Estimation of aquifer scale proportion using equal area grids: assessment of regional scale groundwater quality

The proportion of an aquifer with constituent concentrations above a specified threshold (high concentrations) is taken as a nondimensional measure of regional scale water quality. If computed on the basis of area, it can be referred to as the aquifer scale proportion. A spatially unbiased estimate of aquifer scale proportion and a confidence interval for that estimate are obtained through the use of equal area grids and the binomial distribution. Traditionally, the confidence interval for a binomial proportion is computed using either the standard interval or the exact interval. Research from the statistics literature has shown that the standard interval should not be used and that the exact interval is overly conservative. On the basis of coverage probability and interval width, the Jeffreys interval is preferred. If more than one sample per cell is available, cell declustering is used to estimate the aquifer scale proportion, and Kish's design effect may be useful for estimating an effective number of samples. The binomial distribution is also used to quantify the adequacy of a grid with a given number of cells for identifying a small target, defined as a constituent that is present at high concentrations in a small proportion of the aquifer. Case studies illustrate a consistency between approaches that use one well per grid cell and many wells per cell. The methods presented in this paper provide a quantitative basis for designing a sampling program and for utilizing existing data.