Finite-sample Truncation in Empirical Multivariate Drought Indices Leads to Systematic Underestimation of Extreme Compound Droughts

Compound drought assessment requires indices that distinguish concurrent meteorological, agricultural, and hydrological deficits. Empirical multivariate drought indices such as TSDI commonly estimate joint probabilities using calendar-month rank-based plotting positions to preserve seasonality, but this reduces effective sample size and can truncate extreme severity. This study derives the Gringorten lower-bound expression, tests finite-sample effects through trivariate Monte Carlo experiments for 20–50-year records and evaluates the truncation mechanisms using observed drought records from the Seyhan and Çoruh River basins in Türkiye. In the 40-year baseline experiment, the empirical lower bound was approximately −2.20. For analytical severity below −2.0, TSDI bias was 0.403, whereas KMDI reduced bias to 0.048 and lowered RMSE by 73.6%; RMSE reductions remained 73–76% across tested record lengths. Basin results confirmed that TSDI reached the theoretical floor, while KMDI resolved lower-tail values below it. Finite-sample resolution should therefore be explicitly considered in compound drought-risk assessment.