Reduction of soil water spatial sampling density using scaled semivariograms and simulated annealing

Abstract

Spatial sampling density influences the reliability and feasibility of environmental studies. Optimizing spatial sampling schemes is important, particularly when multiple observations must be repeated over extended periods. The goal of this study was to develop a sampling density reduction method for a network of 57 soil water content (SWC) measurement locations in an 8-ha microwatershed, given observations taken at five different dates. We sought a subset of 10 points that would best predict (via spatial interpolation) the SWC at the remaining locations. Three observation dates (calibration set) were used to develop the method, and the remaining two (validation set) were used to test it. Calibration date semivariograms were coalesced into one scaled semivariogram, used with ordinary kriging to predict SWC outside the chosen subset. We defined four different scenarios by combining two simulated annealing algorithms, Sacks and Schiller (S&S) and Spatial Simulated Annealing (SSA), and two fitness functions, one based on scaled kriging variance (SKV), and the other based on actual mean squared prediction error (scaled mean squared error, SMSE). We searched for an optimal subset in each calibration scenario; each was then used to predict SWC throughout the microwatershed on the validation dates. The results were compared with those of regular grids and randomly generated patterns. Temporal stability was tested by analyzing deviations between individual and field average observations and using Spearman's rank correlation. The S&S and SSA algorithms performed similarly well, although SSA converged better. The SKV-based scenarios had lower SKV in the calibration and validation sets than the SMSE-based scenarios, the regular grids, and the random patterns. However, the SMSE-based scenarios produced an optimal subset having minimal SMSE over both data sets vs. the other methods. This subset produced mostly low relative errors: for January 25, 1993, 50% of the predicted points fell within ±5%, 82% within ±10%, and 6.5% fell outside 15%; for December 23, 1993, 35% were within ±5%, 72% within ±10%, and 23% fell beyond 15%. However, kriging assumptions were violated on December 23. The SMSE-based scenarios predicted validation set SWC better than the SKV scenarios because they included microwatershed locations that did not obey the stationarity assumptions of kriging but were temporally stable and captured the full range of SWC variation. Modifying the proposed method to perform kriging with a physically based trend model will further improve its predictive accuracy.