Statistical distributions for monthly aggregations of precipitation and streamflow in drought indicator applications

Abstract

Drought indicators are used as triggers for action and so are the foundation of drought monitoring and early warning. The computation of drought indicators like the standardized precipitation index (SPI) and standardized streamflow index (SSI) require a statistical probability distribution to be fitted to the observed data. Both precipitation and streamflow have a lower bound at zero, and their empirical distributions tend to have positive skewness. For deriving the SPI, the Gamma distribution has therefore often been a natural choice. The concept of the SSI is newer and there is no consensus regarding distribution. In the present study, twelve different probability distributions are fitted to streamflow and catchment average precipitation for four durations (1, 3, 6, and 12 months), for 121 catchments throughout the UK. The more flexible three‐ and four‐parameter distributions generally do not have a lower bound at zero, and hence may attach some probability to values below zero. As a result, there is a censoring of the possible values of the calculated SPIs and SSIs. This can be avoided by using one of the bounded distributions, such as the reasonably flexible three‐parameter Tweedie distribution, which has a lower bound (and potentially mass) at zero. The Tweedie distribution has only recently been applied to precipitation data, and only for a few sites. We find it fits both precipitation and streamflow data nearly as well as the best of the traditionally used three‐parameter distributions, and should improve the accuracy of drought indices used for monitoring and early warning.

Spatial and temporal patterns, trends and teleconnection of cumulative rainfall deficits across Central America

“…For this regional study, we selected the widely used and simple SPI originally proposed by McKee and Kleist (). Recent criticism of the SPI relates to the a priori selection of a statistical distribution function (gamma distribution) to approximately normalize the rainfall data (Svensson et al ., ), which in cases does not reflect the empirical distribution of measured monthly rainfall totals. Further, the SPI requires rather long data records (recommendation by McKee and Kleist () is to use a minimum of 30 years) to incorporate most of the natural climate variability for the classification of droughts (Wu et al ., ).…”

Historic hydrological droughts 1891–2015: systematic characterisation for a diverse set of catchments across the UK

“…The 3-month accumulation period (SSI-3) characterises short-term seasonal river flow deficits and impacts on smaller, single season reservoirs. The SSI was calculated using the Tweedie distribution, which has been found to have the best fit for observed river flow data for UK Benchmark catchments (Svensson et al, 2017). Due to the uncertainties associated with extreme SSI values (e.g.…”

Computation of monthly runoff coefficients for Istanbul

“…5, for each month, together with a fitted Gaussian. The Gamma probability distribution is a generally accepted model for monthly precipitation data [16]. We compute the parameters of the best fitting Gamma distribution for each month, using the statistical toolbox of MATLAB and on fig.…”