Sampling the soil in long-term forest plots: The implications of spatial variation

Long-term monitoring of forest soils as part of a pan-European network to detect environmental change depends on an accurate determination of the mean of the soil properties at each monitoring event. Forest soil is known to be very variable spatially, however. A study was undertaken to explore and quantify this variability at three forest monitoring plots in Britain. Detailed soil sampling was carried out, and the data from the chemical analyses were analysed by classical statistics and geostatistics. An analysis of variance showed that there were no consistent effects from the sample sites in relation to the position of the trees. The variogram analysis showed that there was spatial dependence at each site for several variables and some varied in an apparently periodic way. An optimal sampling analysis based on the multivariate variogram for each site suggested that a bulked sample from 36 cores would reduce error to an acceptable level. Future sampling should be designed so that it neither targets nor avoids trees and disturbed ground. This can be achieved best by using a stratified random sampling design.

Relevance of sampling schemes in light of Ruelle's linear response theory

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We �rst show that by using a general functional decomposition for space-time dependent forcings, we can de�ne elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the de�nition of SRB measure, we then study the consequence of taking di�erent sampling schemes for analysing the response of the system. We show that only a speci�c choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula �rst presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be �ne-tuned to make the de�nition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.