Articles | Volume 24, issue 9
https://doi.org/10.5194/hess-24-4541-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-24-4541-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
21 Sep 2020
Research article |
| 21 Sep 2020
| 21 Sep 2020
A universal Standardized Precipitation Index candidate distribution function for observations and simulations
Patrick Pieper
CORRESPONDING AUTHOR
Institute of Oceanography, Center for Earth System Research and Sustainability, Universität Hamburg, Hamburg, Germany
André Düsterhus
Irish Climate Analysis and Research UnitS (ICARUS), Department of Geography, Maynooth University, Maynooth, Ireland
Johanna Baehr
Institute of Oceanography, Center for Earth System Research and Sustainability, Universität Hamburg, Hamburg, Germany
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- A scientific-based protocol for the calculation of two standardized drought indices using NASA POWER data L. Martins et al. https://doi.org/10.1007/s12040-024-02446-5
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- The PowerSDI: an R-package for implementing and calculating the SPI and SPEI using data from the NASAPOWER project G. Blain et al. https://doi.org/10.1590/1678-4499.20230260
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- The Standardized Wind Speed Index: a multiscalar indicator of wind speed variability with a focus on wind droughts M. Andres-Martin et al. https://doi.org/10.1016/j.atmosres.2026.108967
- Appropriate statistical rainfall distribution models for the computation of standardized precipitation index (SPI) in Cameroon A. Fotse et al. https://doi.org/10.1007/s12145-023-01188-0
- Multiscale analysis of drought, heatwaves, and compound events in the Brazilian Pantanal in 2019–2021 M. Calim Costa et al. https://doi.org/10.1007/s00704-023-04655-2
- Attribution of air temperature and precipitation to the future global drought events R. Fu et al. https://doi.org/10.1088/2515-7620/acde37
- Unveiling Asymptotic Behavior in Precipitation Time Series: A GARCH-Based Second Order Semi-Parametric Autocorrelation Framework for Drought Monitoring in the Semi-Arid Region of India N. Choudhari et al. https://doi.org/10.3390/hydrology12100254
- How standard are standardized drought indices? Uncertainty components for the SPI & SPEI case J. Laimighofer & G. Laaha https://doi.org/10.1016/j.jhydrol.2022.128385
- Enhancing drought projection reliability: a framework for optimal GCM selection, aggregation, and trend analysis under shared socioeconomic pathways M. Shakeel et al. https://doi.org/10.1007/s00704-025-05443-w
- Utilizing Logistic Regression and Random Forest to Model Meteorological Drought Persistence Across Seasonal Transitions A. Hussain et al. https://doi.org/10.1007/s41748-025-00682-3
- Designing an Interactive Visual Analytics System for Precipitation Data Analysis D. Jeong et al. https://doi.org/10.3390/app15105467
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- An Alternative Approach for Computing the Standardized Precipitation-Evapotranspiration Index (SPEI) T. Raziei & M. Miri https://doi.org/10.1007/s11269-023-03542-9
- Effect Analysis of Probability Estimators on Parameter Estimation of the Three-Parameter Weibull Distribution X. Yang et al. https://doi.org/10.1142/S0219455424500093
- On interval estimation methods for the location parameter of the Weibull distribution: An application to alloy material fatigue failure data X. Yang et al. https://doi.org/10.1080/03610926.2023.2242984
- Multi-model assessment of seasonal rainfall and temperature forecast skill for operational drought prediction in India P. Deb et al. https://doi.org/10.1007/s00382-025-08024-9
- Multi-Secular Trend of Drought Indices in Padua, Italy F. Becherini et al. https://doi.org/10.3390/cli12120218
- Development of a Novel Non-Stationary Daily Hydrological Drought Index C. Yu et al. https://doi.org/10.1007/s11269-026-04777-y
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- Methodology for Developing Severity‐Duration‐Frequency Curves for Drought Assessment in South Africa J. du Plessis & E. Smith https://doi.org/10.1002/hyp.70185
- A Skewness–Kurtosis Adjusted Expansion of the Standardised Precipitation Index for Drought Analysis M. Gül & Y. Güçlü https://doi.org/10.1002/joc.70531
- Determining optimal probability distributions for gridded precipitation data based on L-moments M. Li et al. https://doi.org/10.1016/j.scitotenv.2023.163528
- A Computational Platform for Exploring Brazilian Rainfall Data P. Oliveira et al. https://doi.org/10.3390/data11090232
- Improving the normalization procedure of the simplified standardized precipitation index (SSPI) using Box–Cox transformation T. Raziei https://doi.org/10.1007/s00477-022-02317-9
- Improving seasonal predictions of meteorological drought by conditioning on ENSO states P. Pieper et al. https://doi.org/10.1088/1748-9326/ac1cbb
- SPI-3 Analysis of Medjerda River Basin and Gamma Model Limits in Semi-Arid and Arid Contexts Z. Kebaili Bargaoui & S. Jemai https://doi.org/10.3390/atmos13122021
- Truncated distributions for the Standardized Precipitation Index (SPI) and Standardized Streamflow Index (SSI) in a tropical basin L. Lopes Martins et al. https://doi.org/10.1080/02626667.2025.2576493
- Contrasting CESM and ECMWF for predictive modeling of spatial heterogeneity of drought indices across Colorado and Louisiana regions of the USA N. Choudhari et al. https://doi.org/10.1016/j.ejrh.2026.103351
58 citations as recorded by crossref.
- New Insights into Meteorological and Hydrological Drought Modeling: A Comparative Analysis of Parametric and Non-Parametric Distributions A. Abu Arra & E. Şişman https://doi.org/10.3390/atmos16070846
- Using a regional frequency analysis approach for calculating the Standardized Precipitation Index: an operational approach based on the two-parameter gamma distribution E. dos Santos Junior et al. https://doi.org/10.1007/s00704-022-03989-7
- Propagation in the Drought Cascade: Observational Analysis Over the Continental US D. Entekhabi https://doi.org/10.1029/2022WR032608
- Spatial and temporal variability of meteorological droughts including atmospheric circulation in Central Europe A. Wałęga et al. https://doi.org/10.1016/j.jhydrol.2024.131857
- The SPIChanges R-package: Improving the interpretation of the standardized precipitation index under changing climate conditions G. Blain et al. https://doi.org/10.1016/j.envsoft.2025.106573
- Improving the interpretation of standardized precipitation index estimates to capture drought characteristics in changing climate conditions G. Blain et al. https://doi.org/10.1002/joc.7550
- Monitoring meteorological drought in Hoa Vang district, Da Nang City, using Google Earth Engine and satellite-derived precipitation data combined with ground-based weather stations L. Hanh et al. https://doi.org/10.2166/wcc.2024.214
- Modified standardized precipitation index for skewed hydro-meteorological data M. Gül & Y. Güçlü https://doi.org/10.1016/j.pce.2025.104234
- A scientific-based protocol for the calculation of two standardized drought indices using NASA POWER data L. Martins et al. https://doi.org/10.1007/s12040-024-02446-5
- Exploring the joint probability of precipitation and soil moisture over Europe using copulas C. Cammalleri et al. https://doi.org/10.5194/hess-28-103-2024
- Intensified drought and vegetation-specific responses in the Tianshan Mountains, Central Asia H. Wang et al. https://doi.org/10.1016/j.catena.2026.110132
- The PowerSDI: an R-package for implementing and calculating the SPI and SPEI using data from the NASAPOWER project G. Blain et al. https://doi.org/10.1590/1678-4499.20230260
- Rethinking standardized drought indices for critical drought evaluation C. Ercan et al. https://doi.org/10.2166/wcc.2025.037
- Optimal distribution functions for drought characterization across Europe’s climatic gradient B. Mohammadi et al. https://doi.org/10.1016/j.ejrh.2026.103907
- Drought analysis in the Seyhan River Basin based on standardized drought indices using a new approach considering seasonality T. Terzi & B. Önöz https://doi.org/10.1007/s12665-024-12039-6
- تحلیل و ارزیابی اثرات خشکسالی در حوزۀ دریایی شمال ف. حسن زی et al. https://doi.org/10.62810/jns.v8iSpecial.Issue.507
- Standardized precipitation evapotranspiration index (SPEI) for Canada: assessment of probability distributions B. Tam et al. https://doi.org/10.1080/07011784.2023.2183143
- Spatial-temporal dynamics of meteorological and soil moisture drought on the Tibetan Plateau: Trend, response, and propagation process H. Lin et al. https://doi.org/10.1016/j.jhydrol.2023.130211
- Adapting the regional frequency analysis based on L-moments to improve the standardized precipitationevapotranspiration index L. Martins et al. https://doi.org/10.1590/1678-4499.20240029
- PyDRGHT: A comprehensive python package for drought analysis T. Terzi https://doi.org/10.1016/j.envsoft.2025.106847
- Optimal Probability Distribution and Applicable Minimum Time-Scale for Daily Standardized Precipitation Index Time Series in South Korea C. Lee et al. https://doi.org/10.3390/atmos14081292
- Multi-Index evaluation of meteorological drought across Türkiye: a temporal and seasonal perspective B. Selek et al. https://doi.org/10.1007/s11069-025-07961-2
- Accuracy Evaluation of Standardized Precipitation Index (SPI) Estimation under Conventional Assumption in Yeşilırmak, Kızılırmak, and Konya Closed Basins, Turkey M. Hinis et al. https://doi.org/10.1155/2023/5142965
- A Common Factor Analysis Based Data Mining Procedure for Effective Assessment of 21st Century Drought under Multiple Global Climate Models M. Ahmad et al. https://doi.org/10.1007/s11269-023-03581-2
- The Standardized Wind Speed Index: a multiscalar indicator of wind speed variability with a focus on wind droughts M. Andres-Martin et al. https://doi.org/10.1016/j.atmosres.2026.108967
- Appropriate statistical rainfall distribution models for the computation of standardized precipitation index (SPI) in Cameroon A. Fotse et al. https://doi.org/10.1007/s12145-023-01188-0
- Multiscale analysis of drought, heatwaves, and compound events in the Brazilian Pantanal in 2019–2021 M. Calim Costa et al. https://doi.org/10.1007/s00704-023-04655-2
- Attribution of air temperature and precipitation to the future global drought events R. Fu et al. https://doi.org/10.1088/2515-7620/acde37
- Unveiling Asymptotic Behavior in Precipitation Time Series: A GARCH-Based Second Order Semi-Parametric Autocorrelation Framework for Drought Monitoring in the Semi-Arid Region of India N. Choudhari et al. https://doi.org/10.3390/hydrology12100254
- How standard are standardized drought indices? Uncertainty components for the SPI & SPEI case J. Laimighofer & G. Laaha https://doi.org/10.1016/j.jhydrol.2022.128385
- Enhancing drought projection reliability: a framework for optimal GCM selection, aggregation, and trend analysis under shared socioeconomic pathways M. Shakeel et al. https://doi.org/10.1007/s00704-025-05443-w
- Utilizing Logistic Regression and Random Forest to Model Meteorological Drought Persistence Across Seasonal Transitions A. Hussain et al. https://doi.org/10.1007/s41748-025-00682-3
- Designing an Interactive Visual Analytics System for Precipitation Data Analysis D. Jeong et al. https://doi.org/10.3390/app15105467
- Uncertainty analysis of SPI and SRI calculation using bootstrap in the Mediterranean regions of Algeria M. Achite et al. https://doi.org/10.1007/s11069-024-06642-w
- Assessment of future meteorological droughts in Iran B. Ghazi et al. https://doi.org/10.1038/s41598-026-65752-6
- Drought cascade lag time estimation across Africa based on remote sensing of hydrological cycle components A. Amazirh et al. https://doi.org/10.1016/j.advwatres.2023.104586
- Development of co-integrated standardized procedure for the joint monitoring, forecasting and probabilistic characterization of climate extremes under global climate models A. Batool et al. https://doi.org/10.1007/s00704-026-06089-y
- Development of climate indices relevant for agriculture in Africa under different climate change scenarios based on GCM and RCM ensembles K. Ziegler et al. https://doi.org/10.1088/2752-5295/ad9f94
- Future meteorological drought in Ethiopia using better performed ensemble Coupled Model Intercomparison Project 6 (CIMP6) climate models Z. Kebede & G. Wedajo https://doi.org/10.1016/j.nhres.2025.08.006
- Assessing Drought Vulnerability in the Brazilian Atlantic Forest Using High-Frequency Data M. Chaves et al. https://doi.org/10.3390/meteorology3030014
- An Alternative Approach for Computing the Standardized Precipitation-Evapotranspiration Index (SPEI) T. Raziei & M. Miri https://doi.org/10.1007/s11269-023-03542-9
- Effect Analysis of Probability Estimators on Parameter Estimation of the Three-Parameter Weibull Distribution X. Yang et al. https://doi.org/10.1142/S0219455424500093
- On interval estimation methods for the location parameter of the Weibull distribution: An application to alloy material fatigue failure data X. Yang et al. https://doi.org/10.1080/03610926.2023.2242984
- Multi-model assessment of seasonal rainfall and temperature forecast skill for operational drought prediction in India P. Deb et al. https://doi.org/10.1007/s00382-025-08024-9
- Multi-Secular Trend of Drought Indices in Padua, Italy F. Becherini et al. https://doi.org/10.3390/cli12120218
- Development of a Novel Non-Stationary Daily Hydrological Drought Index C. Yu et al. https://doi.org/10.1007/s11269-026-04777-y
- GRACE-based hydrological droughts are less frequent but more severe than meteorological droughts in global major basins C. Ren et al. https://doi.org/10.1016/j.jhydrol.2025.134582
- SWAT Model and Drought Indices: A Systematic Review of Progress, Challenges and Opportunities L. Martins et al. https://doi.org/10.3390/w18010041
- On the relation between antecedent basin conditions and runoff coefficient for European floods C. Massari et al. https://doi.org/10.1016/j.jhydrol.2023.130012
- Methodology for Developing Severity‐Duration‐Frequency Curves for Drought Assessment in South Africa J. du Plessis & E. Smith https://doi.org/10.1002/hyp.70185
- A Skewness–Kurtosis Adjusted Expansion of the Standardised Precipitation Index for Drought Analysis M. Gül & Y. Güçlü https://doi.org/10.1002/joc.70531
- Determining optimal probability distributions for gridded precipitation data based on L-moments M. Li et al. https://doi.org/10.1016/j.scitotenv.2023.163528
- A Computational Platform for Exploring Brazilian Rainfall Data P. Oliveira et al. https://doi.org/10.3390/data11090232
- Improving the normalization procedure of the simplified standardized precipitation index (SSPI) using Box–Cox transformation T. Raziei https://doi.org/10.1007/s00477-022-02317-9
- Improving seasonal predictions of meteorological drought by conditioning on ENSO states P. Pieper et al. https://doi.org/10.1088/1748-9326/ac1cbb
- SPI-3 Analysis of Medjerda River Basin and Gamma Model Limits in Semi-Arid and Arid Contexts Z. Kebaili Bargaoui & S. Jemai https://doi.org/10.3390/atmos13122021
- Truncated distributions for the Standardized Precipitation Index (SPI) and Standardized Streamflow Index (SSI) in a tropical basin L. Lopes Martins et al. https://doi.org/10.1080/02626667.2025.2576493
- Contrasting CESM and ECMWF for predictive modeling of spatial heterogeneity of drought indices across Colorado and Louisiana regions of the USA N. Choudhari et al. https://doi.org/10.1016/j.ejrh.2026.103351
Saved (final revised paper)
Latest update: 21 Sep 2026
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 using a previously mostly overlooked PDF, namely the exponentiated Weibull distribution. The proposed PDF ensures the normality of the index. We demonstrate 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...
