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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/hess-2019-614
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2019-614
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 02 Jan 2020

Submitted as: research article | 02 Jan 2020

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

Global and regional performances of SPI candidate distribution functions in observations and simulations

Patrick Pieper1, André Düsterhus2, and Johanna Baehr1 Patrick Pieper et al.
  • 1Institute for Oceanography, Center for Earth System Research and Sustainability, Universität Hamburg, Hamburg, Germany
  • 2ICARUS, Department of Geography, Maynooth University, Maynooth, Ireland

Abstract. The Standardized Precipitation Index (SPI) is a widely accepted drought index. Its calculation algorithm normalizes the index via a distribution function. Which distribution function to use is still disputed within literature. This study illuminates the long-standing dispute and proposes a solution which ensures the normality of the index for all common accumulation periods in observations and simulations.

We compare the normality of SPI time-series derived with the gamma, Weibull, generalized gamma, and the exponentiated Weibull distribution. Our normality comparison evaluates actual against theoretical occurrence probabilities of SPI categories, and the quality of the fit of candidate distribution functions against their complexity with Akaike's Information Criterion. SPI time-series, spanning 1983–2013, are calculated from Global Precipitation Climatology Project's monthly precipitation data-set and seasonal precipitation hindcasts from the Max Planck Institute Earth System Model. We evaluate these SPI time-series over the global land area and for each continent individually during winter and summer. While focusing on an accumulation period of 3-months, we additionally test the drawn conclusions for other common accumulation periods (1-, 6-, 9-, and 12-months).

Our results suggest to exercise caution when using the gamma distribution to calculate SPI; especially in simulations or their evaluation. Further, our analysis shows a distinctly improved normality for SPI time-series derived with the exponentiated Weibull distribution relative to other distributions. The use of the exponentiated Weibull distribution maximizes the normality of SPI time-series in observations and simulations both individual as well as concurrent. Its use further maximizes the normality of SPI time-series over each continent and for every investigated accumulation period. We, therefore, advocate to derive SPI with the exponentiated Weibull distribution, irrespective of the heritage of the precipitation data or the length of analyzed accumulation periods.

Patrick Pieper et al.
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Patrick Pieper et al.
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Short summary
The Standardized Precipitation Index (SPI) is a widely accepted drought index. SPI normalizes the precipitation distribution via a probability density function (PDF). However, which PDF properly normalizes SPI is still disputed. We suggest to use a previously mostly overlooked PDF, namely the exponentiated Weibull distribution. The proposed PDF ensures the normality of the index. We show this – for the first time – for all common accumulation periods in both observations and simulations.
The Standardized Precipitation Index (SPI) is a widely accepted drought index. SPI normalizes...
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