Predicting Threshold Exceedance by Local Block Means in Soil Pollution Surveys

Soil contamination by heavy metals and organic pollutants around industrial premises is a problem in many countries around the world. Delineating zones where pollutants exceed tolerable levels is a necessity for successfully mitigating related health risks. Predictions of pollutants are usually required for blocks because remediation or regulatory decisions are imposed for entire parcels. Parcel areas typically exceed the observation support, but are smaller than the survey domain. Mapping soil pollution therefore involves a local change of support. The goal of this work is to find a simple, robust, and precise method for predicting block means (linear predictions) and threshold exceedance by block means (nonlinear predictions) from data observed at points that show a spatial trend. By simulations, we compared the performance of universal block kriging (UK), Gaussian conditional simulations (CS), constrained (CK), and covariance-matching constrained kriging (CMCK), for linear and nonlinear local change of support prediction problems. We considered Gaussian and positively skewed spatial processes with a nonstationary mean function and various scenarios for the autocorrelated error. The linear predictions were assessed by bias and mean square prediction error and the nonlinear predictions by bias and Peirce skill scores. For Gaussian data and blocks with locally dense sampling, all four methods performed well, both for linear and nonlinear predictions. When sampling was sparse CK and CMCK gave less precise linear predictions, but outperformed UK for nonlinear predictions, irrespective of the data distribution. CK and CMCK were only outperformed by CS in the Gaussian case when threshold exceedance was predicted by the conditional quantiles. However, CS was strongly biased for the skewed data whereas CK and CMCK still provided unbiased and quite precise nonlinear predictions. CMCK did not show any advantages over CK. CK is as simple to compute as UK. We recommend therefore this method to predict block means and nonlinear transforms thereof because it offers a good compromise between robustness, simplicity, and precisio

Robuste geostatistische Methoden zur räumlichen Analyse und Kartierung von Bodeneigenschaften

Die von Künsch et al. (2010) entwickelte robuste geostatistische Methode erlaubt die räumliche Analyse von Zusammenhängen mit der Zielvariablen (Strukturmatrix). Die Schätzung der Regressionskoeffizienten der räumlichen Trendmodellierung erfolgt simultan mit der robusten Schätzung der Kovarianzfunktion. Der Einfluss lokaler „Extremwerte“ kann hierbei wahlweise mehr oder weniger stark mit einer Gewichtungsfunktion eingeschränkt werden. Vor dem Hintergrund heterogener Datensätze für Bodeneigenschaften, welche aus unterschiedlichen Datenquellen stammen, liefert die robuste Schätzmethode zuverlässigere Schätzwerte (und Schätzvarianzen) als die klassische Kriging-Methode

Organic Wheat Farming Improves Grain Zinc Concentration

Zinc (Zn) nutrition is of key relevance in India, as a large fraction of the population suffers from Zn malnutrition and many soils contain little plant available Zn. In this study we compared organic and conventional wheat cropping systems with respect to DTPA (diethylene triamine pentaacetic acid)-extractable Zn as a proxy for plant available Zn, yield, and grain Zn concentration. We analyzed soil and wheat grain samples from 30 organic and 30 conventional farms in Madhya Pradesh (central India), and conducted farmer interviews to elucidate sociological and management variables. Total and DTPA-extractable soil Zn concentrations and grain yield (3400 kg ha-1) did not differ between the two farming systems, but with 32 and 28 mg kg-1 respectively, grain Zn concentrations were higher on organic than conventional farms (t = -2.2, p = 0.03). Furthermore, multiple linear regression analyses revealed that (a) total soil zinc and sulfur concentrations were the best predictors of DTPA-extractable soil Zn, (b) Olsen phosphate taken as a proxy for available soil phosphorus, exchangeable soil potassium, harvest date, training of farmers in nutrient management, and soil silt content were the best predictors of yield, and (c) yield, Olsen phosphate, grain nitrogen, farmyard manure availability, and the type of cropping system were the best predictors of grain Zn concentration. Results suggested that organic wheat contained more Zn despite same yield level due to higher nutrient efficiency. Higher nutrient efficiency was also seen in organic wheat for P, N and S. The study thus suggests that appropriate farm management can lead to competitive yield and improved Zn concentration in wheat grains on organic farms

3D-Digital soil property mapping by geoadditive models

ISSN:1029-7006ISSN:1607-796

Predicting threshold exceedance by local block means in soil pollution surveys

Soil contamination by heavy metals and organic pollutants around industrial premises is a problem in many countries around the world. Delineating zones where pollutants exceed tolerable levels is a necessity for successfully mitigating related health risks. Predictions of pollutants are usually required for blocks because remediation or regulatory decisions are imposed for entire parcels. Parcel areas typically exceed the observation support, but are smaller than the survey domain. Mapping soil pollution therefore involves a local change of support. The goal of this work is to find a simple, robust, and precise method for predicting block means (linear predictions) and threshold exceedance by block means (nonlinear predictions) from data observed at points that show a spatial trend. By simulations, we compared the performance of universal block kriging (UK), Gaussian conditional simulations (CS), constrained (CK), and covariance-matching constrained kriging (CMCK), for linear and nonlinear local change of support prediction problems. We considered Gaussian and positively skewed spatial processes with a nonstationary mean function and various scenarios for the autocorrelated error. The linear predictions were assessed by bias and mean square prediction error and the nonlinear predictions by bias and Peirce skill scores. For Gaussian data and blocks with locally dense sampling, all four methods performed well, both for linear and nonlinear predictions. When sampling was sparse CK and CMCK gave less precise linear predictions, but outperformed UK for nonlinear predictions, irrespective of the data distribution. CK and CMCK were only outperformed by CS in the Gaussian case when threshold exceedance was predicted by the conditional quantiles. However, CS was strongly biased for the skewed data whereas CK and CMCK still provided unbiased and quite precise nonlinear predictions. CMCK did not show any advantages over CK. CK is as simple to compute as UK. We recommend therefore this method to predict block means and nonlinear transforms thereof because it offers a good compromise between robustness, simplicity, and precision

constrainedKriging : an R-package for customary, constrained and covariance-matching constrained point or block kriging

The article describes the R-package constrainedKriging, a tool for spatial prediction problems that involve change of support. The package provides software for spatial interpolation by constrained (CK), covariance-matching constrained (CMCK), and customary universal (UK) kriging. CK and CMCK yield approximately unbiased predictions of nonlinear functionals of target quantities under change of support and are therefore an attractive alternative to conditional Gaussian simulations. The constrainedKriging package computes CK, CMCK, and UK predictions for points or blocks of arbitrary shape from data observed at points in a two-dimensional survey domain. Predictions are computed for a random process model that involves a nonstationary mean function (modeled by a linear regression) and a weakly stationary, isotropic covariance function (or variogram). CK, CMCK, and UK require the point–block and block-block averages of the covariance function if the prediction targets are blocks. The constrainedKriging package uses numerically efficient approximations to compute these averages. The article contains, apart from a brief summary of CK and CMCK, a detailed description of the algorithm used to compute the point-block and block-block covariances, and it describes the functionality of the software in detail. The practical use of the package is illustrated by a comparison of universal and constrained lognormal block kriging for the Meuse Bank heavy metal data set

Life beyond MSE and R2 — improving validation of predictive models with observations

ISSN:1029-7006ISSN:1607-796