Modeling and estimation of snow depth spatial correlation structure from observations over North America

Estimation of spatial correlations should be an integral part of objective analysis of geophysical variables. However, a statistical assessment of spatial correlations has been absent from studies of objective analysis of snow depth since its debut over 2 decades ago. We show a method for computing regional spatial correlations of observed snow depth and the daily snow depth increment and fitting them to correlation functions to estimate the correlation scale parameters. Both horizontal and vertical distance correlations are computed from station observations over a well sampled part of North America. The vertical and horizontal distance correlations are fitted to exponential functions using the least square method to estimate the correlation scale parameters including the amplitude, which represents short distance correlation. Our assessment suggests a large horizontal e-folding correlation scale for both the observed snow depth and the daily increment, with implications for improving predictions in poorly monitored areas with relatively flat topography. Over mountainous terrain, vertical e-folding correlation scale for observed snow depth is much smaller than that for the daily snow depth increment and for the snow depth increment used in operational snow analyses. That means that optimal interpolation-based analysis of the increments may be more accurate than the interpolation of snow depth data.