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COMPARISON OF THE METHODS OF ESTIMATING MEAN AREAL RAINFALL
VlJAY P. SlNGH and YUKSEL K. BIRSOY
New Mexico Institute of Mining and Technology Socorro, New Mexico, U.S.A.
A comparison of nine different methods ofestimating mean areal rainfall is made. Five areas from three continents of the world are selected for application of the methods. The methods are utilized to estimate mean areal rainfall for daily, monthly and yearly values. It is shown that all methods generally yield comparable results, and that for most hydrologic problems simpler methods of estimating mean areal rainfall are sufficiently accurateanobservation contradicting the traditional belief.
Determination of the average amount of rain which falls on a watershed during a given storm is a fundamental requirement for many hydrologic studies. Of practical necessity rainfall is measured at a number of sample points, and the amounts recorded a t these points are utilized to form a n estimate of mean areal rainfall for the storm of interest.This estimate will, however, differ from the true mean areal rainfall for three reasons:
I . The sample points may be unrepresentative of the watershed in that no gauge may lie in the section of watershed having extreme rainfall. 2. The record may be constantly higher or lower than the true rainfall a t that sample point. 3. Factors may combine to cause the rainfall amounts recorded at gauges todiffer from their true values in an unsystematic manner.
It is, therefore, not surprising that little is known about the accuracy of the mean areal rainfall estimates; both the ease of making accurate point meas-
Comparison of the Methods of Estimating Mean Areal Rainfall Table I .
Sources of information on methods of estimating mean areal rainfall. Method UM GAAM TP AAM TAM MYER IS0TREN RDS Source of information Whitmore et al. (1961); Rainbird (1967). Whitmore et al. (1961). Thiessen (1911); Whitmore et al. (1961); Bruce & Clark (1966); Rainbird (1967); Hutchinson (1969); Diskin (1969, 1970). Whitmore et al. (1961). Whitmore et al. (1961). Myers (1959); Whitmore et al. (1961). Reed & Kincer (1917); Butler (1957); Whitmore et al. (1961); Bruce & Clark (1966); Rainbird (1967);Diskin & Davis (1970). Dawdy & Langbein (1960); Sutcliffe & Carpenter (1967); Unwin (1969); Chidley & Keys (1970); Shaw & Lynn (1972); Lee et al. (1974). McGuiness & Harold (1965); Solomon et al. (1968); Pentland & Cuthbert (1971); Wei & McGuiness (1973).
urements of rainfall and the simplicity of determining the mean areal rainfall are indeed deceptive. Nevertheless, several techniques ofestimating mean areal rainfall are available. Some of them are simple, but normally adequate for practical purposes, although they tend to be employed without sufficient appreciation of their limitations. Others are relatively new and demand the use of considerable skill, and even judgement in some cases, on the part of the user. The question arises: How do these techniques compare? Is one techniquesuperior to the other? Are these techniques simply different alternatives to estimate mean arean rainfall or have they led to an increased understanding of spatial distributional characteristics of rainfall? These are the questions the present study attempts to answer.
METHODS OF ESTIMATING MEAN AREAL RAINFALL
T h e following methods were considered: 1. 2. 3. 4. 5. Unweighted mean (UM)Grouped area aspect weighted mean (GAAM) Individual area weighted mean, Thiessen polygon (TP) Individual area altitude weighted mean (AAM) Triangular area weighted mean (TAM)
Vijay P. Singh and Yiiksel K. Birsoy
6. Myers method, grouped mean weighted for distance and altitude (MYER)
7. Isohyetal method (ISO) 8. Trend surface analysis (TREN) (a) Linear function (LIN), a simple TREN (b)...