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Track Stability Management
Track Stability Management
DOCUMENT CONTROL SHEET
Document:
Title: Track Stability Management: Development of Rail-Temperature
Prediction Model and Software
CRC for Rail Innovation
Floor 23, HSBC Building
Brisbane Qld 4000
Project Leader: Nirmal Mandal
GPO Box 1422
Brisbane Qld 4001
Authors:
Ying Min Wu
Associate Professor Mohammad Rasul
Professor Masud Khan
Tel: +61 7 3221 2536
Fax: +61 7 3235 2987
Reviewers
Professor Colin Cole (Program Leader, CQUniversity)
John Powell (Project Chair), QR
www.railcrc.net.au
Project No: R3.112
Project Name: Track Stability Management
Synopsis: The main goal of this study was to develop a model and software to accurately predict rail-track
temperatures 24 hours in advance, in order to provide data that can be used in managing rail buckling.
Three major tasks were undertaken to achieve this goal: designing field experimentation and procedures;
developing a multivariate regression model of rail-track temperatures; and verifying the regression model
against measured rail temperatures.
The researchers concluded that Australian Bureau of Meteorology NWP ACCESS-A* data can be used to
accurately predict rail temperatures 24 to 48 hours in advance, using a software code developed in MATLAB.
Data produced in this way could give rail-industry operators at least one day’s advance notice of when rail
temperatures may become critical. This has the potential to deliver substantial benefits to operators and their
customers.
* Numerical weather prediction Australian Community Climate and Earth-System Simulator
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Established and supported under the Australian Government’s Cooperative Research Centres Programme
Copyright © 2012
This work is copyright. Apart from any use permitted under the Copyright Act 1968, no part may be reproduced by any
process, nor may any other exclusive right be exercised, without the permission of Central Queensland University.
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Table of Contents
Abbreviations and Acronyms ................................................................................................................... v
Executive Summary ................................................................................................................................. vi
1.
Introduction .......................................................................................................................... 1
1.1 Background and Significance .............................................................................................................. 1
1.2 Objectives ........................................................................................................................................... 2
1.3 Scope and Limitations of the Study .................................................................................................... 2
1.4 Outline of Chapters ............................................................................................................................ 3
2 Literature Review .................................................................................................................................. 4
2.1 Methods for Predicting Weather Conditions ..................................................................................... 4
2.1.1 Predicting Solar Irradiance—Empirical Methods ....................................................................... 4
2.1.2 Spatial and Time Scales of Weather Forecasts ........................................................................... 6
2.1.3 Forecasting Methods ................................................................................................................. 7
2.1.4 NWP Forecasting Procedure .................................................................................................... 10
2.1.5 Australian Community Climate and Earth-System Simulator (ACCESS) Model ......................... 11
2.1.6 ACCESS Products Particulars .................................................................................................... 12
2.1.7 ACCESS-A and Surface-weather Element Verification .............................................................. 12
2.2 Effect of Temperature Change on Buckling ...................................................................................... 14
2.2.1 Minimum Potential Energy Buckling Theory ............................................................................ 14
2.2.2 Three-dimensional Modelling of Forces due to Temperature Fluctuation ............................... 16
2.3 Surface and Internal Temperature of the Rail .................................................................................. 19
2.4 Frictional Heat Generation ............................................................................................................... 21
2.4.1 Curved Track Heat Addition Due to Friction ............................................................................ 21
2.4.2 Tangent Track Heat Addition Due to Friction ........................................................................... 23
2.5 Existing Rail-temperature Models .................................................................................................... 24
2.5.1 Empirical Relationships ........................................................................................................... 24
2.5.2 RSSB UK Rail-temperature Model ........................................................................................... 27
2.5.3 FRA Rail-temperature Model................................................................................................... 32
2.6 Concluding Remarks on Existing Rail-temperature Prediction ......................................................... 35
3.
Research Methodology ....................................................................................................... 36
3.1 Weather Predictions......................................................................................................................... 36
3.1.1 Tasks Involved in Producing a Downscaled Weather Forecast ................................................. 36
3.1.2 Network Common Data Format (netCDF) files ........................................................................ 37
3.1.3 Cubic Spline Interpolation ....................................................................................................... 37
3.2 Predicting the Temperature of the Rail Track Due to Weather Conditions ..................................... 38
3.2.1 Tasks Involved in Producing Rail-temperature Prediction ....................................................... 38
3.2.2 Multivariate Linear Regression ................................................................................................ 39
3.3 Frictional Heat Quantification .......................................................................................................... 39
3.4 Statistical Analysis of Measured Data and BoM Data ...................................................................... 39
4.
iii
Experimental Design ........................................................................................................... 42
Track Stability Management
4.1 Site Layout ........................................................................................................................................ 42
4.2 Thermocouples and Rail-temperature Measurements .................................................................... 43
4.2.1 Thermocouple Set-up on Rail Profile ....................................................................................... 44
4.2.2 Laboratory Test of Thermocouples .......................................................................................... 45
4.3 Weather Station ............................................................................................................................... 46
4.4 Rail Stress Modules (RSMs) .............................................................................................................. 47
5.
Rail-temperature Prediction Software ............................................................................... 49
5.1 Operating the Program .................................................................................................................... 49
5.2 Program Disclaimers......................................................................................................................... 52
5.3 Program Run Times .......................................................................................................................... 52
1.
6. Results and Discussion .................................................................................................... 54
6.1 Weather Variables Comparison: Weather Station and BoM data ................................................... 55
6.1.1 Screened Air Temperature ...................................................................................................... 57
6.1.2 Relative Humidity .................................................................................................................... 60
6.1.3 Surface Air Pressure ................................................................................................................ 62
6.1.4 Zonal Winds (U) ....................................................................................................................... 63
6.1.5 Meridional Winds (V) .............................................................................................................. 64
6.1.6 Overall Statistical Weighted Factor ........................................................................... 65
6.2 Comparison of Temperature Difference over the Rail Surface .................................................... 67
6.2.1 Sensor in the Same Orientation but on Different Rails ............................................................ 68
6.2.2 Different Positions on the Profile on the Same Rail ................................................................. 70
6.2.3 Rail Temperatures on Rail Sitting on Sleeper and Rail sitting above Ballast ............................. 72
6.2.4 RSMs and Thermocouple Rail-temperature Comparison ......................................................... 73
6.3 Rail-temperature Prediction ............................................................................................................. 74
6.3.1 Real-time Predictions .............................................................................................................. 75
6.3.1.1Validation Analysis of Real-Time Predictions .......................................................... 75
6.3.2 Future Predictions ................................................................................................................... 78
6.3.2.1 Validation of Future Predictions ............................................................................. 79
6.3.3 BoM Raw Data and BoM Interpolated Predictions .................................................................. 85
6.3.3.1 Interpolated This-day Predictions .......................................................................... 86
6.3.3.2 Interpolated next-day predictions .......................................................................... 88
6.4 Empirical Prediction Drawbacks ....................................................................................................... 91
6.5 Frictional Temperature Increase ...................................................................................................... 92
6.6 Sensors and Prediction: the Argument for Rail-Temperature Prediction ........................................ 94
7.
Conclusion .......................................................................................................................... 95
References .............................................................................................................................................. 96
iv
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Abbreviations and Acronyms
ACCESS
ARTC
AWS
BoM
CACWR
CFD
CSIRO
CWR
DAQ
ECM
FEA
FRA
GCM
GMT
MOS
NCAR
NMOC
NOAA
NWP
RSMs
RSSB
PP
SCI
WOLO
v
Australian Community Climate and Earth-System Simulator
Australian Rail Track Corporation
Automated weather station
Bureau of Meteorology (Australia)
Centre for Australian Weather and Climate Research
Computational fluid dynamics
Commonwealth Scientific and Industrial Research Organisation (Australia)
Continuous Welded Rail
Data acquisition system
Expectation condition maximisation
Finite element analysis
Federal Railroad Association (USA)
General circulation model
Global mean time
Model output statistics
National Center for Atmospheric Research (USA)
National Meteorological Operations Centre (Australia)
National Oceanic and Atmospheric Administration (USA)
Numerical weather prediction
Rail stress modules
Rail Safety and Standards Board (UK)
Perfect Prog
Statistical climate inversion
Welded track—restrictions on speed of operation of locomotive
Track Stability Management
Executive Summary
Background
Railway-track buckling occurs due to inadequate rail-stress adjustment, which is greatly influenced by variations
in weather-induced rail temperatures and the rigidity of track structures. Climate change and increases in
extreme temperature variations have made buckling a more prevalent problem.
The ultimate goal of any research into managing track stability is to allow operators to comprehensively manage
rail buckling and the management procedures that follow buckling. The first step in developing a comprehensive
management plan is to clearly understand how environmental conditions influence changes in rail-track
temperatures. The second step is to accurately predict environmental conditions at least 24 hours in advance so
that management procedures can be put in place.
Study Goal
The goal of this study was to develop a model and software to accurately predict rail-track temperatures 24 hours
in advance, so that this data can be used to help manage rail-track buckling.
Methodology
Two distinct and separate mathematical manipulations were performed to achieve this goal. First, weather
forecasts from the Australian Bureau of Meteorology (BoM) were used to forecast the weather at specific railtrack locations selected for the study. This involved using three-dimensional cubic interpolation (that is, weather
parameters were interpolated in two dimensions geographically, and then in one dimension through time). The
result was a series of forecasts updated every 15 minutes for locations every 3.06 km along the rail track.
Second, multivariate linear regression was used to predict rail temperatures on the tracks 24 to 48 hours in
advance.
To validate the rail-temperature predictions, a three-month field test was conducted on a section of Queensland
Rail’s coal-network track in central Queensland from June to August 2010. This involved erecting an automated
weather station (AWS) and attaching temperature sensors to a section of track. The AWS model WXT520,
produced by Vaisala (Vaisala 2009), was used. This is an off-the-shelf product similar to what some rail operators
already use for continuous monitoring of critical sites.
Temperature sensors (surface thermocouples) and Salient Systems’ rail-stress modules (another off-the-shelf
product) were used to measure rail surface temperatures on both rails of the track (Salient Systems Inc 2009). The
sensors were attached to the surface of the track to directly measure temperature changes in the rail profile
throughout the diurnal cycle. Statistical correlations between the different measured points of the rail profile
were evaluated in relation to the diurnal cycle to assess the accuracy of current rail-temperature measuring
practices.
Statistical evaluation was used to assess how well the BoM predictions compared with weather parameters at the
field experimentation site. Similarly, statistical evaluation was used to assess the accuracy of the rail-temperature
method developed. Prediction methods were also compared with existing empirical methods identified in the
literature review, and with an assessment of track conditions.
Conclusions
Using a test-case scenario, the researchers concluded that it is possible to accurately predict rail-track
temperatures in advance without using on-track weather instrumentation, and that the accuracy of predictions
made in this way is as good as, if not better than, predictions made using instrumentation calculation. While the
accuracy of the method has been assessed only for the track configuration, materials and location used in this
study, further research could develop the method for other tracks.
This is a flagship study in Australia, with significant potential benefits for rail operators and their customers.
vi
1. Introduction
1.1 Background and Significance
For rail tracks to remain stable, a balance must be achieved between environmentally induced
changes in rail-track temperature (which cause thermal expansion and subsequent instability), and
the counteracting resistive forces provided by sleepers and ballast (which keep tracks in position).
Rail tracks become unstable and buckle due to inadequate rail-stress adjustment and weatherinduced track elongation, which can, ultimately, cause derailments.
As ambient temperatures have increased and extreme heatwaves have become more prevalent in
Australia (Parliament of Australia, 2009), rail temperatures have also increased, and track instability
has become more common. While substantial research in the field of track stability has been
conducted in the USA and UK, much of this research is not readily transferable to Australia, where
weather conditions and track standards are significantly different from those in the northern
hemisphere.
Australian research in track stability has been hampered due to fragmentation of the railway
industry and the lack of any centralised national knowledge-base on track stability. Studies in track
stability have not been revised nor progressed since the 1980s (Bartlett et al. 1961; Hunt 1994;
Esveld 2001). Considering advances in track standards and weather-forecasting technology in the
last 30 years, the issue is overdue for revision and ready for new approaches that engage with
current technology.
Two distinct areas of research arise naturally out of track-stability studies: first, the stresses that
cause instability in rails, and, second, the environmental conditions that cause these stresses. This
study focuses on environmental effects on rail-track temperatures.
Currently, the railway industry assesses weather parameters by using an empirical formula based on
maximum ambient air temperature (Whittingham 1969; Hagaman and Kathage 1988). This is then
used to estimate rail temperatures and, if necessary, issue slow orders to operators when the
calculated maximums exceed safe levels.
A second level of monitoring occurs on sections of track that are known to be particularly
susceptible to environmental conditions such as flooding and buckling. When temperatures on these
sections exceed alarm levels, monitoring devices communicate this directly to the central railway
hub, acting as an emergency warning system. An example of such an alarm-monitoring system is the
WOLO speed restriction system implemented by the Australian Rail Track Corporation (ARTC) (2005).
The current Australian standards for unsafe temperature increases in rail tracks were developed as a
result of a 15-month study conducted by the Australian Bureau of Meteorology (BoM) in 1951. Using
the results of the BoM study, Whittingham (1969) developed an empirical relationship between airscreened temperature and rail temperature for sunny cloudless, windless, and light-wind days in the
metropolitan area of Brisbane, Queensland. This relationship was interoperated for Australianrecorded extreme maximum screened air temperatures to develop a contoured isothermal map of
the expected maximum rail temperatures for Australia, which is still used for alarm-level settings.
Empirical weather-prediction methods have a number of shortcomings. A scan of the literature
indicates that empirical methods are either inaccurate for rail-temperature purposes, or require a
long period to gather observations.
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Furthermore, existing rail-temperature models do not take into account heat transfer on the bottom
surface of the rail, or consider frictional heat addition inputs. Both of these areas are explored in this
study.
Advances in weather forecasting mean that it should now be feasible to develop a predictive
simulation model that calculates rail temperatures dynamically for each section of track. The goal of
such a model would be to develop more accurate predictions of high rail temperatures. In practical
terms, this could mean the difference between blanket speed restrictions in hot weather (with all
the costs and inconvenience that they involve), and focused operational management based on
localised risk conditions determined by a scientific approach.
1.2 Objectives
The main goal of this study was to develop a model and software to predict rail-track temperatures
24 hours in advance, in order to provide data for use in managing rail buckling.
Three major tasks were undertaken to achieve this goal: designing field experimentation and
procedures, developing a multivariate regression model of rail-track temperatures, and verifying the
regression model against measured rail temperatures. These tasks can be further broken down into
the following objectives:
1. to measure rail temperature and weather conditions on an in-situ rail track
2. to perform mathematical manipulation of different temperature models reported in the relevant
literature
3. to quantify the accuracy of the numerical weather prediction (NWP) product produced by the
BoM against weather parameters measured using weather stations
4. to quantify surface-temperature differences over the rail profile
5. to quantify the temperature difference between the same position geographical on different rails
6. to quantify the measurement difference between rail stress modules (RSMs) and thermocouple
sensors
7. to quantify the frictional heat generated by train passage over the rail
8. to develop a code in MATLAB software that interacts with the user and produces a graphic
representation of rail temperature over the next two days
9. to recommend steps for further development.
1.3 Scope and Limitations of the Study
Australia is a large country, with railway networks a prominent feature across its 7,692,030 km²
landmass. Because of the limited resources and time available to this study, it was restricted to
developing a method that would accurately predict rail temperatures for a section of rail track within
the Queensland Rail (QR) coal-network region in central Queensland.
Variations in track materials, construction and orientation affect the heating profile of a rail, causing
potential temperature variations between different tracks, even when they are in the same
geographic location. This study was limited to considering a concrete-sleepered, narrow-gauge track
running east–west, in the central Queensland area of Australia.
Because any weather model developed would not have equalled the quality of the BoM weather
forecast, BoM forecast data was purchased. The BoM data was from the Australian Community
Climate and Earth-System Simulator (ACCESS) model, which has been developed in conjunction with
Australia’s Commonwealth Scientific and Industrial Research Organisation (CSIRO).
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The study considered a standard 60 kg rail-track profile, which is rated for heavy haul. Track features
such as cuttings, bridges, and points, which are known to cause track instabilities, were not
considered.
1.4 Outline of Chapters
Chapter 2 presents a review of the literature relevant to this study, including techniques and
methods commonly used to predict rail temperatures.
Chapter 3 describes the study methodology, including the theory and processes of the methods
used.
Chapter 4 describes instrumentation and field experimentation details, and discusses the type of
instrumentation, how it was used, and the accuracy of different types of instrumentation.
Chapter 5 discusses the rail-temperature prediction software developed as a part of this study,
including how to use it. Screen-shots and descriptions of function files are included.
Chapter 6 contains results and discussion, including analysis of data from field instrumentation and
the BoM data. This section also discusses limitations in the mathematical manipulations, and
outlines further recommended areas of research arising from this study.
Chapter 7 outlines the study’s main findings and discusses their implications for the rail industry.
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2 Literature Review
A review was conducted of the literature relating to:





available methods for predicting weather conditions
the effect of temperature change on rail buckling
surface and internal rail temperatures
the generation of frictional heat by wheel contact with rails
existing rail-temperature models.
A separate review of literature related to the rail-buckling mechanism was also conducted, and is
presented in other report (Shah’s work).
2.1 Methods for Predicting Weather Conditions
Weather studies consider the effects of the atmosphere over a short period of time, while climate
research considers long-term atmospheric patterns that may indicate general trends and averages
over a number of years (Gutro 2005). The current study focused exclusively on weather prediction
for a 24-hour period, and did not include long-term issues such as climate change or monthly
average predictions.
All weather is caused directly or indirectly by the interactions of the earth, its atmosphere, and the
sun. A substantial part of the literature review focused on solar radiation, which is the main source
of heating for natural and artificial structures. The review first considered solar-radiation and
air-temperature data freely available from BoM national forecasts, and how it could be used to
predict weather conditions. It then reviewed empirical, semi-empirical and NWP models for weather
prediction.
2.1.1 Predicting Solar Irradiance—Empirical Methods
Solar irradiance is the intensity of solar radiation per unit area, which is affected by the earth’s
rotation and orbits around the sun, and by gaseous particles in the atmosphere. Various estimations
of solar irradiance are available for engineering purposes. These are based on the Angstrom-Prescott
equations, which account empirically for specific locations the amount fraction of average global
solar radiation to extraterrestrial radiation. The Angstrom-Prescott equation (Njau 1995) is:
G
 a  bS
G0
2.1
where:
G = average solar radiation [W/m2]
G0 = extraterrestrial radiation [W/m2]
S = sunshine factor (see Equation 2.1)
a = coefficient (between 1 and 0)
b = coefficient (between 1 and 0 )
The coefficients a and b are calculated from measured solar radiation, which modifies solar radiation
according to the pollutants and atmospheric conditions particular to a location. This is unique for
each location. S can be expressed in terms of hours of sunshine (Iqbal 1983):
S
n
Nd
2.2
where:
n = monthly average number of instrument-recorded bright sunshine hours per day [h/day]
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N d = average day length [h]
For a given month, the average day-length N d can be calculated from (Iqbal 1983):
Nd 
1 n n2  2

cos 1   tan  tan   


n2  n1 n n1 15

2.3
where:
n1 = day number at the beginning of the month (1 to 365)
n2 = day number at the end of the month (1 to 365)
 = latitude [⁰]
δ = solar declination [⁰]
Numerous modifications have been made to the basic Angstrom-Prescott equation. These aim to
relate the equation to climatological variables, rather than keeping it as a purely experiment-based
equation.
The agricultural industry also uses empirical methods based on air temperature and rainfall to
calculate irradiance. A detailed review of these methods in the Australian environment was
conducted in 2000 by Liu and Scott (Liu & Scott 2000). After comparing methods that used air
temperature only, rainfall only, and a combination of air temperature and rainfall, Liu and Scott
found that using air temperature as the main parameter and rainfall as 1 for presence of rainfall and
0 as no rain gave the best results.
The equation that best described the Rockhampton region relevant to this study was:
Q  Q0 a[1  exp(b  Dc )](1  dR j 1  eR j  fR j 1 )  g
2.4
where:
Q = solar radiation reaching the earth’s surface [W/m2]
D = diurnal range of air temperature [⁰C] (Equation 2.5)
R = transformed rainfall data where if P>0, R=1; P=0, R=0
a,b,c,d,e,f = coefficients determined by regression for Rockhampton (Liu & Scott 2000):
a=0.700
b=0.026
c=1.874
d=0.034
e=0.038
f=0.124
g=-0.020
j = the current day
J+1 = the next day
D  Tmax 
Tmin ( j )  Tmin ( j  1)
2
2.5
where:
Tmax = current maximum temperature [⁰C]
Tin (j) = minimum temperature current day [⁰C]
Tmin( j+1) = minimum temperature the next day [⁰C]
SHAZAM software was used for non-linear least square regression (Liu & Scott 2000), and this
equation was found to have a regression coefficient R2 of 0.77 between estimated and observed
irradiances, and an RMSE of 2.58 MJ m-2.
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The main criticism of these empirical statistical methods is not that they are inaccurate. After all, the
R2 findings of Liu and Scott ‘s equations were all 0.69 and above, and the RMSEs were all 2.53 MJm-2
and below. However, their applicability is highly localised—for example, the model developed for
Darwin can only be used for Darwin, and cannot be transferred to Cairns, even though Cairns has a
similar climate classification.
In Liu’s paper, measurements of climatological parameters were taken over a four-year period and
repeated for each location of interest. While Liu and Scott tried to develop empirical radiation
equations for locations by using climate data from other locations that had a similar climate, their
over mean had an R2 of 0.45 and an RMSE of 3.08 MJm-2 (Liu & Scott 2000).
This indicates that, although it is possible to develop empirical relationships for locations using data
from similar climatic regions, results are not very accurate, and nowhere near accurate enough for a
24-hour advanced forecast model of track temperatures. Furthermore, given that railway networks
cover large geographic areas with varied topographical features, it is neither practical nor desirable
to implement weather stations in a 20 km grid formation around Australia, collect data for a couple
years, and then develop a rail-temperature model. Indeed, models developed in the USA (explained
in Section 2.1.4) use NWP to solve an initial value problem (Zhang & Lee 2008).
2.1.2 Spatial and Time Scales of Weather Forecasts
In meteorology, the scale or resolution of the forecast is important, because different weather
phenomena occur over a range of space and time scales. One boundary-condition measurement
may be important in one scale and inconsequential in another (Whiteman 2000; Pielke SR 2002).
Meteorology is classified into three basic scales: large-scale or synopticscale, mesoscale, and
microscale.
Large-scale or synopticscale meteorology considers global circulation systems, including hemispheric
wave patterns called Rossby waves; monsoons; high- and low-pressure centres; and fronts.
Temperature, humidity, pressure, and wind measurements are collected simultaneously all over the
world, and atmospheric dynamics are solved for the entire earth. Synopticscale meteorology has a
resolution greater than 200 km and lifetimes (time scales) of days to months (Whiteman 2000).
Mesoscale weather events include diurnal systems such as mountain wind systems, including
breezes, sea breezes, thunderstorms, and other phenomena with horizontal scales that range from
2 km to 200 km and lifetimes that range from hours to days. Mesoscale meteorologists use networks
of surface-based instruments, weather balloon measurements, and remote sensing systems such as
radar and aircraft to make observations.
Microscale meteorology focuses on local or small-scale atmospheric phenomena with resolutions
below 2 km and lifetimes from seconds to hours. These include gusts and turbulence, dust devils,
thermals, and certain cloud types (Whiteman 2000).
A fourth scale in between mesoscale and synopticscale is also widely used. It is the regional scale,
and relates to circulations and weather events occurring on horizontal scales from 500 km to
5000 km (Whiteman 2000).
For railway applications, synopticscale and regional scales are too large to allow for local variation of
weather parameters on the track. An average section of track between joints is around 3 km, and
the required time scale is 24 hours in advance, whereas the timescale for synoptic and regional
predictions is days to months, and these models have too coarse a resolution for this application.
Given that track features such as orientation and surrounding vegetation can change within a couple
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of kilometres, mesoscale weather prediction is most appropriate for this study. Literature on
mesoscale modelling is reviewed below.
2.1.3 Forecasting Methods
Similar forecasting methods can be used for climate-change studies and operational forecasts.
However, the literature on meteorological modelling is usually published for climate case-studies,
such as those related to large eddy motion (Moeng et al. 2006), or the weather particular to one
geographic location (Wilby et al. 1999). Therefore, this review focused on modelling techniques used
in relevant climate studies that were directly analogous to the techniques required for the current
study.
Currently, all operational meteorological forecasts start off with a general circulation model (GCM)—
a synopticscale NWP model that solves for conservation of mass, momentum and energy equations
for the different atmospheric species, where the resolution is 1000 km or greater. GCMs give coarse
general information that corresponds to large-scale forcings such as the earth’s orbit, and determine
the general order of weather events and characterise the climate of a region (Giorgi & Mearns
1991). To gain meaningful forecasts for a particular city or area, GCM model output is downscaled to
a finer resolution, because GCM output is often unreliable at individual grid and sub-grid box scales
(Wilby et al. 1999).
There are several ways to obtain a finer resolution, including purely empirical methods in which
forcing is not explicitly accounted for. Methods are:
 weather forecasts using instrumental data records
 semi-empirical methods using GCMs to describe the atmospheric response to large-scale forcings
of relevance to climate change
 empirical techniques to account for the effect of mesoscale forcings
 dynamic modelling approaches, in which mesoscale forcings are described by increasing the
model resolution only over the area of interest. (Giorgi & Mearns 1991)
GCMs are NWP models that produce a numerical simulation of atmospheric variables such as
temperature and wind for the whole world. Grid sets are divided into latitude and longitude points
and vertical levels above the ground, so that the simulated data is three-dimensional.
Purely empirical methods involve the assumption that, independent of the nature of the forcing
mechanism, under similar lower-boundary conditions (such as ocean to land surface topography),
the general circulation will eventually adjust itself to give a similar response to different forces. This
assumption is supported by the fact that similar latitudinal near-surface GCM responses are
obtained even for increased greenhouse gas concentration and increased values of the solar
constant (Giorgi & Mearns 1991).
Most empirical methods use data from recent instrumental records. There are two main ways of
doing this. One is to group different periods of recorded data that have similar attributes (e.g. warm
years or cold years, or different seasons), then develop characteristics such as precipitation and
cloudiness for these different groups. A statistical relationship is then developed between the type
of year or season and a weather variable, and future information is simulated through this
relationship.
The second way is to develop linear statistical relationships between climate variables such as
temperature and precipitation averaged over a given region and then averaged annually or monthly.
These relationships are then used to estimate possible future climate data (Giorgi & Hewitson 2001).
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This is the same approach Whittingham (1969) took in developing a relationship between rail
temperature and air temperature.
The main problem in using these purely empirical approaches for the current study was their
susceptibility to the availability and quality of observational data (Giorgi & Mearns 1991). Records
collected over several decades have been used to develop these empirical models. In capital cities
such as Melbourne or Sydney, weather data go back to the late 1890s. However, regional and
remote areas of Australia have only been collecting weather data since the 1980s, if at all. Also,
empirical methods can only be used for the regional climates that they are developed for, as Liu and
Scott (2000) found in relation to solar radiation. For rail networks that cover large areas, including
regional and remote areas, not enough observational data exists to develop an accurate empirical
model.
Semi-empirical models or statistical climate inversions (SCI), translate large-scale, coarse-resolution
GCM information into local, high-resolution statistics of surface climatic variables of interest, using
empirically derived relationships between large-scale and local surface variables. GCMs are used to
explicitly account for large-scale forcings, and empirical methods to account for mesoscale forcings
(Giorgi & Hewitson 2001). There are four main SCI methodologies:
 statistical difference schemes
 regression schemes
 Perfect Prog (PP)
 model output statistics (MOS).
The underlying assumption for the differences schemes is that the inaccuracy due to the GCM
resolution is reduced when simulated GCM-produced and observed high-resolution data are added
to the GCM output for forecasting. However, this technique can be misleading, because mesoscale
forcing in different locations within a GCM grid box is widely variable and probably nonlinear (Giorgi
& Mearns 1991). The same problem identified in using purely empirical methods applies to using
differences schemes to account for mesoscale forcing: there is not the necessary quantity of data or
density of observation stations to make it viable for this study.
In a regression downscaling scheme, multivariate regression is conducted for a series of observed
variables in a given region. Another regression is then conducted on a series of the same variables,
but averaged. These data-sets are obtained from the same set of observations for the same period.
The relationship between the averaged regression and observed regression values is then applied to
the forecast GCM produced over that region in order to infer the surface variables (Giorgi & Mearns
1991).
Like the methods discussed above, regression schemes depend on the accuracy and validity of the
observations used in their development. They also rely on a good theoretical understanding of the
surface-variable meteorological interactions, so that relevant variables can be included in the
regression. For the purposes of the current study, this would have been too time-intensive, given
that that study’s focus was to develop a predictive rail-temperature model rather than a
downscaling regression scheme. Therefore, the researchers decided that it would more prudent to
combine this method with an already scaled-down NWP product, rather than downscaling from
purely observational data.
PP and MOS methods are similar to the regression scheme in that both use multivariate regression.
However, instead of developing a relationship between two current regressions of averaged and
observed values, PP and MOS develop relationships between observed surface-weather variables
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and observed or model-produced suitable free-atmosphere and surface-weather predictors (Giorgi
& Mearns 1991).
For MOS, the predictors (the independent variables) are model forecast variables; the predictands
(dependent variables) are weather-station observations valid at the same time as the forecast. An
error function between the predicted weather-station observation and the actual observation is
used as a factor that is fed back into a regression relationship, so that the MOS prediction equation
continuously becomes closer to the variables observed by the weather station (Kalnay 2003).
Whereas MOS uses both forecast model data and observed data, PP only uses observation data. The
regression equations are derived using the observed variables, and the outputted model analysis
assumes a perfect forecast, so an error function is developed between the regression-predicted
forecast and the actual observed forecast. PP uses two sets of observed variables from different
intervals in time (Marzban et al. 2005).
Again, these two empirical methods suffer from a lack of accurate data for remote and regional
areas, and using them would have required at least a few years of observations for the specific
regions being studied. However, MOS and PP techniques are also used for post-processing, where
atmospheric predicted variables are statistically modified so that they resemble more realistic values
near the surface (Kalnay 2003).
Dynamic modelling approaches involve increasing the NWP grid resolution to a higher resolution
over the region of interest. This is achieved by nesting or embedding a finer-grid NWP model
(regional model) inside the coarse-grid NWP model (host model)—that is, the grid points of the
coarse NWP model are used as the boundary conditions of the fine NWP model (Giorgi & Mearns
1991).
This can be achieved by either one-way nesting or two-way nesting. One-way nesting consists of
boundary conditions being fed into the regional model. This leads to abrupt changes in resolution,
and there is no modification of the host model by the regional model. This has some advantages, as
it allows for independent development of the regional model, and the host model can be run for
long integrations without being influenced by the problems associated with non-uniform resolution
from the regional model (Kalnay 2003).
Two-way nesting is when the solutions of regional models are fed back into the host model and
modify the host model. This gives a more accurate result because there is better continuity of
information between the two models (Kalnay 2003). The disadvantage of the two-way nested model
is that the fine resolution of the regional model may distort the host model and give unrealistic
variables (Kalnay 2003).
Using a nested NWP downscaling procedure allows predictions to be made for regional and remote
areas of Australia, without having to wait for empirical data to be collected using observation or
weather stations. Existing GCM and mesoscale model products available from the BoM (see
Appendix A) can cut down the computational time of running an NWP model if only a small region is
considered (e.g. each city hub for train operations could run their own nested NWP area for
surrounding regions). Because NWP nesting procedure does not need empirical data or an advanced
knowledge of theoretical meteorology to use the correct variables for regression, it is also easier to
implement—although it does require more computational effort.
Due to the intensive computation and simulation cost of implementing an NWP model to downscale
the GCM points, an existing NWP downscaled product was purchased for the purposes of this study.
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2.1.4 NWP Forecasting Procedure
NWP forecasting requires the solving of equations that govern the movement of the atmosphere for
seven unknown variables. While a wide variety of standard numerical procedures are used for
different NWP models, only basic concepts of NWP modelling are discussed here. The NWP model
used is the ACCESS (Australian Community Climate and Earth-System Simulator) model.
ACCESS solves the equations in orthogonal coordinate form, as listed below (Kalnay 2003).
1. Newton’s second law or conservation of momentum (three equations for the three velocity
components)
2. Continuity equation or conservation of mass
3. Equation of state for ideal gases
4. First law of thermodynamics or conservation of energy
5. Conservation equation for water mass
Into these equations, appropriate boundary conditions at the bottom and top of the atmosphere are
used to calculate a full numerical solution. The governing equations are in Lagrangian definition for
the movement of a parcel of air in an arbitrary coordinate system origin at the centre of the earth
and z-axis along the axis of rotation.
The governing equations are (Kalnay 2003):
dv
 p    F  2 v
dt

   (  v)
t
p  RT
dT
dp
Q  Cp

dt
dt
 q
   (  vq)   ( E  C )
t
(2.6)
(2.7)
(2.8)
(2.9)
(2.10)
The unknown variables that need to be solved for are:
v = the velocity vector v =(u,v,w)
u = velocity in the x direction [m/s]
v = velocity in the y direction [m/s]
w = velocity in the z direction [m/s]
T = temperature [K]
p = pressure [pa]
3
 = density [kg/m ]
q = mixing ratio of water vapour and dry air mass
The other variables are:
1
the specific volume [m3/kg]






i
j  k = gradient operator
x
y
z
  g  g e  2l = apparent gravity
ge  e gravitation accelerations vector
e = Newtonian gravitational potential of the earth [J/kg]
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 = angular velocity [rad/s]
l = position vector from the axis of rotation parcel of air
F = friction force [N]

= compressibility of the air parcel
t
R = universal gas constant for air [J/kg⁰ K]
Q = heat energy [J/kg]
Cp= specific heat at constant pressure of air [J/kg⁰K]
dT
= change in temperature over time
dt
dp
= change in pressure over time
dt
 q
= change in mixing water vapour mixing ratio q
t
E = evaporation [kg/m2s]
C = condensation [kg/m2s]
These equations are solved for all parcels of air in the atmosphere using numerical methods;
solutions themselves correspond to wave forms which relate directly to physical variables.
2.1.5 Australian Community Climate and Earth-System Simulator (ACCESS)
Model
Each climate-research organisation, government department or research body runs their own NWP
model with varying initial conditions, boundary assumptions and numerical schemes designed to
serve their own purposes. ACCESS is an Australian government model that solves the abovementioned governing equations to predict weather variables days and months in advance.
In August 2010, the Australian BoM switched from their previous in-house model to the ACCESS
model for both research and operational forecasts (Bureau of Meteorology 2010). Evening weather
forecasts are now based on ACCESS data combined with the experience of forecasters who decipher
ACCESS outputs to make a weather prediction. Data is outputted from the ACCESS model in several
formats and resolutions, available to the public for a subscription fee.
The ACCESS-A product, which has a resolution of 0.11⁰ or 12 km grids for single-level fields, was used
in this study. It was chosen because it offered the smallest-resolution weather output that
encompassed the central Queensland area relevant to the study. Single-level fields were chosen
because multi-level fields had weather data not only on the surface of the earth but at intervals into
the earth’s atmosphere, and this vertical information was not relevant to the study.
The ACCESS model is based on the UK Met Office Unified Model/Variational Assimilation (UM/VAR)
system. It was developed and tested in Australia by Dr Kamal Puri of the Earth System Modelling
Programme at the Centre for Australian Weather and Climate Research (CAWCR). It was
implemented by the Operational Development Subsection of the National Meteorological
Operations Centre (NMOC) (Bureau of Meteorology 2010).
Specifications of the ACCESS model are as follows (Bureau of Meteorology 2010).
 Equation set is non-hydrostatic.
 Arakawa-C grid is used in the horizontal plane and Charney-Phillips is used in the vertical.
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 Advection is solved with two-time-level, semi-Lagrangian integration scheme, with noninterpolating scheme for vertical advection of temperature. An exception for solving is density,
which uses a Eulerian scheme.
 Acoustic terms are treated using a semi-implicit approach.
 Cloud prediction uses a diagnostic cloud scheme based on conserved variables of liquid/frozen
water temperature and total water content (TL and qT), and a sub-grid scale probability
distribution of these variables (Smith 1990). Cloud amounts and water content are found using an
assumed critical relative humidity. The BoM modifies the scheme such that only water clouds are
defined from TL and qT, and a sub-grid probability distribution. Ice water content is determined
by the prognostic mixed-phase microphysics scheme, with ice-cloud fraction calculated
diagnostically from ice-water content.
 The radiation scheme used is a modified version of the Edwards and Slingo scheme (Edwards &
Slingo 1996), which is based on rigorous solution of the two stream-scattering equations,
including partial cloud cover with full treatment of scattering and aerosols and consistent
treatment of cloud radiative properties in solar and thermal regions of spectrum.
 Precipitation is solved by using a single-moment bulk microphysics scheme (Wilson & Ballard
1999), with explicit calculation of transfers between vapour, liquid and ice phases.
 Convection uses a modified mass-flux scheme based on Gregory and Rowntree (Gregory &
Rowntree 1990).
2.1.6 ACCESS Products Particulars
The ACCESS model is a GCM model, which is downscaled using NWP nesting by the Australian BoM.
As Table 2.1 indicates, several products are available for public consumption in various resolutions,
domain sizes, durations, runs, and types.
From Table 2.1, ACCESS-A is the product that has the smallest resolution and encompasses the
central Queensland region. Its resolution is approximately 12 km, and it can predict weather
conditions up to 48 hours in advance, 4 times a day at 00hr, 06hr, 12hr, and 18hr (GMT). This
product was chosen for use in this study.
Table 2.1: Description of ACCESS Products Provided by the BoM (Bureau of Meteorology 2010)
2.1.7 ACCESS-A and Surface-weather Element Verification
After the BoM switched to the ACCESS model in August 2010, several verifications were performed
by Tomasz Glowacki of CAWCR to verify that ACCESS-A was as accurate as the BoM’s previous
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MESOLAPS model, using all available Australian surface observations from 10 to 18 July 2010
(Bureau of Meteorology 2010).
Figure 2.1 compares the forecasts produced by the two models. It shows:
 forecast RMS error and bias of mean sea-level pressure
 screen-level temperature (PT)
 screen-level dewpoint temperature (D2)
 zonal (U) and meridional (V) components of the 10 m wind.
The blue line in Figure 2.1 is the output of the MESOLAPS model, while the green line is the
ACCESS-A output. For any particular hour of the day, the latest available model forecast for that time
was used (Bureau of Meteorology 2010).
Figure 2.1 gives an estimation of the average errors and biases found in the short-term forecasts
available throughout the day. ACCESS-A generally shows smaller RMS errors than MESOLAPS for
most hours of the day, particularly for the mean sea-level pressure, temperature, and wind fields.
Biases are also significantly better for most fields throughout the day, except for the 10 m zonal
wind component, which tends to display a slightly greater (0.1–0.2 m/s) negative bias than
MESOLAPS during the evening and overnight (Bureau of Meteorology 2010).
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Figure 2.1: Comparison of Hourly Forecast RMSE (left) and Bias (right) for ACCESS-A (Green) and
MESOLAPS (Black) 10 –18 July 2010
2.2 Effect of Temperature Change on Buckling
Buckling occurs because of thermal expansion—that is, a steel rail’s natural tendency to expand
when temperatures increase. Because rails are continuously welded, they do not have adequate
space to expand, and the rail is placed under thermal stress as it becomes warmer. If the stress
reaches a critical point, the rail will curve out of shape and buckle (ARTC 2005). Buckling occurs on
both straight tangent tracks and on curved tracks, which buckle into different shapes from each
other. As this study focuses on well-maintained tangent tracks, the theory discussed is limited to
those.
“Rail-neutral temperature” (also known as “stress-free temperature”) is the temperature at which a
rail does not experience any thermal stresses. This is usually the temperature at which the railway
track was built, although neutral temperature can decrease over time due to heating and cooling
cycles. The neutral temperature of two rails on the same track can also differ (Chapman et al. 2008).
2.2.1 Minimum Potential Energy Buckling Theory
Buckling theory is based on elementary beam theory and the principles of minimum potential
energy (Kerr 1976; Samavedam et al. 1993), where the amount of energy needed to cause buckling
is then used as a parameter for track stability (Samavedam et al. 1993). The discussion of buckling
here is based largely on parametric buckling analysis conducted by the USA Federal Railroad
Administration (Samavedam et al. 1993).
Two different types of buckling can occur in the horizontal plane of the track, both pictured in Figure
2.2 (Kerr 1975). The focus is on buckling in the horizontal plane because buckling in the vertical plane
occurs only when lateral resistance is insufficient, and does not occur when the track is sufficiently
maintained (Kerr 1975). Of the two prevalent buckling shapes formed by tangent tracks , the main
focus of this study was on the antisymmetric mode.
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Figure 2.2: Mode Shapes of Tangent-track Buckles in Horizontal Plane (Kerr 1975)
Energy required for buckling is represented by a potential energy balance equation:
  (V2  V1 )  W
(2.11)
where:
V1 = strain energy in the rails at a stable pre-buckled [J]
V2= strain energy in the rails after a buckle [J]
W = work done against resistance by moving track from pre-buckled position to buckled position [J]
 = potential energy required to move track from pre-buckled position to buckled position [J]
Potential energy and temperature can be solved numerically when values for resistance and buckling
shape are substituted into the potential energy equation. The result of temperature against energy
is shown in Figure 2.3. The resistance values used in solving Equation 2.11 are given in Table 2.2.
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Figure 2.3: Temperature versus Buckling Energy Solution to Equation 2.11 (Samavedam et al. 1993)
Table 2.2: Resistance Values Used in Solving Equation 2.11 (Samavedam et al. 1993)
In Figure 2.3, a clear maximum temperature and minimum temperature can be seen on the graph.
The TB,MAX is about 121⁰F (or 49.4⁰C) and the value of TB,MIN is 76⁰F (or 24.4⁰C). If these values in
Equation 2.11 are used in a graph of lateral displacement versus temperature increase (shown in
Figure 2.4), they clearly indicate an unsafe band of rail temperatures.
Figure 2.4: Graph of Temperature Increase versus Lateral Displacement (Samavedam et al. 1993)
The upper critical buckling temperature TB,MAX represents a track position that is infinitesimally
stable—that is, without any disturbance or energy input, the track will naturally buckle out to
Position C, which is stable. From Position A, the track will buckle to Position S only with sufficient
external energy input. The minimum buckling temperature increase is TB,MIN. The absolute
temperature of the track is the sum of the critical temperature rise and the rail-neutral temperature
(Samavedam et al. 1993).
2.2.2 Three-dimensional Modelling of Forces due to Temperature
Fluctuation
Another way of evaluating buckling behavior and thermal forces applied to a railway-track structure
is to develop a three-dimensional finite element analysis (FEA) model for the track structure (Lim &
Sung 2004).
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In Lim and Sung’s model (Lim et al. 2003), the track consisted of two parallel rails resting on a series
of sleepers, which were attached to the rail by fasteners. Lim considered the fasteners to have finite
rotational and translational resistances; this implies that the movement (translational and
rotational) of the sleeper can be different from that of the rails. The sleeper will always exert an
opposing force to any displacement of the rails. Lim modeled the non-uniform ballast resistance as
non-linear lateral spring elements. Rails were modeled as a thin-walled mono-symmetric opensection beam element with 7 degrees of freedom. The sleepers were modeled as solid beams on
elastic foundation elements with 6 degrees of freedom.
Through experimentation, it was found that the applied force and displacement on the sleeper
varied linearly for small displacements and non-linearly for large displacements. Therefore, Lim
modeled ballast as an elastic and inelastic element. Lim modeled the pad-fastener system as an
elastic spring element with 6 degrees of freedom per node. The elastic spring element had two
nodes but the length of the element is zero. Each pad fastener had six springs with three springs for
force-displacement and three springs for moment-rotation. Lim’s configuration is shown in Figure
2.5.
Figure 2.5: Cross-section View of CWR Tracks (Lim et al. 2003)
In the potential energy study (Samavedam et al. 1993), the lateral and longitudinal resistance of the
CWR was represented as an elasto-perfect plastic model (as shown in Figure 2.6), rather than as an
infinite series that took into account distributed load and material properties. The lateral and
longitudinal resistance was assumed to be linear-elastic until the lateral forces had reached their
peak value, then the ballast starts to yield and plastic deformations starts to increase.
Figure 2.6: Pad-fastener Element as Represented in Lim (2004) Model
The track parameters shown in tables 2.3, 2.4 and 2.5 were used in numerical simulations.
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Table 2.3: FEA Model Track Properties (Lim & Sung 2004)
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Table 2.4: Rail RE132 Properties (Lim & Sung 2004) Table 2.6: Wooden Sleeper Properties (Lim & Sung 2004)
Table 2.5: Fastener Material Properties (Lim & Sung 2004)
In the tables above, ties are used instead of sleepers. Similar graphs of above-neutral temperature
and lateral displacement are plotted for the FEA model as shown in Figure 2.7.
Figure 2.7: Graph of Temperature Increase versus Lateral Displacement (Lim & Sung 2004)
Both approaches produce a graph with a similar shape; however the TB,MAX and TB,MIN values are a
little different due to slight differences in the track parameters used in the two models. A review of
the buckling analysis revealed that temperature considerations were limited to a bulk-deformation
temperature, with possible flow-on problems for field testing where only the surface temperature of
a rail can be measured. These critical rail temperatures are calculated from loading, but how surface
temperatures relate to the bulk-deformation temperature is a separate issue that needs to be
quantified.
2.3 Surface and Internal Temperature of the Rail
Quantifying a single temperature over the whole rail profile is problematic, as it is unclear which
temperature measured on the rail corresponds to the bulk-deformation temperature that is
calculated in buckling studies.
A study was conducted by the UK’s Rail Safety and Standards Board (RSSB) into rail surface
temperature and the bulk-deformation temperature of rail steel to quantify a temperature
measurement (Ryan 2005). Ryan conducted several laboratory tests using a test rail section
(CEN60E1, 898  1 mm long), which was polished to simulate in-situ rail-head wear. The rail was on
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wooden blocks to simulate wooden sleepers, which in turn rested on a small bed of ballast to
simulate real track conditions. Rail sleeper and ballast configuration was set up 590 mm off ground
height. Two dual-filament radiant heaters rated at 3 kW per heater were used to induce
temperature change in the rails.
The bulk-deformation temperature was found using thermal expansion with Equation 2.12.
(2.12)
L  LT
where:
L = the change in length [mm]
L = original length of the rail [mm]
T =increase in temperature from ambient [⁰C]
 = thermal expansion coefficient of rail steel ( 11.5 106 m/m⁰C-1)
Figure 2.8 shows Ryan’s findings.
Figure 2.8: RSSB Study—Temperature versus Time Both Sides Heated (Ryan 2005)
It is interesting to note that, except between 90 and 100 minutes, average surface temperature is
lower than the bulk temperature, even though the rails were heated externally. Logically, the
surface or average surface temperature for rails heated horizontally on both sides should be
consistently higher than bulk temperatures. Ryan (2005) does not explain this result; however, it
could be due to the polished rail-head, which would have had a higher emissivity than rusted
surfaces and might therefore have retained less heat and given a lower result. It might also be due
to wind or to a convective heat transfer on the surface of the rail during Test 1. Furthermore, the
complex geometric shape of the rail profile was not considered in Ryan’s calculations for bulk
temperature, and this may have over-simplified calculations somewhat. However, Ryan does not
discuss details of incidents during the test, and any number of external influences could have caused
the counter-intuitive result.
The main information to take from Ryan is that surface temperature and bulk temperature are
closely related, as seen by the R-squared value of 1, which indicates that an experimental design
with surface-temperature measurements is possible. However, a discrepancy still exists between
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surface and bulk temperatures, and some post-experiment analysis on temperature variations over
the rail profile are performed.
2.4 Frictional Heat Generation
Although quantifying frictional heat generation is not a major objective of this study, frictional heat
does affect operational rail tracks. Friction, and the subsequent wearing away of the track, is the
main by-product of train travel. How much of this friction translates into heating on the overall rail
profile is unclear.
Many wear studies concentrate on the surface-heating characteristics of rail–wheel interaction for
wear purposes (Knothe & Liebelt 1995; Ahlstrom & Karlsson 1999; Ertz & Knothe 2002; Olofsson &
Telliskivi 2003). How well these theories translate to overall rail-profile heating has been quantified
in various field tests. Two references that include field experimentation were reviewed to give an
overview of the conflicting information on frictional heat generation.
2.4.1 Curved Track Heat Addition Due to Friction
Tests were conducted by Transnet Freight Rail in South Africa to quantify friction and management
of friction on rail-gauge face temperatures on the high rail of a curved track (Frohling et al. 2008).
The site had a radius of curvature of 604 m, 59/9 km south of Vryheid on a coal export line. The cant
(tilt) of the track was 20 mm. Over a three-day period, 57 trains passed this test site.
The temperature sensors used were bead-type thermistors, which were embedded into the gauge
corner of the rail and logged using an HOBO external temperature logger. Figure 2.9 shows the
sensor configuration.
Figure 2.9: Vryheid Field Test Thermistor Location on Rail Profile (Frohling et al. 2008)
Trains with different types of wheel axles or bogies passed this curved section, with the increase in
temperature grouped for different bogies.
A bogie is a structure incorporating suspension elements and fitted with wheels and axles, used to
support rail vehicles at or near the ends, and capable of rotation in the horizontal plane. It may have
one, two or more axle sets, and may be the common support of adjacent units of an articulated
vehicle (IGA 2003).
The four different types of bogies identified in the South African study were:
 200 wagons at 26-ton axle load [23.58 tonnes], fitted with self-steering three-piece bogies
 100 wagons at 20-ton [18.14 tonnes] and 100 wagons at 26-ton [23.58 tonnes] axle load, fitted
with self-steering three-piece bogies
 85 to 112 general freight wagons with axle loads less than 20 tons [18.14 tonnes], fitted with a
mix of standard and self-steering three-piece bogies
 fewer than 50 general freight wagons with an axle load of less than 20 tons [18.14 tonnes], fitted
with standard three-piece bogies.
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The temperature rises recorded on the gauge side of the track directly under the train’s passage
were very high—up to 25ºC for 26-ton axle loads and 16ºC for less than 20-ton axle loads (see Figure
2.10a and Figure 2.10b).
These peak temperatures even out and remain for up to 400 seconds, a substantial amount of time.
Frohling et al. (2008) focused on practical measurements of coefficient and temperature increase, so
the time it takes for this temperature to dissipate and its effect on overall track temperature were
not discussed.
Figure 2.10a (left): Temperature Increase versus Time 26-ton Axle Load Left (Frohling et al. 2008)
Figure 2.10b (right): Temperature Increase versus Time 20-ton Axle Load Right (Frohling et al. 2008)
Frohling (2008) found:
 no correlation between increases in rail temperature and the speed of trains
 a strong correlation between increases in rail temperature and the length of trains
 that the increase in rail-gauge face temperature on the high rail was dominated by the duration
and magnitude of flange forces above a 1.5-ton threshold exerted on the rail
 that, on average, the high-rail gauge corner increased by 0.000506ºC/ton for 26-ton axle-load
trains, 0.000529ºC/ton for 20-ton and 26-ton wagons with self-steering bogies, and
0.01019ºC/ton for a less than 20-ton axle load.
Frohling (2008) conducted a second test on six 800 m right-hand curves and one tangent section. For
this test, temperature sensors were located at Position 5 in Figure 2.9. The rail was not lubricated for
four days; because it rained after one day’s measurement, which changed the rail’s friction and
lubrication characteristics, it was regarded as inconclusive (Table 2.6).
Table 2.6: Description of Instrumented Rail Sections and Average Speeds (Frohling et al. 2008)
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As can be seen in Figure 2.11, although the tangent track S2 has a lower temperature, the additional
heat due to friction is still around 5ºC for each passing train. Curved tracks had higher temperatures,
which varied depending on the radius of the curvature. Similar travelling speeds on curved track S1
produced almost double or more the temperature increase found on tangent track S2.
Figure 2.11: Rail Temperatures versus Train Passing for Different Sections of Rail (Frohling et al.
2008)
Note that Frohling’s test results conflict with Chapman’s findings presented in the RSSB report from
the UK (Chapman et al. 2005).
2.4.2 Tangent Track Heat Addition Due to Friction
Frictional heat-generation results for tangent tracks presented in Chapman’s report (Chapman et al.
2005) are shown in Figure 2.12.
Figure 2.12: Rail Surface Temperature versus Time Tangent Track (Chapman et al. 2005)
Again, a large discrepancy exists between the temperature increases reported by Frohling et al.
(2008) and those reported by Chapman et al. (2005). Whereas Frohling et al. (2008) found at least a
5⁰C increase in tangent-track measurements, Chapman et al. (2005) found an increase of around
0.1⁰C in rail temperature.
Many experimental design factors could have contributed to this difference. For example, Frohling et
al. (2008) placed sensors on the gauge corner of the rail, which is much closer to the wheel-contact
area than the foot of the rail, where the sensors were located for the study carried out by Chapman
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et al. (2005). Also, while Chapman did not note the type or the bogie of passing trains, the
Winterbourne location used for the UK study would not have been a freight line. Furthermore,
Frohling et al. used thermistors, whereas Chapman et al. used thermocouples, so there may have
been differences in the accuracy of instrumentation. Having said this, however, such a large
discrepancy between measurements is unlikely to be due solely to instrument placement or type,
given the large thermal conductivity and diffusion factors of rail steel.
Frohling et al. (2008) found a strong correlation between train lengths (which are an indication of
actual loads that a track experiences) and temperature increase. The current study is specific to a
coal rail line in Queensland, which has similar loads to those studied by both Frohling et al. (2008)
and Chapman et al. (2005). Therefore, despite the discrepancies between previous studies, the
researchers concluded that frictional heat addition should be explored as part of the current study.
2.5 Existing Rail-temperature Models
Many models have been devised to quantify changes in rail temperature due to environmental
conditions. The most recent models are reviewed below.
2.5.1 Empirical Relationships
Hunt (1994) developed an empirical formula for rail to air temperature given below:
Trail  1.5  Tair
Trail  Tair  17
(2.13)
(2.14)
where:
Trail = temperature of the rail track [°C ]
Tair = temperature of the air [°C]
Equation 2.13 is used for sunny days and Equation 2.14 is used for cloudy days.
Esveld (Esveld 2001) developed a similar relationship using finite element software and buckling
theory. A comparative study using these results and measured trail temperatures was conducted by
Chapman et al. (2005) (see Figure 2.13).
Figure 2.13: Temperature of the Foot versus Air Temperature (Chapman et al. 2005)
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It can been seen from Figure 2.13 that, taking only air temperature into account, the empirical
formulas are within the same range as the actual measured temperature of the rail foot, but there is
a large variance in rail temperature that these equations cannot account for. Chapman et al.
hypothesise that a data envelope (or look-up chart) would be more useful than an empirical linear
relationship because this would give an indication of the range of the rail temperature.
This current empirical relationship would be too inaccurate for a day-to-day real-time prediction of
rail temperature, although the equations give an indication of what the range of rail temperatures
may be, and could be used for design standards. For example, the analysis by Esveld (2001) came
very close to predicting the upper boundaries of the rail temperature relationship, and could be used
for design or industry standards. However, it is not accurate enough for real-time prediction.
In Australia, similar empirical equations were developed by BoM researcher Whittingham (1969),
who conducted a 15-month experiment on a piece of exposed railway rail in an instrumented
enclosure at the bureau’s Brisbane office. Details of the experiment are as follows:
 geographical location latitude 27⁰28’S, longitude 153⁰02’E
 piece of rail was 82 lb [37.2 kg] and 11 ft [3.35 m] long
 rail was laid on 18-inch [0.46 m] long sleepers at 2 ft [0.61 m] intervals
 rail and sleepers were then laid on 1¼-inch [0.032 m] grade ballast
 head was not polished to replicate the wear band that would be present on in-situ rails.
Hourly temperature measurements were taken in two ways. The first involved inserting a dial
thermometer into a 1¼-inch [0.032 m] fishbolt hole in the centre of the web. The second used a
fishbolt hole 13/16 inch [20.64 mm] in diameter and 1 ¼ inches [0.032 m] in depth on the head
surface of the rail. The head hole was filled with mercury, and a standard mercury-in-glass
thermometer with a range from 20⁰F to 230⁰F [−6. 67⁰C to 110⁰C] was used. Due to the inaccuracies
of the dial thermometer, its measurements were discarded, and the focus was on the mercury-inglass thermometer measurements.
The problem was simplified by considering the components of heat balance only at the upper
horizontal surface of the rail. This was justified by saying that, under normal conditions, the
maximum temperature within the rail would be on the upper surface, which was directly exposed to
the sun and would, therefore, experience the maximum temperature conditions.
This assumption has some flaws. As Ryan (2005) showed, the surface head temperature was, in fact,
cooler than the internal temperature, even when radiant heaters were directly 45⁰ at the head
surface. This is because wear on the head or upper horizontal surface causes it to become very
polished, so that most short-wave radiation is reflected. In fact, more heat is absorbed on the web
and foot because it is rusted and has a much lower albedo than the upper horizontal surface. Again,
this is demonstrated in the RSSB report (Ryan 2005).
Whittingham (1969) defined heat flow as positive when directed towards the reference level, and
used the conservation of energy equation given below.
Rn  H  Q  0
(2.15)
where:
Rn = radiation component
H = convection component
Q =conduction component
The prediction developed for maximum rail temperatures for Brisbane is shown in Equation 2.16:
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Trx  1.228Tx  9.7
(2.16)
where:
Trx = maximum temperate in the rail [⁰F]
Tx =the screened maximum temperature [⁰F]
This equation had a correlation coefficient R of 0.866 and a standard error of estimation of 4.13⁰F
[2.3⁰C]. However, it was developed in the 1960s, and instrumentation accuracy has improved
dramatically since then. Rail profiles and track structures have also changed substantially. For these
reasons, this equation may not be accurate for current track configurations and materials.
Whittingham (1969) also used this maximum temperature equation to draw up a map of Australia
with an isotherm of recorded average maximum screened air temperatures. The argument for this
was that the maximum screened temperature corresponded to when the sun was at its maximum
meridian altitude over Brisbane. Whittingham found that the maximum rail temperature coincided
with the maximum screened temperature. He also found that, throughout the year, the maximum
meridian altitude angle in Brisbane (range greater than 70⁰ to 90⁰) corresponded to the maximum
meridian altitude for Southern Tasmania and the tropics respectively. In this way, he extrapolated
the Brisbane equation for other areas of Australia.
Both the assumptions used by Whittingham were proven incorrect in subsequent experiments
conducted by Chapman et al. (2005), who found that rail temperature is affected by air temperature,
humidity, and orientation. These factors have a substantial effect on rail temperature, and are very
different in Brisbane than they are in the tropics or southern Tasmania.
Figure 2.14 shows the maximum expected rail temperatures in Australia as determined by
Whittingham, converted to degrees centigrade by Hagaman and Kathage (1988) as a part of rail
design standards in Australia.
Figure 2.14: Maximum Expected Rail Temperatures in Australia (Hagaman & Kathage 1988)
From July 2008 to February 2010, Munro (2009) conducted an experiment similar to that carried out
by Whittingham, this time on Victoria’s regional rail network. Munro’s aim was to establish whether
the information shown in Figure 2.14 was accurate, and whether a modification of Equation 2.16
would be more accurate for the temperate Victorian climate.
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Munro instrumented six sites around regional Victoria with weather stations and the in-situ
stress-monitoring product RSMs. Munro used regression equations with data from weather stations
located next to the tracks and from the nearest BoM weather station. Equations 2.17 and 2.18 were
used to calculate the rail temperature.
Trail  a  Tair
Trail  aT
. air  b.S  cW
. n  d .H
(2.17)
(2.18)
where:
Trail &Tair = defined previously
a,b,c,d = experimentally determined coefficients
S = solar radiation [MJ/m2]
Wn = wind intensity [km/h]
H = relative humidity [%]
Munro‘s findings are given in Table 2.7.
Table 2.7: Munro’s Main Findings (Munro 2009)
Parameter
Rail elevation
Rail orientation (N–S or
E–W)
Sleeper material
Relative humidity
Wind intensity
Data from BoM and
from weather station
beside track
Effect on rail temperature
No significant correlation found between the sites with highest and
lowest elevation (~400 m difference); however, more investigation is
required to increase the sample size.
N–S direction has higher rail temperatures relative to E–W rails.
Rails on timber sleepers are 7–15% hotter than rails on concrete
sleepers.
Effects on prediction were minimal (0.5–1% improvements in
regression accuracy).
Wind effects were non-linear and specific to each site.
Rail-temperature regression equations found from BoM data had an
average correlation factor of 0.796 with data measured trackside,
whereas trackside weather-station data and rail temperature had a
correlation factor of 0.918.
Both the map of isomers (Figure 2.14) and Munro’s results face the same problems as the methods
used by Hunt (1994) and Esveld (2001)—that is, they are not suitable for use as a real-time
prediction tool because of the large variations in rail temperature that any location would
experience. In fact, Munro notes that real-time temperature calculations using AWSs on sites with
critical rail temperatures are an expensive solution to predicting rail temperatures.
2.5.2 RSSB UK Rail-temperature Model
Chapman et al. (2005) developed a rail-temperature model using a simplified profile of the rail
shown in Figure 2.2a.
Chapman et al. validated their findings by conducting two field tests. Site 1 was at Winterbourne,
with a small section of rail clamped onto two sleepers sitting on a bed of ballast to UK standards,
fitted with screened air temperature sensors. Three Type K magnetic thermocouples were adhered
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to the head, web and foot1 of the rail, and the head of the rail was polished to simulate the wear
band present on in-situ rails. Site 2 was at Leominster, next to a ”live” track, where a weather station
was installed and rail temperature was measured using a temperature sensor secured to the rail foot
(Hima Sella sensor, with the sensor electrically insulated from the track to prevent interference with
signalling).The study team collected data over a 12-month period from June 2003 to June 2004.
The study found that it was not uncommon for the temperature of the rail-head to be twice that of
the air temperature (⁰C) in the afternoon, but that it was more common for the rail to be cooler than
the ambient air temperature because of the high thermal conductivity and diffusivity of the rail
steel’s microstructure. The largest difference in profile temperatures was between the head and the
foot in summer months. This difference reached a maximum of 3.7⁰C, with similar differences found
between the web and the foot temperatures.
Chapman et al. also found that the differences in profile temperatures of tracks orientated north–
south were greatest in the afternoon because the west-facing side of the web and head was in direct
sunlight. The highly reflective polished head absorbed less direct-beam radiation, whereas the
unpolished and rusted rail web received more radiation and heated up more. Chapman et al.
observed that rail-profile temperature differences increased throughout the day and peaked in late
afternoon, then decreased with the onset of dusk. After sunset, the profile temperature differences
became negligible as the rail rapidly cooled. Profile temperature differences were short-lived and
the differences minimal.
Chapman et al. found that the presence of moisture was very important. The large difference
between air and rail temperature in summer was not observed when heavy rainfall and high
humidity caused convective cooling of the rail and clouds blocked beam radiation. When there were
intervals of rainfall and sunshine, the rail adjusted to changes in incoming solar radiation and
moisture, although time lags in heating and cooling were observed.
Chapman et al. found a non-linear relationship existed between maximum rail and air temperatures
as a result of environmental factors such as track orientation, exposure to sun or wind, humidity,
precipitation and cloud cover. While empirical relationships such as those stated by Hunt (1994) and
Esveld (2001) provide good results for tracks from which data can be collected, they cannot be used
for tracks where similar direct-measurement data cannot be collected, because of these
environmental factors. Chapman et al. proposed a more sophisticated method using a zerodimension energy balance approach to predict an equilibrium service temperature with the
simplified rail track geometry seen in Figure 2.15b.
1
Note that Chapman et al. use the term “soffit” to imply the whole rail foot, even though “soffit” is
generally used to refer only to the underside of the rail foot. In this discussion, the term “foot” is
used to refer to what was called “the soffit” in the original work.
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Figure 2.15a: Cross-section of Rail Profile (Chapman et al. 2005)
Figure 2.15b: Schematic of the simplified model rail (Chapman et al. 2005)
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By balancing the energy of three types of heat transfer—conduction, convection and radiation—net
radiation flux of the rail web and the rail-head can be calculated. The governing equations are shown in
Equation 2.19 to Equation 2.21.
 RN H  H H  LEH  QSH  0
(2.19)
 RNWsun  HWsun  LEWsun  QSWsun  0
(2.20)
 RNWshade  HWshade  LEWsun  QSWshade  0
(2.21)
where:
RN = net radiation flux [W/m2]
H = sensible heat flux [W/m2]
L E= latent heat flux [W/m2]
QS = thermal conduction [W/m2]
Subscript W = rail web
Subscript H = rail-head
Subscript shade = rail track surface in shade
Subscript sun = rail track surface in sun
Chapman et al. further developed a prediction equation for the rail foot, as they believed that the rail
foot was the most practical place for rail personnel to measure rail temperatures. However, they
admitted that it might not be the most representative of rail temperatures—as confirmed by Ryan
(2005).
A two-dimensional diffusion equation was used to calculate heat flow within the track, which could be
used for the head and web of the rail:
  2T  2T 
T
 K S  2  2 
t
z 
 x
where:
Ks = thermal diffusivity of rail
T= temperature
(2.22)
t = the local apparent solar time
x and z = dimensions shown in Figure2.19b
Chapman et al. simplified the problem by assuming that:
 there was no heat exchange between underneath the foot and the air
 some parts of the foot surface would be exposed to direct beam radiation.
This prediction equation was tested against the physical measurements over a 200-day period at the
Winterbourne site. Weather data was collected from the weather station located at the site, but cloud
conditions were not measured at Winterbourne, so those from the nearest UK meteorological office
(Coleshill— 9 miles [14.48 km] from Winterbourne) were used.
Chapman et al. used statistical analysis on predicted temperature and actual measured temperature to
find the overall bias and root mean square error as shown in equations 2.23 and 2.24.
Overall bias equation is presented in Equation 2.23:
Modeli  Actuali
n
i 1,24
n

(2.23)
where:
Every 24 measurement was taken
Overall bias = 0.2°C
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Maximum temperature bias = −0.36°C
Minimum temperature bias = −0.21°C.
Root means square error was calculated:
n

i 1,24
 Modeli  Actuali 
2
(2.24)
n
Chapman et al.’s overall root mean squared error (RMSE) = 2.5°C, maximum temperature RMSE =
2.53°C, and minimum temperature RMSE = 2.02°C.
The mean maximum temperature lag was −44 minutes, and mean minimum temperature lag was −19
minutes.
The Chapman et al. model tends to underestimate rail temperatures, which may make it problematic to
use as part of a buckling-prevention system. The actual temperature of the rail may be higher than the
predicted temperature, and the time that the actual maximum occurs may be sooner than predicted.
This could result in a rail experiencing a larger-than-expected temperature increase sooner than
expected. Also, Chapman’s simplification of the model may artificially reduce the heat-transfer
properties of the rail, as an actual rail has a much larger surface area than the simplification. This makes
the model susceptible to underestimating a rail’s convective heat transfer. However, because wind does
not move at high speeds near the ground, this may not be a problem.
Chapman et al. also performed a sensitivity test on the model, using the methodology developed by
Thornes and Shao (1991) to assess the impact of various parameters in the model on rail-temperature
forecast curves.(Thornes and Shao 1991)
Chapman et al. used hypothetical data, consisting of constant values of relative humidity = 70%, wind
speed = 3 ms-1, precipitation = 0, cloud cover = 4 oktas, and cloud height = medium, with rail and air
temperatures varying throughout the day consistent with real data.
The results from the sensitivity test were:
1. Latitude: did not change maximum temperatures but increased minimum temperatures at higher
latitudes, because increases in latitude result in longer hours of sunlight.
2. Rail orientation: magnitude of maximum temperatures varied only slightly, but the maxima occurred
at different times of the day. A double peak is clearly seen in the rails oriented north–south, where
the reflective properties of the rail-head reduced the temperature of the rail at midday. The hottest
rails were found in the north–west/south–east orientations. In explaining this, Chapman et al. noted
that direct-beam radiation coincided with the maximum air temperatures for the day, creating
slightly higher rail temperatures. Rails oriented north–east/south–west were found to be the coldest.
3. Rail inclination: the simplification made at the beginning of the model made any subtle changes to
the rail geometry minimal; the result of difference is negligible.
4. Air temperature: decrease or increase in air temperature resulted in a decrease or increase in air
temperature. Any constant change in air temperature had no effect on the timing of the forecast
rail-temperature maxima and minima.
5. Relative humidity: increase or decrease in relative humidity resulted in a small increase or decrease
in forecast rail temperatures. The model was most sensitive to changes in humidity when forecasting
minimum temperatures in winter, where an increase or decrease in humidity of 20% could change
the temperature by around 1°C.
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6. Cloud cover: change from 3–5 oktas of cloud cover to 8 oktas reduced the maximum temperature
forecast by 6.15°C; a change from 3–5 oktas to clear skies increased the forecast by 1.27°C. Cloud
cover had negligible effects on the minimum temperature forecast, the time at which neither
maxima occurred, and the general shape of the temperature variation of the rail over the diurnal
cycle.
7. Cloud height: a small increase in rail temperatures was seen when cloud height was increased from
medium to high, and a small decrease in temperature occurred when cloud height was changed from
medium to low. There was also a reduction in the magnitude of the curve; the double peak seen with
the north–south orientation was far less obvious.
8. Wind speed: increase and decrease in wind speed produced lower maximum and overall rail
temperatures. Variations in wind speed appeared to have no effect on the timing of maximum
temperatures.
9. Precipitation: rain had a significant impact on suppressing maximum temperature. When the rail was
wet, there was an 8.16°C decrease in average and maximum temperatures compared with dry
conditions. Temperatures tended to peak slightly earlier when there was rain.
Although the model used by Chapman et al. was quite accurate, with a 0.2 overall bias and 2.5 RMSE,
simplifying the rail profile to a rectangular structure resulted in negligible effects for rail elevation. The
prediction equation was conducted for the rail foot. However, as Ryan (2005) demonstrated, variations
of up to 3.7°C can arise between the rail-head and foot because of rail-head emissivity and direct-beam
radiation. Potentially, there can be an under-estimate of approximately 5°C between the predicted foot
temperature and the head temperature of the rail, which corresponds better to the bulk-deformation
temperature (Ryan 2005).
Chapman et al. also omitted the ballast and track structure from the energy balance equation, and
assumed no heat transfer on the bottom of the foot, so any long-wave ballast inputs were not
accounted for. No heat transfer on the bottom of the foot can be justified for rails sitting entirely on
sleepers, because sleepers are non-conductive materials, but in-situ rails would have 130 mm sections in
contact with sleepers and then 550 mm without contact (and so on), so the proportion of rail not in
contact with sleepers would be much higher than that in contact with sleepers. This assumption will be
tested in this study.
2.5.3 FRA Rail-temperature Model
A model predicting rail-track temperatures for up to nine hours in advance was developed for the northeastern region of the United States by the Federal Railroad Association (FRA) in conjunction with Ensco,
Inc (Kesler & Zhang 2007; Zhang & Lee 2008).
The model uses existing numerical weather model temperatures, and the transient heat transfer of a
floating body to represent a finite rail element. The energy equilibrium equation used is a first-order,
non-linear, non-homogeneous, ordinary differential equation as stated in Equation 2.23 (Kesler & Zhang
2007; Zhang & Lee 2008):
Eabsorbed  Eg  Eout  Est
(2.23)
where:
Eabsorbed = rate of energy absorbed by rail from the sun and atmospheric irradiation [W/m2]
2
Eout = rate of energy emitted from the rail through convection, conduction and radiation [W/m ]
2
Eg = rate of energy generation due to conversion of energy forms (latent heat) [W/m ]
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Est = rate of energy change [W/m2]
The energy balance is affected by weather conditions, rail metallurgical properties, rail size, shape
factors and other environmental parameters
k s AsGs cos( )   hconv AC (Tr  T )   Ar (Tr 4  Tsky 4 )  Eother    cV
dTr
dt
(2.24)
where:
k = atmospheric filtering factor [ #]
 s = solar absorptivity
[#]
As = area of rail surface exposed to the sun [mm2]
Gs= solar constant [W/m2]
=
solar angle [⁰]
hconv= convective coefficient [W/m2K]
AC = area of rail surface subject to convection heat transfer [mm2]
Tr = rail temperature [⁰K]
T = ambient air temperature [⁰K]
 = emissivity of rail [#]
 = Stefan-Boltzmann constant [ W/m2K4]
Ar= area of rail surface subject to radiation heat transfer [mm2]
Tsky = atmospheric sky temperature above the cloud level [⁰k]
Eother = term for heat exchange at the interface of the rail–sleeper and rail–ballast
interfaces
 = density of rail steel [kg/m3]
c = specific head of rail steel [J/KgK]
V = volume of rail [mm3]
dTr
= change of rail temperature over time
dt
Zhang et al. (2008) used a dedicated weather-prediction service to provide a short-wave solar radiation
factor so that the factors that modify incoming environmental radiation were automatically calculated.
Zhang et al. would have needed to take a similar approach to Chapman et al. (2005) if MetwiseTM (a
commercial division of the USA National Weather Service) had not been used.
The convective heat transfer coefficient was found using Equation 2.25.
a  bvwin , for v win  5m/s
hconv  
0.78
 c(vwin ) , for v win > 5m/s
where:
a = 5.6
b = 4.0
c = 7.2
Vwin = wind velocity m/s
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Equation 2.25 is an empirical equation, developed by the USA’s National Institute of Standards and
Technology. As Zhang et al. noted, there was no standard method for determining the heat-transfer
coefficient, but it was sufficient for rail predictions.
Like Chapman et al. (2005), Zhang et al. simplified the model so that the heat exchange between the
sleeper and the ballast was assumed to be zero (no heat transfer). Zhang et al. assumed that there was
no energy generation due to energy conversion. However, because of the height of the rails, there
would be phase transformations in atmospheric species from evaporation, so it is unclear why Zhang et
al. assumed no energy conversion in the energy balance.
Sky temperature was used to find outgoing net heat from the rail; this was estimated to be −20°C below
air temperature. The true value for this variable would have been affected by cloud, aerosols, and
particles in the atmosphere, so this simplification was used. As Zhang et al. admit, this is highly
inaccurate, but there were no other simple ways to quantify this top-of-atmosphere temperature.
Zhang et al. developed a flow chart (shown in Figure 2.16), to show where rail-temperature prediction
could be used in the operation and management architecture of railways.
Figure 2.16: Flow Chart of Rail Representation of Influencing Factors (Kesler & Zhang 2007)
The forecast results produced by Zhang et al. were validated against results obtained from a 9 km x 9 km
area covering 10 north-eastern USA states. There was a maximum difference of 2°C and 4°C for windy
days between predicted temperature and measured temperature. The discrepancy was largest on windy
days because the forecast wind speed differed significantly from local values. This could have been due
to a number of factors. Wind speed and direction at the point where an anemometer is installed can
vary significantly from track level, while obstacles such as trees, bushes and buildings can shield the
track from wind so that it is not cooled as much as expected.
The correlation of forecast rail temperature and actual measured rail temperature is shown in Figure
2.17:
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Figure 2.17: Predicted and Measured Daily Maximum Rail Temperatures (Zhang & Lee 2008)
Both Chapman et al. (2005) and Zhang et al. (2008) have developed models that are relatively accurate
for predicting rail temperature. However, improvements can be made by more realistically modelling
the surface of the rail, and by taking into account the bottom surface of the rail foot and its heat
transfer.
Both models were also developed for sections of rail, rather than for in-situ rails with passing trains.
While Chapman et al. had a temperature sensor on the rail foot, it was used only for validation rather
than to collect data to develop the model. The current study will be the first to use in-situ rail profile
temperatures.
2.6 Concluding Remarks on Existing Rail-temperature Prediction
This review of the literature has found that empirical weather-prediction methods are either inaccurate
for the purpose of predicting rail temperature, or require an observation-gathering period that is too
long for the time available for this study.
The review has also found that existing rail-temperature models do not take into account heat transfer
on the bottom surface of the rail, or the additional heat inputs of frictional heat . Chapman et al. (2005)
did consider friction, but ruled it out as a heat source because their empirical data showed only a very
small increase in temperature caused by friction. However, this was contrary to empirical data later
collected by Frohling et al. (2008). In addition, the placement of sensors on the in-situ track used by
Chapman et al. (2005) was shown to be not the most representative of rail temperature in the railtemperature report produced by Ryan (2005).
The current study aims to:
 verify if there is heat exchange on the bottom of the rail foot
 quantify if heat generated by friction should be considered in a rail-temperature model.
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3. Research Methodology
3.1 Weather Predictions
Australia’s railway networks extend over large, often remote, geographic areas, where there are no
permanent weather stations operated by the BoM or other enterprises. Therefore, weather predictions
must be accurate over large geographic areas to meet the operational needs of the railway industry.
Furthermore, the horizontal resolution of the forecast is also important. Railway networks pass over and
through various topological features (e.g. mountains, valleys, built-up areas), all of which may influence
weather patterns and must be accounted for in weather predictions. Thus, any resolution chosen must
take into account the orographic forcing caused by topology (Pielke SR 2002).
In the initial stages of this study, the available weather services and forecasts provided by the BoM were
audited. From this audit, it emerged that the BoM offers a subscription service providing 48-hour
advance weather predictions for all locations in Australia, with an 11 km resolution. The predictions are
generated using BoM’s ACCESS-A NWP product (Bureau of Meteorology 2010).
For the purposes of the study, the aims of the weather prediction were to:
 verify the accuracy of the unmodified ACCESS-A NWP product against the measured weather
variables at the field experiment site
 downscale the ACCESS-A NWP data at a specific location into a 3.06 km horizontal and 15-minute
time resolution from the original 11 km horizontal and 1-hour time resolution. This would allow it to
be applied to more specific track locations.
3.1.1 Tasks Involved in Producing a Downscaled Weather Forecast
Figure 3.1 shows a flow chart of the tasks involved in producing a downscaled weather forecast.
BOM
forecasted
data at
Relevant
location is
found close
to the field
experiment
al site
Interpol
ation
Forecast data
at
approximatel
y 3km
horizontal
Data is
rearranged
from a
geographic
location
Data can
be used
for
multivari
ate
Figure 3.1: Flow Chart of Predictive Weather Model
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Figure 3.1 shows both unmodified (or raw) BoM data as well as the interpolated BoM data.
The accuracy of a weather prediction is important to any subsequent rail-temperature predictions, so
any modifications needed to be as accurate as the unmodified product. Different function codes in
MATLAB were written to transform ACCESS-A into a useable format for multivariate regression.
Functions were written to:
1. extract the relevant weather variables from netCDF format into a .mat format, which is easily
processed by MATLAB
2. target the geographic locations of interest within the ACCESS-A domain
3. interpolate all the weather variables in two dimensions
4. rearrange a matrix field of weather variables in the geographic domain into a matrix field of weather
variables in the time domain
5. interpolate all weather variables in time.
3.1.2 Network Common Data Format (netCDF) files
The netCDF format was chosen for the BoM weather prediction data because this format has a set of
access libraries for C, and MATLAB software Version 2008b has functions that use these C libraries, in
particular for indexing files.
netCDF is a set of interfaces for array-oriented data access, with a freely distributed collection of dataaccess libraries for C, Fortran, C++, Java, and other languages (Rew 2010). According to Rew (2010), the
main features of netCDF are as follows:
 netCDF files include information about the data they contain
 netCDF files can be accessed by computers with different ways of storing integers, characters, and
floating-point numbers
 a small subset of a large dataset may be accessed efficiently
 data may be appended to a properly structured netCDF file without copying the dataset or redefining
its structure
 one writer and multiple readers may simultaneously access the same netCDF file.
The netCDF file format and subsequent software were developed by Glenn Davis, Russ Rew, Ed Hartnett,
John Caron, Steve Emmerson, and Harvey Davies at the Unidata Program Centre in Boulder, Colorado,
with contributions from many other netCDF users (Rew 2010).
3.1.3 Cubic Spline Interpolation
Cubic spline interpolation was used to interpolate between the latitude and longitude points within the
horizontal BoM data, in order to find a resolution of 3.06 km from the original 11 km resolution.
The MATLAB function for bi-cubic spline interpolation ‘griddata’, with the method ‘cubic’, was used. This
was decided in consultation with Mr Ivor Blockley from Operations Development at the BoM’s NMOC
(Blockley 2010), who advised that a more advanced scheme similar to cubic interpolation is used for
operational forecasts.
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The theory behind the MATLAB function is the quick hull algorithm for convex hulls (Barber et al. 1996).
The one-dimensional interpolation through time uses the MATLAB function ‘spline’, which in turn uses
the spline interpolation algorithm described by de Boor (1978).(De Boor 1978)
3.2 Predicting the Temperature of the Rail Track Due to Weather
Conditions
ACCESS-A weather variables were used in a multivariate linear regression analysis with the measured
averaged rail temperatures to find a rail-temperature regression equation.
A selection of the full ACCESS-A weather variable fields was used for the rail-temperature regression
analysis. Variables such as below-ground soil temperatures, horizontal visibilities, etc., were not used
because they would not affect rail temperature.
ACCESS-A variables used in the regression analysis were:
1. v10: meridional component wind at 10 m height [m/s]
2. u10: zonal component wind at 10 m height [m/s]
3. temp_scrn: screen level temperature [⁰k]
4. dewpt_scrn: dewpoint screened temperature
5. sfc_pres: surface pressure [Pa]
6. accum_prcp: accumulated precipitation [kg m-2]
7. mslp: mean sea-level pressure [Pa]
8. accum_evap: accumulated evaporation [kg m-2]
9. av_lat_hflx: average surface latent heat flux [Wm-2]
10. av_lwsfcdown: average downwards longwave radiation at the surface [Wm-2]
11.av_netlwsfc: average net longwave radiation at the surface [Wm-2]
12.av_netswsfc: average net shortwave radiation at the surface [Wm-2]
13. av_olr: average outgoing longwave radiation at the surface [Wm-2]
14.av_sens_hflx: average sensible heat flux [Wm-2]
15.av_sfc_sw_dif: average surface shortwave diffuse radiation flux [Wm-2]
16.av_sfc_sw_dir: average surface shortwave direction radiation flux [Wm-2]
17.av_swirrtop: average incoming shortwave radiation flux [Wm-2]
18.av_swsfcdown: average downwards shortwave radiation at the surface [Wm-2]
19. mid_cld: mid cloud cover [0–1]
20.qsair_scrn: screen level (1.5 m) specific humidity [kg kg-1]
21.sens_hflx: surface sensible heat flux [Wm-2]
22.sfc_temp: surface temperature [⁰K]
23.soil_mois: soil moisture [kg m-2]
24.soil_temp: soil temperature [⁰K]
25. tmax_scrn: screen level (1.5 m) maximum temperature [⁰K]
26.tmin_scrn: screen level (1.5 m) minimum temperature [⁰K]
27.ttl_cld: total cloud cover [0–1]
28.z0: roughness length [m].
3.2.1 Tasks Involved in Producing Rail-temperature Prediction
Figure 3.2 is a flow chart of the tasks involved in producing a rail-temperature prediction.
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Weather
data
formatted by
MATLAB into
the time
domain
Multivariate
linear
regression
Rail
temperatur
es
Figure 3.2: Flow Chart of Predictive Rail-Temperature Model
Figure 3.2 shows the linear progression of inserting the weather data and generating rail-temperature
predictions. One function in MATLAB was written to perform regression analyses on the weather
variables.
3.2.2 Multivariate Linear Regression
Multivariate linear regression was chosen as the method to calculate rail temperatures from the
weather variables.
This is this same method used by Whittingham (1969) and Munro (2009) to calculate rail temperatures.
The MATLAB function used for multivariate linear regression is ‘mvregress’. ‘mvregress’ uses an
expectation condition maximisation (ECM) algorithm, which is an iterative method that finds maximum
likelihood in incomplete data-sets (Meng & Rubin 1993). In this study, the ECM algorithm was used for a
full data-set; thus, the ECM is a specialised case of a cyclic coordinate accent method for function
maximisation in the optimisation literature on iterative proportional fitting (Zangwill 1969; Haberman
1974).
3.3 Frictional Heat Quantification
Heat generated by train passage was captured by the field experimentation described in Chapter 4.
The data from this the field experiment was analysed statistically to quantify the temperature increase
due to train passage over the rail. The variance and standard deviation of the measurements were used
to indicate heat added to the track as a result of the train passage. The formulas used to calculate
variance and standard deviation are listed below in Equation 3.1 and Equation 3.2 respectively
(Weisstein 2010).
(3.1)
1 N
2
2
S 
S
where:
S = variance
S2= standard deviation
N =total number of samples [#]
N
1
N
 x  x 
i 1
i
N
  xi  x 
2
(3.2)
i 1
i = the sample number within the set of data
x = the value of the data
x = the mean of the data-set
3.4 Statistical Analysis of Measured Data and BoM Data
Some information is repeated between field experimentation data (as described in Chapter 4) and
purchased BoM data. Both the weather station and the BoM provided weather information about the
site, and both the thermocouple sensors and the RSMs provided rail-temperature information.
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Repeated values were checked for consistency, and then used in further analysis. Consistency checks
included:
 comparing predicted BoM variables with those measured by the weather station for the month
 comparing the surface profile temperature over the measurement period (this included the RSMs
rail-temperature data).
Data from both the weather station and the BoM were used in the regression analysis. The weather
station provided a set of real-time weather variables, while the BoM provided a set of predictive
variables.
Statistical comparisons between measured and calculated temperatures included:
1. comparing real-time, future predictive rail temperatures and empirical methods for accuracy
2. comparing BoM-interpolated temperatures with the raw BoM-predicted rail temperatures for
accuracy.
In addition, statistical comparisons included:
 taking the difference between the variables measuring the same phenomenon
 finding the correlation, overall average bias and overall average root mean squared error (RMSE)
between the calculated and measured rail temperatures.
The equations to calculate correlation, overall average bias, and overall average RMSE are listed in
equations 3.3, 3.4 and 3.5 respectively.
(3.3)
1 N
( xi  x )( yi  y )

N  1 i 1
r
N
1
1 N
( xi  x ) 2 
( yi  y ) 2


N  1 i 1
N  1 i 1
(3.4)
x y
Biasoverall 
RMSEoverall 
where:
N = total number of samples [#]
x = measured variable
x = mean of the measured variables

N
  x  y
2
(3.5)
N
y = predicted variable
y = mean of the predicted variable
i = the sample number within the set of data
Figure 3.3 shows the statistical comparisons and analyses carried out during the study.
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BOM
forecasted
data at 11km
Data is
reduced to
relevant
geographic
area
Interpolatio
n
Forecast data
at 3km
horizontal
resolution for
specific site
location
Comparison 1
BOM
forecasted
data at 11km
Data is
reduced to
relevant
geographic
area
Data is
rearranged from
geographic
domain to time
domain
Weather
measured
data
Multivariate
regression
Comparison
3
Comparison 2
List of rail
temperature
values from
interpolated
BoM data
List of rail
temperature
values from
unmodified
BoM data
List of rail
temperature
values (from
weather
station
regression)
Measured rail
temperatures
from
thermocouples
Measured rail
temperatures
from RSM
Figure 3.3: Flow Chart of Methodology
Figure 3.3 shows that statistical analysis was performed at several stages of the study, and that data
sources and the study results were evaluated.
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4. Experimental Design
The aim of this study was to develop software to enable the accurate prediction of rail-track
temperatures. While other Australian projects have attempted to calculate rail temperatures
(Whittingham 1969; Munro 2009), this is the first attempt to predict rail temperatures using an NWP
product.
An important part of the current study was to compare the accuracy of the new software with that of
existing technology and methods for predicting rail temperatures. In order to compare the new method
to previous research (Whittingham 1969; Munro 2009), an experimental design similar to that used by
Munro (2009) was devised.
This field experiment employed:
 an automated weather station (AWS) to measure weather variables
 thermocouple temperature sensors to measure rail surface temperatures
 RSMs (rail stress modules), an off-the-shelf product to measure rail temperatures.
Each played a different function in the study.
 The weather station provided the screened air temperatures and wind velocities used by
Whittingham (1969). It also provided the necessary information to check the accuracy of the NWP
product, ACCESS-A, purchased from the BoM.
 The thermocouples provided rail surface temperatures across the profile of the rail.
 The RSMs allowed the researchers to compare the accuracy of the program developed for this study
to an existing product that monitors rail temperature.
The equipment and configuration of the field experiment are described in more detail below.
4.1 Site Layout
The field test site was at Edungalba, central Queensland, on the QR national coal network, located at
latitude 23.7⁰, longitude 49.9⁰.
The thermocouples and RSMs were installed on a 4 m section of the right rail and a 6 m section of the
left rail. The different rail lengths were chosen for ease of identification (the thermocouple
configurations were different on the two rails).
The rail track was located on an embankment approximately 3 m above the ground level of the rail
corridor. Under QR National’s track-safety protocol, none of the data acquisition system (DAQ)
equipment or power supply could be installed within 3 m of the track centre-line (known as the “danger
zone”).
Accordingly, the DAQ box was installed just outside of the danger zone, and the power supply (which
was larger) was installed in the rail corridor below the embankment. A network cable connecting the
DAQ box to the power supply enabled study personnel to download the thermocouple data without
having to walk near the danger zone. A diagram of the instrumentation rail sections as installed on the
real track is shown in Figure 4.1.
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Figure 4.1: Instrumented Rail Sections Installed on the Track
(NB: Figure 4.1 also includes strain gauges, which were not used for this study but related to another
study that also used the track instrumentation.)
4.2 Thermocouples and Rail-temperature Measurements
A thermocouple is a device that converts thermal energy into electrical energy. Thermocouples work on
the Seebeck, Peltier and Thomson effect (Pollock 1993). The type of thermocouple sensor used for this
study is shown in Figure 4.2.
Figure 4.2: Cement on Polyimide Thin-film Thermocouple (TC Direct 2009)
The thermocouple sensors chosen for this study are cement on polyimide thin-film thermocouples—
aerostructure grade (TC Direct 2009). Their specifications are as follows:
 Type T Class 1
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 temperature measurement range of −250⁰C to 300⁰C
 accuracy of +/−0.004*(temperature measured) or 0.5⁰C at all other temperatures
 dimensions are 20 mm x 10 mm x 0.13 mm thick.
Before field installation, the thermocouples were compared with existing Type K thermocouples to
check for consistency of temperature measurement.
4.2.1 Thermocouple Set-up on Rail Profile
Fifteen thermocouples were adhered to the surface of the two rail sections. The configuration of the
set-up is shown in figures 4.3a and 4.3b.
Figure 4.3a: Position of Thermocouples on Rail Profile
Figure 4.3b: Numbered Thermocouple Sensors for Easy Identification
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There were 17 surface thermocouples in total, with 15 sensors actively taking measurements and 2
residual sensors in Position 8 and Position 16. The two residual sensors were backups in case Sensor 7 or
Sensor 17 was damaged during installation.
The left rail does not have a bottom-of-rail foot sensor because this section of the rail is placed on top of
a sleeper, whereas the right thermocouple has a bottom-of-rail foot sensor (Sensor 13) because it sits on
top of the ballast. This was to gauge whether temperature transfers from the bottom surface were
significant to the heating pattern of the rail overall.
Thermocouple measurements were recorded in the field by a National Instrument Compact Rio DAQ (NI
2011). The saved file format was ‘.tdms’. A MATLAB program was written using a National Instrument
‘tdms’ wrapper to import and analyse the results.
4.2.2 Laboratory Test of Thermocouples
Thin-film surface thermocouples were installed in the laboratory using adhesive proxy. They were
checked for operation by placing two 500 W lamps at a 45⁰ angle approximately 10–20 cm from the
sensors. The experimental set-up is shown in Figures 4.4a and 4.4b.
Figure 4.4a: Laboratory Experimental Set-up Right rail
Figure 4.4b: Thermocouple Sensors
Four additional Type K surface thermocouples (lab thermocouples) for each rail were temporarily
adhered to the rail with masking tape, and read at 10-minute intervals to check for consistency. An
example of the data produced by this comparison is shown in Figure 4.5.
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sensor comparison
80
75
70
Temp deg C
65
60
55
DAQ channel 4
Thermocouple sensor 2
50
45
40
35
0
200
400
600
800
time intervals (/10s)
1000
1200
1400
Figure 4.5: Graph of Thermocouple on Right Web
Figure 4.5 shows good correlation between the installed thermocouples and the lab thermocouples
(although, because the thermocouples were in different positions and had different accuracies, an exact
match was not expected). From Figure 4.5, it was concluded that the field-experiment thermocouples
were in working order and the rails could be installed in the field.
4.3 Weather Station
Weather variables were measured using a standard weather station WXT50, produced by Vaisala. This
was installed approximately 20 m away from the instrumented track section and 10 m above ground
level. The weather station measured:
 screened air temperature [⁰C]
 relative humidity [%]
 wind speed [m/s]
 wind direction [⁰ from north]
 rainfall—intensity [mm/h], accumulation [mm], and duration [s].
This automated weather station (AWS) conforms to the regulations in the World Meteorological
Organisation standard for installing an AWS (WMO 2008). It took measurements every 10 minutes,
which were logged in the DAQ and downloaded once every 4 weeks. An image of the weather station
and DAQ configuration is shown in Figure 4.6.
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Figure 4.6: Weather Station and DAQ Set-up
The measurement range and accuracy of the weather variables measured are listed in Table 4.1 below.
Table 4.1: Variables Measured by Weather Station: Measurement Range and Accuracy
Weather variable
Measurement range
Accuracy
Barometric pressure
600~1100 hPa
Air temperature
Wind speed
−52⁰C~60⁰C
0~60 m/s
Wind direction
Relative humidity
0~360⁰ (from azimuth)
0~100%
Rainfall accumulation
Rain duration
Rain intensity
0.01 mm
10-second increments
0~200 mm/h
+/− 0.5 hPa at 0⁰C to30⁰C
+/− 1hPa at −52⁰C to 60⁰C
+/− 0.3⁰C
+/−0.3 m/s or +/−3% between
0–35 m/s
+/−5% between 36–60 m/s
+/−3.0⁰
+/−3% at 0–90%RH
+/−5% at 90–100%RH
5%
(NB: Where lines are blank in the “Accuracy” column, it is because accuracy in these cases depends
largely on other measured variables, such that accuracy is greatly variable.)
The recorded weather measurements were saved in a ‘.csv’ format with a date stamp per measurement.
4.4 Rail Stress Modules (RSMs)
Two RSMs (see Figure 4.7) were installed alongside the thermocouples as a second way to measure rail
surface temperature. The RSMs were designed to measure both surface strain and surface temperature
on the neural axis of the rail, but, for this study, only the rail temperature was used.
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RSMs use an integrated temperature sensor, which has:
 an accuracy of +/−10C from −200C to +600C
 a battery life of 10 years
 a storage memory of 7.5 months when using 10-minute measurement intervals (Salient Systems Inc
2009).
The wayside weather monitor shown in Figure 4.6 contained a radio that communicated with the RSMs
shown in Figure 4.7. The wayside monitor allowed the data stored in each RMS to be downloaded
remotely via the phone network.
Figure 4.7: RSMs Installed on the Rail in the Field Experiment
The RSMs outputted their files in Excel format. A program was written in MATLAB to import and analyse
the results.
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5. Rail-temperature Prediction Software
As a part of this study, interactive rail-temperature prediction software was written in MATLAB. The
software converts the ACCESS-A netCDF files from the BoM into a graphical forecast of rail temperatures
based on Equation 6.15 and Table 6.10 as outlined in Section 6.4.
The software consists of one main program, three main functions and an update to the numberconservations program written by Ameya Deoras (Deoras 2010), which is covered by a Berkeley
Software Distribution licence and is free for public use. The script for the program is:
1. main.m
2. readncfile.m
3. interpolate.m
4. resize.m
5. dynamicDateTicks.m. (Deoras 2010)
A library file beta.mat also needs to be included for the software to run. The user is prompted for the
path to this file in the main program. All the above-mentioned files need to be saved in the same
directory for the program to run.
The program was developed using the July 2010 weather-parameter data-set for the track in the east–
west orientation. In addition, it was developed for a Linux system. If it was to be run on a Windowsbased system, alterations to the path import/export routines would need to be made.
In the future, these program scripts could be developed into a stand-alone program or excitable
software by using the MATLAB compiler (Mathworks 2008). The program is designed to be read in one
run of ACCESS-A from BoM at a time.
5.1 Operating the Program
The file ‘main.m’ is the main file program that controls all operations and interacts with the user. It calls
up the function ‘readncfile’ to read ACCESS-A files in netCDF format, and uses the functions ‘resize’ or
‘interpolate’ depending on whether the user wants to use raw ACCESS data or interpolated ACCESS data.
At the start, the program asks the user for the location of ACCESS-A files on the computer, as shown in
Figure 5.1a and Figure 5.1b.
Figure 5.1a: Program Prompt to Specify Path to Files
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Figure 5.1b: Folder Selection Prompt for Location of ACCESS-A Files
The program then asks the user to specify the location of interest in latitude and longitude in degrees.
The latitude is positive in the northern hemisphere and negative in the southern hemisphere.
ACCESS-A has domain limits of latitude −55.00S to 4.73 N, longitude 95.00E to 169.69E. Figure 5.2 shows
the prompt for the user to enter the location of the rail.
Figure 5.2: Prompt to Enter Latitude and Longitude of the Location of the Rail
After the prompt, the program asks the user if they would like to save the output of the file in the
current working directory. This is shown in Figure 5.3.
Figure 5.3: Prompt for Location to Save Output Files
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If ‘Yes’, is selected, the output results are saved to the MATLAB working directory, where the program
scripts are located. If ‘No’ is selected, another location-selection window prompt will appear, in the
same format as Figure 5.1b.
The main program then inserts the location of the specified folder and the geographic location of
interest in the ‘readncfile’ function. The ‘readncfile’ function imports the netCDF file format into a
MATLAB multidimensional structure array format, with a domain of 5.39⁰x5.39⁰ of latitude and
longitude surrounding the geographic location of interest. The MATLAB array ‘varnc’ is passed back to
the main program, then main asks the user if interpolation of the data is required, as shown in the
prompt box in Figure 5.4.
Figure 5.4: Prompt Asking if Data Should Be Interpolated
If ‘interpolate’ is chosen, the ‘varnc’ variable and the latitudes and longitudes previously entered by the
user are fed into the function ‘interpolate’, which interpolates the ACCESS-A variables in the
geographical plain and then in the time plain. The function ‘interpolate’ then rearranges the ACCESS-A
variables into time-dependent variables in a multidimensional structure array ‘vars’, which has as its
fields the variable names from ACCESS (i.e. vars.temp_scrn, vars.v10, vars.sfc_temp, etc.).
If ‘raw’ is chosen, the 'varnc' variable and the latitudes and longitudes entered by the user are fed into
the function ‘resize’, which rearranges the raw ACCESS-A variables into the multidimensional structural
array ‘vars’.
If ‘both’ is chosen, the ‘varnc’ is fed both into the ‘interpolate’ and the ‘resize’ function and the
operations described above are performed.
Once the variable ‘vars’ is passed back to the main program, it prompts the user for the location of the
library file ‘beta.mat’, which contains the regression coefficients listed in Table 6.10 in Chapter 6 of this
report. After the location of ‘beta.mat’ is established, the main program loads the ‘beta.m’ file.
The main program then asks the user if they would like to include Whittingham’s equation calculations
(Whittingham 1969) or Hunt’s sunny- and cloudy-day equation calculations (Chapman et al. 2005). If
option ‘all’ is chosen, the screened-temperature variable from the ACCESS-A files is used in the empirical
relationships to calculate a rail temperature.
The main program then calculates rail temperatures accordingly and produces a graph (an example of
which can be seen in Figure 5.5). The graph depicts rail temperatures over the period specified in the
ACCESS-A files, and saves to the user-specified folder in the ‘.mat’ format of date and time and rail
temperatures.
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Figure 5.5: Sample Output of Software with Options of Using Raw BoM Data
5.2 Program Disclaimers
The program was developed using data from July 2010, for rail in an east–west orientation, with steel
sleepers and fist-clip fasteners, in the central Queensland area.
Using the program outside of these parameters may produce results that are not as accurate as the rail
predictions listed in Section 6.4 of this report. However, the program could be made more generic if
statistical regression factors are found for each season and more samples of rail temperatures and rail
configurations are entered as different options.
5.3 Program Run Times
The run time of the program was calculated using a quad core Linux system. Run times were
approximately:
1. 2 minutes to read in 49 ACCESS-A files
2. 5 seconds to rearrange the ACCESS-A variables into the time domain
3. 3 minutes for the two-dimensional cubic interpolation
4. 19 minutes for the one-dimensional cubic spline interpolation of the already interpolated twodimensional data.
It took approximately 25 minutes to run the program interpolating the raw BoM data, and 2 minutes to
run the program with only the raw BoM data.
Depending on a user’s computer, run times could be faster or slower.
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1. 6. Results and Discussion
All field experiments carry the risk of equipment damage. In the case of this study, out of the three
data-collection methods (weather station, thermocouples, and RSMs) only the RSMs (a commercial
product designed for the railway environment) survived the three-month period in the field.
The weather station recorded the full set of weather variables from 31 March 2010 to 8 August 2010. On
18 August 2010, study personnel found a DAQ malfunction that had occurred on 8 August 2010. A visual
inspection of the DAQ revealed that the only noticeable fault related to the memory card. A new
memory card was installed on the next track visit on 13 October 2010; however, on the next site visit on
11 November 2010, the weather station was found to be recording only wind and precipitation
variables. Air temperature, relative humidity, and air pressure were not recorded after 8 August 2010.
Due to time constraints, no attempt was made to repair the weather station DAQ.
The thermocouples recorded the full set of rail temperatures at one-hour intervals from 30 May 2010 to
13 August 2010. On the track visit on 18 August 2010, study personnel found that the thermocouple
DAQ was not recording because the memory card was full, and had stopped recording on 13 August
2010. Also on 18 August 2010, personnel noted that Thermocouple 9, located on the side of the railhead on the right rail (shown in Figure 4.3b), was damaged. Unfortunately, Thermocouple 9 was not
repaired and the DAQ was not restarted because the main electrical technician who implemented the
DAQ system was not present. On a track visit on 13 October 2010, the DAQ was restarted with new
software. The measurement interval was 1 sample per minute and the DAQ was automatically triggered
to take 70 samples per second when trains passed the instrumented site. On the track visit on
11 November 2010, the thermocouple DAQ was found to have recorded only three days of data from
13 October 2010 to 16 October 2010. Because of time constraints, no attempt was made to repair the
thermocouple DAQ.
The RSMs, which also record rail temperature, were installed on 8 March 2010, and are still recording
data.
ACCESS-A data from the BoM before 26 May 2010 was validation-stage data, as the BoM had only
recently moved to ACCESS-A from its previous LAPS NWP product. From 1 March 2010 to 26 May 2010,
the ACCESS-A model was running on an SX6 supercomputer and the 6-hour run and 18-hour run were
only forecast to +9 hours. Full ACCESS-A data from the BoM was available from 27 May 2010 to 05
December 2010.
The period for which all data-sets are available is 30 May 2010 to 8 August 2010—that is, two full
months of data in the winter 2010 period. This is not ideal for a study investigating rail buckling due to
high temperatures.
The data-sets for each analysis are listed below:
 July 2010 data-set (31 days, 744 samples ) was used for rail-temperature regression analysis
 June 2010 data-set (30 days, 720 samples ) was used to validate the regression analysis
 July 2010 data-set (30 days 744 samples) was used to check for consistency between BoM data and
weather-station data
 30 May 2010 to 13 August 2010 data-set (76 days 1824 samples) was used to check for consistency
between thermocouple data and RSMs data
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 30 May 2010 to 13 August 2010 data-set (76 days 1824 samples) was used to quantify the
temperature change over the rail profile and between the left and right rail.
6.1 Weather Variables Comparison: Weather Station and BoM data
The BoM prediction data was compared with actual measured data from the weather station. The BoM
data came in a gridded format, where the weather station is located at latitude −23.7⁰, longitude 149.9⁰.
BoM data geographically closest to this location were chosen, and several other surrounding BoM points
were chosen to gauge how much the weather variables differed within a 0.2⁰ change in latitude and
longitude. Figure 6.1 shows the configuration of BoM data-points in relation to the weather station.
Lon:149.67
Lat:-23.65
Lon:149.7
8lat:-23.65
Lon:149.89
Lat:-23.65
Lon:150
Lat:-23.65
Weather station
Lat:-23.71
Lon:149.9
Lon:149.67
Lat:-23.76
Lon:149.67
Lat:-23.87
Lon:149.78
Lat:-23.76
Lon:149.78
Lat:23.87
Lon:149.89
Lat:-23.76
Lon:149.89
Lat:-23.87
Lon:150
Lat:-23.
Lon:150
Lat:-23.87
Figure 6.1: Location of Weather Station Between Grid Locations of BoM Data
The BoM data also came in several runs, with a new prediction file for the next 48 hours made available
four times a day, so there is considerable overlap between each prediction file. This is shown in detail in
Figure 6.2.
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0 6 1 1 24 3 3 4
H H 2 8 H 0 6 2
R R H H R H H H
R R
R R R
4
8
H
R
Figure 6.2: ACCESS-A Predictions of Each Run and Their Overlap
Figure 6.2 shows that the prediction data in Run 1 overlaps 42 hours with Run 2, 36 hours with Run 3
and 32 hours with Run 4.
How accurately each run predicts the measured weather variables is not constant; there are slight
variations in accuracy between each run. This may be because of variations in the observational data
gathered for various runs. For example, Run 1 is a morning run, with the largest number of observations
included for the prediction output. On the other hand, night-time runs do not include observation data
from radiosonde balloons, which are launched only in the morning in most Australian cities.
The correlation coefficients, bias, and root mean squared errors of each run for each location were
performed. Overall, Run 1 was found to be most accurate in forecasting most weather variables. The
comparisons between each weather-station-measured variable and the BoM equivalent are detailed in
sections 6.2.1 to 6.2.6.
Run 1 itself had some overlap in predictions, as shown in Figure 6.3. The BoM provides its NWP model
with observational data before each run, so shorter-term forecasts should be more accurate than
longer-term forecasts (because a longer time elapses between when observational data is taken and
when predicted weather will occur for longer-term forecasts). This was confirmed by separating Run 1
into a 1–24-hour forecast and a 25–49-hour forecast.
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0 6 1 18 24 30
HR H 2 H HR H
R H RUN
R 1 (dayR1)
R
3 42 48
6 H H
H R R
R
RUN 1 (day2)
0 6
HR H
R
1 18 poi 30
2 H
H
R
H R
R
3 42 48
6 H H
H R R
R
Figure 6.3: ACCESS-A Predictions of the First Run of Each Day and Its Overlaps
BoM data forecasts are also in one-hour intervals; that is, only one instantaneous prediction
measurement is given for the hour, with the measured weather-station variables gathered every 10
minutes (i.e. the BoM forecast is not an average, but an instantaneous point prediction). Therefore, to
compare data-sets, weather-station data was not averaged but was sampled for every sixth 10-minute
measurement (i.e. every hour). Thus the time of the measured variable corresponds to the time of the
predicted variable.
6.1.1 Screened Air Temperature
The BoM variable of screened air temperature is predicted at 1.5 m above ground in degrees Kelvin.
Screened air temperature does change with elevation above ground level; however, as a 10 m elevation
is within 0.1⁰C of the screened temperature at 1.5 m (Blockley 2010), this was assumed to be
insignificant. The BoM variable temp_scrn was converted to degrees Celsius by subtracting 273.15. The
graph for July 2010 is shown in Figure 6.4.
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Figure 6.4: Screened Air Temperature July 2010
The temperature variation plotted corresponds very well with the measured temperature, although
there are some minimum temperature extremes around 19 and 20 July and 23 and 24 July that the
predicted temperature does not account for. After checking the rain-gauge measurement for these
days, study personnel found that there were large amounts of precipitation on those days, which could
account for the temperature difference in predicted and measured values. The screened temperature
corresponded well with the actual measured air temperature; the correlation factor, overall average
bias, and overall root mean squared error are tabulated in Table 6.1. The formula for calculating the
correlation coefficient is explained in Chapter 3 of this report.
Table 6.1: Correlation Coefficients of Screened Air Temperature
Screened Air Temperature Correlation Coefficient
Run 1 (1–24-hour prediction)
Run 1 (25–49-hour prediction)
lon:149.67 lat:–23.65
0.945
0.916
lon:149.78 lat–23.65
0.943
0.918
lon:149.89 lat:–23.65
0.940
0.921
lon:150 lat:–23.65
0.938
0.923
lon:149.67 lat:–23.76
0.943
0.915
lon:149.78 lat:–23.76
0.941
0.916
lon:149.89 lat:–23.76
0.940
0.920
lon:150 lat:–23.76
0.939
0.923
lon:149.67 lat:–23.87
0.938
0.913
lon:149.78 lat:23.87
0.938
0.913
lon:149.89 lat:–23.87
0.936
0.916
lon:150 lat:–23.87
0.936
0.919
From Figure 6.4, it can be seen that screened air temperature is a very stable variable, reflected in the
consistently high correlation coefficients shown in Table 6.1. The fact that the geographically closest
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points do not have the highest correlation coefficients (which are bolded) is unexpected but not
impossible, because the difference in correlation is within +/−0.025 at about 0.942 and the variable does
not vary overly much across the landscape. It is possible that a grid point had very similar temperatures,
which coincidently corresponded slightly better with the measured temperature. The correlation was
separated into the first 1–24-hour prediction and the 25–49-hour prediction. As expected, the forecast
decreased in accuracy over time. For a detailed explanation of overall bias calculation, see Chapter 3 of
this report. The overall biases in degrees Celsius are listed in Table 6.2.
Table 6.2: Screened Air Temperature Overall Bias
Screened Air Temperature Overall Bias
Run 1 (1–24-hour prediction)
Run 1 (25–49-hour prediction)
lon:149.67 lat:–23.65
–0.816
–0.889
lon:149.78 lat:–23.65
–0.792
–0.856
lon:149.89 lat:–23.65
–0.677
–0.751
lon:150 lat:–23.65
–0.550
–0.632
lon:149.67 lat:–23.76
–0.739
–0.809
lon:149.78 lat:–23.76
–0.719
–0.770
lon:149.89 lat:–23.76
–0.585
–0.642
lon:150 lat:–23.76
–0.478
–0.547
lon:149.67 lat:–23.87
–0.604
–0.667
lon:149.78 lat:23.87
–0.642
–0.687
lon:149.89 lat:–23.87
–0.482
–0.534
lon:150 lat:–23.87
–0.365
–0.396
From the overall bias, it can be seen that the location with the highest correlation factors actually has
the highest bias, which indicates that the reasoning behind the discrepancy of correlation is sound.
Overall RMSE was performed on the data-sets to see what difference existed between the measured
and predicted samples. This is presented in Table 6.3.
Table 6.3: Screened Air Temperature Overall RMSE
Screened Air Temperature Overall RMSE
Run 1 (1–24-hour prediction)
Run 1 (25–49-hour prediction)
lon:149.67 lat:–23.65
1.980
2.343
lon:149.78 lat:–23.65
1.992
2.303
lon:149.89 lat:–23.65
1.976
2.243
lon:150 lat:–23.65
1.954
2.172
lon:149.67 lat:–23.76
1.992
2.331
lon:149.78 lat:–23.76
1.992
2.305
lon:149.89 lat:–23.76
1.969
2.234
lon:150 lat:–23.76
1.934
2.160
lon:149.67 lat:–23.87
2.051
2.347
lon:149.78 lat:23.87
2.031
2.330
lon:149.89 lat:–23.87
2.029
2.280
lon:150 lat:–23.87
1.997
2.207
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Table 6.3 shows that the lowest overall RMSE is at the BoM data-point longitude 150, latitude –23.65,
which corresponds to one of the nearest geographical locations of the BoM data-points. It should be
noted that correlation coefficient, although a good indicator of correlation, does not necessarily indicate
the closest geographic location when the variable is highly stable across the landscape. Statistically, the
geographic BoM data-points do not vary greatly for screened air temperature. This indicates that a
weighted combination of the statistical factors needs to be considered when deciding which raw BoM
data-point should be used, because correlation alone is not the best indication in this instance.
A weighted correlation, bias, RMSE factor for screened air temperature is calculated using Equation 6.1
below.
(6.1)
R
 Correlation 10  bias  RMSE
screen _ temp
where Rscreen_temp is the weighted factor for screened air temperature.
A factor table is included below.
Table 6.4: Weighted Factor for Screened Air Temperature
Rscreen_temp
lon:149.67 lat:–23.65
lon:149.78 lat:–23.65
lon:149.89 lat:–23.65
lon:150 lat:–23.65
lon:149.67 lat:–23.76
lon:149.78 lat:–23.76
lon:149.89 lat:–23.76
lon:150 lat:–23.76
lon:149.67 lat:–23.87
lon:149.78 lat:23.87
lon:149.89 lat:–23.87
lon:150 lat:–23.87
Run 1 (1–24-hour prediction)
6.656
6.645
6.751
6.881
6.696
6.703
6.845
6.980
6.723
6.710
6.850
6.995
Run 1 (25–49-hour prediction)
5.924
6.024
6.212
6.428
6.009
6.089
6.324
6.520
6.115
6.115
6.345
6.591
From the weighted factor Rscreen_temp, it can be seen that the geographic location of the BoM data closest
to the location of the actual weather station does correspond; however, this could not be used to decide
which raw BoM data-point should be used in analysis until other weather variables had been checked.
6.1.2 Relative Humidity
Relative humidity is not a quantity in the BoM data fields; however, the BoM data fields do include
dewpoint temperature and screened air temperature, which can be used to calculate relative humidity.
The relative humidity conversion formula (Lowe & Fickle 1974) in equations 6.2, 6.3, and 6.4 was used to
convert the two BoM field quantities into relative humidity. Relative humidity is a calculation of the
moisture content in the atmosphere, so both the dewpoint (the temperature at which air can no longer
hold all of its water vapour, and some must condense into liquid) and the actual air temperature need to
be considered.
RH 
(6.2)
e(TD )
100
e(T )
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


e  a0  T a1  T a2  T a3  T  a4  T  a5  T  a6  

e  min ewater , eice  , 50C  T  100C
(6.3)
(6.4)
where:
RH = relative humidity [%]
TD = dewpoint temperature [⁰C]
T = the screened air temperature [⁰C]
e = vapour pressure of water (Equation 6.3)
Table 6.5: Coefficients to Calculate Vapour Pressure of Water
Vapour pressure of water factors
Water
Ice
a0
6.107799961
6.109177956
a1
4.436518521x10-1
5.034698970x10-1
a2
1.428945805x10-2
1.886013408x10-2
-4
a3
2.650648471x10
4.176223716x10-4
a4
3.031240396x10-6
5.824720280x10-6
a5
2.034080948x10-8
4.838803174x10-8
-11
a6
6.136820929x10
1.838826904x10-10
After the BoM fields of dewpoint temperature and screened air temperature were converted into
relative humidity, they were graphed in Figure 6.5 below for the month of July 2010.
Figure 6.5: Relatively Humidity July 2010
Relative humidity is, again, a very stable weather variable, with no large sudden fluctuations over the
month of July. The BoM raw data have similar results to screened air temperature when the two are
statistically compared. The correlation coefficient, overall bias and overall RMSE are calculated in the
same way as for screened air temperature and can be found in Appendix I.
As the prediction moves further out in time from the observation input, the relative humidity bias has in
some cases doubled in magnitude from the 1–24-hour to the 25–49-hour predictions for the same BoM
geographic location. Again, the BoM data location closest to the weather station did not have the lowest
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bias; however, as in the case of screened air temperature, this is due to the stable nature of the variable.
Further information is needed to decide on the best raw BoM data-point to use for calculations. The
RMSE of relative humidity is far larger than that for screened air temperature, due mostly to relative
humidity being a percentage variable.
Overall, the RMSE is out by approximately 10%. If a percentage calculation was taken for screened air
temperature, a number similar in magnitude would be observed. Taking the percentage into account, a
weighted factor analysis was performed on relative humidity, shown in Equation 6.5 below.
(6.5)
RRH  Correlation 10  0.1 bias  0.1 RMSE
The weight factor of relative humidity is listed in Appendix I. The weighted factor RRH of the geographic
location of the BoM data-point closest to the location of the actual weather station does correspond
well. However, this is not conclusive, as the weighted factors are all very close to each other. A more
dynamic weather variable needs to be considered for a final analysis.
6.1.3 Surface Air Pressure
Surface pressure is the air pressure at the surface. The weather-station pressure unit was the hectorPascal (hPa), while the BoM field output was supplied in Pascals, so the BoM field was multiplied by 10
to provide consistent units. A graph of surface air pressure for the month of July 2010 is show in Figure
6.6 below.
Figure 6.6: Surface Air Pressure July 2010
In Figure 6.6, the measured pressure is consistently around 5 hPa higher than predicted pressures.
Although there is a slight elevation in the weather-station measurement, this would not equate to a
5 hPa increase. This is due to the discrepancy between the BoM model topography elevation at the
location and the elevation. Pressure typically drops by about 1 hPa for every 10 m increase in altitude.
This suggests that the model topography is in the order of 40–50 m higher in elevation than the real
topographic height at the weather-station location. This discrepancy seems large but not impossible
(Blockley 2010). The correlation coefficient, overall bias, and overall RMSE were calculated in the same
way as for screened air temperature.
The pressure bias and RMSE for surface air pressure were constantly 4 hPa and 15 hPa respectively less
than the measured pressure. Therefore, for surface pressure, the weight factor should take into account
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the correlation more than the bias or RMSE, as these are consistently large. The weight factor for
pressure is shown in Equation 6.6. This factor weights the correlation coefficient more heavily than
either bias or RMSE compared to the weighted factor for screened air temperature and surface air
pressure.
Rsurface _ pres  Correlation 10  0.01 bias  0.01 RMSE
(6.6)
From the weighted factor Rsurface_pres, it can be seen that the geographic location of the BoM data on the
latitude line –23.65⁰ corresponds most closely to the actual weather-station data. However, this is not
conclusive, as the weighted factors are all very close to each other. A more dynamic weather variable
needs to be considered in the final analysis.
6.1.4 Zonal Winds (U)
Zonal wind components are the wind magnitudes parallel to lines of constant latitude, that is, along the
x-axis in the Cartesian plane, while meridional wind components are parallel to lines of constant
longitude—that is, along the y-axis in the Cartesian plane. The weather station measured winds in
magnitude and wind direction in degrees from north.
However, if the zonal and meridional winds were transformed into magnitude and direction, analysing
the two data-sets would be problematic, because when the wind direction is nearing 0⁰ it is also nearing
360⁰. Thus, the decision was made to transform the wind magnitude and wind direction measured by
the weather station into the zonal and meridional wind fields that BoM fields provide. This task was
carried out using equations 6.7 and 6.8 (Blockley 2010).
(6.7)
U  r  sin( )
(6.8)
V  r  cos( )
where:
U = zonal winds [m/s]
V = meridional winds [m/s]
r = wind magnitude [m/s]
θ = wind direction [⁰]
The graph of the zonal winds in Figure 6.7 shows large deviations and a very noisy wind pattern.
Although the general trend of wind is present, there is too much fluctuation for the prediction data to
be as close to the measured data as that for the other weather variables. This does not affect the results
greatly, because the rail track is located near the ground surface, where wind effects are greatly reduced
(whereas the data-sets compared in this section are elevated 10 m above the ground surface).
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Figure 6.7: Zonal Winds July 2010
The correlation coefficient, overall bias, and overall RMSE are calculated and listed in tables 6.14, 6.15
and 6.17 below. As expected from Figure 6.7 above, the correlation coefficients for zonal winds are far
less than those of screened air temperature, surface pressure, or relative humidity. The correlation
coefficient, overall bias, and overall RMSE are calculated in the same way as for screened air
temperature.
The overall bias and the overall RMSE of zonal winds reflect a not very skilful forecast, but, due to the
nature of wind and the strong influences of topology, this is not surprising. The BoM model from which
the data is extracted has a grid resolution of 11 km. With a low-topology resolution, the wind variable
prediction would be smoothed out compared to measured winds. Although the wind forecast is not very
skilful, it does give some information about the forecast, so a similar weighted factor is found for the
zonal wind magnitudes as shown in Equation 6.9.
(6.9)
RU  Correlation 10  0.1 bias  0.1 RMSE
From the weighted factor RV, it can be seen that, similar to surface pressure, the geographic location of
the BoM data on the latitude line –23.65⁰ corresponds better to the actual weather-station data.
6.1.5 Meridional Winds (V)
A similar process was performed for meridional winds. Surprisingly, the meridional winds graphed in
Figure 6.8 below appear to be better correlated with the measured data than the zonal winds.
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Figure 6.8: Meridional Winds July2010
Calculations using the correlation coefficient listed in Appendix G show that the correlation coefficient
of meridional winds is indeed much larger than those for the zonal winds. However, a large overall bias
and large overall RMSE exist, as shown in tables 6.19 and 6.20 below.
Similar to the zonal winds, a weighted factor is calculated for the meridional winds, using the formula as
for zonal wind calculation and listed in Appendix G.
(6.10)
RV  Correlation 10  0.1 bias  0.1 RMSE
From the weighted factors RV and RU, it can be seen that forecasting wind is not very effective for the
BoM model; however, wind prediction can be used as an indication of a closer geographic location. Thus
a combined and overall weighted statistical factor was found to indicate how well the BoM data forecast
the weather at the field location and which raw BoM data-point was to be used in further analysis.
6.1.6 Overall Statistical Weighted Factor
An overall weighted factor for all of the weather variables was calculated using Equation 6.11 and the
values in Table 6.6.
(6.11)
Rscreen _ temp  RRH  Rsurface _ pres  RV  RU
Roverall 
5
This weighted overall factor averages all the weighted factors, so that an overall indication of
“goodness” of prediction can be found for the raw BoM data.
Table 6.6: Weighted Overall Goodness of Prediction Factor
Roverall
lon:149.67 lat:–23.65
lon:149.78 lat:–23.65
lon:149.89 lat:–23.65
lon:150 lat:–23.65
lon:149.67 lat:–23.76
lon:149.78 lat:–23.76
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6.505
6.495
6.465
6.500
6.431
6.446
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6.132
6.078
6.064
6.108
6.102
6.053
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lon:149.89 lat:–23.76
lon:150 lat:–23.76
lon:149.67 lat:–23.87
lon:149.78 lat:23.87
lon:149.89 lat:–23.87
lon:150 lat:–23.87
6.426
6.507
6.261
6.324
6.266
6.315
6.021
6.103
5.980
5.982
5.903
5.950
The closest geographic locations to the actual weather station have higher goodness of prediction
factors for Run 1 (1–24-hour predictions) than those located further way from the geographic location,
with the exception of a few locations such as longitude 149.67, latitude −23.65. Latitude −23.87,
although only one latitude grid away, gives a noticeable margin of 0.2–0.3 less in the goodness of
prediction factor compared to the other location for Run 1 (1–24-hour predictions). This could be
because of the hilly nature of the area, where the BoM data has a low resolution of the terrain, which
affects the wind variables the most and other variables to a lesser extent. This could also be why some
locations near latitude −23.65, longitude 149.67 have high goodness of prediction factors, because the
BoM model has terrain that better matches the weather station’s location. This does not imply that that
location is closer to the actual weather station, rather that there are terrain differences between the
actual field site and what the BoM model expects to be there.
Goodness of prediction is noticeably less for Run 1 (25–49-hour prediction) than for Run 1 (1-24-hour
prediction). This indicates that, as prediction time becomes further away from the model run, it
becomes less accurate. Also, as accuracy decreases, the variation in the goodness predictor decreases.
Thus the decision was made that the BoM data-point at latitude −23.76, longitude 150 should be used as
the example of the ”raw BoM data”. It was also decided that interpolated data-points surrounding the
weather station’s location would be used for comparison, to see whether interpolation in between
geographic- and time-interpolated data-sets would reduce the accuracy of the rail-temperature
prediction. The following points around the weather station were used:
 longitude 149.9725, latitude −23.7050
 longitude 150, latitude −23.7050
 longitude 149.9725, latitude −23.7325
 longitude 150, latitude −23.7325.
The interpolated data-points can be seen in Figure 6.9 below.
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Lon:149.89
Lat:-23.65
Lon:149.9175
lat:-23.65
Lon:149.9450
Lat:-23.65
Lon:149.9725
Lat:-23.65
Lon:149.89
Lat:-23.6775
Lon:149.9175
lat:-23.6775
Lon:149.9450
Lat:-23.6775
Lon:149.9725
Lat:-23.6775
Lon:149.89
Lat:-23.7050
Lon:149.9175
lat:-23.7050
Lon:149.9450
Lat-23.7050
Lon:149.9725
Lat-23.7050
Weather station
Lon:149.87
Lat:-23.71
Lon:149.89
Lat:-23.7325
Lon:149.89
Lat:-23.76
Lon:149.9175
Lat:-23.7325
Lon:149.9175
lat:-23.76
Lon:149.9450
Lat:-23.7325
Lon:149.9450
Lat-23.76
Lon:149.9725
Lat:-23.7325
Lon:149.9725
Lat-23.76
Figure 6.9: Configuration of Interpolated BoM Data-points in Relation to Weather Station
6.2 Comparison of Temperature Difference over the Rail Surface
Fifteen surface thermocouples were attached over two rails (see Chapter 4 of this report for a detailed
description of sensor placement). It was theorised that:
 sensors on the same sides of the rail should have the same heating pattern as each other
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 over the profile of any one rail, there should be distinct differences in temperature at critical points
in the day such as sunrise, sunset and at maximum air temperatures
 there should be some slight variation between the rail sitting directly on a sleeper and the rail
suspended above the ballast.
For this reason, the following analysis of rail temperature over the surface profile is divided into three
sections relating to:
1. sensors in the same orientation but on different rails
2. sensors in different positions on the profile on the same rail
3. rail temperatures of rail sitting on sleeper and rail sitting on ballast.
6.2.1 Sensor in the Same Orientation but on Different Rails
Corresponding sensors on the left and right rails are graphed together in Figure 6.10 below. From this
figure, it can be seen that, between 12 July 2010 and 14 July 2010, although there is a slight difference
between maximum temperatures, it is not consistent or large. Further analyses in terms of overall bias
and root mean squared error between the two sensors were done using equations 6.12 and 6.13.
(6.12)
T
T
Biasoverall 

RMSEoverall 
left _ rail
right _ rail
no.samples
 (T
left _ rail
(6.13)
 Tright _ rail )2
no.samples
where:
Tleft_rail is the rail-temperature sensor on the left rail
Tright_rail is the corresponding rail-temperature sensor on the right rail
no.samples is the number of samples
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th
Rail temperature deg C
Rail temperature deg C
5
10
15
20
25
30
10
20
30
40
5
10
15
20
25
30
06/12-2010
06/12-2010
06/12-2010
Date
06/13
Date
06/13
Date
06/13
Left rail field side web
Right rail gauge side web
06/14
06/14
Left rail gauge side top of foot
Right rail field side top of foot
06/14
Left rail gauge side under side of head
Right rail field side under sid eof head
Rail temperature deg C
Rail temperature deg C
CRC for Rail Innovation
Rail temperature deg C
Rail temperature deg C
5
10
15
20
25
30
10
15
20
25
30
5
10
15
20
25
30
06/12-2010
06/12-2010
06/12-2010
Left rail field side top of foot
Right rail gauge side top of foot
06/14
06/14
Left rail gauge side web
Right rail field side web
Date
Left rail field side under side of head
Right rail gauge side under side of head
06/13
06/14
Date
06/13
Date
06/13
Rail surface thermocouple sensor measurement
Track Stability Management
In
these
calcula
tions,
bias is
the
consist
ent
tempe
rature
differe
nce
betwe
en two
sensor
s at
the
same
orient
ation
on the
left
and
right
rail,
which
can be
either
a
negati
ve or
positiv
e
numbe
r, and
the
RMSE
is a
measu
re of
the
absolu
te
differe
nce
betwe
en the
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Track Stability Management
two sensors. The results of the overall bias and RMSE appear in Table 6.7.
Table 6.7: Overall Bias and RMSE of Thermocouples in Same Orientation but on Different Rails
Overall bias (⁰C)
Overall RMSE (⁰C)
Left rail gauge side under head and
0.206
0.737
right rail field side under head
left rail gauge side web and right rail
0.108
0.673
field side web
left rail gauge side top foot and right
0.016
0.710
rail field side top food
left rail field side top foot and right rail
0.056
0.654
gauge side top foot
left rail field side web and right rail
0.136
0.628
gauge side web
left rail field side under head and right
0.180
0.693
gauge side under head
Overall, calculating the bias and RMSE from 30 May to 13 August 2010 (1824 samples), there is less than
a +/−1 ⁰C difference for both bias and RMSE. This magnitude is within sensor accuracy range, indicating
that two sensors in the same orientation and on the same position of the profile have virtually the same
heating profiles. This occurs even when the two sensors are placed 300 mm apart longitudinally and on
different rails. It is conclusive that, within small distances such as sleeper spacing and crib distances, the
temperature profiles of both rails can be regarded as the same at different positions on the profile.
6.2.2 Different Positions on the Profile on the Same Rail
Sensors placed in different positions across the surface of the same rail record a different result. There is
a noticeable and consistent variation between the thermocouples across the profiles of both rails as
shown in Figure 6.11 below. This is consistent with past research (Ryan 2005), which showed distinct
heating differences between different areas on the rail’s surface. On the east–west rail used for this
study, the differences in temperature were more pronounced at sunrise, as seen around 5am (19:00
GMT) on 12 and 14 June. At this time of day, some sensors would be in direct sunlight and others not.
Also, as demonstrated by the maximum temperatures around 1pm (3:00 GMT) on 12, 13 and 14 June, at
this time of day, the sensors under the head of the rail would be in direct shade and would record lower
temperatures than those exposed to direct sunlight. Statistically, the percentage variance and
percentage standard deviation in degrees Celsius are graphed in Figure 6.12 below.
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Rail temperature deg C
9 August 2011
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0
-1
10
20
30
40
-0.5
10
15
20
25
30
35
0
-1
5
10
15
20
25
30
35
40
45
50
0.5
1.5
12:00
2
18:00
Degree C variance
1
3
06/13-00:00
2.5
06:00
3.5
12:00
0
-1
10
20
30
40
-0.5
18:00
0.5
1
1.5
06/14-00:00
06:00
Degree C standard deviation
0
12:00
2
18:00
2.5
Gauge side under head
Gauge side web
Gauge side top foot
Field side top foot
Field side web
Field side under head
Field side side head
Left rail percentage standard deviation from mean May-August2010
-0.5
06:00
0
0.5
1.5
12:00
2
18:00
Degree C variance
1
3
06:00
3.5
12:00
0
-1
Date and time (GMT)
06/13-00:00
2.5
5
10
15
20
25
30
35
40
-0.5
Right rail surface temperatures
45
50
18:00
0.5
1
1.5
06/14-00:00
06:00
Degree C standard deviation
0
12:00
2
18:00
2.5
Field side side head
Field side under head
Field side web
Field side top foot
Bottom foot middle
Gauge side top foot
Gauge side web
Gauge side under head
Date and time (GMT)
Right rail percentage variance from mean May-August2010
Right rail percentage standard deviation from mean May-August2010
06:00
0
Percentage % of occurance
over the May-August 2010 period
50
Left rail surface temperatures
Left rail percentage variance from mean May-August2010
5
06/11/10-18:00 06/12-00:00
Rail temperature deg C
5
06/11/10-18:00 06/12-00:00
10
15
20
25
30
Percentage % of occurance
over the May-August 2010 period
Percentage % of occurance
over the May-August 2010 period
CRC for Rail Innovation
Percentage % of occurance
over the May-August 2010 period
50
Track Stability Management
Page 71
Figure 6.12 shows that although there are instances where the variation and deviation of
temperature indicate a real difference in temperature across the profile (that is, above 1⁰C), the vast
majority of the time, variance and standard deviation are within 0.5⁰C of the mean rail temperature.
Therefore, as in the study conducted by Ryan (2005), the current study took the mean surface
temperature as the rail temperature for further calculations involving rail temperature as a variable.
6.2.3 Rail Temperatures on Rail Sitting on Sleeper and Rail sitting above
Ballast
The literature review (Chapter 2) noted that previous studies have found that a rail’s location on
sleepers or above ballast is largely insignificant in overall considerations of rail temperature. This
somewhat surprising finding was deemed worthy of further investigation in the current study.
Therefore, care was taken to mount sensors on one rail sitting on a sleeper with fist clips, and on
another rail that was above ballast. This could be one reason for greater variance and standard
deviation on the right rail, which sat above ballast, than on the left, which sat on a sleeper. The
difference between thermocouples has been plotted in Figure 6.13 below. From Figure 6.13, it can
be seen that there is a larger percentage of foot top differences between 0⁰C and −1⁰ C (i.e. the right
rail is consistently warmer than the left rail, as the difference was Tleft_rail-Tright_rail).
Distrubiton of difference between left and right rail sensors
11
Left rail gauge under head, right rail field under head
left rail gauge web and right rail field web
left rail gauge top foot and right rail field top food
left rail field top foot and right rail gauge top foot
left rail field web and right rail gauge web
left rail field under head and right gauge under head
The foot sensors have
10percentage
larger
difference
9
Percentage occurance
8
7
6
5
4
3
2
1
0
-2
-1
0
1
2
3
Degrees difference between left and right rail
Figure 6.13: Differences between Thermocouples
Results from the sensors on the foot of the rails indicate that the right rail (rail above ballast) is
generally marginally warmer than the left rail (rail on sleeper). However, this difference is within the
range of sensor accuracy and the results are not conclusive. Therefore, more analysis was performed
on the daily maximum and minimum temperatures and the difference between the mean
temperature and the bottom-of-foot temperature. This is graphed in Figure 6.14.
In the 76-day period, the foot of the right rail, which was never exposed to direct sunlight, could, at
maximum rail temperature, be warmer than the average surface temperature of the rail. Around
10% of the time, it was more than 1⁰C warmer than the average rail temperature. However, for a
majority of the time, the rail temperature on the bottom surface was cooler than the average rail
temperature. This distributed temperature difference between mean and foot temperature was
closely related to weather phenomena. If rain was falling or winds were high, the right rail top
_________________________________________________________________________________
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surface was exposed to more convective cooling than the foot, which was insulated by the ballast,
resulting in a higher foot temperature than the mean. Where there was incident radiation on the
other surface, the foot in shade was lower in temperature. This is an important issue for further
research if a generic model of rail temperature is to be attempted.
Daily minimum temperature differences between the foot and the mean right-rail temperature were
also calculated. The distribution of the daily minimum temperatures was more regular than that of
daily maximum temperatures. This issue would also need to be researched further in the
development of any more generic rail-temperature model.
Maximum temperature differences right rail mean- bottom of foot sensor
Percentage % of maximum
temperature difference
6
5
4
3
2
1
0
-3
-2
-1
0
1
Degree C difference
2
3
4
Minimun temperature differences right rail mean- bottom of foot sensor
Percentage % of minimum
temperature difference
12
10
8
6
4
2
0
-1.5
-1
-0.5
0
Degree C difference
0.5
1
1.5
Figure 6.14a (top): Difference of Maximum Rail Temperatures between Mean and Bottom of Foot
Figure 6.14b (bottom): Difference of Minimum Rail Temperatures between Mean and Bottom of
Foot
Generally, then, the rail sitting on sleepers was marginally warmer than the rail sitting above ballast.
For maximum average temperatures, the sleepered rail was overall 0.7⁰C warmer than the rail on
ballast. However, as this is in the same magnitude as the sensor accuracy range, it is not a conclusive
finding. A more generic model, using thermodynamic principles, needs to be developed for this
finding to be verified. While it can hypothesised that smaller sleeper spacing would have an overall
effect on rail temperature, this would also need further investigation.
6.2.4 RSMs and Thermocouple Rail-temperature Comparison
RSMs are a commercially available product that was used in this study partly as robust
instrumentation to verify thermocouple measurements. The RSMs are encased in a hollow metal
casing as protection for their sensors. The average left- and right-rail temperatures were compared
with the sampled results from the RSMs. From the graphs (as seen in Figure 6.15), it was found that
RSMs data was noisier than the thermocouple measurements. This noise corresponded to the times
when a train passed over the sensors. The RSMs recorded a noisy signal at train passage that was
not present in the thermocouple data. There was also a time delay between the measurements
recorded by the thermocouples and those recorded by the RSMs. At times there was a 1.5- to 2-hour
difference between the measured maximums of the day, as can be seen in Figure 6.15.
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Left rail temperatures 4th -6th June 2010
Temperature deg C
45
RSM rail temp
mean thermocouple rail temp
measured air temp
40
35
30
25
20
15
10
06/04/10-00:00
06:00
12:00
18:00
06/05-00:00
06:00
12:00
18:00
06/06-00:00
06:00
Date and time (GMT)
Right rail temperatures 4th -6th June 2010
45
RSM rail temp
mean thermocopule rail temp
measured air temp
Temperature deg C
40
35
30
25
20
15
10
5
06/04/10-00:00
06:00
12:00
18:00
06/05-00:00
06:00
12:00
18:00
06/06-00:00
06:00
12:00
Date and time (GMT)
Figure 6.15a (top): Mean, RSMs Left-rail Temperature and Air Temperature, 4–6 June 2010
Figure 6.15b (bottom): Mean, RSMs Right-rail Temperature and Air Temperature, 4–6 June 2010
This is in part due to the thermal mass of the RSMs unit, which insulates its rail-temperature sensors
from the elements, and in part due to the fact that the changes in rail temperature are most
pronounced on the surface of the rail, where the thermocouples were located. This second factor
was mitigated somewhat by taking the average temperature of the thermocouple measurements.
Readings showing the actual air temperature of the day are the red line in Figure 6.15 above. Air
temperature maximums correspond well with the maximum RSMs measurements but, again, this
can be deceptive. As seen in results from Chapman et al. (2005), the timing of rail temperature
maximums in relation to air temperature depends largely on rail orientation and seasonal changes.
Both of these factors would have contributed to the time difference between the RSMs and
thermocouple measurements. The RSMs and thermocouples correlate well, with the left rail having
a coefficient of correlation of 0.902 and the right rail 0.879. However, further analysis of the RSMs
measurements would be required in order to validate the RSMs product in Australia.
6.3 Rail-temperature Prediction
Rail-temperature regression equations for both BoM and weather-station data were formulated
using multivariate linear regression (as outlined in Chapter 2). July 2010 was chosen as the month for
use because it was the only month where data from all four sources was available. Previous research
(Chapman et al. 2005) indicates that one month of regression data is not robust enough for future
prediction. However, with the limited data available, a distinction between the formulation data-set
and the validation data needed to be maintained for a non-biased assessment of the accuracy of any
regression equation developed. The average left-rail temperature was chosen to represent
measured rail temperature because it had less variance and deviation (as explained in Section 6.3.2
below).
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6.3.1 Real-time Predictions
A real-time predictions equation was formulated from weather-station measurements. It was called
“real-time” because the weather-station measurements occurred at the same time as the railtemperature measurements, so there was no lead time between predicting rail temperature and it
occurring. Real-time rail-temperature prediction was developed for the July 2010 data-set (31 days
at 744 samples). Equation 6.14 (with coefficients in Table 6.8) was the result.
Trail  1Tair  2U wstat  3Vwstat   4 RH  5 Pr es
where:
Tair = screened air temperature [⁰C]
Uwstat = zonal winds [m/s]
Pres = air pressure [hPa]
(6.14)
Vwstat = meridional winds [m/s)
RH = relative humidity [%]
Table 6.8: Real-time Rail-temperature Prediction Coefficients
Variable
Coefficient
α1
−0.653448202389647
α2
0.637206478633606
α3
0.218464524148432
α4
2.12553852746129
α5
−0.0545025911532638
This weather-station regression equation is compared for the month of June with the empirical
relationships of Whittingham’s maximum-rail-temperature equation (1969) and Hunt’s sunny- and
cloudy-day equations ( 1994). These four different rail-temperature predictions are all classified as
real-time, because their empirical relationships use a real-time air-temperature measurement from
the weather station. This is discussed further in Section 6.4.1.1 below.
6.3.1.1Validation Analysis of Real-Time Predictions
The coefficients in Table 6.9 above are used for the weather-station data in June 2010, and
compared to the mean left-rail temperature in June 2010. Temperatures from 9 –12 June 2010 are
graphed in Figure 6.16.
June validation rail temperatures
35
Temperature deg C
30
25
20
15
10
5
average left rail temperature
Hunt's cloudy rail temp
Hunt's sunny rail temp
Whittingham's max rail temp
weather station regressoin
air temperature
0
06/09/10-18:00
06/10-00:00
CRC for Rail Innovation
06:00
12:00
18:00
06/11-00:00
06:00
12:00
18:00
Date
and Time (GMT)
th
9 August 2011
06/12-00:00
06:00
12:00
18:00
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06/13-00:00
Track Stability Management
Figure 6.16: Validation Graph of Real-time Rail-temperature Predictions 9–13 June 2010
Figure 6.16 shows that all the empirical relationships consistently overestimate the rail temperature,
even when real-time air temperature is used. This is consistent with the purpose of the empirical
relationships, which was to find a critical maximum temperature of the day using predicted air
temperature. The correlation coefficient of the empirical equations is only slightly lower (0.858
compared with the weather station equation of 0.896). However, the overall bias and RMSE of the
empirical relationships (listed in columns 2 and 3 of Table 6.9) show that the bias is magnitudes
larger than the weather-station equation. An exception is Hunt’s sunny-day equation, which
performs better than both Whittingham’s equation and Hunt’s cloudy-day equation, because most
of the days in June 2010 were sunny. The overarching concern with the empirical real-time
equations is that there is no accurate time of critical temperature. An empirical relationship may find
a satisfactory maximum rail temperature, but these equations do not accurately indicate when this
maximum temperature will be reached and how long the maximum will remain.
Table 6.9: Statistical Comparison of Real-time Rail-temperature Predictions
Correlation Coefficient
Average overall bias
Average overall
R2
⁰C
RMSE ⁰C
Real-time prediction (air temperature is measured at the same time as rail temperature)
Whittingham’s
0.858
−8.722
10.149
equation
Hunt’s sunny-day
0.858
−3.227
5.806
equation
Hunt’s cloudy-day
0.858
−12.497
13.742
equation
Weather-station
0.896
0.659
4.193
prediction
Over the 720 measurements that were taken in the month of June 2010, the difference between the
measured mean temperature and various relationships were calculated and graphed in Figure 6.17
below. Figure 6.17b shows that Hunt’s sunny-day equation performs better than previous empirical
relationships; however, the weather-station equation for the site is better distributed around 0⁰ C
differences, whereas Hunt’s sunny-day equation has maximum occurrence at around 5⁰C higher
than actual rail temperature. This is as expected, because the weather-station relationship was
developed for the site of validation, whereas the other equations were developed in other locations
around the world.
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Hunt sunny day equation
Occurences within the June 30 days
Occurences within the June 30 days
Whittingham equation
120
100
80
60
40
20
0
-20
-15
-10
-5
0
5
10
15
Temperature difference measured -predicted degC
20
100
80
60
40
20
0
-20
-15
-10
-5
0
5
10
15
Temperature difference measured -predicted degC
Weather station regression
400
Occurences within the June 30 days
Occurences within the June 30 days
Hunt cloudy day equation
350
300
250
200
150
100
50
0
-20
-15
-10
-5
0
5
10
15
Temperature difference measured -predicted degC
20
20
100
80
60
40
20
0
-20
-15
-10
-5
0
5
10
15
Temperature difference measured -predicted degC
20
Figure 6.17a (top left): Real-time Rail-temperature Prediction using Whittingham’s Equation (Measured Minus Predicted)
Figure 6.17b (top right): Real-time Rail-temperature Prediction using Hunt’s Sunny-day Equation (Measured Minus
Predicted)
Figure 6.17c (bottom left): Real-time Rail-temperature Prediction using Hunt’s Cloudy-day Equation (Measured Minus
Predicted)
Figure 6.17d (bottom right): Real-time Rail-temperature Prediction Using Weather-station-regression Equation (Measured
Minus Predicted)
The purpose of the research conducted by Hunt (1994) and Whittingham (1969) was to develop a
gauge for maximum rail temperatures so that maximum rail temperatures could be investigated. The
difference between the maximum rail temperature and the maximum predicted temperatures is
graphed in Figure 6.18.
Figure 6.18 shows that, as expected, Whittingham’s equation performs better at predicting
maximum temperatures than all other relationships. Whittingham’s equation predicts the maximum
within a +/−5 ⁰C range 28 out of the 30 days, whereas even the weather-station prediction is in the
0–10⁰C interval less than measured rail temperature for the majority of June 2010. This could be
problematic for operational usage, if the predicted temperature is consistently 5–10⁰C less than the
actual rail temperature. This could be improved if more data-sets were used in the regression
process, given that Whittingham had 15 months of data-sets for his empirical analysis. This was not
possible for the current study, but a hybrid program using Whittingham’s equation for maximumtemperature estimation and the weather-station equation for temperature timings could be a less
time-intensive method of producing a better timed forecast.
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Whittingham equation
Hunt sunny equation
7
Occurances of maximum
temperature differences
Occurances of maximum
temperature differences
10
8
6
4
2
0
-20
-15
-10
-5
0
5
10
15
6
5
4
3
2
1
0
-20
20
Temperature difference measured -predicted degC
Hunt cloudy equation
-10
-5
0
5
10
15
20
Weather station regression equation
6
Occurances of maximum
temperature differences
6
Occurances of maximum
temperature differences
-15
Temperature difference measured -predicted degC
5
4
3
2
1
0
-20
-15
-10
-5
0
5
10
15
5
4
3
2
1
0
-20
20
Temperature difference measured -predicted degC
-15
-10
-5
0
5
10
15
20
Temperature difference measured -predicted degC
Figure 6.18a (top left): Daily Maximum Rail-temperature Differences
between Measured and Whittingham’s Prediction
Figure 6.18b (top right): Daily Maximum Rail-temperature Differences
between Measured and Hunt’s Sunny Day Prediction
Figure 6.18c (bottom left): Daily Maximum Rail-temperature Differences
between Measured and Hunt’s Cloudy Day Prediction
Figure 6.18d (bottom right): Daily Maximum Rail-temperature Differences
between Measured and Weather Station Regression Prediction
6.3.2 Future Predictions
The BoM predicts weather variables 1–48 hours in advance. Practically speaking, files are not
uploaded onto the BoM ftp server for subscribers to download until the third hour of the prediction
because of the size and the number of services that the BoM offers (Blockley 2010). This shortens
the prediction to 1–45 hours; however, this does not detract from the predictive nature of the files.
Thus the runs from BoM have still been separated into 1–24-hour forecasts and 25–48-hour
forecasts as shown in Figure 6.2 in Section 6.2. The multi-variant regression for the 1–24 hour
equation was developed for July 2010 and is shown in Equation 6.15. The BoM predictions for
weather variables that are used in this section are from the location latitude −23.76, longitude 150,
and have not been modified in any way.
Trail  1v10   2u10  3temp _ scrn   4 dewpt _ scrn  5 sfc _ pres
(6.15)
  6 accum _ prcp   7 mslp +8 accum _ evap  9 av _ lat _ hflx 
10 av _ lwsfcdown  11av _ netlwsfc  12 av _ netswsfc  13 av _ olr
 14 av _ sens _ hflx  15 av _ sfc _ sw _ dif  16 av _ sfc _ sw _ dir
 17 av _ swirrtop  18 av _ swsfcdown  19 mid _ cld   20 qsair _ scrn
  21sens _ hflx   22 sfc _ temp   23 soil _ mois   24 soil _ temp 
 25t max_ scrn   26t min_ scrn + 27ttl _ cld + 28 z 0
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where the symbols used are the same as those explained in Section 3.2. The β coefficients are listed
in Table 6.10.
Table 6.10: Coefficients of Regression β
Coefficient
Number
β1
0.0349214685860181
β2
0.300803117783424
β3
3.26127609691842
β4
0.548680299876555
β5
−0.0176241478356276
β6
0.296859695855778
β7
0.0190721105766093
β8
1.08266611560058
β9
− 0.00968231367160908
β10
0.114534168536698
β11
–0.133276582471754
β12
7.95797683959537
β13
0.00914604669678778
β14
0.0120850138461365
β15
–1725.67323763576
β16
–1725.67801531730
β17
0.00230863771581154
β18
1718.97342606071
β19
0.390794423357368
β20
–1002.22138885324
β21
–0.00394730467453745
β22
0.189313674908339
β23
–0.0616725597039408
β24
0.221087658354270
β25
–0.105847604257958
β26
–2.95880644076632
β27
0.635764475671435
β28
–17880.8512663862
6.3.2.1 Validation of Future Predictions
The graph of 13–16 June 2010 appears in Figure 6.19 below. As can be seen in the figure, the BoM
prediction is variable. On 13 June 2010, the prediction is very close to the actual rail temperatures;
on 14 June, it is greater than actual; on 15 June, the prediction is less than actual; and so on. Hunt’s
and Whittingham’s equations were calculated using the BoM screened temperature field
(temp_scrn) and graphed in the figure. Much of Figure 6.19 shows empirical relationships
overestimating rail temperatures when using real-time measured air temperatures. This also occurs
when using the predicted screened air temperatures. Again, the timing of the maximum
temperatures is not well-interpreted by the empirical formulas; at times, the peaks occur three to
four hours after the measured rail temperatures.
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Future prediction temperature validation
40
Temperature deg C
35
30
25
20
15
average left rail temperature
Hunt's cloudy day rail temp
Hunt's sunny day rail temp
Whittingham's rail temp
BoM 1-24 predicted rail temp
air temperature
10
06/13/10-06:0012:00
18:00 06/14-00:00 06:00
12:00
18:00 06/15-00:00 06:00
12:00
18:00 06/16-00:00 06:00
12:00
18:00
Date and time (GMT)
Figure 6.19: Future Predicted Rail Temperature 13–16 June 2010
The correlation coefficient, overall average bias and RMSE were found for the three empirical
formulas by Hunt and Whittingham and for the BoM regression equation and are listed in Table 6.11
below.
Table 6.11: Statistical Comparison of Future Predictions
Correlation
Average Overall
Average Overall
Coefficient R2
bias ⁰C
RMSE ⁰C
Future predictions (air temperature is predicted 1–24 hours in advance of rail-temperature
measurement)
BoM prediction equation
0.963
–0.136
2.560
(1–24hr)
Whittingham’s equation
0.852
–9.717
11.345
Hunt’s sunny-day equation
0.853
–4.44
6.952
Hunt’s cloudy-day equation
0.853
–13.308
14.758
Table 6.11 indicates that the BoM predictions are far better in terms of correlation coefficient bias
and RMSE; Hunt’s sunny-day equations have double the bias and RMSE of the BoM prediction. Even
when compared with the weather-station real-time numbers, the raw BoM prediction correlates
better than the weather-station regression output (correlation coefficient of 0.963 to 0.806
respectively), has an average overall bias of −0.136⁰C compared to 0.659⁰C, and has an RMSE of
2.560⁰C compared to 4.193⁰C. Even though the BoM regression had only July 2010 data in its
formulation, it is still more robust than either the Hunt or Whittingham equations.
Figure 6.20 graphs the temperature difference (measured minus predicted) versus the number of
such occurrences for the four methods shown.
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100
80
60
40
20
0
-20
-15
-10
-5
0
5
10
15
20
Temperature difference measured -predicted degC
Hunt cloudy day equation
400
350
300
250
200
150
100
50
0
-20
-15
-10
-5
0
5
10
15
20
Temperature difference measured -predicted degC
Occurences within the June 30 days
Whittingham equation
120
Hunt sunny day equation
100
Occurences within the June 30 days
Occurences within the June 30 days
Occurences within the June 30 days
Track Stability Management
80
60
40
20
0
-20
-15
-10
-5
0
5
10
15
20
Temperature difference measured -predicted degC
BoM predicted rail temperature
100
80
60
40
20
0
-20
-15
-10
-5
0
5
10
15
20
Temperature difference measured -predicted degC
Figure 6.20a (top left): Occurrence Difference Graph—Whittingham’s Equation as Prediction
Figure 6.20a (top right): Occurrence Difference Graph—Hunt’s Sunny-day Equation as Prediction
Figure 6.20a (bottom left): Occurrence Difference Graph—Hunt’s Cloudy-day Equation as Prediction
Figure 6.20a (bottom right): Occurrence Difference Graph—BoM Regression Equation as Prediction
Figure 6.20 shows that, similar to the real-time prediction, Hunt’s sunny-day equation outperforms
the other empirical equations. Hunt’s sunny-day equation predicts the rail temperature at around 5
⁰C above the measured rail temperature the majority of the time, whereas Hunt’s cloudy-day
equation and Whittingham’s empirical equation are around 15⁰C higher and 10⁰C higher respectively
than the measured temperature. The BoM prediction again outperforms Hunt’s sunny-day equation.
The majority of BoM predictions are within the −5⁰C to 5⁰C range, with the largest occurrences
centring around a +/−2 ⁰C difference, whereas predictions using Hunt’s sunny-day equation are
centred around −6⁰C, with the majority ranging from 10⁰C to 5⁰C above the measured temperature.
The day maximum temperature differences are also plotted in Figure 6.21 for the future predictions.
The figure shows that, again, the BoM prediction has less variation and is closer to the actual
measured temperature than all of the empirical relationships.
It is conclusive that the raw BoM prediction out-performs any existing empirical relationship
currently available for industry use. Also of interest is whether the BoM’s 25–48-hour prediction is
as accurate as the 1–24-hour prediction. This is investigated in the next section.
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Hunt sunny day equation
Whittingham equation
4
Occurences of maximum
temperature differences
Occurences of maximum
temperature differences
6
5
4
3
2
1
3
2
1
0
-20
-10
0
10
20
Temperature difference measured -predicted degC
0
-20
-10
0
10
20
Temperature difference measured -predicted degC
Hunt cloudy day equation
BoM prediction equation
6
Occurences of maximum
temperature differences
Occurances of maximum
temperature differences
6
5
4
3
2
1
0
-20
-10
0
10
20
Temperature difference measured -predicted degC
5
4
3
2
1
0
-20
-10
0
10
20
Temperature difference measured -predicted degC
Figure 6.21a (top left): Daily Maximum Rail-temperature Difference
(Measured minus Whittingham’s Prediction)
Figure 6.21b (top right): Daily Maximum Rail-temperature Difference
(Measured minus Hunt’s Sunny-day Prediction)
Figure 6.21c (bottom left): Daily Maximum Rail-temperature Difference
(Measured minus Hunt’s Cloudy-day Prediction)
Figure 6.21d (bottom right): Daily Maximum Rail-temperature Difference
(Measured minus BoM Regression Equation Prediction)
6.3.2.2 1–24-hour and 25-48-hour Predictions
The BoM ACCESS model depends on weather observations collected by the BoM on a daily to hourly
basis. Thus, as the time period for a forecast increases, its accuracy decreases, because the weather
changes and the initial observations become less valid as the initial conditions of the model.
Considering this, and the fact that each day’s BoM output runs overlap with each other, this study
investigated how the accuracy of BoM predictions changes as the forecast time moves further into
the future. The BoM prediction at latitude −23.76, longitude 150 was separated into “this-day”
predictions (1–24 hours) and “next-day” predictions (25–48 hours). Equation 6.15 and the
coefficients (Table 6.10) from Section 6.4.1 were used to predict rail temperature using both this-day
and next-day variables.
The validation analysis for June 2010 graphed in Figure 6.22 shows that the next-day predictions are
smoother in form than this-day predictions, showing fewer perturbations an exaggerate the
inaccuracies in the BoM predictions. Where the this-day predictions for 20 June predict a higher
maximum rail temperature, the next-day predictions (i.e. temperatures for 20 June as predicted on
18 June, rather than 19 June) show an even higher maximum temperature.
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20th to 23rd June 2010 validation of BoM raw prediction accuracy
35
Temperatures deg C
30
25
20
15
average left rail temperature
BoM predicted (1-24 hr) rail temp
BoM predicted (25-48hr) rail temp
air temperature
10
5
06/20/10-00:0006:00
12:00
18:00 06/21-00:00 06:00
12:00
18:00 06/22-00:00 06:00
12:00
18:00 06/23-00:00 06:00
12:00
Date and time (GMT)
Figure 6.22: BoM Regression-equation Rail-temperature Predictions This-day and Next-day
Comparing this-day and next-day statistics shows that the correlation coefficient reduces by 0.021,
the overall bias increases by 1.246⁰C, and the overall RMSE increases by 0.82⁰C (as seen in Table
6.13).
Table 6.12: Statistical Comparison of BoM This-day and Next-day Predictions
Correlation
Average Overall bias Average Overall RMSE
2
Coefficient R
⁰C
⁰C
Future predictions
BoM this-day
0.963
−0.136
2.560
BoM next-day
0.942
−1.382
3.381
The next-day predictions are less accurate than the this-day predictions. However, the next-day
predictions are still more accurate than the weather-station predictions. The weather station has a
correlation coefficient of 0.896 compared with 0.942 for the next-day prediction, 0.659⁰C bias
compared with −1.382⁰C next-day bias, and 4.193⁰C RMSE compared to 3.381⁰C next-day RMSE (see
Section 6.4.1.1). The rail temperatures calculated by the weather-station variables at the same time
as measured rail temperatures are less correlated and have a larger RMSE than a prediction that was
calculated by BoM data 24 hours before the event. This indicates that the BoM predictions are more
accurate than weather-station predictions.
Similar “occurrences versus difference” graphs have been produced for this-day and next-day
predictions, and are shown in Figure 6.23 below.
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Occurences
within the June 30 days
BoM predicted (1-24 hours)
150
100
50
0
-20
-15
-10
-5
0
5
10
15
20
15
20
Temperature difference measured -predicted degC
Occurences
within the June 30 days
BoM predicted (25-48 hours)
100
80
60
40
20
0
-20
-15
-10
-5
0
5
10
Temperature difference measured -predicted degC
Figure 6.23a (top): Rail Temperatures Occurrences versus Difference
(Measured minus BoM This-day Predictions)
Figure 6.23b (bottom): Rail Temperatures Occurrences versus Difference
(Measured minus BoM Next-day Predictions)
Figure 6.23 shows that the next-day prediction has shifted the difference distribution to predicting
3⁰C above the measured rail temperature rather than centring on the 0⁰C difference. Generally, the
next-day predictions increase the variance of measured-predicted rail temperatures compared with
this-day BoM predictions; however, the next-day predictions differences are similar to the weatherstation predictions. The daily maximum rail temperature versus occurrence is also graphed in Figure
6.24. As in the occurrence difference graphs, the maximum daily temperatures for next-day
predictions have a larger variance when compared with this-day predictions.
BoM prediction (25-48 hours)
BoM predicted (1-24 hours)
5
Occurences of maximum temperature differences
Occurences of maximum temperature differences
6
5
4
3
2
1
0
-20
-10
0
10
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
-20
20
-10
0
10
20
Temperature difference measured -predicted degC
Temperature difference measured -predicted degC
Figure 6.24a (left): Daily Maximum Rail-temperature Difference
(Measured Minus BoM This-day Prediction)
Figure 6.24b (right): Daily Maximum Rail-temperature Difference
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(Measured Minus BoM Next-day Prediction
6.3.3 BoM Raw Data and BoM Interpolated Predictions
The interpolated BoM data located weather parameters much closer to the geographic location of
the actual weather station and also increased the time frequency of the prediction. That is, instead
of a rail-temperature prediction for every hour, a prediction was made for every 15 minutes.
Provided that the accuracy of a prediction is not diminished by interpolation, then a prediction using
a smaller time resolution will more accurately indicate when the maximum temperature will be
reached. The accuracy of the interpolated values was checked using the thermocouple readings,
which only existed for every hour (i.e. the interpolated results were sampled every hour and
compared to the thermocouple readings).
The daily maximum temperature comparison used the full set of interpolated results, found the
maximum value of those for each day, and then compared these with the daily thermocouple
maximums.
The location of the interpolated BoM points is shown in Figure 6.25 below. They are 0.0275⁰ to
0.05⁰ in latitude (3.06 km to 6.12 km) closer to the weather station.
Lo
Lo
n:1
n:
We
49. ath 1
Lo 97
5 Lo
n:125
0 n:
49.Lat
La1
Lon
97 5
t:-Raw
:15
25 23.
0
2BoM
0
Lat70
La
3.data
Lat:
:- 50
7 t:23.
02
23.
73
5 3.
76
25
07
3
2
5
Figure 6.25: Configuration of Interpolated BoM Prediction and Raw BoM Prediction in Relation to
Location of Weather Station
The weather variables were multiplied using the regression coefficients listed in Table 6.10 in Section
6.4.2.Once again, the predictions were separated into this-day and next-day predictions.
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6.3.3.1 Interpolated This-day Predictions
Figure 2.6 shows graphs of rail-temperature predictions and actual measured rail temperatures for
8–10 June 2010. The figure shows that, although all the predictions are similar, the raw BoM
prediction appears to be a closer fit than the other interpolated predictions. Of the interpolated
predictions, the BoM latitude −23.705, longitude 149.4725 outputs appear to be closer to the
measured temperatures than the rest. The correlation coefficient, overall bias, and overall RMSE are
listed in Table 6.14.
Interpolated BoM validation (1-24hr prediction)
mean left rail temperature
raw BoM prediction
BoM lat 023.705 lon:149.4725 predict
BoM lat-23.705 lon:150 predict
BoM lat-23.7325 lon:149.4725 predict
BoM lat-23.7235 lon:150 predict
40
Rail temperature deg C
35
30
25
20
15
10
5
06/08/10-21:00
06/09-00:00 03:00
06:00
09:00
12:00
15:00
18:00
21:00 06/10-00:00 03:00
Date and time (GMT)
06:00
09:00
12:00
15:00
Figure 6.26: Interpolated, Raw BoM Prediction and Measured This-day Rail Temperature 8–10 June
Table 6.13: Statistical Comparison of Interpolated and Raw BoM This-day Rail-Temperature
Prediction Equations
Correlation
Average Overall
Average Overall
Coefficient R2
bias ⁰C
RMSE ⁰C
Future predictions (1–24 hours in advance of rail-temperature measurement)
Raw BoM prediction equation
0.963
−0.136
2.560
(1–24-hour)
BoM lat–23.705 lon:149.4725
0.942
0.645
3.198
BoM lat–23.705 lon:150
0.942
4.718
5.667
BoM lat–23.7325 lon:149.4725 0.941
−1.940
3.699
BoM lat–23.7235 lon:150
0.941
2.173
3.834
Table 6.13 indicates that all of the interpolated predictions correlate well with the measured rail
temperature; the correlation is slightly bettered by the raw BoM prediction by 0.022. However,
when considering bias and RMSE, the raw BoM predictions outperform the other interpolated
results, with the interpolated location at BoM latitude −23.705, longitude 149.4725 performing
better than the rest of the interpolated results. The temperature differences between predicted and
measured are graphed in Figure 6.27.
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raw BoM predicted (1-24 hours)
BoM lat:-23.705 lon:149.4725
120
100
Occurences within
the June 30 days
Occurences within
the June 30 days
150
100
50
0
-20
-10
0
10
80
60
40
20
0
-20
20
Temperature difference
measured -predicted degC
0
10
BoM lat-23.7325 lon:149.4725
BoM lat-23.705 lon:150
120
100
100
100
60
40
20
0
-20
-10
0
10
Temperature difference
measured -predicted degC
20
Occurences within
the June 30 days
120
80
80
60
40
20
0
-20
20
BoM lat-23.7235 lon:150
120
Occurences within
the June 30 days
Occurences within
the June 30 days
-10
Temperature difference
measured -predicted degC
-10
0
10
Temperature difference
measured -predicted degC
20
80
60
40
20
0
-20
-10
0
10
20
Temperature difference
measured -predicted degC
Figure 6.27a (top left): Rail Temperatures Occurrences versus Difference
(Measured minus Raw This-day BoM Predictions)
Figure 6.27b (top right): Rail Temperatures Occurrences versus Difference
(Measured minus This-day BoM lat-23.705 lon:149.4725 Predictions)
Figure 6.27c (bottom left): Rail Temperatures Occurrences versus Difference
(Measured minus This-day BoM lat-23.705 lon:150 Predictions)
Figure 6.27d (bottom middle): Rail Temperatures Occurrences versus Difference
(Measured minus This-day BoM lat-23.7325 lon:149.4725 Predictions)
Figure 6.27e (bottom left): Rail Temperatures Occurrences versus Difference
(Measured minus This-day BoM lat-23.7235 lon:150 Predictions)
Figure 6.27 shows that the range of the measured minus predicted values is similar, between
+/−10⁰C. However, the interpolated predictions tend to skew the maximum occurrences from 0⁰C
difference in the case of both raw BoM prediction and BoM latitude −23.705, longitude 149.4725 to
4⁰C for both BoM latitude –23.705, longitude 150 and BoM latitude –23.7235, longitude 150. –2⁰C
for BoM prediction latitude –23.7325, longitude 149.4725.
The daily maximum differences between measured and predicted temperatures are graphed in
Figure 6.28.
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5
4
3
2
1
-10
Interpolated BoM lat:-23.705 lon:150
5
4
3
2
1
-10
0
10
0
10
Temperature difference
measured -predicted degC
Temperature difference
measured -predicted degC
20
20
5
4
3
2
1
0
-20
-10
0
10
20
Temperature difference
measured -predicted degC
Interpolated BoM lat:-23.7325 lon:149.4725
Interpolated BoM lat:-23.7235 lon:150
5
4
3
2
1
0
-20
-10
0
10
20
Temperature difference
measured -predicted degC
Occurences of
maximum temperature differences
Occurences of
maximum temperature differences
0
-20
0
-20
Interpolated BoM lat:-23.705 lon:149.4725
raw BoM predicted (1-24 hours)
Occurences of
maximum temperature differences
6
Occurences of
maximum temperature differences
Occurences of
maximum temperature differences
Track Stability Management
5
4
3
2
1
0
-20
-10
0
10
20
Temperature difference
measured -predicted degC
Figure 6.28a (top left): Daily Maximum Rail Temperatures Occurrences versus Difference
(Measured minus This-day Raw BoM Predictions)
Figure 6.28b (top right): Daily Maximum Rail Temperatures Occurrences versus Difference
(Measured minus This-day BoM lat-23.705 lon:149.4725 Predictions)
Figure 6.28c (bottom left): Daily Maximum Rail Temperatures Occurrences versus Difference
(Measured minus This-day BoM lat-23.705 lon:150 Predictions)
Figure 6.28d (bottom middle): Daily Maximum Rail Temperatures Occurrences versus Difference
(Measured minus This-day BoM lat-23.7325 lon:149.4725 Predictions)
Figure 6.28e (bottom left): Daily Maximum Rail Temperatures Occurrences versus Difference
(Measured minus This-day BoM lat-23.7235 lon:150 Predictions)
Figure 6.28 shows the variance of difference is still within a 10⁰C range. However, there is a shift in
the range. Whereas the range is from –2⁰C to 8⁰C in the raw BoM prediction, the interpolated
predictions range from –3⁰C to 8⁰C for BoM latitude –23.705, longitude 149.4725 and BoM latitude
–23.705, longitude 149.4725; and from 1⁰C to 12⁰C for BoM latitude –23.705, longitude 150 and
BoM latitude –23.705, longitude 150.
It is conclusive that the raw BoM predictions are more accurate for this-day predictions. However,
the interpolated BoM prediction latitude –23.705, longitude 149.4725 comes close to the accuracy
of the raw BoM prediction and can be used to better understand the time at which maximum rail
temperatures occur.
6.3.3.2 Interpolated next-day predictions
Figure 6.29 shows a graph of rail-temperature predictions and actual measured temperatures for 8 –
10 June 2010 for next-day predictions. This figure shows that all of the next-day predictions, whether
interpolated or raw, look similar. The raw BoM prediction does not appear to be a closer fit than any
of the other interpolated predictions as was the case with the this-day predictions. The correlation
coefficient, overall bias, and overall RMSE are listed in Table 6.14.
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Interpolated BoM validation (25-48hr prediction)
mean left rail temperature
raw BoM prediction
BoM lat 023.705 lon:149.4725 predict
BoM lat-23.705 lon:150 predict
BoM lat-23.7325 lon:149.4725 predict
BoM lat-23.7235 lon:150 predict
40
Rail temperature deg C
35
30
25
20
15
10
5
06/08/10-18:00
06/09-00:00
06:00
12:00
18:00
06/10-00:00
06:00
12:00
18:00
Date and time (GMT)
Figure 6.29: Interpolated, Raw BoM Prediction and Measured Next-day Rail Temperature 8–10 June
Table 6.14: Statistical Comparison of Interpolated and Raw BoM Next-day Rail-temperature
Prediction Equations
Correlation
Average Overall
Average Overall
2
Coefficient R
bias ⁰C
RMSE ⁰C
Future predictions (24–48 hours in advance of rail-temperature measurement)
BoM prediction equation
0.942
–1.382
3.381
(25–48-hour)
BoM lat –23.705 lon:149.4725
0.942
–0.425
3.841
BoM lat –23.705 lon:150
0.911
3.669
5.302
BoM lat –23.7325 lon:149.4725 0.942
–3.014
4.859
BoM lat –23.7235 lon:150
0.942
1.117
3.983
Table 6.14 shows that the accuracy of the raw BoM prediction and interpolated BoM predictions for
the next day are not very different. With the exception of BoM latitude –23.705, longitude 150,
correlation coefficients are the same. With regard to bias, all the predictions are of the same
magnitude; the interpolated BoM latitude –23.705, longitude 149.4725 actually has a lower bias
than the raw BoM next-day predictions. With regard to RMSE, all the predictions are again of the
same magnitude.
Figure 6.30 graphs the temperature differences between predicted and measured for next-day rail
temperatures.
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raw BoM predicted (25-48 hours)
BoM lat:-23.705 lon:149.4725
80
Occurences
within the June 30 days
Occurences
within the June 30 days
100
80
60
40
20
0
-20
-10
0
10
60
40
20
0
-20
20
Temperature difference
measured -predicted degC
BoM lat-23.705 lon:150
40
20
-10
0
10
Temperature difference
measured -predicted degC
20
80
60
40
20
0
-20
20
BoM lat-23.7235 lon:150
Occurences
within the June 30 days
60
10
100
100
Occurences
within the June 30 days
Occurences
within the June 30 days
0
BoM lat-23.7325 lon:149.4725
80
0
-20
-10
Temperature difference
measured -predicted degC
-10
0
10
Temperature difference
measured -predicted degC
20
80
60
40
20
0
-20
-10
0
10
20
Temperature difference
measured -predicted degC
Figure 6.30a (top left): Rail Temperatures Occurrences versus Difference
(Measured minus Next-day Raw BoM Predictions)
Figure 6.30b (top right): Rail Temperatures Occurrences versus Difference
(Measured minus Next-day BoM lat-23.705 lon:149.4725 Predictions)
Figure 6.30c (bottom left): Rail Temperatures Occurrences versus Difference
(Measured minus Next-day BoM lat-23.705 lon:150 Predictions)
Figure 6.30d (bottom middle): Rail Temperatures Occurrences versus Difference
(Measured minus Next-day BoM lat-23.7325 lon:149.4725 Predictions)
Figure 6.30e (bottom left): Rail Temperatures Occurrences versus Difference
(Measured minus Next-day BoM lat-23.7235 lon:150 Predictions)
In Figure 6.30, the range of measured minus predicted values for the interpolated predictions have a
marginally larger range than those of the raw BoM predictions. As in the case of the this-day
prediction, the next-day interpolated predictions tend to skew the maximum occurrences.
Figure 6.31 graphs the daily maximum differences between measured and predicted for next-day
predictions.
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5
Interpolated BoM lat:-23.705 lon:149.4725
Occurences of maximum
temperature differences
Occurences of maximum
temperature differences
raw BoM predicted (25-48 hours)
4
3
2
1
0
-20
-10
0
10
20
Temperature difference
measured -predicted degC
5
4
3
2
1
0
-20
-10
0
10
20
5
4
3
2
1
0
-20
-10
0
10
Temperature difference
measured -predicted degC
20
5
Occurences of maximum
temperature differences
6
Occurences of maximum
temperature differences
Occurences of maximum
temperature differences
Temperature difference
measured -predicted degC
Interpolated BoM lat:-23.705 lon:150 Interpolated BoM lat:-23.7325 lon:149.4725 Interpolated BoM lat:-23.7235 lon:150
4
3
2
1
0
-20
-10
0
10
20
Temperature difference
measured -predicted degC
6
5
4
3
2
1
0
-20
-10
0
10
20
Temperature difference
measured -predicted degC
Figure 6.31a (top left): Daily Maximum Rail Temperatures Occurrences versus Difference
(Measured minus Next-day Raw BoM Predictions)
Figure 6.31b (top right): Daily Maximum Rail Temperatures Occurrences versus Difference
(Measured minus Next-day BoM lat-23.705 lon:149.4725 Predictions)
Figure 6.31c (bottom left): Daily Maximum Rail Temperatures Occurrences versus Difference
(Measured minus Next-day BoM lat-23.705 lon:150 Predictions)
Figure 6.31d (bottom middle): Daily Maximum Rail Temperatures Occurrences versus Difference
(Measured minus Next-day BoM lat-23.7325 lon:149.4725 Predictions)
Figure 6.31e (bottom left): Daily Maximum Rail Temperatures Occurrences versus Difference
(Measured minus Next-day BoM lat-23.7235 lon:150 Predictions)
Figure 6.31 shows the variance of difference is still within a 15⁰C range; however, there is a shift in
the range. Whereas the range was from –7⁰C to 8⁰C in the raw BoM prediction, the interpolated
predictions range from –8⁰C to 5⁰C for BoM latitude –23.705, longitude 149.4725; from –4⁰C to 11⁰C
for BoM latitude –23.705, longitude 150; from –8⁰C to 5⁰C for BoM latitude –23.3725, longitude
179.4725; and from –4⁰C to 11⁰C for BoM latitude –23.7235, longitude 150.
It is conclusive that, for next-day predictions, the interpolated BoM predictions are as skilful as the
raw BoM prediction. There is almost no difference in accuracy between the raw BoM prediction and
the interpolated BoM latitude –23.705, longitude 149.4725.
6.4 Empirical Prediction Drawbacks
The rail-temperature prediction completed in this study depended heavily on empirical data
collected in the field. Although the BoM data is from a dynamic NWP model, the ultimate accuracy
of the rail temperature is based on empirical downscaling.
The field experimentation for this study was oriented in the east–west direction, but it is known that
rail oriented north–south has a distinctly different heating pattern, with higher maximum rail
temperatures (Whittingham 1969; Munro 2009). Track in cuttings, on bridges and in urban areas
would also have a distinctly different heating pattern from that observed in this study. Different
track constructions (such as timber sleepers, larger sleeper spacing, different gauge distances, and
different fasteners) also affect the heating pattern of a rail. Therefore, the findings of this study are
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limited to straight track on embankment configuration, with narrow-gauge distances, concrete
sleepers and fist-clip fasteners. Beyond this scenario, the accuracy of rail-temperature prediction
would differ greatly from what is reported in this study.
The volume of data available for this study also reduces the accuracy of the rail-temperature
prediction described here. Only 744 samples from July 2010 were used to formulate the railtemperature prediction equation, compared with previous research by Whittingham (1969) that
used 15 months of data, Chapman et al. (2005) that used 12 months of data, and Munro (2009) that
used 9 months of data. Due to time constraints and its academic nature, the current study did not
use enough data for a robust empirical analysis. Therefore, the rail-temperature prediction
developed lacks the empirical data to be a truly robust prediction.
The July period in which the data was collected is also problematic. July is winter in Australia, while
most track buckles (which are caused by large rail-temperature variations) occur in spring or
autumn. In a different season, the rail may have had a very different heating pattern. This could not
be considered because of the study’s time constraints.
6.5 Frictional Temperature Increase
On a site visit on 18 October 2010, study personnel found that Thermocouple 9, on the field side of
the right rail-head, was loose and may not have been reading correctly. However, a visual inspection
suggested that the other sensors were intact.
During this visit, the triggering mechanism of the DAQ system was implemented. That is, as a train
passed the instrumented site, measurements of temperature were taken at 70 Hz for 5 minutes,
which was enough time to record any temperature increase due to the train passage. The rail
temperature was averaged over both rails, so a uniform increase in temperature could be gauged.
The variances in rail temperature and standard deviation in rail temperature were found to gauge
the effect of a train passage on the overall temperature of the rail. The measurement for the train
passage was a very noisy signal, so, in lieu of filtering the data, variance and standard deviation were
taken as an indication of the increase in rail temperature.
It was found that temperature change due to train passage varied depending on whether the train
was loaded or empty. Empty trains had no effect on the overall temperature of the rails, regardless
of rail temperature. Average rail temperature during the train passage, variance of rail temperature,
and standard deviation of rail temperature are plotted in Figure 6.32.
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Figure 6.32: Rail-temperature Mean, Variance, and Standard Deviation of Empty Train Passage over
Instrumentation
A total of 25 empty trains passed the instrumented site and temperature changes were recorded.
The average, variance, and standard deviation of rail temperature during the passage show that, on
average, the variation was 0.2⁰C (0.6% of average rail temperature), and the standard deviation was,
on average, 0.3⁰C (1% of average rail temperature), regardless of the average rail temperature. The
range of the variance and standard deviation is within 1% of the average rail temperature, indicating
that an empty train has virtually no effect on rail temperature regardless of whether it is day or night
or what the temperature of the rail is at the time of the train’s passage.
Ten loaded trains with various total wagon numbers passed the instrumented site. The average,
variance, and standard deviation of rail temperatures during the train passage are plotted and
shown in Figure 6.33.
Figure 6.33: Rail-temperature Mean, Variance, and Standard Deviation of Loaded Train Passage over
Instrumentation
The plot of loaded trains (Figure 6.33) shows a very different result from the empty trains.
Depending on the number of wagons, the average overall temperature variance was 4.7⁰C (20.6% of
average rail temperature) and 2⁰C in standard deviation (8.7% of average rail temperature).
However, these large increases were not observed in the next interval measurement of rail
temperature after the train had passed. That is, the high temperatures were sustained for only a
short period and did not add to the rail’s overall temperature increase. This is similar to the findings
of Chapman et al. (2005).
The increase in rail temperature due to train passage varied according to the weight of the train (or
loaded wagons). From the results, it is conclusive that temperature increase due to train passage
does not depend on the rail’s initial temperature.
Temperature increase due to the passage of loaded trains could be problematic when rail
temperature is near critical and a loaded train passes and increases the rail temperature above the
critical limit. Of course, the rail-buckling mechanism depends both on the forces that the train
induces (due to traction) and the residual stress in the rail (which is highly dependent on rail
temperature).
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An attempt was made to quantify the frictional heat generated by train passage over the rail in this
study by calculating the variance and mean of rail temperature at the time of train passage.
However, this is not the usual method for calculating heat addition due to friction. There were some
limitations:
 First, the sensor placement in the field experiment was located at least 10 mm away from the
contact patch. Therefore, the intense heat produced by friction and its subsequent transfer into
the rail could not be studied.
 Second, the sampling rate of 70 Hz was not fast enough to capture the frequencies that are
developed within the wheel rail contact.
 Third, the configuration of the passing trains (i.e. how many wagons were loaded and what kind
of locomotive was present) was not known, so what temperature increase was generated by
what load could not be assessed.
 Fourth, the rail-temperature data-set was not filtered because of the study’s time constraints, so
exactly how much overall rail temperature increased was not quantified.
Therefore, it is not clear whether temperature increase due to train passage can initiate a buckling
event, or if it is the traction forces of a train that initiate buckling. This is beyond the scope of this
study and could be a future area for research.
6.6 Sensors and Prediction: the Argument for Rail-Temperature
Prediction
The rail-temperature prediction developed for this study had an accuracy of:
 +/– 5⁰C approximately 95% of the time for this-day predictions
 +/– 5⁰C approximately 89% of the time for next-day predictions.
Measurement devices currently used to measure rail temperature include Type K Class 1 or Class 2
hand-held surface thermocouples, which have an accuracy of +/– 1.5 ⁰C and +/– 2.5 ⁰C respectively.
Prediction using the NWP product ACCESS is less accurate, but is within the same magnitude as data
gathered by sending personnel to physically measure rail temperatures, or that collected through
continuous monitoring. Therefore, the rail-temperature prediction is on a par with physical
measurement, and is well worth further future development.
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7. Conclusion
This study developed a piece of software to predict rail temperatures using data from the BoM NWP ACCESS-A
product. It is a flagship study for the use of an NWP product in a railway-engineering application in Australia.
The researchers concluded that ACCESS-A can be used to accurately predict rail temperatures 24 to 48 hours in
advance. While the accuracy of the prediction decreases as the length of the prediction time increases, this
decrease in accuracy is within the same magnitudes as that experienced when using rail-temperature
measurements taken by instrumentation. Ultimately, this software could be used to provide the rail industry
with at least one day’s warning of when rail temperatures could become critical.
The accuracy of the method has been tested only for the track configuration, materials and location used in
this study. If the research is further developed for different track configurations, materials and locations, it
could provide rail-network controllers and schedulers with a powerful tool to help decide if it is safe to run
trains at certain speeds. It could also lead to better customer satisfaction for both rail commuters and freight
customers, allowing trains to operate with fewer delays and cancellations, and less uncertainty.
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