Degree-day method
degree-day method, the restricted degree-day
factor (r) for a site is held constant throughout the
The degree-day method is based on eq 16:
snowmelt season.
M = a Td
(16)
Limitations
where M = snowmelt (cm),
Rain infiltration or refreezing within the snow-
a = degree-day factor (cm day1 C 1),
pack is not physically modeled in SRM. Early in
Td = degree-days (C day), the mean daily
the season before the snowpack is ripe, rainfall is
temperature over 24 hr, or the aver-
assumed to add to the snowpack water equiva-
age of the maximum and minimum
lent. Precipitation is added to snowmelt when the
temperature over 24 hr.
snowpack is ripe. The user must specify when the
The degree-day coefficient (a) for a site varies
snowpack becomes ripe based on judgment.
greatly over time as it implicitly represents all
PRMS
terms of the energy budget that account for the
The Precipitation Runoff Modeling System
mass balance of the snowpack. The degree-day
(PRMS) (Leavesley et al. 1983) was developed by
coefficient (a) can be evaluated over time by com-
the U.S. Geological Survey and is an application
paring degree-day values with the daily decrease
of a conceptual two-layer snowpack model devel-
in snow water equivalent. This can be done along
oped by Obled and Rosse (1977). Obled and Rosse
snow courses, or when lysimeter data are avail-
used Anderson's model (Anderson 1968) as a
able. Where such data are unavailable, a can be
starting point for their model development. Data
estimated as a function of snow density (Martinec
from open and forested lysimeter sites (located at
et al. 1994, Martinec 1960).
1350-m elevation, 15 km from Grenoble in the
north French Alps) were used to calibrate and test
Restricted degree-day
the model, and a second lysimeter site (in Davos,
radiation balance approach
Switzerland) was used to verify that the model
The restricted degree-day radiation balance
worked at another site.
approach is as follows:
The snowpack is modeled as a two-layered sys-
M = r Td + mQ R
(17)
tem with a surface layer of 3- to 5-cm thickness.
The snowpack mass balance is computed once a
where M = snowmelt (cm day1),
day and energy balance each 12 hours, represent-
r = constant restricted degree-day factor
ing night and day.
(cm day1 C 1),
When the surface layer temperature (TS) is below
mQ = physical constant converting radia-
freezing (< 0 C), non-melt conditions prevail, and
tion to snow water equivalent [0.026
heat transfer between the surface and snowpack
cm day1 (W m2)1]
occurs by conduction. When the temperature of the
R = net radiation in W m2.
surface snow is at freezing (TS = 0C), an energy
balance (I) at the air/snow interface is computed
The term including the restricted degree-day fac-
for each 12-hr period. If the energy balance is nega-
tor (r) represents melt attributable to turbulent
tive (I<0), there is no melt and the heat transfer
energy exchange, while the second term converts
occurs as conduction between the surface and bot-
net surface radiation (R) to depth of melt in snow
tom layer of snow. If the energy balance is positive
water equivalent. Low r values occur when low
(I>0), the available energy is used to melt snow in
winds reduce sensible heat transfer, and when
the surface layer and conduction is ignored.
low relative humidity increases latent heat loss
Conduction between the snow layers is com-
due to evaporation (Kustas et al. 1994). Martinec
puted by
(1989) showed r values that have much smaller
variation than the original degree-day factor,
KE ∆t
(TS - TP )
ranging between 0.20 and 0.25 cm C 1 through-
ICOND = 2ρsci
(18)
ρsci π
out the ablation period. Brubaker et al. (1996) pro-
vided a method to estimate r from representative
where ρs = snowpack density (g cm3),
meteorological characteristics of the basin that
ci = specific heat of ice (cal g1 C1),
requires wind speed, relative humidity, and air
temperature, and is based on a simplified energy
snow (cal cm1 s1 C1),
balance equation for snowmelt. In contrast to the
7
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