Objective analyses and mapping techniques for rainfall fields: An objective comparison

Abstract

Many methods have been proposed and applied individually to rainfall fields in order to estimate point or average values at ungauged sites. This paper reviews some of the usual as well as some of the more recent techniques. They are classified according to their fundamental principles, optimality criteria, and practical aspects. Some theoretical developments, mostly for the statistically based techniques, are offered, and the practical aspects are mainly directed to the particular case of rainfall fields. A case study is presented for a region with particularly high rainfall variability, providing a good sample of events for testing the sensitivity of the estimation to the different methods used. The identification of statistical structure functions, required by certain methods using regionalized variable concepts, is discussed in detail for the case considered. Method evaluation is based on a classical validation technique that divides the available stations into two separate networks, i.e., a base network is used to perform estimations at the stations of a test network for a set of independent storm events. Careful attention is paid to result interpretation and visualisation. Finally, conclusions are drawn as to which method should be implemented, taking into account cost-efficiency considerations.Many techniques have been proposed for mapping rainfall patterns and for evaluating the average rainfall over a watershed. Some of these are reviewed by Hall and Barclay [1975], although others have been proposed since then [cf. Thorpe et al., 1979;Bethlamy, 1976;Pande et al., 1978].Attempts to evaluate and compare the different methods are much more rare. This is understandable for techniques that estimate spatial averages because of the lack of experimentally measured areal values. However, most techniques may also be used for point values, where ground verification is possible. Point values are also of interest for contouring and for filling in gaps in records of existing stations. This paper proposes an objective comparison of methods estimating point values. The evaluation procedure itself relies on a simple validation technique commonly used in statistics. The methods evaluated are those which are or are becoming commonly used in surface hydrology.Although several other classification systems will be used throughout this paper, the various methods may first of all be separated into simple and sophisticated ones. In the first group are the following:1. The nearest neighbor method. The estimated value at any given point is taken as the observed value at the nearest neighboring station. This represents the simplest possible interpolation scheme and is in fact the basic principle of the Thiessen method, as demonstrated in the automated version proposed by Diskin [1970] and widely used in hydrology for average rainfall estimation. The arithmetic mean.This assumes that the rainfall depth is theoretically constant over a given region and can be estimated by the average of the observed values within this region.In the ...

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