Uncertainties in Estimating Areal Means: With Applications to NADP/NTN Data

Abstract

The National Atmospheric Deposition Program (NADP) and National Trends Network (NTN) have been gathering data to estimate mean deposition of various constituents of precipitation over areas of varying size and time periods of varying length. The mean values are estimated mainly by sampling at various locations and at discrete times. Such estimations introduce uncertainty about the means since the samplers represent only a minute fraction of the total area to be estimated. When two or more such means are compared, some estimation of uncertainties is required to derive the statistical significance. This paper examines two methods capable of estimating such uncertainty - - areal-temporal correlation and kriging approaches. These methods are applied to the NADP/NTN data, and the estimated uncertainties are compared for concentrations of nine constituents, plus conductivity and pH of the rainfall. The estimated root mean square errors (RMSE) of both methods are smaller than the non-weighted standard deviation. The RMSE of the correlation approach is smaller than that of kriging for K, NH4, NO3, pH, and precipitation volume for the 3 U.S. sub-regions. Mixed results occur for other ions.

The work was done while the author was at the Illinois State Water Survey. Now the author is at AT & T Bell Laboratories, Middletown, NJ 07748.