Analysis of Rainfall Data
by Robust Spatial Statistics
using S+SpatialStats

Marc G. Genton, Reinhard Furrer


Abstract

This paper discusses the use of robust geostatistical methods on a data set of rainfall measurements in Switzerland. The variables are detrended via non-parametric estimation penalized with a smoothing parameter. The optimal trend is computed with a smoothing parameter based on cross-validation. Then, variograms are estimated by a highly robust estimator of scale. The parametric variogram models are fitted by generalized least squares, thus taking account of the variance-covariance structure of the variogram estimates. Comparison of kriging with the initial measurements is completed and yields interesting results. All these computations are done with the software S+SpatialStats, extended with new functions in S+ that are made available.

Keywords: Robustness; Trend; Variogram; Generalized least squares; Kriging.


S-Plus functions

Download of the functions for highly robust variogram estimation and generalized least squares fitting. This software may be used, copied and modified freely for scientific and/or non-commercial purposes, provided reference is made.


Highly robust variogram estimation:

READ.ME
variogram.qn.tar

Generalized least squares fitting:

READ.ME
glse.fitting.tar


The authors decline any responsibility of the correctness of the functions and any damages that may occur by using them.
The authors appriciate all comments on the functions.

References

Rousseeuw, P.J. and Croux, C. (1993): "Alternatives to the Median Absolute Deviation," Journal of the American Statistical Association, Vol. 88, 1273-1283.

Genton, M. G. (1996): "Robustness in Variogram Estimation and Fitting in Geostatistics", Ph.D. Thesis #1595, Department of Mathematics, Swiss Federal Institute of Technology.

Genton, M. G., (1998): "Highly Robust Variogram Estimation", Mathematical Geology, Vol. 30, No. 2, p. 213-221.

Genton, M. G., (1998): "Variogram Fitting by Generalized Least Squares Using an Explicit Formula for the Covariance Structure", Mathematical Geology, Vol. 30, No. 4, 323-345.

Genton, M. G., (1998): "Spatial Breakdown Point of Variogram Estimators", Mathematical Geology, Vol. 30, No. 7, 853-871.

Furrer, R. and Genton, M. G. (1998): "Robust Spatial Data Analysis of Lake Geneva Sediments with S+SpatialStats", Systems Research and Information Science, Special Issue on Spatial Data: Neural Nets/Statistics, Vol. 8, No. 4, 257-272.