Model Implementation (1)

If precipitations inputs to the snowpack during the ablation season are small it is possible to calculate snow water equivalent (SWE) as:

Where Mj is the melt flux at time step j, SWEn is the SWE of each pixel at time step n, and SWE0 is the initial SWE or SWE at the time step corresponding to the field campaigns. By knowing any two of the three terms in the above expression the mass balance can be closed.

Research developed by Molotch and Bales raises the following mass balance for the initial snow water equivalent (SWE0)

 

Where SCA represents fractional Snow Covered Area (0-1 values) and Mvj corresponds to the daily potential maximum melt flux, which are calculated based on characteristics snow parameters (Brubaker et al, 1996).

  

 

Where:

: incoming solar radiation

: snow surface albedo (0-1 values)

: incoming thermal radiation

: outgoing thermal radiation

: energy to water depth conversion

: average daily air temperature above 0°C

: restricted degree day coefficient (0.09 cm/°C) [Brubaker et al., 1996].

Hereafter we refer to the product of Tdj and ar as turbulent transfer although it is actually a parameterization rather than an explicit calculation.

A potential melt flux (Mv) corresponds to the amount of water stored within the snowpack which potentially is available to be melted. Summation of this fluxes does not necessarily represent snowmelt runoff, since in its determination we are not including importants effects such as storage, sublimation, evaporation, etc.

This simulation is based on a reconstruction. We say reconstruction because we obtain snow water equivalent once the snow has already melted, i.e., this modeling corresponds to a post-factum estimation.

Figure: Snow accumulation/Snow melt periods representation

The snow has its own natural cycle of accumulation and melting. The accumulation period is determined by the first and last snowfall of the season, and certainly the period of melting corresponds to the inverse period. Broadly speaking in central Chile melting period starts in September and ends in February next year. The importance of a correct determination of the melting period is that the model does not consider the accumulation stage, and then any snowfall that occurs during the melting period is not being quantified in the mass balance. 

(1) Molotch, N.P., and R.C. Bales (2006), Comparison of ground-based and airbone snow surface albedo parameterizations in an alpine watershed: Impact on snowpack mass balance, Water Resour. Res., 42, W05410, doi:10.1029/2005WE004522.