Multivariate Spatial Prediction in the Presence of Non‐linear Trend and Covariance Non‐stationarity

Abstract

When two or more spatial processes are punctually observed over a region, a multivariate predictor can account for spatial cross‐covariance among the variables and thus potentially yield more reliable predictions and lower estimated prediction standard errors. If the spatial processes exhibit first‐ and/or second‐order non‐stationarity, however, standard cokriging‐based predictors may not be adequate. A new cokriging‐based multivariate predictor is presented capable of modelling non‐linear trend, non‐stationary spatial covariance, and the case where the covariable also enters as a covariate. This method is used to predict 1991 sulphate deposition over the conterminous US with the aid of the more spatially dense National Weather Service precipitation data. It is found that there are only small differences between sulphate predictions and estimated prediction standard errors and those computed under enforced zero cross‐covariance. Failing to include the covariate effect of precipitation, however, results in non‐negligible differences in such predictions and prediction standard error estimates.

Bivariate geostatistical modelling: a review and an application to spatial variation in radon concentrations

“…In the traditional geostatistics literature, bivariate spatial prediction is called co-kriging (Ver Hoef and Cressie 1993;Haas 1996). In this technique, a two-dimensional point prediction S(x) = (S 1 (x), S 2 (x)) at location x is constructed as the linear combination of the data Y that minimises the mean squared prediction error.…”

Moving window kriging with geographically weighted variograms

“…Haas (1990) was the first to counter this approximation and actually fit a variogram within each OK neighbourhood. 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).…”

“…In any case, CV/WLS variogram fits have been the usual choice for most MWK studies (e.g. Haas 1990Haas , 1996.…”

Book Reviews

“…In this situation, the author acknowledges that the classical cross-semivariogram cannot be estimated (p. 145). At least in the environmental sciences, as data from different monitoring efforts are pooled to give more cost-effective estimates of environmental status, analysis of data from noncoincident networks will become more frequent (see, e.g., Haas 1996).…”