Estimating the Amount of Snowmelt
Based on Viscous Compression Model of Snow
Yuji Kominami1, Yasoichi Endo 2, and Shoji Niwano 2
This study proposes a method to estimate the amount of snowmelt, using hourly data of total snow
depth and precipitation. First, a snow cover is divided into a large number of thin snow layers named
ti-layer (i=1,2,...,n), which was deposited for one hour to time ti. Assuming that a change in thickness
of ti-layer by snow melting from time tn-1 to tn is resulted after deformation of ti-layer by viscous
compression, let h'i (tn) and hi(tn) be respectively the thickness of ti-layer at time tn deformed by
viscous compression and resulted from both compression and melting. Then, thickness D(tn) of
snow deposited or melted on the snow surface for one hour from time tn-1 up to tn is given by
tn -1
∑ h'i (t a ) ,
D(t) = H(t) -
i -1
where H(tn) is total snow depth lying at time tn. Assuming that a relation between compressive
viscosity η and dry density ρ dry of snow is expressed by η = C(ρ dry)n with constants of C and a, we
derived theoretically an equation giving thickness h'i (tn) of ti-layer from weight wj(tn-1) (ji) of each
snow layer lying at time tn-1 on ti-layer and hourly precipitation at time tn, and computed h'i (tn) of
every ti-layer to obtain the index D(tn). In a case of D(tn)0, the value is considered to indicate a
thickness hn(tn) of tn-layer deposited newly on the snow surface, and a weight wn(tn) of tn-layer at
time tn is given by hourly precipitation p(tn) at time tn. In the other case of D(tn) < 0, thickness hi(tn)
and weight wi(tn) of snow layers lying to the depth of D(tn) from the surface come to zero, because
the value shows a thickness of snow melted on the surface. Supposing that hourly precipitation in the
case of D(tn) < 0 is supplied as rain, which is distributed with melt water downward according to
such a simple tank model that water percolates into lower snow layer only in a case that water
content αi(tn) of a snow layer exceed 15% by weight, we computed water content αi(tn) and weight
wi(tn) of each ti-layer. Computing in order from time t1 by such a procedure, we can obtain thickness
hi(tn), weight wi(tn), and water content ai(tn) of each ti-layer at time tn from hourly total snow depth
and precipitation. So depth of snowmelt was estimated by subtracting measured thickness of snow
depth reduction and estimated thickness of snow compaction. The amount of snowmelt was esti-
mated as the estimated dry weight of these snow layers, which was lost by snowmelt. The approxi-
mated results were found to be in good agreement with estimated results by the other methods in
Tohkamachi in 1994/95.
1
Kansai Research Center, Forestry and Forest Products Research Institute, Momoyama-cho, Fushimi-ku,
Kyoto 612 Japan
2 Tohkamachi Experiment Station, Forestry and Forest Products Research Institute 614 Tatsuotsu, Tohkama-
chi City, Niigata, 948 Japan
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