Monitoring and quantifying future climate projections of dryness and wetness extremes: SPI bias

Abstract. The adequacy of the gamma distribution (GD) for monthly precipitation totals is reconsidered. The motivation for this study is the observation that the GD fails to represent precipitation in considerable areas of global observed and simulated data. This misrepresentation may lead to erroneous estimates of the Standardised Precipitation Index (SPI), evaluations of models, and assessments of climate change. In this study, the GD is compared to the Weibull (WD), Burr Type III (BD), exponentiated Weibull (EWD) and generalised gamma (GGD) distribution. These distributions extend the GD in terms of possible shapes (skewness and kurtosis) and the behaviour for large arguments. The comparison is based on the Akaike information criterion, which maximises information entropy and reveals a trade-off between deviation and the numbers of parameters used. We use monthly sums of observed and simulated precipitation for 12 calendar months of the year. Assessing observed and simulated data, (i) the Weibull type distributions give distinctly improved fits compared to the GD and (ii) the SPI resulting from the GD overestimates (underestimates) extreme dryness (wetness).