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Simple and ordinary kriging assume a constant mean and variance of the soil variable of interest. This assumption is often implausible because the mean and/or variance are linked to terrain attributes, parent material or other soil forming factors. In kriging with external drift (KED) non-stationarity in the mean is accounted for by modelling it as a linear combination of covariates. In this study, we applied an extension of KED that also accounts for non-stationary variance. Similar to the mean, the variance is modelled as a linear combination of covariates. The set of covariates for the mean may differ from the set for the variance. The best combinations of covariates for the mean and variance are selected using Akaike's information criterion. Model parameters of the selected model are then estimated by differential evolution using the Restricted Maximum Likelihood (REML) in the objective function. The methodology was tested in a small area of the Hunter Valley, NSW Australia, where samples from a fine grid with gamma K measurements were treated as measurements of the variable of interest. Terrain attributes were used as covariates. Both a non-stationary variance and a stationary variance model were calibrated. The mean squared prediction errors of the two models were somewhat comparable. However, the uncertainty about the predictions was much better quantified by the non-stationary variance model, as indicated by the mean and median of the standardized squared prediction error and by accuracy plots. We conclude that the non-stationary variance model is more flexible and better suited for uncertainty quantification of a mapped soil property. However, parameter estimation of the non-stationary variance model requires more attention due to possible singularity of the covariance matrix. [ABSTRACT FROM AUTHOR]

The accuracy of spatial predictions of rainfall by merging rain-gauge and radar data is partly determined by the sampling design of the rain-gauge network. Optimising the locations of the rain-gauges may increase the accuracy of the predictions. Existing spatial sampling design optimisation methods are based on minimisation of the spatially averaged prediction error variance under the assumption of intrinsic stationarity. Over the past years, substantial progress has been made to deal with non-stationary spatial processes in kriging. Various well-documented geostatistical models relax the assumption of stationarity in the mean, while recent studies show the importance of considering non-stationarity in the variance for environmental processes occurring in complex landscapes. We optimised the sampling locations of rain-gauges using an extension of the Kriging with External Drift (KED) model for prediction of rainfall fields. The model incorporates both non-stationarity in the mean and in the variance, which are modelled as functions of external covariates such as radar imagery, distance to radar station and radar beam blockage. Spatial predictions are made repeatedly over time, each time recalibrating the model. The space-time averaged KED variance was minimised by Spatial Simulated Annealing (SSA). The methodology was tested using a case study predicting daily rainfall in the north of England for a one-year period. Results show that (i) the proposed non-stationary variance model outperforms the stationary variance model, and (ii) a small but significant decrease of the rainfall prediction error variance is obtained with the optimised rain-gauge network. In particular, it pays off to place rain-gauges at locations where the radar imagery is inaccurate, while keeping the distribution over the study area sufficiently uniform. [ABSTRACT FROM AUTHOR]

Many crop growth models require daily meteorological data. Consequently, model simulations can be obtained only at a limited number of locations, i.e. at weather stations with long-term records of daily data. To estimate the potential crop production at country level, we present in this study a geostatistical approach for spatial interpolation and aggregation of crop growth model outputs. As case study, we interpolated, simulated and aggregated crop growth model outputs of sorghum and millet in West-Africa. We used crop growth model outputs to calibrate a linear regression model using environmental covariates as predictors. The spatial regression residuals were investigated for spatial correlation. The linear regression model and the spatial correlation of residuals together were used to predict theoretical crop yield at all locations using kriging with external drift. A spatial standard deviation comes along with this prediction, indicating the uncertainty of the prediction. In combination with land use data and country borders, we summed the crop yield predictions to determine an area total. With spatial stochastic simulation, we estimated the uncertainty of that total production potential as well as the spatial cumulative distribution function. We compared our results with the prevailing agro-ecological Climate Zones approach used for spatial aggregation. Linear regression could explain up to 70% of the spatial variation of the yield. In three out of four cases the regression residuals showed spatial correlation. The potential crop production per country according to the Climate Zones approach was in all countries and cases except one within the 95% prediction interval as obtained after yield aggregation. We concluded that the geostatistical approach can estimate a country’s crop production, including a quantification of uncertainty. In addition, we stress the importance of the use of geostatistics to create tools for crop modelling scientists to explore relationships between yields and spatial environmental variables and to assist policy makers with tangible results on yield gaps at multiple levels of spatial aggregation. [ABSTRACT FROM AUTHOR]

This paper presents a pedometric approach to updating the Dutch 1:50,000 national soil map for the peatlands, and illustrates this approach for a 187,525 ha area in the northern peatlands. This is the first time that digital soil mapping replaces conventional soil mapping in a nationwide, government-funded soil survey program in the Netherlands. Soil classes were updated indirectly through mapping two quantitative diagnostic soil properties: the thickness and starting depth of the peat layer. From these, five major soil groups could be constructed. Because the point data were zero-inflated, a two-step simulation approach was implemented. First, peat presence/absence indicators were simulated from probabilities of peat occurrence that were predicted with a generalized linear model. Second, conditional peat thickness values were simulated from kriging with external drift predictions. The indicator and peat thickness simulations were combined to obtain simulations of the unconditional peat thickness. A similar approach was followed for the starting depth. From the simulated soil properties, probability distributions of soil groups were derived. These groups were refined with information on (static) soil properties derived from the 1:50,000 map to obtain soil classes according to the 1:50,000 legend. The updated raster map was then incorporated in the 1:50,000 polygon map. The prediction models were calibrated with legacy point data, that were updated for peat thickness before being used, in addition to a set of newly acquired point data. The uncertainty associated to the updated peat thickness values in the legacy dataset was quantified and accounted for by the prediction models. The peat thickness map and a map with three soil orders were validated with independent probability sample data. The overall purity of the soil order map was 66% for both subareas. For subarea 1 this was a 12% purity improvement compared to the current 1:50,000 map, for subarea 2 this was 3%. For subarea 1, the mean absolute error of the predicted peat thickness was 23.5 cm, and the R 2 is 0.50. For subarea 2 these accuracy measures were 30.9 cm and 0.65. We conclude that nationwide updating the 1:50,000 map with pedometric techniques is feasible. In order to increase the value and usability of the legacy point data as well as the large set of newly acquired field observations and the updated 1:50,000 map, we recommend installation of a soil monitoring network in the Dutch peatlands. [ABSTRACT FROM AUTHOR]

Abstract: The quality of maps obtained by interpolation of observations of a target environmental variable at a restricted number of locations, is partly determined by the spatial pattern of the sample locations. A method is presented for optimization of the sample pattern when the environmental variable is interpolated with the help of exhaustively known covariates, which are assumed to be linearly related to the target variable. In this method the spatially averaged universal kriging variance (MUKV), which incorporates trend estimation error as well as spatial interpolation error, is minimized. The optimal pattern is obtained using simulated annealing. The method requires that the covariance function or variogram of the regression-residuals is known. The method is tested in a case study on the Mean Highest Water table in a coversand area in The Netherlands. The patterns of 25, 50 and 100 sample locations are optimized and compared with the patterns optimized with the ordinary kriging (OK) model (assuming no trend) and with the multiple linear regression (MLR) model (assuming no spatial autocorrelation of residuals). The results show that the UK-patterns are a good compromise between spreading in geographic space and feature space. The MUKV for the UK-patterns is 19% (n =25), 7% (n =50) and 3% (n =100) smaller than for the OK-patterns. Compared with the MLR-patterns the reduction is 2%, 4% and 4%, respectively. [Copyright &y& Elsevier]

Soils are among the most biodiverse and densely inhabited environments on our planet. However, there is little understanding of spatial distribution patterns of belowground biota, and this hampers progress in understanding species interactions in belowground communities. We investigated the spatial distribution of nematodes, which are highly abundant and diverse metazoans in most soil ecosystems. To gain insight into nematode patchiness, we mapped distribution patterns in twelve apparently homogeneous agricultural fields (100 m × 100 m each) with equal representation of three soil textures (marine clay, river clay and sandy soil). Quantitative PCRs were used to measure the abundances of 48 distinct nematode taxa in ≈1200 plots. Multivariate analysis showed that within this selection of sites, soil texture more strongly affected soil nematode communities than land management. Geostatistical analysis of nematode distributions revealed both taxon-specific and field-specific patchiness. The average geostatistical range (indicating patch diameter) of 48 nematode taxa in these fields was 36 m, and related to soil organic matter. Soil organic matter content affected the spatial variance (indicating within-field variation of densities) in a life-strategy dependent manner. The r-strategists (fast-growing bacterivores and fungivores) showed a positive correlation between organic matter content and spatial variance, whereas most K-strategists (slow-growing omnivores and carnivores) showed a negative correlation. Hence, the combination of two parameters, soil organic matter content and a general life-strategy characterisation, can be used to explain the spatial distribution of nematodes at field scale. • Nematode distribution maps show taxon- and field-specific levels of patchiness • Distributions of nematodes with similar food preferences show little or no overlap • Soil organic matter affects nematode patchiness in a life-strategy dependent manner • Stochasticity is a dominant driving factor for mesoscale distribution of nematodes • Distribution maps enable the design of soil sampling schemes with known accuracies [ABSTRACT FROM AUTHOR]