Incorporating process knowledge in spatial interpolation of environmental variables

Gerard B.M. Heuvelink
Environmental Sciences Group
Wageningen University and Research Centre
P.O. Box 37
6700 AA Wageningen, The Netherlands
Tel.: + 0031 317 474628; Fax + 0031 317 419000


Ordinary kriging is the most commonly used geostatistical interpolation technique. It predicts the value of a spatially distributed environmental variable at an unobserved location by taking a weighed linear combination of neighbouring observations. Ordinary kriging has proven to be very rewarding to the earth and environmental sciences, but a disadvantage is that it is a purely empirical technique that relies solely on point observations of  the target variable. Potentially one ought to be able to do much better by also exploiting all sorts of ancillary information, such as derived from digital terrain models, remote sensing imagery, geological, soil and landuse maps. Knowledge about the physical, chemical, biological or socio-economic processes that caused the spatial variation in the environmental variable is potentially also of much value. This paper explores two recent approaches that incorporate ancillary information and process knowledge in spatial interpolation. Regression kriging differs from ordinary kriging by including a trend function that is steered by ancillary information and process knowledge. Space-time Kalman filtering takes a dynamic approach by formulating a state equation that computes the state of the system at the next time point from driving variables and the current state. The Kalman filter conditions the state predictions to measurements in the measurement update step. Regression kriging and space-time Kalman filtering are compared and their application in practice is illustrated with examples. Incorporating process knowledge in spatial interpolation is advantageous not only because using more information yields more accurate maps, but also because it gives insight into how processes affect the state of the environment and is better suited to make extrapolations. Although these techniques are increasingly applied and have a bright future, several important theoretical and practical issues need to be resolved before routine application is in place.

Keywords: dynamic modelling, geostatistics, Kalman filtering, regression kriging

In: Caetano, M. and Painho, M. (eds). Proceedings of the 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, 5 – 7 July 2006, Lisboa, Instituto Geográfico Português

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