Understanding the Dynamics of Transfer of Satellite Rainfall Error Metrics From Gauged to Ungauged Satellite Gridboxes Using Interpolation Methods

Knowledge of error characteristics of high resolution satellite rainfall data at different spatial/temporal scales is useful, especially when the scheduled Global Precipitation Mission (GPM) plans to provide High Resolution Precipitation Products (HRPPs) at global scales. Satellite rainfall data contain errors which need ground validation (GV) data for characterization, while satellite rainfall data will be most useful in the regions that are lacking in GV data. Therefore, a critical step to bridge this gap is to assess spatial interpolation schemes for transfer of the error characteristics from GV regions to non-GV regions. In this study, a comprehensive assessment of kriging methods for spatial transfer (interpolation) of error metrics is performed. Three kriging methods for spatial interpolation are compared, which are: ordinary kriging (OK), indicator kriging (IK) and disjunctive kriging (DK). Additional comparison with the simple inverse distance weighting (IDW) method is also performed to quantify the added benefit (if any) of using geostatistical methods. Four commonly used satellite rainfall error metrics are assessed for transfer to non-GV satellite gridboxes: Probability of Detection (POD) for rain, False Alarm Ratio (FAR), bias (BIAS), and Root Mean Squared Error (RMSE). Results show that performance of a kriging scheme is strongly sensitive to the timescale for which the errors are interpolated (monthly and weekly) wherein the extent of coverage by GV data plays an equally sensitive role. While most kriging techniques perform well according to correlation measure at climatologic timescales for a range of GV data coverage, only DK and OK appear to retain accuracy at the shorter timescales (monthly and weekly). However, scalar assessment metrics such as mean and standard deviation of error (i.e., difference between true and interpolated errors) reveal a completely different picture of accuracy of each interpolation method. In terms of such assessment measures, the overall performance ranking of the kriging methods is as follows:
${\rm OK}={\rm DK}>{\rm IDW}>{\rm IK}$
. Assessment of kriging methods also revealed that the transfer accuracy is sensitive to error metric type. The ranking of error metrics with highest accuracy in transfer is:
${\rm POD}>{\rm FAR}>{\rm RMSE}>{\rm BIAS}$
. Overall, the assessment of kriging methods revealed that these best linear unbiased spatial estimators may not be appropriate transfer methods for transfer of satellite rainfall error metrics at time scales shorter than a week. It is worthwhile now to pursue more non-linear transfer methods (such as neural networks) and other kriging methods that use additional spatial information on the rainfall process (such as co-kriging) to further constrain the interpolation uncertainty.