## Tag Cloud

spatial_analysis_methods:regression_kriging

# Regression Kriging

Written by Jason Karl

## Other Names:

Kriging with External Drift

## Description

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.

## Output

Prediction map, map of prediction variance, summary statistics of model performance

## Successful Rangeland Uses

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

## Technical References

*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.

## Limitations

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 regression-kriging 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).

## Data Inputs

Field observations with latitude/longitude coordinates, correlated data measured at same locations, or imagery correlated to the field observations.

## Software/Hardware Requirements

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 high-resolution imagery might need to be aggregated to a coarser resolution to avoid out-of-memory errors.

## Sample Graphic

 Predictions of percent sagebrush cover made via regression kriging of 147 field observations. Regression kriging gives variance estimates that vary with distance from the sample point. The maximum variance that is achieved furthest from the sample points is equal to the variance estimate of a standard regression without kriging.

## Who Is Using This Method?

• Idaho Chapter of The Nature Conservancy

Landscape Toolbox Project

`  Contact: Jason Karl, [[jkarl@tnc.org]]`

## References

• Bailey, T.C., Gatrell, A.C. 1995. Interactive spatial data analysis. Addison-Wesley.
• Cigliano, M.M., Kemp, W.P., Kalaris, T.M. 1995. Spatiotemporal characteristics of rangeland grasshopper (Orthoptera: Acrididae) regional outbreaks. Journal of Orthoptera Research
• Cousens RD, Brown RW, McBratney AB, Whelan B, Moerkerk M. 2002. Sampling strategy is important for producing weed maps: a case study using kriging. Weed Science 50:542-6.
• Hengl, T., Heuvelink, G.B.M., Stein, A. 2004. A generic framework for spatial prediction of soil variables based on regression-kriging. Geoderma 120:75-93.
• Karl, J.W. in review Using regression kriging to make spatial predictions of rangeland condition attributes. Rangeland Ecology and Management. jkarl@tnc.org
• Mutanga O, Rugege D. 2006. Integrating remote sensing and spatial statistics to model herbaceous biomass distribution in a tropical savanna. International Journal of Remote Sensing 27(16):3499-514.
• Voltz M, Lagacherie P, Louchart X. 1997. Predicting soil properties over a region using sample information from a mapped reference area. European Journal of Soil Science 48:19-30.