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.

(16)

where *M *= snowmelt (cm),

Rain infiltration or refreezing within the snow-

pack is not physically modeled in SRM. Early in

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

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

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

the model, and a second lysimeter site (in Davos,

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-

(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-

ing night and day.

(cm day1 C 1),

When the surface layer temperature (*T*S) is below

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

surface snow is at freezing (*T*S = 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,

(TS - *T*P )

ranging between 0.20 and 0.25 cm C 1 through-

(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

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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