Charlie H Luce (1)
David G Tarboton (2)
(1) USDA Forest Service, Rocky Mountain Research Station, 316 E Myrtle St., Boise, ID 83702, USA
(2) Utah State University, Utah Water Research Laboratory, 8200 Old Main Hill, Logan, UT 84322-8200, USA

Abstract of Presentation at European Geophysical Society XXVI General Assembly, Nice, France, March 25-30, 2001.  [Powerpoint]

The parameterization of subgrid scale variability in snow accumulation and melt models is analyzed from a physical perspective considering the cause for this variability and covariance between processes that result in snowpack variability. In snow accumulation and melt modeling it is sometimes desirable to use model elements that are larger than the scale of natural variability. This is necessary in cases where the purpose is to represent aggregate inputs or match to large scale observations. A further motivation to increase the support scale of snowmelt models is to take up the opportunities for simplification inherent in using a statistical description of the system as opposed to spatially explicit descriptions of the process throughout the unit of interest. For models at scales where spatial variability in snow water equivalence can be substantial, some parameterization of the variability of the snowpack must be included. The covariance between snow water equivalence and the accumulation rate or melt rate at each point is the source of temporal changes in spatial variance of snow water equivalence. Areal depletion curves relating snow covered area to basin average snow water equivalence have been shown to be an effective parameterization of subgrid variability caused by differential accumulation. We present further theory to improve estimation of depletion curves through examination of the relationship between snow covered area, average snow water equivalence in the snow covered area, and average snow water equivalence in the model element. Information on radiation can be added to depletion curves, thus accounting for information in the joint probability density function of drifting and exposure to direct beam solar radiation. We introduce a "hiding function" approach that further corrects for the fact that snowpack evolution does not depend on element average energy inputs, but on energy inputs to that portion of the model element that is covered by snow. If drifting occurs on north facing slopes, the difference between fractional area coverage and fractional solar exposure can be substantial. The relative role of sources of variability as the support scale increases is discussed.