276 C.E. Kongoli, W.L. Bland Agricultural and Forest Meteorology 104 2000 273–287
where C
v
is an empirical extinction coefficient and d
s
is the grain size diameter of ice crystals mm. Grain size is calculated from Anderson 1976:
d
s
= G
1
+ G
2
ρ
s
ρ
l 2
+ G
3
ρ
s
ρ
l 4
6 where G
1
, G
2
and G
3
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 us- ing the ‘lag and route’ approach originally adopted
by Anderson 1976 and incorporated into the SHAW model by Flerchinger 1995, 1997. Melt water pro-
duced in a snow layer begins to percolate after its wa- ter liquid holding capacity, often called the irreducible
water saturation, is satisfied. The irreducible water sat- uration is analogous to the so-called field capacity of
soil physics. The value of W
e
is assumed to be at a minimum W
e
min
if snow density exceeds a threshold value ρ
e
. If snow density is less than this threshold value, W
e
is computed using the expression W
e
= W
e
min
+ W
e
max
− W
e
min
ρ
e
− ρ
sp
ρ
sp
7 where W
e
max
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 differ-
Table 1 Weather stations studied
Weather station
Altitude m
Latitude Longitude
Simulation period
Madison 622
43
◦
08
′
89
◦
20
′
1975–1990 Milwaukee
220 42
◦
57
′
87
◦
54
′
1975–1990 Green Bay
211 44
◦
30
′
87
◦
07
′
1978–1990 Minneapolis
83 44
◦
53
′
93
◦
13
′
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 km
2
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 Ser-
vice System. Data were obtained from CD-ROMs produced by EarthInfo Inc. 1998a,b, which contain
hourly values of air temperature, dew point tempera- ture, 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 radia- tion was estimated by partitioning the daily values
according to hourly potential radiation. Snow depth readings were taken every day at 06.00 LST, nomi-
nally 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 measur- ement ground area was covered by snow. For compu-
tational 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, preci-
pitation 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 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
