Preserving first and second moments of the slope area relationship during the interpolation of digital elevation models

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Accurate representation of terrain with appropriate reproduction of topographic characteristics is important for increasingly sophisticated physically-based models of natural processes. Recently investigators have successfully enforced slope area relationships to interpolate more realistic topographies from the sparse data. The limitation of those procedures is that, for the most part, they preserve only the first moment (the mean), when scaling slope with contributing area. Here we present a simple approach to also enforce the second moment, the variance, during landscape evolution simulations or physically-based spatial interpolations.