A Winter Duration Index (WDI) for Dhaka: Constructing, Validating, and Forecasting a Dated Measure of Winter Length from a Single ERA5 Grid Cell, 1990–2050

Abstract Bangladesh's winter is among the fastest-warming seasons, but existing research measures how cold it gets, not how long it lasts. This study builds a dated Winter Duration Index (WDI) for Dhaka, which, to the author's knowledge, is the first such measure for Bangladesh: an onset date, withdrawal date, and duration in days each year, from a smoothed daily-mean climatology and a fixed percentile threshold. Using 320,688 hourly ERA5 observations (1990–2026) at the grid cell nearest Dhaka, the climatology was smoothed with a three-harmonic fit, threshold set at the 25th percentile (22.55°C). Across 36 winters (1990–2025), mean duration was 89.6 days (SD = 9.8, range 73–114), with mean onset on 23 November and mean withdrawal on 21 February. Because the threshold is a fixed percentile, the mean duration largely reflects that choice; interannual variability and trend are the informative quantities. WDI was not significantly correlated with the same-series ETCCDI Cold Spell Duration Index (r = 0.18, p = 0.293; ρ = 0.19, p = 0.267), so this comparison provides no positive evidence of convergent validity. A Hamed–Rao Modified Mann-Kendall test found no significant trend in onset, withdrawal, or duration (all p > 0.5); with only 36 winters the test has low power and cannot exclude a modest trend. ARIMA(0,1,1) had a lower test-set RMSE than an ETS benchmark (6.66 vs. 8.53 days; seven test winters), but the difference was not statistically significant (Diebold–Mariano p = 0.126). Refit on the full series, the forecast stays flat near 89 days through 2050; this is a statistical extrapolation of a trendless series, not a climate projection. The WDI is offered as a baseline that complements Bangladesh's severity-focused literature; it is a single-grid-cell, reanalysis-based result that has not yet been validated against station records.