Characterizing the uncertainty and assessing the value of gap-filled daily rainfall data in Hawaii

Almost all daily rainfall time series contain gaps in the instrumental record. Various methods can be used to fill in missing data using observations at neighboring sites (predictor stations). In this study, five computationally simple gap-filling approaches-normal ratio (NR), linear regression (LR), inverse distance weighting (ID), quantile mapping (QM), and single best estimator (BE)-are evaluated to 1) determine the optimal method for gap filling daily rainfall in Hawaii, 2) quantify the error associated with filling gaps of various size, and 3) determine the value of gap filling prior to spatial interpolation. Results show that the correlation between a target station and a predictor station is more important than proximity of the stations in determining the quality of a rainfall prediction. In addition, the inclusion of rain/no-rain correction on the basis of either correlation between stations or proximity between stations significantly reduces the amount of spurious rainfall added to a filled dataset. For large gaps, relative median errors ranged from 12.5% to 16.5% and no statistical differences were identified between methods. For submonthly gaps, the NR method consistently produced the lowest mean error for 1- (2.1%), 15- (16.6%), and 30-day (27.4%) gaps when the difference between filled and observed monthly totals was considered. Results indicate that gap filling prior to spatial interpolation improves the overall quality of the gridded estimates, because higher correlations and lower performance errors were found when 20% of the daily dataset is filled as opposed to leaving these data unfilled prior to spatial interpolation.