Methods, calendars, and interpretation
We fit log(yield) = intercept + linear time trend + β × Niño 3.4 separately for every unit, crop, and season. The sensitivity is 100[exp(β) − 1]. Variance explained is 100[1 − SSE(linear ENSO model)/SSE(trend-only model)]. Both trend and climate terms are estimated jointly. We also fit a quadratic ENSO term and a hinge at zero with separate warm and cold slopes.
Validation holds out five consecutive calendar years and excludes the adjacent year on each side from training. We repeat validation with block boundaries anchored at 1980 and 1982. All models use identical held-out observations within a layout. Each fold requires 12 training observations and three observations on each side of neutral ENSO. We report skill only with at least 15 scored years and three folds. Gain is 100[1 − MSE(nonlinear)/MSE(linear)]; each gain map displays the smaller gain across the two layouts.
A nonlinear candidate requires the same nonlinear form to beat both the linear ENSO model and the trend-only model under both validation layouts. A further trend check repeats the 1980 layout with a quadratic time trend. Candidate labels describe this screening rule. We calculate no uncertainty intervals, p-values, or multiplicity adjustments. Searching many units and two nonlinear forms can produce candidates by chance. These maps do not establish statistical significance or out-of-sample performance of a selected model.
We preserve the established climate windows for the earlier 21 panels. Processed rice forms and components inherit the corresponding paddy-rice window. Other seasonal windows follow season_calendar_asia_v0.2.csv, including its unresolved year assignments. Remaining annual records use January–December of the reported year, except Indian Whole Year records, for which we assume January–December of the following year. The window note above each map identifies these assumptions. Differences across countries can reflect crop calendars, yield denominators, available periods, and reporting practices as well as climate responses.
We retain every crop label, including processed forms and total/component series, as separate views. Their counts overlap and cannot be added as independent agricultural outcomes. Positive yields require complete production and the applicable planted/harvested area. Zero-yield observations are excluded by the logarithmic model. We normalize Vietnamese Summer Rice season labels to Autumn Rice. We correct East Java’s 2017 total-paddy yield using the previously verified BPS area of 2,285,232 ha and production of 13,060,464 tonnes; supplied files remain unchanged. Other source anomalies remain and are flagged when yields fall outside 0.05–30 t/ha; this flag is crop-dependent and does not imply an error.
Maps use the supplied stable administrative boundaries, projected separately for each country with a Lambert azimuthal equal-area projection. Boundaries are simplified by 800 m for display. Gray includes short or incomplete series and units without that crop. Color scales are fixed across selections; values outside the limits saturate. Hover text and tables retain the full estimates. Small countries and large countries have different map scales.