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 National Climate Data Center EarthInfo Inc., 1998b
Air temperature National Climate Data Center EarthInfo Inc., 1998a
Wet bulb temperature National Climate Data Center EarthInfo Inc., 1998a
Dew point temperature National Climate Data Center EarthInfo Inc., 1998a
Humidity National Climate Data Center EarthInfo Inc., 1998a
Wind speed and direction National Climate Data Center EarthInfo Inc., 1998a
Cloud cover National Climate Data Center EarthInfo Inc., 1998a
Incoming solar radiation Potential solar radiation estimated from Weiss and
Norman 1985 and modeled daily solar radiation from the Midwestern Climate Center
Snow depth Midwestern Climate Center
Clear sky emissivity Estimated from Campbell and Norman 1998
Long wave atmospheric emittance Estimated from Monteith and Unsworth 1990
Doesken and Judson, 1996. Table 2 gives the weather inputs to ALEX and the sources from which
they were obtained andor estimated. Precipitation type observations were used in ancillary analysis but
are not used as input in model simulations.
4. Model development
Initial model development was conducted with the 1975–1985 Madison data. This work identified the
need to adjust three parameters: critical air temper- ature at which rain and snow can be differentiated
T
c
, a snow correction factor SCF for efficacy of gauge catch, and the minimum water holding capac-
ity W
e
min
of the melting snowpack. The first two pa- rameters 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 parame-
ters, 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 anal- ysis guided selection of a single set of values that pro-
vided 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 lit- erature as described in Table 3. Each of the adjusted
parameters is discussed in greater detail in the follow- 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.
4.1. Parameterization of the form of precipitation The first parameter we investigated in detail was
the critical air temperature at which precipitation can be differentiated as rain or snow T
c
. Accurate deter- mination of the form of precipitation is widely rec-
ognized as critical to snowmelt-runoff modeling US Army Corps of Engineers, 1956; World Meteorologi-
cal Organization, 1986; Leavesley, 1989; Braun, 1991; Rohrer et al., 1994. Regardless of whether it is con-
sidered a model parameter, critical air temperature is also a climatological parameter that can be established
outside the model through analysis of local obser- vations. 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 fol- lowed by another in short time intervals. Precipitation
form could be required as model input or predicted from more readily available weather variables. Even
278 C.E. Kongoli, W.L. Bland Agricultural and Forest Meteorology 104 2000 273–287
Table 3 Parameter values for the calibrated snow energy model
Identifier Description
Value Source
T
c
Critical air temperature
◦
C tested: −2 to +2
◦
C Calibrated against weather data
and verified against snow depth Z
Roughness length 0.0015 m
Anderson 1976 C
3
Destructive metamorphism 0.001 h
− 1
Anderson 1976 G
1
Grain size parameter 0.16 mm
Anderson 1976 G
2
Grain size parameter 0 mm cm
6
g
− 2
Anderson 1976 G
3
Grain size parameter 110 mm cm
12
g
− 4
Anderson 1976 C
v
Solar radiation extinction coefficient 1.77 cm
12
mm
0.5
g
− 1
Barry et al. 1990 C
1
Compaction parameter 0.01 cm
− 1
h
− 1
Anderson 1976 C
2
Compaction parameter 21 cm
3
g
− 1
Anderson 1976 C
4
Destructive metamorphism parameter 0.04 K
− 1
Anderson 1976 C
5
Melt metamorphism parameter 2
Anderson 1976 SNO
max
Threshold snow density metamorphism parameter 0.15 g cm
− 3
Anderson 1976 W
e
max
Maximum water holding parameter 0.1
Anderson 1976 W
e
min
Minimum water holding capacity 0 tested: 0–0.03
Calibrated against snow depths ρ
e
Lower density to use W
e
min
0.2 g cm
− 3
Anderson 1976 CW
1
Maximum lag parameter 10 h
Anderson 1976 CW
2
Actual lag parameter 1 cm
− 1
Anderson 1976 CW
3
Recession parameter 5 h
Anderson 1976 CW
4
Attenuation parameter 450 cm
3
g
− 1
Anderson 1976 SCF
Snow correction factor 1.3 tested: 1–2
Calibrated against snow depth
if precipitation form is required as an input, relative amounts during mixed or short-term interval transi-
tional events cannot be readily detected by visual ob- servations or by the most sophisticated precipitation
sensors in use today.
Most parameterization studies evaluate air tem- perature as predictor of precipitation form calibrated
against direct observations e.g. Rohrer et al., 1994. These studies suggest that T
c
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 de- termined T
c
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 T
c
= 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 T
c
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 Wiscon-
sin stations in Table 1, limited to days of year 1–100. From these records, we computed the amounts of liq-
uid precipitation in the form of snow, mixed rain and snow, and rain that would be misclassified at pre-
scribed air temperature values. The best value of T
c
minimized total liquid equivalent of misclassified pre- cipitation. In the second, we compared evaluations of
model performance at various values of T
c
. 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 273–287 279
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
