Spatial Interpolation and its Uncertainty Using Automated Anisotropic Inverse Distance Weighting (IDW) - Cross-Validation/Jackknife Approach
Journal of Geographic Information and Decision Analysis, Vol. 2., No. 2, pp. 18-30, 1998.
In order to estimate rainfall magnitude at unmeasured locations, this entry to the Spatial Interpolation Comparison of 1997 (SIC'97) used 2-dimensional, anisotropic, inverse-distance weighting interpolator (IDW), with cross-validation as a method of optimizing the interpolator's parameters. A jackknife resampling was then used to reduce bias of the predictions and estimate their uncertainty. The method is easy to programme, "data driven", and fully automated. It provides a realistic estimate of uncertainty for each predicted location, and could be readily extended to 3-dimentional cases. For SIC97 purposes, the IDW was set to be an exact interpolator (smoothing parameter was set to zero), with the search radius set at the maximum extend of data. Other parameters were optimized as follows: exponent = 4, anisotropy ratio = 4.5, and anisotropy angle = 40?. The results predicted by the IDW interpolator were later compared with the actual values measured at the same locations. The overall root-mean-squared-error (RMSE) between predicted and observed rainfall for all 367 unknown locations was 6.32 mm of rain. The method was successful in predicting 50% and 65% of the exact locations of the twenty highest and lowest measurements respectively. Of the measured values, 65% (238 out of 367 data points) fell within jackknife-predicted 95% confidence intervals, uniquely constructed for each predicted location.
KEYWORDS: cross validation, jackknife, uncertainty, IDW, anisotropic, automated, spatial interpolation, GIS.