Prognosticative De-Volatility Modeling for Empirically Quantifying CESM and ECMWF Space-Time Heterogeneity of Drought Indices Across Colorado and Louisiana Regions of the USA

Although drought indices can be evaluated employing linear and non-linear algorithms, most contributions in the literature have not adequately quantified geospatial-temporal volatility, leading to Type II errors. This study addresses these gaps by comparing ten drought indices across the Colorado and Louisiana regions of the United States over 75 years, examining non-linear and spatio-temporal patterns to ensure a robust assessment of drought. High-resolution European Centre for Medium-Range Weather Forecasts (ECMWF) gridded monthly total precipitation data for 75 years (1950-2024) were used to evaluate the drought indices. The spatial clustering of precipitation patterns was quantified using the second-order semi-parametric eigen-decomposition geospatial autocorrelation to geolocate hot and cold spots of precipitation. We employed the Autoregressive Integrated Moving Average (ARIMA) model, coupled with the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model, and compared five ARIMA-GARCH variants across nine error distributions to address non-asymptotic conditional volatility and temporal persistence in precipitation. Drought indices were examined across five temporal scales and contrasted with simulated parameters derived from the Community Earth System Model (CESM). The temporal lag relationship between meteorological and agricultural droughts was evaluated using the non-parametric Time-Varying Distance Cross-Correlation Function (TV-DCCF). The findings revealed that the ARIMA-eGARCH(1,1) model with a Student’s t distribution precisely detected the non-asymptotic conditional volatility in the precipitation time series. The Standardized Precipitation Index (SPI), China Z Index (CZI), and Z-Score Index (ZSI) were the most applicable indices for drought monitoring in both regions. TV-DCCF revealed that meteorological droughts significantly influenced agricultural droughts, with a lag of up to four months. CESM-derived drought indices were mainly within the ERA5-Land uncertainty range, except for CZI and aSPI, attributable to CESM’s lower spatial resolution and limited sensitivity to localized extreme events.

Keywords: Standardized Precipitation Index (SPI); Global Moran’s Index; Autoregressive Moving Integrated Average (ARIMA); Generalized Autoregressive Conditional Heteroscedastic Model (GARCH); ERA5-Land; Community Earth System Model (CESM).