How we tracked returning rain

Edition dated 4 September 2026. Back to the analysis · Română

The calculator follows precipitation recorded at Romanian stations. For a chosen station, time of year and preceding spell length, it shows how many episodes were followed by at least one day above a rainfall threshold. The records cover 1961–2025. These are historical frequencies; present conditions require a weather forecast.

What “a dry month” means here

The opening example uses Constanța and 30 consecutive days with at most 5 mm of precipitation per day. Day 30 must fall in June, July or August. Lighter rain may occur throughout those 30 days; the definition allows rainfall up to and including the threshold.

Across the 64 Constanța episodes, total precipitation during the 30 preceding days ranges from 0 to 25.3 mm, with a median of 4.6 mm. Only one episode records no precipitation at all. The history table includes each episode's total, showing how much water fell during the interval called “dry”.

This definition makes a frequency calculable from daily observations. Assessing meteorological drought requires a precipitation deficit relative to the local climate over a specified period. Agricultural drought requires information about soil water and crop needs. The calculator does not estimate these indicators, and its station map does not outline drought-affected regions. See the WMO/GWP handbook of drought indicators, chapters 1 and 7.

The Constanța archive supplies 64 eligible episodes across 51 years. At least one day above 5 mm followed within a week in 12 episodes, or 18.75%, and within two weeks in 28 episodes, or 43.75%. Every deadline follows the same 64 episodes.

From an observation to an episode

We use daily PRCP precipitation from NOAA GHCN-Daily, version 3.34, snapshot 3.34-upd-2026090318, downloaded on 4 September 2026. The 30 stations come from NOAA's Romanian inventory. Accepted observations mostly originate in ECA&D; NOAA's inventory does not cover the entire Romanian meteorological archive.

The archive records precipitation in tenths of a millimetre. We exclude missing or negative values, values with quality-control flags and values flagged “missing presumed zero”. After a day without an accepted observation, spell length remains unknown until the next observed day above the threshold. Missing observations never become dry days.

Counting starts after an observed day above the threshold. At a duration of 30 days, each episode enters once, on its 30th consecutive day with at most 5 mm. The calculator also offers other durations and thresholds. Duration zero identifies the day above the threshold itself, so the daily curve's zero point has a different starting condition from points following days with at most 5 mm.

The assessment day is excluded from the following window. Every episode requires accepted observations for all 28 subsequent days, even when displaying only the next-day result. This rule preserves one denominator for the 1-, 7-, 14- and 28-day deadlines. It can exclude an episode with early rain if a later day in that window lacks an accepted observation.

Summer, the warm season and historical periods

“Summer” covers June–August. The “warm season” covers April–September and the “cold season” October–March. An all-months option is also available. Season selection refers to the assessment day's month. An episode assessed in late August may have following days in September; its preceding 30 days may begin in May.

Historical periods are 1961–2025, 1961–1990 and 1991–2025. The entire required history and all 28 subsequent days must fall within the selected period. Counting continues across 31 December when both sides remain inside that period and no observations are missing.

The history on the main page lists precisely the 64 episodes used in the Constanța example. Each entry identifies the assessment date and the first subsequent day above 5 mm, if it falls within the next 28 days. If no day exceeds the threshold within that window, the archive entry leaves the later return of rain unspecified.

Which stations and estimates appear

A station is eligible within a period if it has accepted observations for at least 90% of days and at least 25 years with 90% coverage. For 1961–2025, 23 of the 30 stations qualify, supplying 544,103 valid station-days. Four stations have large gaps in the recent period, and three series mainly derived from synoptic observations have insufficient coverage. The map locates stations; their percentages are not weighted to estimate a national average.

A numerical estimate requires at least 30 episodes and 10 years containing episodes. Below either threshold, the calculator reports insufficient data. For example, Băneasa has only 28 episodes that reach 30 consecutive days with at most 5 mm and are assessed in summer. The display rule suppresses a percentage for that selection. Passing the rule does not guarantee precision for rare episodes.

Calculation and uncertainty

Frequency is k / n, where n is the number of eligible episodes and k counts those followed by at least one day above the threshold within the chosen window. The Constanța opening example gives 12 / 64 = 18.75% within seven days. Its approximate 95% interval is 10.5%–27.8%.

We estimate intervals through 1,000 resampling draws of whole calendar years, using shared weights for every duration and reference within a period. The limits are the 2.5th and 97.5th percentiles. For reproduction, the random seed is 20260904 plus the number of years in the selected period.

Resampling preserves dependence within each year, including overlapping outcome windows. The intervals are pointwise and conditional on accepted observations. They exclude measurement error, some dependence between years and uncertainty across all the exploratory comparisons taken together. If every episode has the same outcome, we show the frequency and explain that this resampling cannot assess its uncertainty.

Why the following window matters

In a hypothetical example with a constant 10% daily probability and independent days, the probability of at least one rainy day within w days is 1 − (1 − 0.10)^w. It reaches about 52% within a week and 77% within two weeks, while daily probability stays unchanged. This is a mathematical identity, not a model fitted to the weather observations.

A cumulative frequency that rises with the allowed window therefore cannot by itself establish that daily rain probability increased after a long spell with little rain. The calculator shows the next-day curve separately.

Two calendar comparisons

Rainfall varies between months and years. The calculator supplies two descriptive references, weighted to the months of the selected episodes:

• Frequency after days in the same calendar months across the selected period.
• Frequency after days in the same months and years as the selected episodes.

The references also require 28 complete subsequent days. They may include an episode's own assessment day and outcomes that overlap in time. The displayed difference is the observed frequency minus the reference, calculated before rounding.

At Constanța, the seven-day frequency of 18.75% compares with 31.46% for the same months, but 14.27% for the same months and years. The differences are −12.71 and +4.48 percentage points respectively. Choosing a reference changes the question; these comparisons do not isolate a causal effect of waiting or ritual.

The connection to research on prayer

Radu Umbreș's post prompted the project. Praying for Rain, by Espín-Sánchez, Gil-Guirado and Ryan, proposes a mechanism through which prayer timing and the properties of rainfall may help sustain belief in rituals.

The article compares cultural groups, fits a flexible model of daily rain probability and classifies its slope at the local 99th percentile of intervals between days above the threshold. The 44% and 30% figures in supplement Table D11 are raw frequencies of documented rain rituals in the two categories. Their unit differs from the weather episodes in this calculator.

This analysis calculates empirical frequencies and keeps next-day probability separate from cumulative probability over a week or longer. The daily comparison between durations of 7 and 30 days does not reproduce classification at the 99th percentile. The data contain no systematic registry of prayers, locations and event dates. Ritual effects in Romania remain outside this estimate.

Sources, verification and remaining limits

The series have not undergone additional homogenisation. Instrument histories, observation times and station moves were not checked. Missing observations may be selective, and a station can draw on several data sources over time. NOAA's S flag calls for additional caution with precipitation; the source ledger records the checks performed.

At Constanța, the 30 days in June 2024 carry flag S. Treating them as missing before counting episodes gives a seven-day frequency of 11/62 = 17.74%, compared with 12/64 = 18.75% in the primary calculation. This sensitivity uses the same method; it does not establish instrument homogeneity.

We also inspected the public RoCliHom file on Zenodo. The checked file has columns id,year,month,variable,value,flag, no day field, and 921,024 rows, exactly 156 × 123 × 12 × 4. It distributes monthly values, although the research description mentions daily source observations. This file cannot reconstruct daily spells and was excluded. That conclusion concerns the inspected file; it does not establish the absence of other Romanian daily records.

The source ledger preserves the limits of each claim. The review dossier distinguishes numerical verification from synthetic review by AI agents. No scientist or cited author has reviewed or endorsed the project. The reproduction package contains the observations and calculations; the instructions explain how to rerun them. A separate protocol for future research describes the ritual evidence that would need to be collected.