New rainfall index captures how many days deliver heavy rain

Two years can rack up almost exactly the same total rainfall and still tell completely different stories about how wet the year actually felt. One year may dump its water in a handful of violent downpours; another may spread the same accumulation across dozens of steady, soaking days. A new open-access study in Discover Atmosphere, published on 8 September 2026, introduces a single number designed to capture that difference, and it does so without asking the analyst to choose any threshold at all.

The metric is called the Rainfall Magnitude–Rank Index, or RMRI, and its definition is disarmingly simple. For a given calendar year, sort all daily precipitation values from largest to smallest. RMRI is the largest integer k such that the kth-largest daily rainfall value is at least k millimeters. In other words, at least k days in that year recorded rainfall of k millimeters or more. If the 26th-ranked day brought at least 26 millimeters but the 27th-ranked day fell short of 27 millimeters, the year’s RMRI is 26. If no day records at least 1 millimeter, the index is 0.

Lead author Ren Zhang points out that the construction has a clean geometric interpretation. When the ranked daily rainfall curve is plotted against rank, it declines monotonically, and the identity line, where rainfall equals rank, cuts through it. The intersection occurs at a point (k, k) where the rainfall magnitude and the number of days sharing at least that magnitude are equal. Graphically, this point defines the largest square that can be inscribed beneath the ranked rainfall curve. In a worked example using New Orleans data from 2013, the intersection fell at k = 26, meaning 26 days that year recorded at least 26 millimeters of rain. The authors note that the formulation is conceptually analogous to the h-index used to rank scientific output, and that the same magnitude–rank framework was recently applied to daily PM2.5 concentrations in United States metropolitan areas.

To see how the index behaves in the real world, the study drew daily precipitation records from the NOAA Global Historical Climatology Network–Daily database. Twelve long-term stations were selected to span a deliberately wide range of climates: Phoenix in a desert setting, Albuquerque in a semi-arid high-altitude environment, Tunis with a Mediterranean regime, marine west coast Seattle, continental Minneapolis, high-latitude and cold Enontekio, humid subtropical Miami, continental monsoon Shenyang, tropical monsoon Darwin, and the wet-tropical stations Hilo, Vacoas, and Cayenne. Together they span six continents. The analysis covered calendar years 1994 through 2023, with 1991–2020 data used only to define station-specific reference thresholds for one comparison index.

Quality control was strict. Values coded as missing or carrying a nonblank quality flag were treated as unavailable, trace precipitation was counted as zero, and no missing observations were imputed. A station-year was retained only when at least 95 percent of expected daily observations were valid, which corresponds to at least 347 valid days in an ordinary year and 348 in a leap year. Applying that criterion yielded 329 complete station-years, with individual stations contributing between 18 and 30 years of data. A sensitivity analysis using a stricter 98 percent completeness requirement, retaining 310 station-years, produced essentially unchanged results.

Across the pooled 329 station-years, RMRI correlated strongly with conventional measures of annual precipitation. The strongest Spearman correlations were with the annual precipitation total, the annual count of days with at least 10 millimeters, and the annual count of days with at least 20 millimeters, each at ρ = 0.98. The index also correlated positively with precipitation accumulated on very wet days above the station-specific 1991–2020 wet-day 95th percentile (ρ = 0.89), the Simple Daily Intensity Index (ρ = 0.87), the annual maximum 1-day precipitation (ρ = 0.86), and the annual number of wet days (ρ = 0.81). It was weakly inversely correlated with the Precipitation Concentration Index, which describes how concentrated annual precipitation is among months, at ρ = −0.24.

Because pooled correlations mix differences between wetter and drier stations with year-to-year variation within stations, the authors also calculated station-centered correlations, subtracting each station’s mean from each index before pooling. Most associations were attenuated, indicating that part of the pooled correlation structure reflected persistent differences between stations. Even so, RMRI remained strongly associated with the count of days at or above 20 millimeters (ρ = 0.80) and the annual total (ρ = 0.78), retained substantial associations with the 10-millimeter day count (ρ = 0.70) and the Simple Daily Intensity Index (ρ = 0.69), showed a moderate association with very-wet-day precipitation (ρ = 0.53), and weaker associations with wet-day count (ρ = 0.34) and maximum 1-day precipitation (ρ = 0.32). The station-centered correlation with the Precipitation Concentration Index was negligible at ρ = 0.01. The authors interpret this pattern as showing that RMRI primarily reflects the combined occurrence and magnitude of moderate-to-heavy rainfall rather than being determined by a single extreme event, the total number of wet days, or seasonal concentration.

The index’s real selling point emerges when years with nearly identical totals are compared. Hilo in 2012 and Miami in 2020 provide an illustrative case: their annual totals were 2310.6 and 2199.9 millimeters respectively, yet Hilo’s ranked curve intersected the identity line at rank 19 while Miami’s stayed above it through rank 27, yielding RMRI values of 19 and 27. Miami had a higher RMRI despite a slightly lower total, indicating that its accumulation was distributed across daily magnitudes differently. Examined systematically, among 129 same-station year pairs whose annual totals differed by no more than 1 percent, the median absolute RMRI difference was 1, with an interquartile range of 1 to 2; 18.6 percent of these pairs differed by at least 3 RMRI units, 2.3 percent by at least 5 units, and the maximum difference was 6. Similar distributions appeared at the broader 2 percent and 5 percent tolerances, which included 271 and 646 pairs respectively, with the median difference remaining 1 at both thresholds. The authors conclude that RMRI is closely related to annual precipitation total but not interchangeable with it.

Geographically, annual RMRI distributions differed markedly among the twelve stations. The lowest values occurred primarily at the arid and semi-arid stations, Phoenix and Albuquerque, while the highest appeared at the wet-tropical and monsoonal stations, particularly Cayenne, Hilo, and Darwin, with Miami and Vacoas also relatively high and Seattle, Minneapolis, Shenyang, Tunis, and Enontekio generally in lower-to-intermediate ranges. Within-station variation was also evident, with several stations showing appreciable year-to-year shifts and partial overlap among stations from different climate regimes. The authors caution that RMRI should not be read as a categorical classifier of climate regime; it summarizes the realized annual distribution of daily precipitation magnitudes at a given location and year, and evaluation in larger station networks will be needed to establish wider generalizability.

The study also spells out clear limitations. RMRI is an annual summary of ranked daily precipitation and does not capture seasonality, event sequencing, clustering, or temporal autocorrelation, so years with identical daily distributions but different temporal ordering receive the same score. It does not distinguish among storm types, it is scale dependent, varying with the precipitation unit and temporal resolution, and it does not represent sub-daily dynamics. The twelve-station sample is not globally representative. The authors propose that future work evaluate seasonal and sub-daily formulations, larger station networks, and the index’s hydrological relevance for runoff and flooding. As it stands, RMRI offers forecasters, hydrologists, and climatologists a threshold-free, interpretable companion to established indices: a single number that answers, for any year, the deceptively simple question of how many days delivered rain heavy enough to match their own rank.

Subject of Research: A new annual rainfall metric, the Rainfall Magnitude–Rank Index, that integrates daily precipitation magnitude and frequency without requiring thresholds

Article Title: An annual rainfall metric integrates daily magnitude and frequency

Article References: Zhang, R. (2026). An annual rainfall metric integrates daily magnitude and frequency. Discover Atmosphere, 4(1), Article 23. https://doi.org/10.1007/s44292-026-00091-9

Image Credits: AI Generated

DOI: 10.1007/s44292-026-00091-9

Keywords: RMRI, rainfall, precipitation, climatology, hydrology, GHCN-Daily, extreme precipitation, h-index analogy, annual precipitation indices, daily rainfall, Spearman correlation, climate metrics