A Cross Validation of Interpolated Tropical Pacific Rainfall

Experimental 0.25-degree gridded monthly atoll rainfall, first published on the Pacific Rainfall (PACRAIN) project website in February 2017, have been updated and extended in coverage. The interpolation scheme used to produce the gridded product has also been improved and updated. Semivariograms for the Kriging procedure are obtained for each field of rainfall reports, rather than locally for limited neighborhoods, and their model parameters are optimized with respect to the mean squared error resulting from their use. The result is a more robust estimate of atoll-derived gridded rainfall across the tropical Pacific.

This paper shows and describes the results from an extensive cross validation of estimated and observed rains, as well as for theoretical and observed standard errors. The cross validation demonstrates the unbiasedness of the gridded product and is used to develop a statistical model of interpolation error based on relationships between the actual distributions of interpolation errors and theoretical distributions of Kriging errors. The resulting model provides a tool for estimating uncertainty due to interpolation throughout the grid domains.

The uncertainty estimation procedure is explained in detail and spatial distributions of quantile thresholds are shown. Errors due to data sparseness, heteroscedasticity and departures of raw rainfall distributions from the normal are discussed along with the effects of increasing averaging scales on uncertainty estimates. In addition, procedures for training and validation site selection, for semivariogram model parameter training, and for the Kriging scheme are shown. The overall results of this effort illustrate the potential usefulness of the gridded atoll product, as well as provide a way to gauge the accuracy of the individual values.