C.E. Kongoli, W.L. Bland Agricultural and Forest Meteorology 104 2000 273–287 279
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 calibra- tion 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 sea- sons, and for wind speeds between 2.2 and 4.6 ms
at gauge height he found SCF values between 1 and 1.25.
4.3. Discussion of W
e
min
Minimum irreducible water saturation W
e
min
im- pacts the amount of liquid water retained by the
snowpack Eq. 7, which, in turn, affects meltwa- ter 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 Ander- son, 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 equa- tion. 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 param- eters 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 T
c
, followed by the statistical measure- ments of model accuracy and sensitivity analysis. We
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 precipi-
tation 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 T
c
, 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
Fig. 1. Average annual misclassified liquid precipitation as a func- tion of air temperature over the simulation period for A Madi-
son, B Green Bay, and C Milwaukee. Snow equivalents of pre- cipitation represent the recorded values. Mixed precipitation was
treated as rain since it produces little snow accumulation.
280 C.E. Kongoli, W.L. Bland Agricultural and Forest Meteorology 104 2000 273–287
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
56 33 70 50
1.3
a
52 35 47 32
45 34 1.5
51 34 53 35
53 42 RMS
1 86 67
68 51 83 69
1.3
a
62 50 60 39
60 51 1.5
60 49 78 64
69 61 Mean bias
1 −
69 −44 −
46 −25 −
55 −37 1.3
a
− 29 −19
10 7 −
16 −9 1.5
− 1 0
41 34 24 21
a
The calibrated parameter value.
Madison, and only 10 for Green Bay and Milwau- kee. Misclassified precipitation was the same at 0 and
0.5
◦
C because temperatures were reported with a res- olution of 1
◦
F, or 0.56
◦
C. A single threshold of 0
◦
C is appropriate for the three stations, as the difference be-
tween 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 simu- lated and measured snow depths Tables 4–6. These
Table 5 Snow depth statistics for ALEX output with respect to W
e
min
W
e
min
Madison mm
Milwaukee mm
Green Bay mm
Absolute departure
a
52 35 47 32
45 34 0.02
59 45 60 49
49 40 0.03
60 50 64 56
51 46 RMS
a
62 50 60 39
60 51 0.02
70 60 74 65
64 59 0.03
70 63 77 71
66 64 Mean bias
a
− 1 0
10 7 −
16 −9 0.02
18 19 34 30
− 1 5
0.03 25 20
42 36 13 3
a
The calibrated parameter value. Table 6
Snow depth statistics for ALEX output with respect to critical temperature T
c
Air temperature
◦
C Madison
mm Milwaukee
mm Green Bay
mm Absolute departure
− 1
77 50 55 33
72 52 0 0.5
a
52 35 47 32
45 33 1
70 51 56 40
48 36 1.5
73 54 71 52
55 42 RMS
− 1
88 70 66 51
89 74 0 0.5
a
62 50 60 39
60 51 1
82 72 70 61
61 53 1.5
86 77 87 77
69 60 Mean bias
− 1
− 69 −44
− 29 −13
− 52 −35
0 0.5
a
− 1 0
10 7 −
9 −16 1
22 19 28 25
− 3 1
1.5 30 25
46 38 9 7
a
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 statis- tics 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 mod- eled 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 underestima- tion 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 correc-
tion 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 273–287 281
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 W
e
min
sig- nificantly 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 disappear-
ance and overall model performance. We also found that at W
e
min
= 0.03, snow densities generated by the
model during snowmelt were unreasonably high. Set- ting 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 T
c
, lowest depar- tures 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 dis- appearance 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
W
e
min
= 0.
all major events, and errors resulting from misclassi- fications are relatively minor, as previously discussed.
Improved classification of precipitation type will likely require a parameterization involving more than T
c
, 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 ac- cumulation and ablation in a wide variety of situations
Figs. 3–6. Figures show the 9 years with the great- est snow depths observed during the period of simu-
lation. 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 disappear-
ance does provide one unambiguous check on model estimates of total liquid equivalent of the snowpack
Fig. 2.
Major departures apparently resulted from misclas- sification of precipitation, blowing snow, and varia-
tions of new snow density not captured by current empiricisms Table 7 and Figs. 3–5. Departures gen-
erally 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 se-
lected T
c
, 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 be- comes important, whereas in rugged terrain relocation
282 C.E. Kongoli, W.L. Bland Agricultural and Forest Meteorology 104 2000 273–287
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 overestima-
tion 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 accompa-
nied the event. At Green Bay in 1978, discrepancy be- tween modeled and measured snow depths began on
day 25. According to the weather records, weather on day 25 and thereafter included blowing snow. No ex-
planation 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 in- vestigated, 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 clas- sified 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 pre-
dicted by the model, i.e. the snow was of exceptionally low density. The presence of snow lighter than pre-
dicted 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 underes-
timated snow accumulation, yielding a maximum de- parture 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 liq-
uid precipitation for Madison than for Milwaukee or Green Bay. In this case, however, a near-by observa-
tion 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 simula-
tion years, for days with snow on the ground average bias was 20 mm, average correlation 0.85, average ab-
solute 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
284 C.E. Kongoli, W.L. Bland Agricultural and Forest Meteorology 104 2000 273–287
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 Wiscon- sin, this is not the case with the Minneapolis records.
This test and the sensitivity analysis for the other sites
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
1979 Underestimation of simulated snow depths; lighter snow during major events
Green Bay 1978
Overestimation of simulated snow depths; blowing snow during one major event Green Bay
1983 Underestimation of simulated snow depths
Madison 1986
Freezing rain misclassified as snow on several events Milwaukee
1979 Overestimation of simulated snow depths; freezing drizzle misclassified as snow for one major event
Milwaukee 1982
Overestimation of simulated snow depths; blowing snow during one major event
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-
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
