Ridge Regression-Time Extrapolation Applied to Hawaiian Rainfall Normals

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Abstract
In this paper ridge regression is introduced as a technique for extrapolating long-period normal rainfalls from short records. The data used are the annual totals for selected stations on the island of Oahu, Hawaii. It has been shown that when the predictor variables are not mutually independent, as is often the case in meteorology, it is unlikely that the estimates of the coefficients obtained through unbiased multiple linear regression will be close to the correct values. In such cases a method of biased estimation, such as the so-called ridge regression, will yield more accurate estimates of the true regression coefficients. Ridge regression is shown to be superior to ordinary least-squares regression and double-mass analysis, and is a robust estimator of central tendency for extrapolating Hawaiian rainfall normals. Mention is also made on the choice of normal statistic and on the selection of the base period of record. Since there is such a diversity of both topographic and climatological regions on Oahu Island it is expected that this method should be applicable in many other locales. Furthermore, the method is not limited to rainfall data; statistical relationships among other meteorological variables, such as model output statistics, may be similarly determined using this technique.

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