Estimation of regionalized phenomena by geostatistical methods: lake acidity on the Canadian Shield

This paper describes a geostatistical technique based on conditional simula tions to assess confidence intervals of local estimates of lake pH values o n the Canadian Shield. This geostatistical approach has been developed to d eal with the estimation of phenomena with a spatial autocorrelation structu re among observations. It uses the autocorrelation structure to derive mini mum-variance unbiased estimates for points that have not been measured, or to estimate average values for new surfaces. A survey for lake water chemis try has been conducted by the Ministere de l'Environnement dir Quebec betwe en 1986 and 1990, to assess surface water quality and delineate the areas a ffected by acid precipitation on the southern Canadian Shield in Quebec. Th e spatial structure of lake pH was modeled using two nested spherical vario gram models, with ranges of 20 km and 250 km, accounting respectively for 2 0% and 55% of the spatial variation, plus a random component accounting for 25%. The pH data have been used to construct a number of geostatistical si mulations that produce plausible realizations of a given random function mo del, while 'honoring' the experimental values (i.e., the real data points a re among the simulated data), and that correspond to the same underlying va riogram model. Post-processing of a large number of these simulations, that are equally likely to occur, enables the estimation of mean pH values, the proportion of affected lakes (lakes with PR less than or equal to 5.5), an d the potential error of these parameters within small regions (100 km X 10 0 km). The method provides a procedure to establish whether acid rain contr ol programs will succeed in reducing acidity in surface waters, allowing on e to consider small areas with particular physiographic features rather tha n large drainage basins with several sources of heterogeneity. This judgmen t on the reduction of surface water acidity will be possible only if the am ount of uncertainty in the estimation of mean pH is properly quantified.