Expected annual minima from an idealized moving-average drought index
<p>Numerous drought indices originate from the Standardized Precipitation Index (SPI) and use a moving-average structure to quantify drought severity by measuring normalized anomalies in hydroclimate variables. This study examines the theoretical probability of annual minima based on such a pr...
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Copernicus Publications
2025-02-01
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| Series: | Hydrology and Earth System Sciences |
| Online Access: | https://hess.copernicus.org/articles/29/719/2025/hess-29-719-2025.pdf |
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| author | J. H. Stagge K. Sung K. Sung I. F. Munyejuru M. A. I. Haidar |
| author_facet | J. H. Stagge K. Sung K. Sung I. F. Munyejuru M. A. I. Haidar |
| author_sort | J. H. Stagge |
| collection | DOAJ |
| description | <p>Numerous drought indices originate from the Standardized Precipitation Index (SPI) and use a moving-average structure to quantify drought severity by measuring normalized anomalies in hydroclimate variables. This study examines the theoretical probability of annual minima based on such a process. To accomplish this, we derive a stochastic model and use it to simulate 10 <span class="inline-formula">×10<sup>6</sup></span> years of daily or monthly SPI values in order to determine the distribution of annual exceedance probabilities. We believe this is the first explicit quantification of annual extreme exceedances from a moving-average process where the moving-average window is proportionally large (5 %–200 %) relative to the year, as is the case for many moving-window drought indices. The resulting distribution of annual minima follows a generalized normal distribution rather than the generalized extreme-value (GEV) distribution, as would be expected from extreme-value theory. From a more applied perspective, this study provides the expected annual return periods for the SPI or related drought indices with common accumulation periods (moving-window length), ranging from 1 to 24 months. We show that the annual return period differs depending on both the accumulation period and the temporal resolution (daily or monthly). The likelihood of exceeding an SPI threshold in a given year decreases as the accumulation period increases. This study provides clarification and a caution for the use of annual return period terminology (e.g. the 100-year drought) with the SPI and a further caution for comparing annual exceedances across indices with different accumulation periods or resolutions. The study also distinguishes between theoretical values, as calculated here, and real-world exceedance probabilities, where there may be climatological autocorrelation beyond that created by the moving average.</p> |
| format | Article |
| id | doaj-art-5912ede35c3e4b6a88b8ee3548a9b3c8 |
| institution | Kabale University |
| issn | 1027-5606 1607-7938 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Hydrology and Earth System Sciences |
| spelling | doaj-art-5912ede35c3e4b6a88b8ee3548a9b3c82025-02-07T06:56:15ZengCopernicus PublicationsHydrology and Earth System Sciences1027-56061607-79382025-02-012971973210.5194/hess-29-719-2025Expected annual minima from an idealized moving-average drought indexJ. H. Stagge0K. Sung1K. Sung2I. F. Munyejuru3M. A. I. Haidar4Department of Civil, Environmental and Geodetic Engineering, The Ohio State University, Columbus, OH 43210, USADepartment of Civil, Environmental and Geodetic Engineering, The Ohio State University, Columbus, OH 43210, USAKorea Adaptation Center for Climate Change, Korea Environment Institute, Sejong, Republic of KoreaDepartment of Civil, Environmental and Geodetic Engineering, The Ohio State University, Columbus, OH 43210, USADepartment of Civil, Environmental and Geodetic Engineering, The Ohio State University, Columbus, OH 43210, USA<p>Numerous drought indices originate from the Standardized Precipitation Index (SPI) and use a moving-average structure to quantify drought severity by measuring normalized anomalies in hydroclimate variables. This study examines the theoretical probability of annual minima based on such a process. To accomplish this, we derive a stochastic model and use it to simulate 10 <span class="inline-formula">×10<sup>6</sup></span> years of daily or monthly SPI values in order to determine the distribution of annual exceedance probabilities. We believe this is the first explicit quantification of annual extreme exceedances from a moving-average process where the moving-average window is proportionally large (5 %–200 %) relative to the year, as is the case for many moving-window drought indices. The resulting distribution of annual minima follows a generalized normal distribution rather than the generalized extreme-value (GEV) distribution, as would be expected from extreme-value theory. From a more applied perspective, this study provides the expected annual return periods for the SPI or related drought indices with common accumulation periods (moving-window length), ranging from 1 to 24 months. We show that the annual return period differs depending on both the accumulation period and the temporal resolution (daily or monthly). The likelihood of exceeding an SPI threshold in a given year decreases as the accumulation period increases. This study provides clarification and a caution for the use of annual return period terminology (e.g. the 100-year drought) with the SPI and a further caution for comparing annual exceedances across indices with different accumulation periods or resolutions. The study also distinguishes between theoretical values, as calculated here, and real-world exceedance probabilities, where there may be climatological autocorrelation beyond that created by the moving average.</p>https://hess.copernicus.org/articles/29/719/2025/hess-29-719-2025.pdf |
| spellingShingle | J. H. Stagge K. Sung K. Sung I. F. Munyejuru M. A. I. Haidar Expected annual minima from an idealized moving-average drought index Hydrology and Earth System Sciences |
| title | Expected annual minima from an idealized moving-average drought index |
| title_full | Expected annual minima from an idealized moving-average drought index |
| title_fullStr | Expected annual minima from an idealized moving-average drought index |
| title_full_unstemmed | Expected annual minima from an idealized moving-average drought index |
| title_short | Expected annual minima from an idealized moving-average drought index |
| title_sort | expected annual minima from an idealized moving average drought index |
| url | https://hess.copernicus.org/articles/29/719/2025/hess-29-719-2025.pdf |
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