Methods & Derivation · v1.0

How the likelihood ratio was derived

Everything required to reproduce, check, or contest the engine behind the ENSO Risk Translator. Sources are primary and openly available. This page is public and intended to be citable.

1 · Design

Question	By how much does an El Niño state during the Indian summer monsoon change the odds of an all-India drought?
Design	Retrospective cohort of monsoon seasons; exposure and outcome both classified independently of one another.
Window	1950–2015. n = 66 monsoon seasons. Chosen because NOAA CPC ONI classification is authoritative from 1950; pre-1950 values carry materially greater uncertainty.
Exposure	Monsoon-season ONI, defined as mean(JJA, JAS) from the NOAA CPC ERSSTv5 series. El Niño ≥ +0.5 °C; La Niña ≤ −0.5 °C; neutral otherwise.
Outcome	All-India JJAS rainfall below −10% of the long-term mean — the India Meteorological Department drought threshold. Census taken from Borah et al., Table S1 (IITM homogeneous series).
Reference group	ENSO-neutral seasons. La Niña seasons are reported separately rather than pooled into the reference.
Statistics	Wilson score intervals for proportions; Woolf logit intervals for the odds ratio with Haldane–Anscombe correction where a cell is zero; Fisher exact test.

2 · Result

Monsoon-season state	Seasons	Droughts	Rate	95% CI (Wilson)	LR vs neutral
La Niña (ONI ≤ −0.5)	15	0	0.0%	0.0 – 20.4%	0.15 [0.01–2.77]
Neutral — reference	35	6	17.1%	8.1 – 32.7%	1.00
El Niño (ONI ≥ +0.5)	16	10	62.5%	38.6 – 81.5%	8.06 [2.11–30.78]
All seasons	66	16	24.2%	—	—

Fisher exact p = 0.0026 · RR 3.65 · ARI +45.4 pp · NNE 2.2 · AF_e 72.6% · PAF 39.1%

External corroboration

The India Meteorological Department, briefing on the 2023 seasonal outlook, reported 15 El Niño years between 1951 and 2022 of which six saw normal-to-above-normal rainfall — implying a below-normal rate near 60%. The derivation here, on a different outcome definition and a different window, gives 62.5%. Independent method, convergent result.

3 · Falsification recorded

Deleted from the tool: the El Niño intensity ladder

Version 1.0 of the Risk Translator graded the likelihood ratio by event intensity (weak 1.8, moderate 2.6, strong 3.2), on the assumption that stronger El Niños carry higher drought risk. The census refutes it.

weak (0.5–0.99) 6/9 = 66.7% · moderate (1.0–1.49) 2/4 = 50.0% · strong (≥1.5) 2/3 = 66.7%

Non-monotonic, with every subgroup interval overlapping every other. This reproduces the finding of Kumar et al. (2006) that stronger El Niños were not necessarily associated with a weaker monsoon.

The control was deleted rather than retained with a caveat. A graded input the evidence cannot support is an invitation to over-read, and the caveat never travels with the screenshot.

The two strongest events in the record make the point unaided: 1997 (ONI +1.75) — no drought. 2015 (ONI +1.74) — drought.

4 · Sensitivity to exposure definition

The definition was varied across five reasonable specifications. Every one yields a lower confidence bound above 1.

Definition	n El Niño	Drought \| El Niño	Drought \| neutral	RR	LR	95% CI
JJA only ≥ +0.5	14	57.1%	19.4%	2.94	5.52	1.44 – 21.14
mean(JJA, JAS) ≥ +0.5 — primary	16	62.5%	17.1%	3.65	8.06	2.11 – 30.78
JAS only ≥ +0.5	16	62.5%	17.6%	3.54	7.78	2.03 – 29.77
mean ≥ +0.7	11	63.6%	17.1%	3.71	8.46	1.87 – 38.31
mean ≥ +1.0	7	57.1%	17.1%	3.33	6.44	1.14 – 36.57

Stability checks

Check	Result	Reading
Leave-one-year-out	LR 7.25 – 9.67	No single season drives the estimate.
Era split 1950–1982	LR 5.42 [0.88–33.36]	Same direction; underpowered in isolation.
Era split 1983–2015	LR 13.33 [1.71–103.76]	Same direction, larger; intervals overlap, so no claim of temporal change.

5 · Limitations

Stated in full, and to be quoted alongside any citation of the result.

Mixed sources. Exposure from NOAA CPC ERSSTv5; outcome from the IITM homogeneous rainfall series. This is standard practice in the literature but is not a single-source analysis, and small classification differences between datasets are possible.
Small n. Sixteen exposed seasons. Every subgroup analysis is underpowered — which is precisely why intensity tiers were removed rather than reported with wide intervals.
All-India only. Regional teleconnection strength varies substantially; the 1997 season was near-normal nationally while several central and southern subdivisions were deficient throughout. A district-level user should substitute a local baseline and ideally re-derive on a local census.
The La Niña estimate is fragile. Zero droughts in fifteen seasons is a real and striking observation, but the interval rests on a continuity correction. Read it as “strongly protective, magnitude uncertain.”
Modifiers are not derived. The Indian Ocean Dipole, North Atlantic SST, Pacific flavour and snow-cover adjustments available in the tool have literature-supported directions and illustrative magnitudes. They are disabled by default; output computed with them enabled is flagged and should not be cited.
Index continuity. The Oceanic Niño Index was superseded by the Relative Oceanic Niño Index for official CPC monitoring in February 2026. The historical derivation is unaffected, but any live-data implementation should track RONI.

6 · Sources

Role	Source
Exposure series	NOAA Climate Prediction Center, Oceanic Niño Index (ERSSTv5), oni.ascii.txt
Drought census	Borah, Rai, Krishnan et al., Role of the North Atlantic in Indian monsoon droughts — Table S1
Flavour dependence	Kumar, Rajagopalan, Hoerling, Bates & Cane (2006), Science — central-Pacific warming and Indian drought
IOD modulation	Ashok, Guan & Yamagata (2001, 2004) — complementary IOD–ENSO influence on Indian monsoon rainfall
1997 season	IMD and IITM season summaries — all-India rainfall 102% of long period average
2002 season	IMD end-of-season report — 19% below normal; July 49% deficient, worst in recorded observational history

Citation

Sundaravelan, D. C. (2026). Deriving a likelihood ratio for El Niño and all-India monsoon drought, 1950–2015: methods for the ENSO Risk Translator v2.0. VELANS Climate Risk Intelligence. https://climate.velansai.in/methods.html

Changelog

v2.0 — 2026-08 · Engine rebuilt on the derived likelihood ratio. Intensity ladder removed following falsification. Confidence intervals propagated to posterior risk. Modifier panel separated, disabled by default, and flagged as illustrative. Third verdict state added for estimates whose interval straddles the action threshold.

v1.0 — 2026-08 · Initial release with illustrative likelihood ratios throughout, including an intensity-graded El Niño term subsequently shown to be unsupported.