TY - JOUR

T1 - Analyzing spatial data

T2 - an assessment of assumptions, new methods, and uncertainty using soil hydraulic data

AU - Zimmermann, Beate

AU - Zehe, Erwin

AU - Hartmann, Niklas

AU - Elsenbeer, Helmut

PY - 2008

Y1 - 2008

N2 - Environmental scientists today enjoy an ever-increasing array of geostatistical methods to analyze spatial data. Our objective was to evaluate several of these recent developments in terms of their applicability to real-world data sets of the soil field-saturated hydraulic conductivity (Ks). The intended synthesis comprises exploratory data analyses to check for Gaussian data distribution and stationarity; evaluation of robust variogram estimation requirements; estimation of the covariance parameters by least-squares procedures and (restricted) maximum likelihood; use of the Matérn correlation function. We furthermore discuss the spatial prediction uncertainty resulting from the different methods. The log-transformed data showed Gaussian uni- and bivariate distributions, and pronounced trends. Robust estimation techniques were not required, and anisotropic variation was not evident. Restricted maximum likelihood estimation versus the method-of-moments variogram of the residuals accounted for considerable differences in covariance parameters, whereas the Matérn and standard models gave very similar results. In the framework of spatial prediction, the parameter differences were mainly reflected in the spatial connectivity of the Ks field. Ignoring the trend component and an arbitrary use of robust estimators would have the most severe consequences in this respect. Our results highlight the superior importance of a thorough exploratory data analysis and proper variogram modeling, and prompt us to encourage restricted maximum likelihood estimation, which is accurate in estimating fixed and random effects.

AB - Environmental scientists today enjoy an ever-increasing array of geostatistical methods to analyze spatial data. Our objective was to evaluate several of these recent developments in terms of their applicability to real-world data sets of the soil field-saturated hydraulic conductivity (Ks). The intended synthesis comprises exploratory data analyses to check for Gaussian data distribution and stationarity; evaluation of robust variogram estimation requirements; estimation of the covariance parameters by least-squares procedures and (restricted) maximum likelihood; use of the Matérn correlation function. We furthermore discuss the spatial prediction uncertainty resulting from the different methods. The log-transformed data showed Gaussian uni- and bivariate distributions, and pronounced trends. Robust estimation techniques were not required, and anisotropic variation was not evident. Restricted maximum likelihood estimation versus the method-of-moments variogram of the residuals accounted for considerable differences in covariance parameters, whereas the Matérn and standard models gave very similar results. In the framework of spatial prediction, the parameter differences were mainly reflected in the spatial connectivity of the Ks field. Ignoring the trend component and an arbitrary use of robust estimators would have the most severe consequences in this respect. Our results highlight the superior importance of a thorough exploratory data analysis and proper variogram modeling, and prompt us to encourage restricted maximum likelihood estimation, which is accurate in estimating fixed and random effects.

KW - Soil Hydrology

KW - spatial variability

KW - geostatistics

KW - restricted maximum likelihood

KW - Matérn function

KW - nugget variance

KW - saturated hydraulic conductivity

KW - Hydrologic scaling

KW - Soils

KW - Spatial analysis

KW - Vadose zone

U2 - 10.1029/2007WR006604

DO - 10.1029/2007WR006604

M3 - Journal article

VL - 44

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 10

M1 - W10408

ER -