Multidimensional modeling of cumulative rainfall: Parameter estimation and model adequacy through a continuum of scales

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Abstract
This paper presents the multidimensional representation of the cumulative rainfall process and derives a closed‐form expression for the mean and space‐time covariance functions. A parameter estimation procedure is developed. Sensitivity analysis provides useful information for devising the parameter estimation strategy. The cumulative rainfall model is applied to 8 years of digitized rain gage data from the Walnut Gulch Experimental Watershed. The most useful feature of the model is its self‐consistency, implying that even after using information from a given limited set of data it still leads to realistic parameters which reproduce historical statistics at several levels of time and space scales.

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