has been developed by Melloh et al. (1997). Over
another for clear weather. Cloudy conditions
time we can expect to improve our ability to simu-
are inferred from meteorological records, by
whether or not rainfall was reported. When there
late and forecast snowmelt runoff with these new
is rain, cloudy conditions are presumed and melt
tools. Here we review the major operational mod-
els of past years and contrast these with two
is calculated as
snowmelt algorithms developed at CRREL that
Melt = C1 [(0.029 + 0.0084kv
are candidates for use in distributed operational
models.
+ 0.007Pr) (TaTb) + 0.09]
(2)
MODEL DESCRIPTIONS
where Melt = snowmelt (in. day1)
k = basin convectioncondensation
HEC-1
constant (0 to 1, dimensionless),
HEC-1, a single-event model, uses either a
v = mean wind speed at 50-ft height
degree-day temperature index method or a sim-
(mi hr1),
plified energy balance approach. The equations
used are a subset of those set forth in EM-1110-2-
Ta = temperature of saturated air at 10
1406 (U.S. Army Corps of Engineers 1960), a docu-
ft (F),
ment which summarizes equations derived from
Tb = base temperature at which melt
snow hydrology studies by the North Pacific Di-
will occur, usually 32F,
vision, Corps of Engineers, and the U.S. Weather
C1 = coefficient used in HEC-1 to account
Bureau at the Central Sierra Snow Laboratory
(CSSL) (latitude 3922'N), near Soda Springs, Cali-
for variation from the generalized
snowmelt equation and is dimen-
fornia (U.S. Army Corps of Engineers 1956).
sionless.
Temperature index degree-day method
The temperature index degree-day method
This equation is from U.S. Army Corps of Engi-
uses the following equation:
neers (1960) with coefficients fixed to assume
100% cloud cover and a canopy intermediate
M = Cd (Ta Tb)
(1)
between open and dense forest. The convection
condensation constant (k) represents the mean
where M = snowmelt (in. day1),
exposure of the subbasin to wind, considering
Cd = degree-day melt coefficient (in F1
topographic and forest effects, and is fixed at a
day1),
value of 0.6 in HEC-1. This coefficient should vary
Ta = air temperature (F),
from 1 to 0.3 for unforested plains and dense for-
Tb = base temperature at which melt will
est, respectively. Corrections to wind and tem-
occur, normally 32F.
perature measurement heights must be made
externally to the program input. The first term
EM-1110-2-1406 gives degree-day melt coefficients
(0.029) represents longwave radiation melt with
determined from mean values of snowpack abla-
complete cloud cover. The second term includes
tion related to air temperatures at nearby stations
wind speed ( v) and represents convection-
in the CSSL. The temperature indexes of snow-
condensation melt in open or partly forested
melt were found to be more reliable for forested
areas. Term 3 is melt due to rain (Pr), and term 4
areas than open areas. The term "forest" pertains
is the sum of 0.07 and 0.02 in./day melt due to
to the coniferous forests of the CSSL. Basins of sig-
shortwave radiation in the open and to ground
nificant open, deciduous, or sparse coniferous
heat, respectively.
forest would be modeled less reliably with the
The equation used when there is no rainfall,
index method. This is because temperature is a
assumes no clouds, and 50% forest canopy cover.
better sole indicator of the surface energy balance
This is equation is also from U.S. Army Corps of
in the forest where the canopy diminishes the
Engineers (1960):
direct solar radiation and wind.
(
) (3)
[
]
k (1 F) (0.004I ) (1 α) + k (0.008v) 0.22T ′
Energy balance method
′
i
a
M = C2
(
) (
)
The energy balance method in HEC-1 follows
+k (0.008v) 0.78T ′ + F 0.029T ′
a
two equations, one for cloudy weather, and
d
2
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