Assessment of Meteorological Drought by Temporal Modeling and Innovative Trend Analysis

We present a mathematically rigorous, unified framework for drought assessment and trend diagnostics that (i) evaluates three classical indices SPI, SPEI, and SPTI separately to capture multiple perspectives of drought conditions; (ii) furnishes complete treatment of zero-inflation, multi-month aggregation, and serial dependence; (iii) formalizes Crossing Empirical Trend Analysis (CETA) as a quantile-trend crossing procedure with exact definitions, consistent estimators, and a wild-block bootstrap for valid inference under heteroskedastic AR dependence; (iv) quantifies drought persistence using discrete-state Markov chains with closed-form run-length, recurrence, and stationary properties; and (v) addresses field significance across station networks via false discovery rate (FDR) and Monte Carlo size control under spatial correlation. All derivations are provided in self-contained form. The methodology is designed for a network of 32 stations in Punjab, Pakistan, with monthly data (1981–2021) retrieved from NASA POWER; the study area, climatological context, and figure-based exploratory summaries follow the original manuscript.