A sampling strategy for estimating plot average annual fluxes of chemical elements from forest soils

A sampling strategy for estimating spatially averaged annual element leaching fluxes from forest soils is presented and tested in three Dutch forest monitoring plots. In this method sampling locations and times (days) are selected by probability sampling. Sampling locations were selected by stratified random sampling with five blocks of equal surface area as strata. At each selected day six composite soil solution samples were collected, consisting of five aliquots of equal volume, one per stratum. For most sampling days at some locations no soil solution was collected (non-response), and as a result the average of the six composite sample concentrations (the naïve estimator) is a biased estimator of the plot mean concentration. The plot mean concentration at these days was estimated by ordinary least squares. This estimation method eliminates the bias of the naïve estimator. This estimated concentration was multiplied by the modeled water flux to obtain an estimate of the daily element leaching flux. Sampling times (days) were selected by systematic πps-sampling (sampling with probabilities proportional to size), with precipitation surplus, averaged over the past 30 years, as a measure of size. The spatially averaged annual leaching flux was estimated by the ratio-estimator, accounting for the selection probabilities of the days, using the modeled daily water flux as an auxiliary variable.

Research Highlights
► Probability sampling of locations and days enables estimation of uncertainty in annual flux.
► Use compact geographical strata of equal area to select sampling locations.
► These spatial strata can be constructed by k-means algorithm using R-package spcosa.
► Select days by systematic πps sampling with precipitation surplus as size measure.
► OLS estimation of plot mean when composites are incomplete helps eliminating non-response bias.