New Insights into Meteorological and Hydrological Drought Modeling: A Comparative Analysis of Parametric and Non-Parametric Distributions

Accurate drought monitoring depends on selecting an appropriate cumulative distribution function (CDF) to model the original data, resulting in the standardized drought indices. In the numerous research studies, while rigorous validation was not made by scrutinizing the model assumptions and uncertainties in identifying theoretical drought CDF models, such oversights lead to biased representations of drought evaluation and characteristics. This research compares the parametric theoretical and empirical CDFs for a comprehensive evaluation of standardized Drought Indices. Additionally, it examines the advantages, disadvantages, and limitations of both empirical and theoretical distribution functions in drought assessment. Three drought indices, Standardized Precipitation Index (SPI), Streamflow Drought Index (SDI), and Standardized Precipitation Evapotranspiration Index (SPEI), cover meteorological and hydrological droughts. The assessment spans diverse applications, covering different climates and regions: Durham, United Kingdom (SPEI, 1868–2021); Konya, Türkiye (SPI, 1964–2022); and Lüleburgaz, Türkiye (SDI, 1957–2015). The findings reveal that theoretical and empirical CDFs demonstrated notable discrepancies, particularly in long-term hydrological drought assessments, where underestimations reached up to 50%, posing risks of misinformed conclusions that may impact critical drought-related decisions and policymaking. Root Mean Squared Error (RMSE) for SPI3 between empirical and best-fitted CDF was 0.087, and between empirical and Gamma it was 0.152. For SDI, it ranged between 0.09 and 0.143. The Mean Absolute Error (MAE) for SPEI was approximately 0.05 for all timescales. Additionally, it concludes that empirical CDFs provide more reliable and conservative drought assessments and are free from the constraints of model assumptions. Both approaches gave approximately the same drought duration with different intensities regarding drought characteristics. Due to the complex process of drought events and different definitions of drought events, each drought event must be studied separately, considering its effects on different sectors.