Download Long-term snow depth simulations using a modified atmosphere

Agricultural and Forest Meteorology 104 (2000) 273–287
Long-term snow depth simulations using a modified
atmosphere–land exchange model
C.E. Kongoli, W.L. Bland∗
Department of Soil Science, 1525 Observatory Drive, University of Wisconsin-Madison, Madison, WI 53706, USA
Received 20 October 1999; received in revised form 15 March 2000; accepted 16 June 2000
Abstract
Significant areas of agricultural lands are subject to seasonal, relatively thin snow covers. This cover affects temperature
and moisture in the soil beneath, watershed hydrology, and energy budgets. The depth of snow impacts soil freezing with
implications for soil hydraulic properties and over-winter survival of certain crops. The objective of this study was to incorporate a sophisticated snow cover routine into the atmosphere–land exchange (ALEX) model to simulate snow depths and
dynamics of the relatively thin snowpacks of the US Upper Midwest. The ALEX model is used in several agricultural modeling
projects, and as the land-surface parameterization in a mesoscale forecast model, but with only crude snow cover treatment.
We combined parameterizations and empiricisms from the literature with the ALEX structure. Only three parameters were
adjusted to find a set that worked well for 48 station years from three sites in Wisconsin. These were a correction for gauge
catch deficiency, the air temperature that differentiates rain from snow, and a parameter related to drainage of liquid water
from a melting snowpack. A further independent test included 13 years from one site in Minnesota. The air temperature
differentiating rain from snow was also determined by analysis of weather observations, independently of the snow model.
Both this analysis and the model revealed 0◦ C to be the best choice for this temperature in our region. Results showed that
with a minimum of calibration the model gives good predictions of continuous snow depth, capturing critical processes of
accumulation, ablation and melt in a wide variety of situations. Discrepancies between model and measurements generally
originated from a single event and were mainly attributed to processes of blowing snow, misclassification of precipitation type,
and anomalous new snow densities. Our results demonstrated the robustness of existing parameterizations and empiricisms
for translating environmental observations into snow depth in dynamic simulation models. © 2000 Elsevier Science B.V. All
rights reserved.
Keywords: Snow cover; Snow depth; New snow density; Rain–snow transition temperature; Precipitation; Blowing snow
1. Introduction
Significant areas of agricultural lands are subject to
seasonal snow covers. This cover affects temperature
and moisture in the soil beneath, watershed hydrology,
∗ Corresponding author. Tel.: +1-608-262-0221;
fax: +1-608-265-2595.
E-mail address: [email protected] (W.L. Bland).
and energy budgets. Snow is an appreciable fraction of
soil water recharge in some areas, representing an important source of moisture for agricultural crops (e.g.
western Canadian prairies; Granger and Male, 1978).
The depth of snow regulates soil freezing (Flerchinger,
1991) and influences soil hydraulic properties and the
over-winter survival of certain crops. Decreased hydraulic conductivity of frozen soils increases the potential for high snowmelt runoff losses, while freezing
0168-1923/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 8 - 1 9 2 3 ( 0 0 ) 0 0 1 6 9 - 6
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C.E. Kongoli, W.L. Bland / Agricultural and Forest Meteorology 104 (2000) 273–287
injury can cause yield loss to over-wintering crops,
e.g. alfalfa (Kanneganti et al., 1998).
Motivated by water supply and safety concerns, the
snow literature is dominated by studies of relatively
deep snowpacks of mountainous or forested regions.
Agricultural environments in the US Midwest more
commonly have relatively thin snowpack, and issues
of practical importance can be significantly different
from those surrounding deeper snow. Compared to
deep snowpacks, greater attention may be given to
dates of complete disappearance in agricultural settings. Early ablation, for instance, can have important
implications for alfalfa survival. Responses of environmental factors to thinner snow cover are more rapid
than in deep snow, e.g. to the diurnal cycles of surface
energy fluxes (Granger and Male, 1978).
Snow cover models vary in complexity. An early,
essentially complete physically based model of snow
cover was that of Anderson (1976). This numerical
model included physical descriptions of snowpack
accumulation, change of albedo, settling and compaction, snowmelt, and meltwater retention and percolation as well as the snowpack energy balance.
The major advantage of models of this type is that
they allow mechanistic understanding of snow cover
processes and so should be transportable. However,
their use is limited by data needs and computational
burden. Extensions to Anderson (1976) model expanded the physical system to include the soil beneath (SNTHERM; Jordan, 1991), and vegetation and
residue (SHAW; Flerchinger and Saxton, 1989).
The objective of this study is to test the validity
of Anderson’s parameterizations for the snow depths
and dynamics of the relatively thin snowpacks of
Wisconsin. Additionally, we needed to incorporate a
sophisticated snow routine into the atmosphere–land
exchange (ALEX) model, which we use in several
agricultural modeling products (Anderson et al., 1998;
Bland et al., 1998; Diak et al., 1998). The speed and
simplicity of ALEX is suitable for landscape-to-global
scale applications where calculations must be made
at thousands of locations. One such application is our
project to assess the impact of landscape position and
time of year on optimizing wintertime disposal of animal manure. Additionally, ALEX is the land-surface
parameterization in the CRASS mesoscale forecast
model (personal communication; Diak, 1999), but
with only crude snow cover treatment. Finally, restruc-
turing of the US National Weather Service during the
past decade eliminated many sites where professional
observers recorded snow cover changes. The future
prospect is for fewer observations, so simulation
will play an increasing role in real-time management
problems.
This study is unique in the extent of record used to
demonstrate the validity of the model: four stations
totaling 61 site years of continuous hourly and daily
weather observations. Detailed snow cover models
such as SNTHERM and SHAW have so far been applied to only shorter records for verification purposes
typically extending 1–3 years. In contrast, snow cover
routines subjected to longer-term verifications are
generally less sophisticated (Motoyama, 1990; Yang
et al., 1997). Additionally, the model created here
is both complete in process as defined by Anderson
(1976) and numerically efficient enough to integrate
into a model suitable for mesoscale modeling projects.
Because of computational limitations, snow submodels used in regional or climate studies so far exhibit
low to intermediate complexity (Slater et al., 1998),
typically lacking internal processes (e.g. melt water
retention and percolation) (Yang et al., 1997). In our
work, the snow cover parameters were successfully
applied to the entire data set, covering a wide variety
of snow cover conditions. Results demonstrate that
available parameterizations as implemented in ALEX
are robust.
2. The ALEX model and modifications for snow
2.1. The soil–vegetation system
The ALEX model is a two-source (soil and vegetation) model of heat, water and carbon exchange
between a vegetated surface and the atmosphere
(Anderson et al., 1997; Anderson et al., 2000). Soil is
represented by an arbitrary number of layers, whereas
vegetation is represented as a single layer. This single
vegetation layer allows the model to be used in an inverse mode, for interpreting remotely-sensed temperatures. Each layer is bounded by a pair of nodes and
defined by its unique physical properties with respect
to the transport of heat and water. When vegetation
is present, the top node is at a height above the soil
surface equal to roughness length plus displacement
C.E. Kongoli, W.L. Bland / Agricultural and Forest Meteorology 104 (2000) 273–287
height. Upper boundary conditions are specified at
some measurement height above the top layer, whereas
lower boundary conditions are defined at some depth
within the soil profile. Although the multi-layer structure so defined comprises different materials (soil and
vegetation as top layer), commonality of transport
processes among materials allows ‘binding’ of these
layers into one single computational block. This block
is ‘routed’ into the numerical solution engine at the
beginning of the time step with the new state variables
determined at the end of the time step. For instance,
the soil–vegetation system is treated as one block with
respect to the transport of heat. Similarly, the soil is
treated as another block with respect to infiltration of
water. The solution at the end of each time step is obtained after all the mass and energy balance closures
have been simultaneously satisfied. This structural
simplicity allows addition of a manure layer, which, as
mentioned earlier, is a future improvement needed for
simulations of wintertime disposal of animal waste.
2.2. The modified atmosphere–snow–soil system
Building on the structure of ALEX, we introduced
a snow cover overlaying the soil profile. Similar to
the soil profile, the snow cover consists of an arbitrary
number of layers bounded by pairs of nodes. The
vegetation layer was removed and the series–parallel
resistance network associated with this layer was
replaced with the aerodynamic resistance Ra .
Two major modifications were made to accommodate snow cover processes. One involved representation of processes unique to snow layers (e.g. snow
melt) and the other involved mimicking of a continuously changing snow cover while maintaining the
structural consistency and conceptual simplicity of
ALEX. For the snow layers, soil heat transport equations were modified to include melt energy (Qm ) as
a source, computed as the energy excess above 0◦ C.
The second major modification involved simulation of
an unstable material as part of a multi-layer structure;
unlike soil, snow undergoes significant accumulation,
metamorphosis, compaction and ablation. As a result,
layers of snow are added, expanded, contracted or
disappear continuously. Similarly, nodes associated
with snow layers are added, left out, and reordered
continuously. When no snowpack is present, the system consists of the soil profile and the overlying air.
275
The model updates changes in layers overlying the
soil profile at the end of each time step (hourly).
2.3. Main snow cover routines
Important snow-related equations are discussed in
this section. Values of most of the various empirical
parameters were taken from the literature, as indicated
in Table 3. Parameters that we found necessary to
adjust are discussed later.
The density of new snow is computed according to
a formula given by LaChapelle (1969):
50 + 1.7(Tw + 15)1.5 , Tw > −15◦ C
ρns =
(1)
50,
Tw < −15◦ C
where ρ ns is new snow density in kg m−3 and Tw is
the wet bulb temperature in ◦ C. Compaction of each
layer of snowpack is based on a relationship reported
by Kojima (1967) and Mellor (1964):
1 ∂ρsp
=C1 exp[−0.08(T0 − T )]Ws exp(−C2 ρsp )]
ρsp ∂t
(2)
where Ws is the weight of the overlying snow, ρ sp the
density of the solid phase of snow, T the snow temperature in ◦ C, C1 and C2 are the constants, and
T0 =0◦ C.
Destructive metamorphism is computed by the expressions (Anderson, 1976)
1 ∂ρsp
= C3 exp[−C4 (Tc − T )]
ρsp ∂t
for
ρsp ≤ ρd
(3)
1 ∂ρsp
= C3 exp[−C4 (Tc − T )]exp(−46(ρsp − ρd )]
ρsp ∂t
for ρsp ≥ ρd (4)
where C3 and C4 are the empirical parameters and ρ d
is a threshold density. If melting is under way, Eqs. (3)
and (4) is multiplied by a parameter (C5 ) to account for
the effect on metamorphism of liquid water contained
in the snow layer.
Albedo of the snow is assumed to be independent
of sun angle, and is computed from Anderson (1976):
αsp = 1 − 0.206Cv ds −1/2
(5)
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C.E. Kongoli, W.L. Bland / Agricultural and Forest Meteorology 104 (2000) 273–287
where Cv is an empirical extinction coefficient and ds
is the grain size diameter of ice crystals (mm). Grain
size is calculated from Anderson (1976):
2
4
ρs
ρs
ds = G1 + G2
+ G3
(6)
ρl
ρl
where G1 , G2 and G3 are the empirical coefficients,
ρ s the density of snow at the surface and ρ l is the
density of liquid water. The albedo of snowpacks less
than 4 cm thick is adjusted based on the albedo of the
underlying material.
Melt water percolation in the snow is estimated using the ‘lag and route’ approach originally adopted
by Anderson (1976) and incorporated into the SHAW
model by Flerchinger (1995, 1997). Melt water produced in a snow layer begins to percolate after its water liquid holding capacity, often called the irreducible
water saturation, is satisfied. The irreducible water saturation is analogous to the so-called field capacity of
soil physics. The value of We is assumed to be at a
minimum (Wemin ) if snow density exceeds a threshold
value (ρ e ). If snow density is less than this threshold
value, We is computed using the expression
ρe − ρsp
We = Wemin + (Wemax − Wemin )
(7)
ρsp
where Wemax is the maximum liquid water holding
capacity (Anderson, 1976).
3. Data collection and weather inputs
We investigated the ability of the model to predict
snow depths at Madison, Milwaukee and Green Bay,
WI and Minneapolis, MN during the January–April
winter season for a 16-year period for Madison and
Milwaukee, and a 13-year period for Green Bay and
Minneapolis (Table 1). The stations represent differTable 1
Weather stations studied
Weather
station
Altitude
(m)
Latitude
Longitude
Simulation
period
Madison
Milwaukee
Green Bay
Minneapolis
622
220
211
83
43◦ 080
42◦ 570
44◦ 300
44◦ 530
89◦ 200
87◦ 540
87◦ 070
93◦ 130
1975–1990
1975–1990
1978–1990
1978–1990
ent combinations of latitude and proximity to Lake
Michigan. The official station at Madison was located
at Dane County Regional Airport near southwest shore
of Lake Mendota (approximately 39 km2 in area). The
station at Milwaukee was located about 6 km inland
from Lake Michigan at Mitchell Field Airport. The
Green Bay site was the Austin Straubel Field Airport,
about 17 km from the bay. The Minneapolis site was
the St. Paul Minneapolis International Airport.
During the period simulated, the sites were ‘first
order’ stations within the US National Weather Service System. Data were obtained from CD-ROMs
produced by EarthInfo Inc. (1998a,b), which contain
hourly values of air temperature, dew point temperature, wet bulb temperature, humidity, wind speed and
wind direction, precipitation amount, cloud cover,
and present weather conditions. Modeled estimates
of daily solar radiation and daily measurements of
snow depth were obtained from Midwestern Climate
Center, Champlain-Urbana, IL. Hourly solar radiation was estimated by partitioning the daily values
according to hourly potential radiation. Snow depth
readings were taken every day at 06.00 LST, nominally following standard National Weather Service
procedures. Doesken and Judson (1996) described
these procedures as follows.
Depth of snow on the ground is measured by taking
the average of several depth readings by a snow stake
on a standard-sized plot of open sod near the point of
observation. These plots are selected so that snow
depth reported was the average for unshaded, level and
unpaved areas, not disturbed by human activity in the
vicinity (within several hundred meters) of the weather
station. Depth of snow is measured and reported to the
nearest whole inch, or about 25 mm; if less than
12 mm, it is reported as ‘trace’. Snow depth is also
reported as ‘trace’ when less than 50% of the measurement ground area was covered by snow. For computational purposes, we have set all trace records to zero.
Liquid water equivalent of precipitation was
recorded hourly to the nearest 0.25 mm with a standard
20 cm diameter rain gauge. Snow in the gauge was
melted completely and its equivalent water depth was
measured. Metadata from the National Climate Data
Center also indicate that over the study years, precipitation gauges were shielded against the wind. This
significantly improves catch efficiency especially
when winds near the gauge are extremely strong
C.E. Kongoli, W.L. Bland / Agricultural and Forest Meteorology 104 (2000) 273–287
277
Table 2
The weather inputs to ALEX
Weather input
Source
Precipitation
Air temperature
Wet bulb temperature
Dew point temperature
Humidity
Wind speed and direction
Cloud cover
Incoming solar radiation
National Climate Data Center (EarthInfo Inc., 1998b)
National Climate Data Center (EarthInfo Inc., 1998a)
National Climate Data Center (EarthInfo Inc., 1998a)
National Climate Data Center (EarthInfo Inc., 1998a)
National Climate Data Center (EarthInfo Inc., 1998a)
National Climate Data Center (EarthInfo Inc., 1998a)
National Climate Data Center (EarthInfo Inc., 1998a)
Potential solar radiation estimated from Weiss and
Norman (1985) and modeled daily solar radiation
from the Midwestern Climate Center
Midwestern Climate Center
Estimated from Campbell and Norman (1998)
Estimated from Monteith and Unsworth (1990)
Snow depth
Clear sky emissivity
Long wave atmospheric emittance
(Doesken and Judson, 1996). Table 2 gives the
weather inputs to ALEX and the sources from which
they were obtained and/or estimated. Precipitation
type observations were used in ancillary analysis but
are not used as input in model simulations.
ing sections. All model runs were initialized at the end
of November of the previous year. Criteria for model
performance were overall statistics (e.g. correlation,
bias, absolute departure, and root mean square error
(RMSE)), graphical analysis and dates of complete
melting of snow cover.
4. Model development
4.1. Parameterization of the form of precipitation
Initial model development was conducted with the
1975–1985 Madison data. This work identified the
need to adjust three parameters: critical air temperature at which rain and snow can be differentiated
(Tc ), a snow correction factor (SCF) for efficacy of
gauge catch, and the minimum water holding capacity (Wemin ) of the melting snowpack. The first two parameters are in a sense external to the snow ablation
model, while the third is integral to the snow liquid
retention empiricism (Eq. (7)). For all three parameters, nominal values were obtained from literature, and
adjustments were based on the 1975–1985 Madison
dataset. Next, the adjusted values were applied to the
remainder of the Madison records and to the Green
Bay and Milwaukee datasets. Finally, sensitivity analysis guided selection of a single set of values that provided good model behavior over the complete records
of the Wisconsin sites. This set was then applied to
the Minneapolis site as a final test of the robustness
of the parameter values. Simulations were conducted
using the adjusted parameters and those from the literature as described in Table 3. Each of the adjusted
parameters is discussed in greater detail in the follow-
The first parameter we investigated in detail was
the critical air temperature at which precipitation can
be differentiated as rain or snow (Tc ). Accurate determination of the form of precipitation is widely recognized as critical to snowmelt-runoff modeling (US
Army Corps of Engineers, 1956; World Meteorological Organization, 1986; Leavesley, 1989; Braun, 1991;
Rohrer et al., 1994). Regardless of whether it is considered a model parameter, critical air temperature is
also a climatological parameter that can be established
(outside the model) through analysis of local observations. The ‘present weather’ observations allowed
us to initially derive this relationship independently of
the complete model and then evaluate its impact on
the model through sensitivity analysis.
There are two major model-related problems with
respect to form of precipitation: classification of
precipitation events, and determination of relative
amounts of each form of precipitation when mixed
forms occur or when one form of precipitation is followed by another in short time intervals. Precipitation
form could be required as model input or predicted
from more readily available weather variables. Even
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Table 3
Parameter values for the calibrated snow energy model
Identifier
Description
Value
Source
Tc
Critical air temperature
0◦ C (tested: −2 to +2◦ C)
Z0
C3
G1
G2
G3
Cv
C1
C2
C4
C5
SNOmax
Wemax
Wemin
ρe
CW1
CW2
CW3
CW4
SCF
Roughness length
Destructive metamorphism
Grain size parameter
Grain size parameter
Grain size parameter
Solar radiation extinction coefficient
Compaction parameter
Compaction parameter
Destructive metamorphism parameter
Melt metamorphism parameter
Threshold snow density metamorphism parameter
Maximum water holding parameter
Minimum water holding capacity
Lower density to use Wemin
Maximum lag parameter
Actual lag parameter
Recession parameter
Attenuation parameter
Snow correction factor
0.0015 m
0.001 h−1
0.16 mm
0 mm cm6 g−2
110 mm cm12 g−4
1.77 cm12 mm0.5 g−1
0.01 cm−1 h−1
21 cm3 g−1
0.04 K−1
2
0.15 g cm−3
0.1
0 (tested: 0–0.03)
0.2 g cm−3
10 h
1 cm−1
5h
450 cm3 g−1
1.3 (tested: 1–2)
Calibrated against weather data
and verified against snow depth
Anderson (1976)
Anderson (1976)
Anderson (1976)
Anderson (1976)
Anderson (1976)
Barry et al. (1990)
Anderson (1976)
Anderson (1976)
Anderson (1976)
Anderson (1976)
Anderson (1976)
Anderson (1976)
Calibrated against snow depths
Anderson (1976)
Anderson (1976)
Anderson (1976)
Anderson (1976)
Anderson (1976)
Calibrated against snow depth
if precipitation form is required as an input, relative
amounts during mixed or short-term interval transitional events cannot be readily detected by visual observations or by the most sophisticated precipitation
sensors in use today.
Most parameterization studies evaluate air temperature as predictor of precipitation form calibrated
against direct observations (e.g. Rohrer et al., 1994).
These studies suggest that Tc is generally higher
than 0◦ C, but can vary widely depending on climate,
location and season. US Army Corps of Engineers
(1956) suggested air temperatures in the range of
0.5–1◦ C, whereas Martinec and Rango (1986) and
Braun (1991) referred to maximum values as high as
5.5 and 7◦ C, respectively. Rohrer et al. (1994) determined Tc values for individual weather stations in
Switzerland and found that they are between 0 and
1.5◦ C. Based on about 1000 weather observations of
surface air temperature and precipitation form, Auer
(1974) determined that at Tc =2.5◦ C probabilities of
rain and snow were equal.
Snow cover simulations using rain–snow transition
temperature as a model parameter suggest that its value
can have significant impact. Based on the study of
Auer (1974), Yang et al. (1997) used a critical air tem-
perature of 2.5◦ C as model parameter for long-term
snow cover simulations at six stations located in the
former Soviet Union. However, they found significant
improvement in RMSE of simulated versus measured
snow water equivalents when this parameter was set
at 0◦ C. Yang et al. (1997) attributed the difference
between their results and those of Auer to the effects
of different climates.
We investigated the role and best value of Tc in
our region by two means. In the first, we used hourly
records of precipitation and air temperature along with
the present weather observations (period for Wisconsin stations in Table 1, limited to days of year 1–100).
From these records, we computed the amounts of liquid precipitation in the form of snow, mixed rain and
snow, and rain that would be misclassified at prescribed air temperature values. The best value of Tc
minimized total liquid equivalent of misclassified precipitation. In the second, we compared evaluations of
model performance at various values of Tc .
4.2. Discussion of SCF
The mean SCF corrects for gauge catch deficiency
during snowfall. Precipitation gauges do not collect all
C.E. Kongoli, W.L. Bland / Agricultural and Forest Meteorology 104 (2000) 273–287
precipitation that falls (Doesken and Judson, 1996),
so a factor greater than one should be applied to snow
equivalents of recorded precipitation. Because of the
wide variability of SCF from storm to storm and
the uncertainty associated with its determination, a
mean snow correction factor is applied to all recorded
snow equivalents at a site, and determined by calibration (Anderson, 1973). Wind speed at gauge height
and gauge type are widely recognized as the two
key factors that have a major impact on SCF values
(Goodison, 1978). SCF values can be as high as 2.2
if high wind speeds occur or gauges are unshielded
(Doesken and Judson, 1996; Yang et al., 1997). For
shielded rain gauges, Anderson (1976) determined
snow correction factors for a number of snow seasons, and for wind speeds between 2.2 and 4.6 m/s
at gauge height he found SCF values between 1 and
1.25.
279
then review measured and modeled time series of snow
cover and dates of complete snow disappearance.
5.1. Climatological analysis of critical air
temperature
Results of our climatological analysis show that the
minimum amount of misclassified total liquid precipitation occurred over the 0–0.5◦ C interval for Madison
and Green Bay, and at 1◦ C for Milwaukee (Fig. 1).
At these values of Tc , average annual misclassified
amounts were 12 mm liquid depth for Madison and
Green Bay, and 19 mm for Milwaukee, split roughly in
half between each category (snow and rain). In relative
terms, only 9% of total liquid precipitation that falls
over the first 100 days of year was misclassified for
4.3. Discussion of Wemin
Minimum irreducible water saturation (Wemin ) impacts the amount of liquid water retained by the
snowpack Eq. (7), which, in turn, affects meltwater percolation. This parameter generally has little
effect on snowmelt, except during major melt or
rain-on-snow events (Anderson, 1973). It is generally
a calibrated parameter ranging from 0 to 3% (Anderson, 1973, 1976; Barry et al., 1990; Flerchinger, 1995,
1997). The SNTHERM model (Jordan, 1991) has
incorporated a somewhat different parameterization,
in the form of the empirically derived Darcy’s equation. In this treatment, water transport is governed by
capillary pressure and gravity forces. For the snow
layers, however, capillary pressure is neglected. The
final equation contains a number of empirical parameters related to gravity drainage including minimum
irreducible water saturation. As a result, the physical
basis for Jordan’s equation is similar to Eq. (7). We
chose the expression given by Eq. (7) because it has
fewer empirical parameters.
5. Results and discussion
Results are presented below for the climatological
analysis of Tc , followed by the statistical measurements of model accuracy and sensitivity analysis. We
Fig. 1. Average annual misclassified liquid precipitation as a function of air temperature over the simulation period for (A) Madison, (B) Green Bay, and (C) Milwaukee. Snow equivalents of precipitation represent the recorded values. Mixed precipitation was
treated as rain since it produces little snow accumulation.
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Table 4
Snow depth statistics for ALEX output with respect to SCF
SCF
Madison
(mm)
Milwaukee
(mm)
Green Bay
(mm)
Absolute departure
1
73 (47)
1.3a
52 (35)
1.5
51 (34)
56 (33)
47 (32)
53 (35)
70 (50)
45 (34)
53 (42)
RMS
1
1.3a
1.5
86 (67)
62 (50)
60 (49)
68 (51)
60 (39)
78 (64)
83 (69)
60 (51)
69 (61)
−69 (−44)
−29 (−19)
−1 (0)
−46 (−25)
10 (7)
41 (34)
−55 (−37)
−16 (−9)
24 (21)
Mean bias
1
1.3a
1.5
a
The calibrated parameter value.
Madison, and only 10% for Green Bay and Milwaukee. Misclassified precipitation was the same at 0 and
0.5◦ C because temperatures were reported with a resolution of 1◦ F, or 0.56◦ C. A single threshold of 0◦ C is
appropriate for the three stations, as the difference between the amount of misclassified precipitation at this
value and the amount at 1◦ C for Milwaukee was small.
5.2. Statistical and sensitivity analysis
We calculated several statistics to compare simulated and measured snow depths (Tables 4–6). These
Table 5
Snow depth statistics for ALEX output with respect to Wemin
Wemin
Madison
(mm)
Milwaukee
(mm)
Green Bay
(mm)
Absolute departure
0a
52 (35)
0.02
59 (45)
0.03
60 (50)
47 (32)
60 (49)
64 (56)
45 (34)
49 (40)
51 (46)
RMS
0a
0.02
0.03
62 (50)
70 (60)
70 (63)
60 (39)
74 (65)
77 (71)
60 (51)
64 (59)
66 (64)
Mean bias
0a
0.02
0.03
−1 (0)
18 (19)
25 (20)
10 (7)
34 (30)
42 (36)
−16 (−9)
−1 (5)
13 (3)
a
The calibrated parameter value.
Table 6
Snow depth statistics for ALEX output with respect to critical
temperature (Tc )
Air temperature
(◦ C)
Madison
(mm)
Milwaukee
(mm)
Green Bay
(mm)
Absolute departure
−1
0 (0.5)a
1
1.5
77
52
70
73
(50)
(35)
(51)
(54)
55
47
56
71
(33)
(32)
(40)
(52)
72
45
48
55
(52)
(33)
(36)
(42)
RMS
−1
0 (0.5)a
1
1.5
88
62
82
86
(70)
(50)
(72)
(77)
66
60
70
87
(51)
(39)
(61)
(77)
89
60
61
69
(74)
(51)
(53)
(60)
Mean bias
−1
0 (0.5)a
1
1.5
−69
−1
22
30
a
(−44)
(0)
(19)
(25)
−29
10
28
46
(−13)
(7)
(25)
(38)
−52
−9
−3
9
(−35)
(−16)
(1)
(7)
The calibrated parameter value.
statistics include all years as shown in Table 1.
Reported are average RMSE, absolute departure and
bias for several model runs. Each table reports statistics when one parameter is changed with others set at
the calibrated values. Statistical results summarized
in these tables refer to computations done for days
with measured and predicted snow on the ground, and
for the entire 100-day period of simulation (values in
parenthesis). Correlation between measured and modeled snow depth was calculated, but proved insensitive
to parameter selection, ranging only 0.78–0.9 over
the parameter ranges in Tables 4–6. This insensitivity
is expected when comparing simulated and measured
cumulative time series.
The SCF significantly impacted simulated snow
depths. When this parameter was set at 1 the model
consistently underestimated snow depths throughout
the simulation period for the three stations. The other
possible explanation for the consistent underestimation of snow depth was the rate of compaction and
metamorphosis given by Eqs. (2)–(5). Altering these
improved model performance, but also led to modeled
snow densities significantly lower than suggested by
literature (e.g. Anderson, 1976). A mean snow correction factor of 1.3 for Green Bay and Milwaukee, and
1.5 for Madison yielded the best statistics for the three
C.E. Kongoli, W.L. Bland / Agricultural and Forest Meteorology 104 (2000) 273–287
stations (Table 4), although 1.3 is acceptable also for
Madison. For the estimated mean wind speed around
13 km h−1 at gauge height at each site, a SCF value
of 1.3 is reasonable (e.g. Doesken and Judson, 1996).
Minimum liquid water holding capacity (Wemin ) significantly impacted simulated snow depths, especially
during major melt events, and the date of complete
snow disappearance. When this parameter was set at
the value of 0.03 (Anderson, 1976), delays of melt
occurred irrespective of the value of SCF. Changing
other parameters in Eq. (7) did not significantly affect
model predictions of dates of snow cover disappearance and overall model performance. We also found
that at Wemin =0.03, snow densities generated by the
model during snowmelt were unreasonably high. Setting this parameter at zero eliminated this problem, as
well as improved both predictions of dates of snow
disappearance (Fig. 2) and overall model performance
(Table 5).
For the critical air temperature (Tc ), lowest departures and RMSEs are obtained at 0◦ C for the three
stations (Table 6). This confirms our climatological
analysis on this parameter. At 0◦ C, the model captures
Fig. 2. Measured vs. simulated day of year of snow cover disappearance for accumulations over 0.1 m at the three Wisconsin
stations and Minneapolis, MN. Regression coefficients refer to
simulations done with the calibrated parameter set, for which
Wemin =0.
281
all major events, and errors resulting from misclassifications are relatively minor, as previously discussed.
Improved classification of precipitation type will likely
require a parameterization involving more than Tc ,
perhaps synoptic and upper air weather conditions.
5.3. Reproduction of snow depth patterns and
dynamics
Subjective study of time series of snow depth both
measured and modeled is a powerful demonstration of
the ability of the model. Graphs of simulated versus
measured daily snow depths revealed that the model
captured snow dynamics well, reproducing snow accumulation and ablation in a wide variety of situations
(Figs. 3–6). Figures show the 9 years with the greatest snow depths observed during the period of simulation. At each location years of lower snow depth did
not reveal any model weakness, but did little to prove
its ability. While we do not have water equivalents to
check the model, the date of snow cover disappearance does provide one unambiguous check on model
estimates of total liquid equivalent of the snowpack
(Fig. 2).
Major departures apparently resulted from misclassification of precipitation, blowing snow, and variations of new snow density not captured by current
empiricisms (Table 7 and Figs. 3–5). Departures generally originated from a single event and then caused
poor agreement for many days afterward, e.g. in 1978,
1979 and 1982 at Milwaukee departures originated on
days 27, 45 and 20, respectively (Fig. 5).
Misclassified precipitation by the model results
from snow occurring at air temperatures above the selected Tc , or from rain occurring below this value. For
example, in 1979 at Milwaukee (Fig. 5) departures
resulted from a misclassification on day 45, when
records revealed that this event was accompanied by
freezing rain occurring well below 0◦ C. Similarly, in
1986 at Madison (Fig. 3), the observed freezing rain
on days 32 and 35 was misclassified by the model as
snow.
Redistribution by wind relocates snow covers and
causes sublimation while the snow is in transit. These
processes dominate snow cover development in open,
level, wind-swept areas (e.g. Canadian Prairie) and in
irregular terrain. In open, level areas, sublimation becomes important, whereas in rugged terrain relocation
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Fig. 3. Measured vs. simulated snow depths for the 9 years of greatest snow accumulation during the simulated period at Madison.
of snow by wind predominates (Pomeroy et al., 1998).
Redistribution by wind forms snow covers of highly
variable depth and density (Pomeroy et al., 1997).
Blowing snow may have contributed to overestimation of simulated snow depths in 1979 and 1982 for
Milwaukee. In 1982, for instance, a significant snow
event occurred on day 20, producing a recorded daily
liquid precipitation of 9 mm (as corrected by SCF) and
converted into a daily snow depth increase of about
13 cm by the model. However, recorded snow depth
never reflected that event, suggesting that all of the
new snow may have been transported away from the
site of measurement. This is supported by weather
records, which indicate that blowing snow accompanied the event. At Green Bay in 1978, discrepancy between modeled and measured snow depths began on
day 25. According to the weather records, weather on
day 25 and thereafter included blowing snow. No explanation other than blowing snow is available for the
rapid ablation following day 25. We note that blowing
snow was a frequent event for the three stations investigated, especially for Milwaukee and Green Bay.
However, these events did not prove to cause major
problems other than the few reported above.
Departures also occur during events correctly classified by the model, but for which snow depth is
C.E. Kongoli, W.L. Bland / Agricultural and Forest Meteorology 104 (2000) 273–287
283
Fig. 4. Measured vs. simulated snow depths for the 9 years of greatest snow accumulation during the simulated period at Green Bay.
appreciably underestimated, e.g. 1983 at Green Bay.
Weather records indicated that during the first two
events observed new snowfall per unit of recorded
liquid precipitation was significantly larger than predicted by the model, i.e. the snow was of exceptionally
low density. The presence of snow lighter than predicted by Eq. (1) in the Green Bay vicinity, however,
was not substantiated by weather records at Brillion,
a weather station about 40 km away from Green Bay.
Perhaps discrepancies in observation procedures led
to systematic errors at Green Bay in 1983. Similarly,
in 1979 at Madison, the model significantly underestimated snow accumulation, yielding a maximum departure of about 30 cm. In this year, comparison of
weather records of the three sites revealed similar snow
patterns, but larger snowfall per unit of recorded liquid precipitation for Madison than for Milwaukee or
Green Bay. In this case, however, a near-by observation also recorded anomalously low snow density.
To verify and extend the geographic range of the
model, we chose the Minneapolis station. Good model
accuracy was shown by statistical measures and by
inspection of the time series (Fig. 6). For all simulation years, for days with snow on the ground average
bias was 20 mm, average correlation 0.85, average absolute departure 40 mm, and average RMSE 51 mm.
For the entire 100-day simulation period, average bias
was 11 mm, average correlation 0.90, average absolute
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Fig. 5. Measured vs. simulated snow depths for the 9 years of greatest snow accumulation during the simulated period at Milwaukee.
departure 35 mm, and average RMSE 45 mm. While
there is some ambiguity in the degree of independence
of our assessments of model performance in Wisconsin, this is not the case with the Minneapolis records.
This test and the sensitivity analysis for the other sites
(Table 4) demonstrate that the model formulations and
parameter values are robust for the US Upper Midwest.
The simulations are associated with airports, where the
necessary high-quality datasets were available. These
sites, however, were extensive open areas, represen-
Table 7
Summary of major departures of simulated vs. measured snow depths resulting from events not (correctly) captured by the model
Station
Year
Description of departure
Madison
Green Bay
Green Bay
Madison
Milwaukee
Milwaukee
1979
1978
1983
1986
1979
1982
Underestimation of simulated snow depths; lighter snow during major events
Overestimation of simulated snow depths; blowing snow during one major event
Underestimation of simulated snow depths
Freezing rain misclassified as snow on several events
Overestimation of simulated snow depths; freezing drizzle misclassified as snow for one major event
Overestimation of simulated snow depths; blowing snow during one major event
C.E. Kongoli, W.L. Bland / Agricultural and Forest Meteorology 104 (2000) 273–287
285
Fig. 6. Measured vs. simulated snow depths for the 9 years of greatest snow accumulation during the simulated period at Minneapolis.
tative of many of the region’s agricultural fields. The
physically based nature of the energy balance portions
of the model in principle accommodates differences
among land management, such as presence or absence
of crop stubble.
6. Conclusions
This work extends the ALEX model (Anderson
et al., 2000) for additional applications requiring inclusion of snow cover. We incorporated the basic
compilation of snow processes as defined by Anderson (1976) into the numerically efficient ALEX
model and evaluated the model against 61 site years
of observations from four sites in the Upper Midwest.
With a minimum of calibration, the modified ALEX
model gives good predictions of continuous snow
depth. The model reproduced snow depth patterns
reasonably well for a wide variety of situations. Critical snow cover processes of accumulation, ablation
and melt were well captured. A separate analysis of
the available data set established the best threshold
value of the critical air temperature parameter (Tc )
differentiating rain from snow was 0◦ C for the three
Wisconsin stations. Discrepancies between model and
measurements generally originated from single events
and were mainly attributed to processes of blowing
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snow not represented in the model, misclassification
of form of precipitation, and apparently anomalous
new snow densities. Perhaps improved empiricisms
for Tc and new snow density must involve mesoscale
atmospheric column considerations. These results
demonstrated the robustness of current parameterizations for translating environmental observations into
snow depth.
Acknowledgements
This research was supported by USDA-Hatch funds
through project WIS03954.
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