Humid, overcast conditions are needed for the
perature. The temperature within the snow cover
above equation to apply; therefore, rain must
is represented by a continuous antecedent tem-
exceed 2.5 mm during a 6-hour period before this
perature index, computed from the air tempera-
equation is put to use. Rain falling on snow is
ture time series,
added to surface melt.
ATI2 = ATI1 + TIPM (Ta - ATI1 )
(8)
Non-rain periods
where ATI1 = temperature indices at the begin-
During non-rain periods, a wide range of me-
ning of a 6-hr period (C),
teorological conditions can occur from sunny to
ATI2 = temperature indices at the end of
overcast, dry to humid, and calm to windy. Since
a 6-hr period (C),
these conditions are not well described by air tem-
Ta = air temperature (C),
perature and precipitation data alone, Anderson's
TIPM = weighting multiplier (0.1 to 1.0) for
recourse was the empirical relationship:
previous 6-hr periods.
M = MF (TaTb)
(6)
G a i n or loss of heat from the snowpack is
assumed proportional to the difference between
where M = snowmelt (mm 6 hr1)
the current air temperature and antecedent tem-
MF = p r o p o r t i o n a l i t y, or melt factor
perature index.
(mmC1 6 hr1),
Heat exchange during non-melt periods is,
Ta = air temperature (C),
then,
Tb = base temperature (C).
∆D = NMF (ATI1 - Ta )
(9)
MF varies seasonally due to the increase in incom-
where ∆D = change in snow cover heat deficit
ing solar radiation and decrease in albedo through
spring. The melt factor is important in determin-
expressed in water equivalent (mm
ing the timing of snowmelt runoff. At the Central
6 hr1),
Sierra Snow Laboratory, the melt factor could be
NMF = proportionality factor, referred to as
the negative melt factor (mmC1 6
represented by a sine function of the form
hr1), which represents the rate of
+ MFMIN
M
heat gain or loss per degree Celsius
MF = FMAX
2
and time period, represented by mil-
limeters of water equivalent.
n2π MFMAX + MFMIN
+ sin
(7)
366
The model assumes a seasonal variation in the
2
negative melt factor NMF represented by
where n = day number beginning with 21 March,
MF
MFMAX = MF on 21 June,
NMF =
MaxNMF
(10)
MFMIN = MF on 21 December (mm C 1 6 hr1).
MFMAX
where MaxNMF is a snow model parameter rep-
This MF sinusoid recommended for the con-
resenting the maximum negative melt factor
tiguous United States was based on a snowmelt
(mmC1 6 hr1). The negative melt factor thus
season at the CSSL (Anderson 1968). A modified
increases through the melt season as the melt fac-
sinusoid was recommended for Alaska, based on
tor increases toward its maximum. The idea
studies of the Chena River basin, near Fairbanks.
behind this is that thermal conductivity increases
Typical values of MFMAX and MFMIN are given for
as a function of snow density, and snow density
coniferous, mixed, deciduous, and open sites
increases as the snowmelt season progresses.
(Anderson 1973).
Snow cover heat storage
Non-melt periods
The model keeps a continuous accounting of
Energy exchange between the snow cover and
the heat deficit (Dm) of the snow cover, defined
air is tracked, during non-melt periods, as propor-
as the amount of heat that must be added to re-
tional to a representation of the temperature gra-
turn the snow from below 0C to an isothermal
dient in the top of the snowpack. The surface
state (0C), and computed as
snow temperature is assumed equal to the air tem-
5
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