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Written by Jason Karl
Kriging with External Drift
Kriging is a method of interpolating the values of a variable at points between field observations. Unlike classical statistics which assumes that data points are independent, kriging relies on the fact that observations are NOT independent. Regression kriging is a variation that uses additional – secondary – datasets such as imagery or other correlated observations to improve the quality of the predictions. The method proceeds by using multiple regression to describe the relationship between the variable observed in the field and the secondary data. The kriging then occurs with the regression residuals, and the regression and kriging results are combined to produce the prediction.
Prediction map, map of prediction variance, summary statistics of model performance
Predicting/mapping soil characteristics, mapping continuous vegetation attributes (e.g., percent canopy cover), mapping insect outbreaks
Cousens et al. (2002) weed mapping
Karl (in press)  mapping attributes of rangeland condition
Mutanga and Rugege (2006)  biomass estimation
Voltz et al. (1997)  predicting soil properties
Cousens et al. (2002), Cigliano et al. (1995), Mutanga and Rugege (2006), Karl et al. (in review), Voltz et al. (1997)
*Bailey and Gatrell (1995)  general reference on kriging  see section on Universal Kriging
*Hengl et al. (2003)  good treatment of the specifics of regression kriging. Presents a framework of process steps for implementing regression kriging.  Very useful reference.
Works poorly if there is little correlation between field observations and the secondary data (e.g., imagery). If there is little spatial autocorrelation among the field observations, then regressionkriging will not produce results that are any better than multiple regression. Also, kriging requires enough data points to be able to estimate the spatial dependence among the field observations. A general rule of thumb is that you should have 100 points at varying distances from each other (e.g., some points close, others far away).
Field observations with latitude/longitude coordinates, correlated data measured at same locations, or imagery correlated to the field observations.
Whereas standard kriging can be done in several GIS applications like ESRI’s ArcGIS Geospatial Analyst, regression kriging is a more specialized method and requires a statistics program like R or SAS. Regression kriging can be done on most desktop or laptop PCs, although highresolution imagery might need to be aggregated to a coarser resolution to avoid outofmemory errors.
Landscape Toolbox Project
Contact: Jason Karl, [[jkarl@tnc.org]]
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