Din et al. (2026) Bayesian geostatistical insights into seasonal variability and spatiotemporal structure of precipitation

Identification

• Journal: Acta Geophysica
• Year: 2026
• Date: 2026-01-04
• Authors: Fazal Din, Mohammed M. A. Almazah, Rizwan Niaz, Hefa Cheng, Fathia Moh. Al Samman, Shreefa O. Hilali
• DOI: 10.1007/s11600-025-01728-w

Research Groups

• Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
• Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil, Saudi Arabia
• School of Energy and Environment Science, Yunnan Normal University, Kunming, China
• College of Urban and Environmental Sciences, Peking University, Beijing, China
• Department of Mathematics, College of Science, Northern Border University, Arar, Saudi Arabia
• Department of Mathematics, College of Sciences and Arts (Majardah), King Khalid University, Magardah, Saudi Arabia

Short Summary

This study analyzes the seasonal variability and spatiotemporal structure of precipitation in Punjab, Pakistan, using the Precipitation Concentration Index (PCI) and comparing classical and Bayesian geostatistical methods. It concludes that Bayesian kriging models generally outperform their classical counterparts in spatial modeling of seasonal PCI, with optimal method performance varying by season.

Objective

• To analyze the seasonal variability and spatiotemporal structure of precipitation in Punjab, Pakistan, using the Precipitation Concentration Index (PCI).
• To compare the performance of classical (Ordinary Kriging, Universal Kriging) and Bayesian (Bayesian Ordinary Kriging, Bayesian Universal Kriging) geostatistical methods for spatially mapping seasonal PCI.

Study Configuration

• Spatial Scale: Punjab province, Pakistan, using data from 32 meteorological stations.
• Temporal Scale: Monthly precipitation data from December 1980 to November 2021 (41 years), analyzed seasonally (winter, spring, summer, autumn).

Methodology and Data

• Models used:
  • Precipitation Concentration Index (PCI) calculation.
  • Gibbs sampling for posterior mean estimation of PCI.
  • Geostatistical interpolation methods: Ordinary Kriging (OK), Universal Kriging (UK), Bayesian Ordinary Kriging (BOK), Bayesian Universal Kriging (BUK).
  • Variogram models: Circular, Cauchy, Cubic, Powered exponential, Gneiting.
  • Performance metrics: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Nash-Sutcliffe Efficiency (NSE).
• Data sources:
  • Meteorological data (rainfall, air temperatures, dew point) from 32 stations in Punjab, Pakistan.
  • NASA's POWER database (Data Access Viewer).

Main Results

• Seasonal PCI values indicated uniform rainfall distribution in winter (8.98) and autumn (8.80), moderate concentration in spring, and strongly irregular concentration in summer.
• Bayesian geostatistical techniques generally enhanced the spatial modeling of seasonal precipitation indicators.
• Model performance varied by season: BUK performed best in winter (RMSE: 0.374, NSE: 0.750), UK in spring (RMSE: 0.193, MAE: 0.154, NSE: 0.900), and BOK in both summer (RMSE: 0.250, NSE: 0.910) and autumn (RMSE: 0.472, MAE: 0.357, NSE: 0.898).
• Spatial prediction maps revealed distinct north-to-south gradients in rainfall patterns, with consistently higher precipitation concentration in central Punjab (29-30° N) and lower in southern and northern regions.
• Decadal analysis of PCI showed a rising tendency in concentration across decades, particularly in summer and autumn, indicating altered precipitation patterns.

Contributions

• First study to apply and compare both conventional (OK, UK) and Bayesian (BOK, BUK) kriging methods for mapping the seasonal Precipitation Concentration Index (PCI) in the Punjab region.
• Provides a comprehensive understanding of intra-annual precipitation distribution by focusing on seasonal PCI.
• Offers new insights into spatial prediction accuracy and variability, crucial for agricultural planning, water resource management, and climate change adaptation in a climate-sensitive area.
• Demonstrates that Bayesian geostatistical techniques improve the spatial modeling of seasonal precipitation indicators by incorporating parameter uncertainty, leading to more reliable and stable predictions.

Funding

• King Khalid University, Large Research Project (grant number RGP. 2/103/46).
• Northern Border University, Arar, Saudi Arabia (project number “NBU-FFR-2025-1324-06”).

Citation

@article{Din2026Bayesian,
  author = {Din, Fazal and Almazah, Mohammed M. A. and Niaz, Rizwan and Cheng, Hefa and Samman, Fathia Moh. Al and Hilali, Shreefa O.},
  title = {Bayesian geostatistical insights into seasonal variability and spatiotemporal structure of precipitation},
  journal = {Acta Geophysica},
  year = {2026},
  doi = {10.1007/s11600-025-01728-w},
  url = {https://doi.org/10.1007/s11600-025-01728-w}
}