Spatial prediction of topsoil salinity in the Chelif Valley, Algeria, using local ordinary kriging with local variograms versus whole-area variogram

Abstract

A novel form of ordinary kriging, involving the local estimation and modelling of the variogram at each prediction site (OKLV), is tested at a regional scale on a large data set, in order to adapt to non-uniform spatial structures and improve the assessment of the salinity hazard in the lower Chelif Valley, Algeria. The spatial variability study was carried out on a 38000 ha area using 5141 topsoil electrical conductivity (EC) measurements systematically sampled on a 250 m by 250 m grid. Variography analysis confirmed the existence of large trends in the EC variability with differing spatial structures between sub-areas. OKLV performed better than ordinary kriging with a whole-area variogram (OKWV) in predicting the proportion of high saline soils in large blocks, but the predictions appeared mostly similar. In contrast, the estimation variance maps revealing the uncertainties of the spatial predictions were markedly different between the 2 methods. OKLV integrates the local spatial structure in the uncertainty assessment, whereas kriging with a whole-area variogram only considers the sampling intensity. Comparison with prediction errors on a validation set confirmed the consistency of the OKLV prediction variance. This appears to be a major improvement for decision-making procedures such as delineating areas where remediation should take place.

Movement patterns and habitat use of three declining littoral fish species in a north-temperate mesotrophic lake

“…Lag intervals for computing variograms were 10 m and the number of pairs per lag used to compute mean values of semivariance were never less than 50 in any simulation. Spatial structure of the occurrence of each fish species was quantified and mapped using indicator variograms of semivariance and local indicator kriging in summer of both years (Isaaks & Srivastava, 1989;Haas, 1990;Walter et al, 2001). ''Summer'' included pooled data from June, July, and August of each year.…”

Moving window kriging with geographically weighted variograms

“…Instead, it is MWK's ability to provide kriging variances that reflect local uncertainty accurately that is important. This latter property of MWK has been demonstrated in Van Tooren and Haas (1993), Walter et al (2001) for example; and this improvement alone can justify its use. Commonly, the decision of whether or not to apply MWK over a stationary counterpart (such as BCK) depends on a trade-off between: (a) many ill-fitted local variograms, but with (potentially) more accurate model outputs and (b) a wellfitted (and understood) global variogram with possibly less accurate model outputs.…”

“…Here, it is useful to refer to the empirical studies of Walter et al (2001), Lloyd and Atkinson (2002), Paciorek and Schervish (2006), where prediction using a stationary measure of spatial dependence was just as accurate. Instead, it is MWK's ability to provide kriging variances that reflect local uncertainty accurately that is important.…”

“…Haas (1990Haas ( , 1996 proceeded to develop the MWK approach incorporating lognormal kriging, regression kriging, and cokriging versions. Other notable exponents of MWK include the OK version of Walter et al (2001); the universal kriging (UK) version of Lloyd and Atkinson (2002); the UK (KS-MWK) version of Pardo-Igúzquiza et al (2005); and the IK version of Cattle et al (2002).…”

Second-order non-stationary modeling approaches for univariate geostatistical data

“…Haas (1990a, b) applies this approach to sulfate and sulfuric acid deposition data in the United States. Atkinson (2000, 2002) use moving window based non-stationary modeling approach to mapping digital elevation data while Walter et al (2001) apply it to soil data. Harris et al (2010) replace the moving window estimator of the local stationary spatial dependence structure by a weighted estimator.…”