A Hybrid Precipitation Index Inspired by the SPI, PDSI, and MCDI. Part I: Development of the Index

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Abstract
The filtering properties of the standardized precipitation index (SPI), the Palmer drought severity index (PDSI), and the model calibrated drought index (MCDI) are investigated to determine their relations to past, present, and future precipitation anomalies in regions with a wide diversity of precipitation characteristics. All three indices can be closely approximated by weighted averages of precipitation, but with different weighting. The SPI is well represented by one-sided, uniformly weighted averages; the MCDI is well represented by one-sided, exponentially weighted averages; and the PDSI is well represented by two-sided, exponentially weighted averages with much higher weighting of past and present precipitation than future precipitation. Detailed analyses identify interpretational complications and other undesirable features in the SPI and PDSI. In addition, the PDSI and MCDI are each restricted to single regionally specific “intrinsic” time scales that can significantly differ between the two indices. Inspired by the strengths of the SPI, PDSI, and MCDI, a hybrid index is developed that consists of exponentially weighted averages of past and present precipitation that are implicit in the PDSI and MCDI. The explicit specification of the exponential weighting allows users to control the time scale of the hybrid index to investigate precipitation variability on any time scale of interest. This advantage over the PDSI and MCDI is analogous to the controllability of the time scale of the SPI, but the exponentially fading memory is more physical than the uniform weighting of past and present precipitation in the SPI.

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