External drift kriging of NOx concentrations with dispersion model output in a reduced air quality monitoring network

Abstract

In the mid nineteen eighties the Dutch NO x air quality monitoring network was reduced from 73 to 32 rural and city background stations, leading to higher spatial uncertainties. In this study, several other sources of information are being used to help reduce uncertainties in parameter estimation and spatial mapping. For parameter estimation, we used Bayesian inference. For mapping, we used kriging with external drift (KED) including secondary information from a dispersion model. The methods were applied to atmospheric NO x concentrations on rural and urban scales. We compared Bayesian estimation with restricted maximum likelihood estimation and KED with universal kriging. As a reference we also included ordinary least squares (OLS). Comparison of several parameter estimation and spatial interpolation methods was done by cross-validation. Bayesian analysis resulted in an error reduction of 10 to 20% as compared to restricted maximum likelihood, whereas KED resulted in an error reduction of 50% as compared to universal kriging. Where observations were sparse, the predictions were substantially improved by inclusion of the dispersion model output and by using available prior information. No major improvement was observed as compared to OLS, the cause presumably being that much good information is contained in the dispersion model output, so that no additional spatial residual random field is required to explain the data. In all, we conclude that reduction in the monitoring network could be compensated by modern geostatistical methods, and that a traditional simple statistical model is of an almost equal quality.

Functional zoning for air quality

“…KED implementation follows Van de Kassteele et al (2009) that combine observations and deterministic dispersion model data of atmospheric NO x concentration. Specifically, the kriging is applied on the observed data and the external drift is constituted by the deterministic model output.…”

Geostatistical prediction of nitrous oxide emissions from soil using data, process models and expert opinion

“…They illustrate RK for predicting a hard‐to‐measure soil variable, nitrous oxide (N 2 O) emissions from the soil: the RK predictions are based on direct measurements of the N 2 O emissions and a process model for the emissions, given data on more readily measured input variables for this model. They show that this approach gives better estimates than those from either the process model or geostatistical prediction from data separately; other RK case studies have drawn similar conclusions (Maxwell et al , 2009; van de Kassteele et al , 2009).…”

A model for external drift kriging with uncertain covariates applied to air quality measurements and dispersion model output

“…An earlier study using a comparable data set of NO x concentrations (Van de Kassteele et al, 2005) showed that a large part of the variation in the observations could be explained by the OPS output. This resulted in a high value for the range parameter ($ 1000 km), leading to an almost linear shape of the exponential correlation function on the Dutch scale.…”

“…In the Netherlands, 45 NO 2 monitoring stations, to which secondary information is added from a highresolution dispersion model, are used for this purpose. Kriging with external drift (KED) has been shown to be useful in merging these two sources of information (Van de Kassteele et al, 2005). The primary variable, given by the monitoring data, is combined with a secondary variable, the dispersion model output, as the external drift covering the whole domain.…”