Appropriate application of the standardized precipitation index in arid locations and dry seasons

Abstract

Abstract:The Standardized Precipitation Index (SPI) is now widely used throughout the world in both a research and an operational mode. For arid climates, or those with a distinct dry season where zero values are common, the SPI at short time scales is lower bounded, referring to non-normally distributed in this study. In these cases, the SPI is always greater than a certain value and fails to indicate a drought occurrence. The nationwide statistics based on our study suggest that the non-normality rates are closely related to local precipitation climates. In the eastern United States, SPI values at short time scales can be used in drought/flood monitoring and research in any season, while in the western United States, because of its distinct seasonal precipitation distribution, the appropriate usage and interpretation of this index becomes complicated. This would also be the case for all arid climates. From a mathematical point of view, the non-normally distributed SPI is caused by a high probability of no-rain cases represented in the mixed distribution that is employed in the SPI construction. From a statistical point of view, the 2-parameter gamma model used to estimate the precipitation probability density function and the limited sample size in dry areas and times would also reduce the confidence of the SPI values.On the basis of the results identified within this study, we recommend that the SPI user be cautious when applying short-time-scale SPIs in arid climatic regimes, and interpret the SPI values appropriately. In dry climates, the user should focus on the duration of the drought rather than on just its severity. It is also worth noting that the SPI results from a statistical product of the input data. This character makes it difficult to link the SPI data to the physical functioning of the Earth system.

Evaluation of Drought Indices Based on Thermal Remote Sensing of Evapotranspiration over the Continental United States

“…In addition, SPI-1, SPI-2, and SPI-3 show weak correlations with the USDM in the southwestern United States. Wu et al (2007) demonstrate that short-time-scale SPIs tend to have nonnormal temporal distributions in arid climates where precipitation distribution functions are highly skewed, peaking toward the no-rain case. In these situations, the 3-month SPI will tend to underpredict the severity and frequency of drought events, whereas the 6-month SPI shows more reasonable performance.…”

Inadequacy of the gamma distribution to calculate the Standardized Precipitation Index

“…Accordingly, a great number of drought indices have been proposed to monitor the drought conditions in several parts of the world. Among then, the Standardized Precipitation Index (SPI) has been widely used in both academic and operational modes (Wu et al, 2007;Jain et al, 2010) to detect rainfall deficits summed over several time spans (or timescales).…”

“…Therefore, the confidence in the SPI results may be affected by the use of a distribution that does not provide a suitable goodness-of-fit for the rainfall data (Wu et al, 2005;2007;Sienz et al, 2012;Stagge et al, 2015). Although authors such as Guttman (1999) and López-Moreno & Vicente-Serrano (2008) have already provided evidences indicating that the gamma distribution may not always be the most appropriate choice; this fundamental step is frequently based on this 2-parameter distribution (Wu et al, 2007;Dutra et al 2013; among many others). Moreover, the gamma distribution may not give the best goodness-of-fit for the rainfall data summed over different timescales because it only has two free parameters (Wu et al, 2007).…”

“…The SPI final values are obtained by performing an equiprobability transformation of the cumulative probability estimated in the above-mentioned step (Wu et al, 2007). From a mathematical point of view, the essential goal of this latter step is to transform the SPI series into normally distributed series with zero mean and unitary variance.…”

“…From a mathematical point of view, the essential goal of this latter step is to transform the SPI series into normally distributed series with zero mean and unitary variance. From a meteorological point of view, the essential goal of this transformation is to ensure that the SPI is capable of representing drought and flood events in a similar probabilistic fashion (Wu et al, 2007). Thus, the parametric distribution used to calculate this probabilitybased index should also be capable of providing normally distributed SPI series.…”