Identification of large‐scale spatial trends in hydrologic data

Abstract

It is often useful to distinguish different scales of variability in hydrologic properties such as hydraulic conductivity. In the simplest two‐scale case, large‐scale variations can be viewed as a trend, while small‐scale fluctuations about this trend can be viewed as a random residual. This paper describes a method for estimating spatial trends from scattered field measurements. The basic concept is to treat both the trend and the residual as stationary random functions. These functions are distinguished by their spatial spectral (or covariance) properties, which may be estimated from available data or simply hypothesized. We present two versions of a general algorithm for estimating spatial trends: (1) a discrete version which is useful in practical applications where data are limited and irregularly spaced and (2) a continuous version which can be used to study the effects of using incorrect spectral parameters. Applications of the discrete algorithm to both synthetically generated data and field measurements yield satisfactory trend estimates. An analysis based on the continuous algorithm shows that the estimation error lower bound for these applications depends on two dimensionless ratios, that is, the scale disparity (ratio of the trend and residual correlation scales) and the signal‐to‐noise ratio (ratio of the trend and residual variances). These ratios may be used to evaluate the feasibility of trend estimation before field samples are actually collected.