Download 4.1 Spatial Variability of Rainfall - ISAC

On the Local-scale Spatial Variability of Daily Rainfall in the Highlands
of the Blue Nile: Observational Evidence
Mekonnen Gebremichael1, Menberu Bitew1, Fayera. A. Hirpa1, Yonas Michael2, Yilma
Seleshi2, and Yonas Girma3
Abstract
The HEXB (Hydrological EXperiment in Blue nile) experiment provided an opportunity,
via dense network of rain gauges, to study the spatial variability of daily rainfall at a 5 km 
5 km scale in a tropical and mountainous part of the Blue Nile river basin, for the period of
July 1 – August 9, 2008. The results of daily rainfall spatial analyses are shown in this
paper. High intensity rainfall events have more absolute spatial variability (e.g., standard
deviation) and less relative spatial variability (as measured by coefficient of variation),
compared to lower intensity events. The coefficient of variation varies from 12% to 320%,
with a median of 50%, indicating that there is a significantly large variability from one
gauge observation to the other, and one gauge does not represent 5 km  5 km gridaverage daily values. A careful rain gauge layout design is critical to get accurate
estimates at smaller number of rain gauges.
1. INTRODUCTION
It is known that rainfall events in the tropics can have large spatial variability over short
distances. This variability has implications in the establishment of rain gauge networks
and assessment of spatial sampling uncertainty. However, quantitative information on this
variability is missing in tropical mountainous regions due to the lack of adequate ground
observations.
The HEXB (Hydrological EXperiment in Blue nile) experiment has provided the
opportunity, via a dense network of rain gauges, to explore a range of issues related to
spatial rainfall characteristics. In this study, we consider the variability within a 5 km  5
km area, here called “local” scale, which is commensurate with the resolution of high1
Civil & Environmental Engineering, University of Connecticut, Storrs, CT, USA
Civil & Environmental Engineering, Addis Ababa University, Addis Ababa, Ethiopia
3 Amhara Regional Agricultural Research Institute, Debreberhan Research Center, Debre Berhan, Ethiopia
2
1
resolution satellite rainfall products, such as PERSIANN-CCS (Precipitation Estimation
from Remotely Sensed Information using Artifical Neural Networks – Cloud Classification
System; Hong et al. 2004) and CMORPH (NOAA’s Climate Prediction Center MORPHing
technique; Joyce et al. 2004), and therefore, is important to validate these satellite
products.
Firstly, we characterize the spatial statistics of daily rainfall using marginal statistics
such as the probability distribution, standard deviation, and coefficient of variation.
Secondly, we assess the sampling uncertainty introduced by the use of smaller number of
rain gauges to estimate local-scale-averaged rainfall estimates.
2. THE WATERSHED
The Beressa Watershed is located in the central highlands of Ethiopia, within 93343N
to 94227N and 392834E to 394423E (Fig. 1). It covers an area of 283 km 2.
Geologically, it is part of the highlands that largely owe their altitude to the uplift during the
rifting process. The Beressa watershed is on the western plateau edge of the rift system.
It is characterized by diverse topographic conditions; elevation ranges from 1850 m to
3700 m. Climate is considered humid, with 1100 mm of annual precipitation. Most of the
annual rainfall comes from summer monsoon.
Figure 1. (a) Map of Ethiopia showing the location of the Beressa watershed with respect
to the rift valley. (b) The Beressa Watershed (283 km2) delineated using a 30-m DEM. The
inset contains two grids (5 km  5km) located in the high-elevation and low-elevations
areas of the watershed; and the rain gauges within them. (c) A picture showing an
example of one of the installed non-recording rain gauges.
2
Figure 2. Elevation (m)
of each rain gauge
location over (left panel)
Grid L, and (right panel)
Grid H.
3. THE EXPERIMENT
The HEXB project started in June 2008, with the aim of advancing hydrological science
in a tropical and mountainous region through gaining a better understanding of the spacetime variability of rainfall, as sensed by rain gauges network and remote sensors, and how
this variability influences hydrologic simulation at the catchment scale. The project has
been administered by the University of Connecticut, in collaboration with Addis Ababa
University and the Amhara Regional Agricultural Research Institute-Debreberhan
Research Center. It has been funded by the National Science Foundation.
An important focus of the project was a set of experimental facilities within the Beressa
Watershed. This comprised two new networks of non-recording rain gauges (Fig. 1). The
first network consisted of 21 non-recording rain gauges over a 5 km  5 km area, in the
upstream mountainous region of the watershed, we call “Grid H”. The second network
consisted of 18 non-recording rain gauges over a 5 km  5 km area, in the downstream
hilly region of the watershed, we call “Grid L”. The separation distance between two
neighboring rain gauges was about 1 km, within each grid. Initially, we put rain gauges
every kilometer within each grid, but we lost some of them during the experimental period.
We believe that the remaining density of 18 or 21 rain gauges is adequate to capture the
spatial pattern of rainfall, and to estimate accurately the mean rainfall over each grid.
We selected the two grids to look at the effect of elevation on rainfall’s spatial variability.
Figure 2 presents the elevation of each rain gauge. Grid H’s rain gauges have elevations
ranging from 3100 to 3270 m, while Grid L’s have elevations ranging from 2730 m to 2900
m. Grid H has higher elevation than Grid L. However, both grids have similar sub-grid
variability in elevation; for example, the range of elevations within each grid is about 170
m.
3
The non-recording rain gauges used were the “Tru-Chek®” plastic rain gauges
manufactured by the Forestry Suppliers. The gauges have scales permanently marked on
the front side. We mounted each gauge vertically on a wooden pole at a height of 2 m
above the ground. A typical rain gauge installation is shown in Fig. 1c. Our research
group and trained local research assistants took readings off each rain gauge, every
morning from 7 to 8 am, for the period of July 1 to August 9, 2008. This is the major rainy
period in the region; there were 38 rainy days during the 40-day experimental period.
4. RESULTS AND DISCUSSION
4.1 Spatial Variability of Rainfall
In Figs. 3a and 3b, we show the distributions of spatial variability of daily rainfall within
an area of 5 km  5 km, for Grids L and H. The spatial variability of rainfall varies from day
to day. Higher spatial means tend to have more sub-grid variability than lower ones. We
found a sample correlation coefficient of 0.74 for Grid L (and 0.84 for Grid H) between the
interquantile range (i.e. the difference between the 75% and 25% quantiles of spatial
rainfall) and spatial mean, indicating that the spatial mean explains about 55% for Grid L
(and 71% for Grid H) of the day-to-day variation in the spatial variability of daily rainfall, for
50% of the cases. For 80% of the cases, the spatial mean explains about 65% for Grid L
(and 74% for Grid H) of the day-to-day variation in the spatial variability of daily rainfall.
In Fig. 3c, we present the spatial standard deviation ( ) as a function of the spatial
mean daily rainfall (R ). Overall,  increases with increasing R , indicating that higher
spatial means tend to have more absolute sub-grid spatial variability. However, the
relationship between  and R is non-linear: the slope is steeper and the scatter is
narrower for low R values, than for high values.
The increase in  with increasing R is consistent with the fact that absolute variability
tends to be greater for higher values of measured positively defined random variables than
for small values. To filter out the effect of this fact, we normalized  against R , and
looked at how this relative variability (expressed as coefficient of variation, CV=  / R )
behaves with respect to the spatial mean. Figure 3d shows that, overall, high spatial
means have less sub-grid relative variability than lower spatial means. The relative
variability decreases exponentially with increasing R , for R smaller than 15 mm/day, and
then remains fairly constant for R exceeding 15 mm/day. The CV varies from 12% to
320%, with a median of 50%, indicating that there is a significantly large variability from
one gauge observation to the other. For the days with CV above 100%, the rainfall
intensities were of low to medium intensity.
4
Figure 3. Spatial variability of daily rainfall over each grid. (a) Box plots for the distribution
of spatial rainfall on each day over Grid L. (b) Same as in Fig. (a), but for Grid H. (c)
Spatial standard deviation versus the spatial mean rainfall. (d) Spatial coefficient of
variation versus spatial mean rainfall. The statistics are obtained using all 18 gauges
within Grid L and 21 gauges within Grid L, for each day within the observation period. The
box plots represent 10%, 25%, 50%, 75%, and 90% quantiles, from the bottom up.
4.2 Rain Gauge Spatial Sampling Uncertainty
One of the impacts of the spatial variability of rainfall is the number of rain gauges
required to accurately estimate grid-averages, and the uncertainty level resulting from the
use of smaller number of rain gauges. Let us assume that the spatial mean of rainfall from
all rain gauges within each grid, hereafter referred to as “Reference rainfall R ) represents
the “true” rainfall. The expression for R is:
5
R
1 n
 Ri ,
n i 1
where, i = 1, 2, …, n (number of all rain gauges within Grid L or H).
By sampling smaller number of rain gauges, we can simulate the “Estimated rainfall Re ”
resulting from these gauges::
Re 
1 n
 Ri i ,
n i 1
where, the Kronecker delta function,  i , is one if the rain gauge is selected and zero
otherwise. The estimation error is, therefore, the difference between R and Re , and it
obviously depends on the number of rain gauges as well as the network configuration.
Consider two daily events over Grid H: the July 15 and July 30 events. The July 15
event had a spatial mean of 9 mm/day, which is equivalent to the 50% quantile of the
spatial mean time series data. The July 30 event had a spatial mean of 38 mm/day,
equivalent to the 90% quantile of the spatial mean time series data. So the July 15 event
represents typical event, while the July 30 event represents an extreme event. Our
interest is to quantify Re and estimation error resulting from the use of smaller number of
rain gauges (1, 2, 4, 8, 16) in estimating area-averaged values for these typical and
extreme events. For each gauge density, we simulated 16 realizations of rain gauge
networks by randomly generating each network from a uniform distribution, and show the
results in Figs. 4a and 4b.
Consider the event of July 30 ( R  30 mm/day), which is the 90% quantile extreme
value. When only one rain gauge is used to estimate this grid-average rainfall, the
estimate could be anywhere from 24 to 53 mm/day (equivalent to estimation error of -14 to
15 mm/day, or –37% to 39% of R ) for 80% of the configurations, and from 31 to 48
mm/day (estimation error of -7 to 10 mm/day, or –18% to 26% of R ) for 50% of the
configurations. When four rain gauges are used, the rainfall estimate ranges from 31 to 44
mm/day (estimation error of -7 to 6 mm/day, or –18% to 16% of R ) for 80% of the
configurations, and from 35 to 41 mm/day (estimation error within  3 mm/day, or  8% of
R ) for 50% of the configurations.
6
Figure 4. Distribution of rainfall estimates ( Re ) as a function of rain gauge network density,
for (a) the July 30 extreme event, and (b) the July 15 typical event. The bold dashed line
shows the reference R . The shaded region indicates the 10% deviation.\
Consider the event of July 30 ( R  30 mm/day), which is the 90% quantile extreme
value. When only one rain gauge is used to estimate this grid-average rainfall, the
estimate could be anywhere from 24 to 53 mm/day (equivalent to estimation error of -14 to
15 mm/day, or –37% to 39% of R ) for 80% of the configurations, and from 31 to 48
mm/day (estimation error of -7 to 10 mm/day, or –18% to 26% of R ) for 50% of the
configurations. When four rain gauges are used, the rainfall estimate ranges from 31 to 44
mm/day (estimation error of -7 to 6 mm/day, or –18% to 16% of R ) for 80% of the
configurations, and from 35 to 41 mm/day (estimation error within  3 mm/day, or  8% of
R ) for 50% of the configurations.
Let us look at the corresponding values for the typical event of July 15 ( R  30
mm/day). When one rain gauge is used, the rainfall estimate ranges from 5.3 to 13.5
mm/day (estimation error of -3.7 to 4.5 mm/day, or –40% to 50% of R ) for 80% of the
configurations, and from 5.5 to 10.5 mm/day (estimation error of -3.7 to 4.5 mm/day, or –
39% to 16% of R ) for 50% of the configurations. With four rain gauges, the rainfall
estimate ranges from 6.4 to 11.8 mm/day (estimation error within  2.8 mm/day, or  30%
of R ) for 80% of the configurations, and from 6.4 to 11.4 (estimation error within  2.6
mm/day, or  30% of R ) for 50% of the configurations.
Let us compare and contrast the estimation errors for the two rainy events. The first
feature is that the magnitude of the estimation error is larger for the extreme event than for
the typical event. This can be explained by the fact that strong events have more absolute
spatial variability than those of weaker events (see Fig. 3c). The second feature is that the
proportion of the estimation error to R is smaller for the extreme event than for the typical
7
event. This can be explained by the fact that strong events have less relative variability
than those of weaker events (see Fig. 3d).
How many rain gauges do we need to obtain a reliable estimate of the grid-average
daily rainfall estimate? It depends on the level of uncertainty we accept. Let us say, we
accept 10% level of uncertainty. For the extreme event, this can be achieved by having (i)
16 rain gauges of pretty much any configuration used in this study, or (ii) 2, 4, or 8 rain
gauges with any of the 50% of the configurations used in this study. This indicates that a
careful rain gauge layout design is critical to get accurate estimates at smaller number of
rain gauges. There are studies that looked at optimal network configuration (e.g., Moore et
al. 2000). For the typical event, the 10% uncertainty level can be achieved by having (i) 16
rain gauges of pretty much any configuration used in this study, or (ii) 8 rain gauges having
any of the 50% of the configurations used in this study. Apparently smaller numbers of
rain gauges, that were deemed adequate for the extreme event, were found inadequate for
the typical event. This is due to the fact that our objective measure (i.e. 10% level of
uncertainty) is relative to the actual rainfall value, and strong events have lower
percentage of estimation errors with respect to their rainfall value.
5. CONCLUSIONS
HEXB provided an opportunity, via dense network of rain gauges, to study the spatial
variability of daily rainfall at a 5 km  5 km scale in a tropical and mountainous part of the
Blue Nile river basin. High intensity rainfall events have more absolute spatial variability
(e.g., standard deviation) and less relative spatial variability (as measured by coefficient of
variation), compared to lower intensity events. The coefficient of variation varies from 12%
to 320%, with a median of 50%, indicating that there is a significantly large variability from
one gauge observation to the other, and one gauge does not represent 5 km  5 km gridaverage daily values. The smallest number of rain gauges required to estimate gridaverage rainfall depends on the rainfall magnitude. It is generally smaller for high intensity
events than for low intensity events. A careful rain gauge layout design is critical to get
accurate estimates at smaller number of rain gauges. Four rain gauges with the right
configurations can have better performance than ill-placed 16 gauges.
Acknowledgment. This research was supported by the National Science Foundation
(NSF Grant OISE-0651783).
6. REFERENCES
Hong, Y., K. L. Hsu, S. Sorooshian, and X. Gao, 2004: Precipitation Estimation from
Remotely Sensed Imagery Using an Artificial Neural Network Cloud Classification
System. J. Appl. Meteor., 43, 1834–1852.
8
Joyce, R. J., J. E. Janowiak, P. A. Arkin, and P. Xie, 2004: CMORPH: A method that
produces global precipitation estimates from passive microwave and infrared data at
high spatial and temporal resolution. J. Hydromet., 5, 487-503.
Moore, R. J., D. A. Jones, D. R. Cox, and V. S. Isham, 2000: Design of the HYREX
raingauge network. Hydrol. Earth Sys. Sci., 4(4), 525-530.
9