Extreme Daily Rainfall at Parvathipuram, Andhra Pradesh, 1901–2025: GEV Return Levels with Profile-Likelihood Intervals, an L-Moment Derivation, Trend Tests, and an All-India Field-Significance Test on IMD Gridded Data

Drainage structures on Indian roads are sized for a flood of specified frequency; IRC:SP:13-2004 uses once in 50 years. I estimate the 1-day and 3-day annual-maximum rainfall at the India Meteorological Department (IMD) 0.25° grid cell nearest Parvathipuram (18.75° N, 83.50° E) from the IMD gridded daily series for 1901–2025 (125 years). A generalised extreme value (GEV) distribution fitted by maximum likelihood has shape ξ = 0.191 (s.e. 0.083), a heavy upper tail, and the Gumbel special case is rejected (likelihood-ratio p = 0.009). The 50-year 1-day rainfall is 187.7 mm, with a profile-likelihood 95% interval of [156.5, 253.3] mm; the Gumbel fit gives 158.8 mm, 15% lower. The 50-year 3-day total is 292.0 mm [249.1, 378.6]. I derive the L-skewness of the GEV in closed form and check it by simulation, and a Monte Carlo study shows 93.3% coverage of the nominal 95% profile interval at this sample size. There is no significant trend at the cell (Mann–Kendall p = 0.11; non-stationary GEV p = 0.21). Across India, 25.8% of 4,801 grid cells show a significant increasing trend in 1-day maxima against 2.5% expected by chance; a year-permutation test that preserves spatial dependence rejects the global null (p < 0.005). The last five years at the Parvathipuram cell are all below 62 mm, an event with probability 0.0008 under the fitted model, while annual totals and neighbouring cells are normal; this points to a possible change in the gridding inputs and is reported as an unresolved data issue. The data support using a GEV, not a Gumbel, design value near 190 mm for the 50-year 1-day rainfall at this location, with wide uncertainty.