Ellahi et al. (2025) A framework for spatiotemporal drought analysis using proposed multi-regional weighted aggregative SPI and Bayesian inference

Identification

• Journal: Theoretical and Applied Climatology
• Year: 2025
• Date: 2025-10-17
• Authors: Asad Ellahi, Shreefa O. Hilali, Jorge Alberto Achcar, Ijaz Hussain, Maysaa Elmahi Abd Elwahab, Abdulkareem M. Basheer
• DOI: 10.1007/s00704-025-05774-8

Research Groups

• Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
• Department of Community Medicine, Wah Medical College, National University of Medical Sciences, Rawalpindi, Pakistan
• Department of Mathematics, College of Sciences and Arts (Majardah), King Khalid University, Magardah, Saudi Arabia
• Medical School, University of São Paulo, Ribeirão Preto, São Paulo, Brazil
• Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
• Faculty of Administrative Sciences, Albaydha University, Albaydha, Yemen

Short Summary

This study develops a novel framework for spatiotemporal drought analysis using a proposed multi-regional weighted aggregative standardized precipitation index (MRWASPI) and Bayesian inference, demonstrating its effectiveness in providing insights into drought severity and patterns for homogeneous regions.

Objective

• To develop and validate an efficient and practical framework for spatiotemporal drought analysis in homogeneous regions, utilizing a novel multi-regional weighted aggregative standardized precipitation index (MRWASPI) integrated with Bayesian inference and change-point modeling.

Study Configuration

• Spatial Scale: 132 districts of Pakistan, covering diverse climatic zones (arid, semi-arid, monsoon regions).
• Temporal Scale: Monthly precipitation data over 41 years, from January 1981 to December 2021 (492 months).

Methodology and Data

• Models used:
  • Hierarchical clustering (K-Means) with Canberra distance and SDbw index for optimal cluster identification.
  • Multi-regional weighted aggregation scheme for precipitation data.
  • Multi-regional weighted aggregative standardized precipitation index (MRWASPI) calculation using a 12-Component Gaussian Mixture Distribution (12-CGMD).
  • Non-Homogeneous Poisson Processes (NHPP), specifically Power Law Process (PLP) and Goel–Okumoto Process (GOP), both with and without change points (PLP-CP, GOP-CP), for drought event analysis.
  • Bayesian inference with Markov Chain Monte Carlo (MCMC) method under Gibbs sampling for parameter estimation.
  • Deviance Information Criteria (DIC) for model discrimination.
• Data sources: Monthly average precipitation data for 132 districts of Pakistan, obtained from the NASA POWER platform (https://power.larc.nasa.gov/data-access-viewer/).

Main Results

• Nine optimal homogeneous clusters were identified for the 132 districts of Pakistan based on the lowest SDbw index value of 0.310.
• The weighted aggregation scheme successfully generated representative precipitation vectors for each cluster, with descriptive statistics of weights provided (e.g., Cluster 1: minimum weight 0.00, maximum weight 0.0909, mean 0.0833, standard deviation 0.0185).
• The 12-Component Gaussian Mixture Distribution (12-CGMD) effectively standardized aggregated precipitation data for MRWASPI calculation, indicated by low Bayesian Information Criteria (BIC) values (e.g., Cluster 3: -4925.97, Cluster 2: -1489.999).
• Analysis of accumulated drought events using Non-Homogeneous Poisson Processes (NHPP) revealed that the Power Law Process with Change Point (PLP-CP) was the best-fitting model for all 9 clusters, based on the lowest DIC values (e.g., Cluster 1: DIC = 2067).
• Significant change points in drought occurrence patterns were identified for each cluster, with specific months and years determined (e.g., Cluster 1: January 2005; Cluster 2: February 1986; Cluster 3: December 2001).
• Bayesian inference with MCMC provided precise parameter estimations for NHPP models, indicated by small Monte Carlo (MC) errors.

Contributions

• Proposes a novel, integrated framework for spatiotemporal drought analysis combining hierarchical clustering, a multi-regional weighted aggregation scheme, a new drought index (MRWASPI) using K-CGMD, and Bayesian inference with NHPP and change-point modeling.
• Enhances precision and regional adaptability in drought assessment by capturing regional heterogeneity and providing probabilistic insights into drought occurrence and temporal dynamics, surpassing existing methodologies.
• Introduces the Multi-Regional Weighted Aggregative Standardized Precipitation Index (MRWASPI) to mitigate the impact of extreme values and outliers in aggregated precipitation data.
• Addresses the limitation of univariate models in capturing multimodal precipitation distributions by employing K-CGMD for standardization.
• Utilizes NHPP with change-point detection and Bayesian inference to robustly model variable drought event frequencies and identify temporal shifts, providing crucial information for early mitigation policies.
• Establishes a robust basis for capturing multi-regional precipitation trends and ensuring precipitation pattern homogeneity within groups, independent of geographical proximity.

Funding

• Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2025R913), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
• Large Research Project under grant number RGP. 2/81/46, Deanship of Research and Graduate Studies at King Khalid University.

Citation

@article{Ellahi2025framework,
  author = {Ellahi, Asad and Hilali, Shreefa O. and Achcar, Jorge Alberto and Hussain, Ijaz and Elwahab, Maysaa Elmahi Abd and Basheer, Abdulkareem M.},
  title = {A framework for spatiotemporal drought analysis using proposed multi-regional weighted aggregative SPI and Bayesian inference},
  journal = {Theoretical and Applied Climatology},
  year = {2025},
  doi = {10.1007/s00704-025-05774-8},
  url = {https://doi.org/10.1007/s00704-025-05774-8}
}