The objective analysis of daily rainfall by distance weighting schemes on a Mesoscale grid

Abstract The authors studied the error of spatial interpolation in the context of a climatic data gridding project (Cli‐Grid). Four objective analysis (QA) techniques were implemented: the empirical techniques of Barnes, Cressman and Shepard, and a Gandin‐based statistical technique. These were applied to the interpolation of irregularly distributed daily rainfall data. Spatial resolution of the interpolated arrays was 0.05 degree of latitude by 0.05 degree of longitude. In this experiment, radar rainfall patterns served as reference data for evaluations of O A techniques. Each reference pattern was sampled at the irregularly spaced locations of a climatic rain‐gauge network. The sampled data were then input to one of the four OA techniques. The resulting analysis was subtracted from the corresponding reference pattern. Absolute values of the differences were recorded. This sampling‐to‐difference cycle was repeated with 63 reference patterns. Every map of absolute differences was summed. The resulting map of total errors was normalized by the sum of the reference patterns. Average bias, average RMS error and averages of the ratios of the standard deviations were also computed. All four OA techniques were evaluated separately. The authors recognized that totally unbiased intercomparisons were not possible because of the range in execution parameters for each OA technique. Reasonable efforts were made to minimize subjectivity in the setting of parameters. For application to the specific project grid, the statistical optimal interpolation technique displayed the lowest RMS errors. This technique and Shepard OA, were found more suitable than the other two techniques studied. Statistical and Barnes OA displayed zero average bias and would be useful for areal average computations. The Cressman OA was judged least suitable for interpolation of daily rainfall. An application of the two‐dimensional error maps to network analysis was demonstrated by plotting the relationship between interpolation errors and distance (D) from the closest station. Error increased as D1/2. It was also verified that error and station density were inversely related.