An annual rainfall metric integrates daily magnitude and frequency

Characterizing annual precipitation requires consideration of both daily magnitude and frequency. We introduce the Rainfall Magnitude–Rank Index (RMRI), a simple annual metric that requires no user-selected threshold or tuning parameter. RMRI is the largest integer k such that at least k days in a year record precipitation of at least k mm. For example, an RMRI of 26 indicates that at least 26 days recorded rainfall of 26 mm or more during that year. We evaluated RMRI in 329 quality-controlled station-years from 12 GHCN-Daily stations spanning contrasting hydroclimatic regimes. RMRI varied substantially across stations and years and was closely associated with annual precipitation amount and the frequency of moderate-to-heavy rainfall days. However, it was not interchangeable with annual total: among 129 same-station year pairs whose totals differed by no more than 1%, 18.6% differed by at least 3 RMRI units, with a maximum difference of 6. RMRI provides a concise, interpretable summary of annual daily precipitation magnitude–rank structure that complements established precipitation indices.

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Publication Details

Journal
Discover Atmosphere
Published
2026-09-08
DOI
https://doi.org/10.1007/s44292-026-00091-9
Primary Topic
Hydrology and Drought Analysis
Type
article
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article

An annual rainfall metric integrates daily magnitude and frequency

Ren Zhang
Discover Atmosphere
Hydrology and Drought Analysis
article

An annual rainfall metric integrates daily magnitude and frequency

Ren Zhang
article en

Abstract

Characterizing annual precipitation requires consideration of both daily magnitude and frequency. We introduce the Rainfall Magnitude–Rank Index (RMRI), a simple annual metric that requires no user-selected threshold or tuning parameter. RMRI is the largest integer k such that at least k days in a year record precipitation of at least k mm. For example, an RMRI of 26 indicates that at least 26 days recorded rainfall of 26 mm or more during that year. We evaluated RMRI in 329 quality-controlled station-years from 12 GHCN-Daily stations spanning contrasting hydroclimatic regimes. RMRI varied substantially across stations and years and was closely associated with annual precipitation amount and the frequency of moderate-to-heavy rainfall days. However, it was not interchangeable with annual total: among 129 same-station year pairs whose totals differed by no more than 1%, 18.6% differed by at least 3 RMRI units, with a maximum difference of 6. RMRI provides a concise, interpretable summary of annual daily precipitation magnitude–rank structure that complements established precipitation indices.

Discover AtmosphereVol. 4(1)
Wayne State University (US)
Climate action
Openalex Percentile: Top 13%
Hydrology and Drought Analysis
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An annual rainfall metric integrates daily magnitude and frequency — Ren Zhang · Discover Atmosphere (2026) | TGRS Research Map | TGRS