Temporal and Spatial Interpolation of the Standardized Precipitation Index for Computational Efficiency in the Dynamic Drought Index Tool

Abstract

he feasibility of interpolating gamma-distribution parameters between different precipitation accumulation intervals (durations) is statistically evaluated. The interpolation of these parameters for a specific accumulation interval, but ending on different dates, is similarly assessed. Such interpolation increases the computational efficiency of drought-monitoring tools that require calculation of the standardized precipitation index (SPI) for any user-specified accumulation period on any given day. Spatial interpolation of the distribution parameters is also assessed. Given a 60-yr period of record, few statistically significant differences were found between gamma-distribution percentiles interpolated between fixed base durations and those computed directly. Shorter interpolation intervals (generally 30 days) were required for the shortest (e.g., 30 days) durations, whereas interpolation over periods of as long as 180 days could be used for the longest (between 360 and 720 days) durations. Interpolating the distribution parameters to different ending dates on the basis of those computed for the end of each month was also appropriate. The spatial interpolation of gamma-distribution parameters, although viable in practice for monitoring large-scale drought conditions, was associated with larger SPI differences than was the spatial interpolation of the SPI index itself or the interpolation of historical precipitation and the subsequent calculation of gamma-distribution parameters on the basis of these values.