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<br />1468
<br />
<br />JOURNAL OF APPLIED METEOROLOGY
<br />
<br />VOLUME 20
<br />
<br />On the Sampling Variance of Raingage Networks
<br />
<br />BERNARD A. SILVERMAN AND LINDA KOSHIO ROGERS
<br />
<br />Division of Atmospheric Resources Research, Bureau of Reclamation, Denver, CO 80225
<br />
<br />DAVID DAHL
<br />
<br />Los Alamos Scientific Laboratory, Los Alamos, NM 87545
<br />
<br />(Manuscript received 15 April 1980, in final form 24 June 1981)
<br />
<br />ABSTRACT
<br />
<br />A study has been conducted which examines the sampling variance of raingage networks, the most
<br />commonly used precipitation estimating system, The study is b(lsed on the use of computer-simulated
<br />isohyetal patterns of known characteristics (absolute ground truth) which were calibrated against measured
<br />isohyetal patterns from convective storms that are reported in the literature, The sampling variance of
<br />raingage networks is quantitatively related to both the raingage density and the characteristics of the
<br />isohyetal pattern, It was found that the sampling variance or coefficient of variation is inversely proportional
<br />to the number of gages per surface raincell and directly proportional to the gradient of rainfall.
<br />These results have been used to assess the relative contribution of the sampling variance of raingage
<br />networks and the natural variability of rainfall to the estimated experimental unit sample size requirements
<br />for evaluating precipitation augmentation experiments, The convective storm rainfall data for the Miles
<br />City, Montana, area, gathered as part of the Bureau of Reclamation's HIPLEX (High Plains Cooperative
<br />Program), formed the basis of this analysis, For these rainfall characteristics, it was found that sampling
<br />variance is responsible for no more than 10% of the total sample size requirement with a gage density of
<br />at least an average of four gages per storm (gage density on the order of 80 km2 per gage), The contribution
<br />of network sampling variance to the sample size requirement becomes significant for gage densities less
<br />than one gage per storm or for significantly lower natural rainfall variabilities,
<br />
<br />1. Introduction
<br />
<br />The statistical characteristics of rainfall are im-
<br />portant considerations in many climatological, agri-
<br />cultural, hydrological and weather modification ap-
<br />plications. Of the various statistical properties, the
<br />variability of rainfall is, perhaps, the most important,
<br />especially in the evaluation of precipitation augmen-
<br />tation experiments in which rainfall is the primary
<br />response variable. Estimates of the natural variabil-
<br />ity of rainfall, however, are compounded by variance
<br />components that are introduced by the method of
<br />measurement, namely those due to sampling and
<br />measurement errors. It is the purpose of this paper
<br />to examine the sampling variance of raingage net-
<br />works, the most commonly used precipitation mea-
<br />surement system, and quantitatively relate this vari-
<br />ance to both the density of raingages and the
<br />characteristics of the isohyetal pattern.
<br />The variance due to sampling results from the
<br />necessity of estimating areal rainfall values from
<br />point measurements of a storm footprint that con-
<br />tains spatial gradients. This is especially true for con-
<br />vective storms which are of primary interest in this
<br />study. The estimation procedure is usually based on
<br />
<br />the assumption that a point measurement by a pre-
<br />cipitation gage is representative of the area that sur-
<br />rounds it. Thus, depending on just how the storm
<br />passes over the gage network, the precipitation is
<br />usually either under or overestimated.
<br />A number of investigators (e.g., Light, 19471; Lin-
<br />sley and Kohler, 1951; McGuinness, 1963; Huff,
<br />1970; Woodley et al., 1975; Eddy, 1976) have tried
<br />to obtain estimates of the average sampling error in
<br />determining areal mean rainfall from precipitation
<br />gage measurements. The usual procedure is to rep-
<br />resent the sampling error as the difference between
<br />the best estimate of the true mean obtained from the
<br />maximum density of gages and sample means cal-
<br />culated from successively reduced gage densities.
<br />Sampling errors calculated in this way are at best
<br />relative errors since the true mean is not known ip
<br />an absolute sense. The approach used herein differs
<br />from those of previous studies in that the isohyetal
<br />patterns of interest are not initially derived from
<br />
<br />I Light, p" 1947: Hydrologic aspects of thunderstorm rainfall.
<br />Hydrometeor, Rep, No.5, U,S, Weather Bureau-Corps of En-
<br />gineers, 260-268,
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