Geoscience Reference
In-Depth Information
In its simplest form, the degree-day method predicts a daily melt rate from
M
=
F
max(0
, T
−
T
F
)
(B3.3.1)
where
M
is melt rate as a water equivalent per unit area [LT
−1
],
F
is the degree-day factor
[LT
−1
K
−1
],
T
is mean daily air temperature [K], and
T
F
is a threshold temperature [K] close to
the freezing point of water. Thus, in its simplest form, the degree-day method takes no account
of the temperature of the snowpack; variations in local radiation balance due to slope, aspect,
cloudiness, changing albedo, partial snow cover and vegetation projecting above the snow;
inputs of heat associated with rainfall, changing snow pack area, etc., except in so far as these
can be accounted for by adjusting either
F
or the temperature values. The degree-day method
works best when the snow pack has ripened to the melting temperature, but even then the
diurnal changes in air temperature and day-to-day weather conditions can lead to variations
in melt rates in both time and space. It is not expected, however, that the degree-day method
will be accurate at all points in space, only that it will produce reasonable estimates of melt
and the lifetime of a pack over an area, given some knowledge of the snow water equivalent
at the end of the accumulation period.
Various modifications to the degree-day method have been made to try to extend the basic
concept of a temperature-dependent melt. In the ETH-4 version of the method (Hottelet
et
al.
, 1993), a continuous balance of water equivalent and snowpack temperature is maintained
throughout the winter period. This version of the degree-day method was used by Ambroise
et al.
(1996b) in modelling the small Ringelbach catchment in the Vosges, France.
In the ETH-4 model, when precipitation occurs, it is added to the pack water equivalent as
liquid water, snow or a mixture of the two depending on the air temperature at the time relative
to two threshold temperatures. Above
T
rain
, all precipitation is assumed to be in liquid form;
below
T
snow
, all precipitation is assumed to occur as snow. Between the two, the proportion
of snowfall is given as the ratio (
T
j
−
T
snow
)
/
(
T
rain
−
T
snow
) where
T
j
is the air temperature at
time step
j
. Any precipitation in the form of snow is added directly to the pack.
At each time step, the temperature of the pack,
T
j
, is updated according to the equation
T
j
=
C
T
T
j
−
C
T
)
T
j
−1
+
(1
(B3.3.2)
Rainfall is added to the pack at a rate depending on the pack surface temperature. If
T
j
is less
than a threshold temperature
T
c
(which need not be the same as
T
F
), all rainfall is assumed to be
frozen into the pack. Otherwise, if
T
j
>T
c
then the rainfall is added to the pack as liquid water
content. Part of this liquid water content may freeze at a rate proportional to the temperature
difference between the pack temperature and the threshold temperature. If there is some liquid
water content, the increase in snowpack water equivalent is calculated as
S
j
=
S
j
−1
+
C
T
(
T
j
−
T
c
)
(B3.3.3)
The model is completed by conditions to ensure that there is not more melt or freezing than
available water equivalent.
This simple snowmelt model already contains a number of parameters that must be cali-
brated. These are the coefficients
F
,
C
T
, and
C
T
and the threshold temperatures
T
F
and
T
c
.
These might vary with location; it has long been recognised that the melt coefficient
F
is not
generally constant but increases during the melt season (Figure B3.3.2). The World Meteo-
rological Organisation (WMO, 1964) recommends values of the degree-day coefficient that
increase through the melt season. Hottelet
et al.
(1993) represent this change as a gradually in-
creasing sine curve defined by maximum and minimum values of
F
, resulting in one additional
parameter to be estimated.
