Sensitivity of SPI to Distribution Functions and Correlation Between its Values at Different Time Scales in Central Africa

Abstract

This paper studies sensitivity of Standardized Precipitation Index (SPI) to statistical distribution functions used in SPI computation procedure, in order to find out which are more appropriate and to assess SPI shift if using inappropriate distribution functions. Results may explain one of the reasons why spatial SPI computed with unique distribution function as usually, sometimes does not give better drought description. Central Africa is chosen as the study area because of its importance in climate change perspective and the necessity to use improved tools for drought quantification in this region. Monthly precipitation data for the period 1951–2016, both from the Climatic Research Unit (CRU) and Global Precipitation Climatology Centre (GPCC) were used. They were first aggregated at various time scales and four statistical distribution functions (gamma, weibull, exponential and lognormal) were tested to select the best-fit. Next, SPI was calculated for various time scales using the best fit function at each grid point and results were compared to those computed assuming a same distribution function at all grid points. Results show that, from 1- to 9-month time scales, observed spatial patterns of distribution functions were more homogeneous and the weibull function had the highest extended spatial rate, followed successively by gamma, lognormal and exponential. From 12-month time scale, spatial patterns were inhomogeneous, and no gridded precipitation followed the exponential function. The study of cross-correlations showed significant resemblance between SPIs at different time scales, leading to reduce the studies from 1- to 15-month. SPI values were affected if inappropriate distribution functions were used and the shift increases in correlation with the increase of time scale. The two datasets CRU and GPCC showed similar results, but GPCC’s SPIs were wetter and distribution functions somewhat more dispersed spatially from 12-month time scale. For SPI calculation in Central Africa, the weibull and gamma functions if used lead to good SPI results at short time scales (not more than 9-month) compared to SPI calculated using exponential or lognormal function. From 12-month time scale, it is recommended to choose the best fit distribution function at each grid point in order to expect good SPI results and then better drought description.