Two-Stage Zero Inflated Forecasting of Monthly Monsoon Rainfall: A Evaluation with Decision Focused Metrics

Abstract

Monthly rainfall in north-west India is strongly seasonal, right-skewed and, in the dry season, zero-heavy, and it is
usually evaluated by aggregate error measures that may hide failures in the months that matter for agriculture. This
study proposes a decision-focused evaluation protocol and applies it to a 124-year series of monthly rainfall for the
Haryana-Chandigarh-Delhi region (1,488 months, 1901-2024). A two-stage forecaster, which multiplies the probability
of a wet month (rainfall above 5 mm) from a gradient-boosted classifier by the expected amount in wet months from a
gradient-boosted regressor, is compared with nine benchmarks (persistence, seasonal naive, monthly climatology,
ridge regression, a Tweedie generalised linear model, a random forest, single-stage boosting with squared and Poisson
loss, and a two-stage linear model) in an expanding-window, one-month-ahead evaluation over 1926-2024 (1,188
forecasts) with annual re-estimation. Accuracy is assessed by MAE and RMSE on all, monsoon and wet months, by the
Brier skill score and calibration for occurrence, by drought-month recall, flood-month precision and onset detection,
and by stability across 25-year blocks, with Diebold-Mariano tests and a block bootstrap. The main finding is negative
and informative: no model beats the climatological benchmark. The two-stage boosted model has an MAE 7.3% above
climatology (bootstrap interval 1.031–1.110) and a Jun-Sept MSE skill of -0.152, and is statistically indistinguishable
from single-stage boosting (Diebold-Mariano p = 0.83 for absolute error). The best-calibrated probabilistic forecast
is climatology itself (Brier skill scores of all other forecasters are negative). Decision-focused metrics rank models
very similarly to aggregate metrics, drought recall (0.32-0.46 at a 20% alarm rate) and flood precision (0.15-0.25 at
a 15% alarm rate) differ among models by amounts well inside bootstrap uncertainty, and onset predictions do
no better than always predicting July. Monthly anomalies have almost no autocorrelation (0.035 at lag 1), and the
calendar month alone explains 63% of the variance; the remainder is not predictable from past rainfall alone. Skill
relative to climatology does not change systematically across 25-year blocks, and there is no significant trend in
monsoon rainfall (Kendall τ = -0.02, p = 0.74). The results show that the benefit of two-stage structure depends on
the presence of predictable occurrence and amount signals, which are absent in rainfall-history-only forecasting at
monthly resolution, and they provide a reproducible benchmark and protocol for evaluating richer predictors such as
sea-surface temperature or other states’ rainfall.