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<p>Accurate assessment and estimation of precipitation across spatial and temporal scales are crucial for addressing various environmental and resource management challenges, such as reducing soil erosion, evaluating agricultural productivity, conserving wetlands, assessing the impacts of climate change, and planning sustainable water resources. Precipitation features such as frequency, intensity, and total accumulation are crucial indicators; yet, their impact varies considerably among geographies and temporal contexts due to differing environmental and climatic variables. This study utilized a Bayesian spatio-temporal framework to estimate precipitation at ungauged locations and time intervals over 14 designated sites in Pakistan’s Indus Basin. Within a Bayesian framework, the study employs the hierarchical nugget effect model (HNEM), which integrates Gaussian Process (GP) modeling for spatial patterns and Auto-Regressive (AR) modeling for temporal dynamics to analyze spatio-temporal data effectively. Results show that the AR model improves temporal forecast accuracy, with a mean absolute error (MAE) of 6.31. In contrast, the GP model performs better in spatial prediction, achieving a MAE of 24.33. The model’s predictive performance significantly improves when the Matérn covariance function is combined with a square root transformation of the data.</p>

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Advanced Bayesian spatio-temporal frameworks for predicting precipitation at ungauged sites and times

  • 期刊论文

  • 发表日期：

    2026年4月10日

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  • Muhammad Asif Khan,
  • Rangjian Qiu,
  • Muhammad Zubair,
  • Shah Fahd,
  • Zeeshan Zafar

摘要

Accurate assessment and estimation of precipitation across spatial and temporal scales are crucial for addressing various environmental and resource management challenges, such as reducing soil erosion, evaluating agricultural productivity, conserving wetlands, assessing the impacts of climate change, and planning sustainable water resources. Precipitation features such as frequency, intensity, and total accumulation are crucial indicators; yet, their impact varies considerably among geographies and temporal contexts due to differing environmental and climatic variables. This study utilized a Bayesian spatio-temporal framework to estimate precipitation at ungauged locations and time intervals over 14 designated sites in Pakistan’s Indus Basin. Within a Bayesian framework, the study employs the hierarchical nugget effect model (HNEM), which integrates Gaussian Process (GP) modeling for spatial patterns and Auto-Regressive (AR) modeling for temporal dynamics to analyze spatio-temporal data effectively. Results show that the AR model improves temporal forecast accuracy, with a mean absolute error (MAE) of 6.31. In contrast, the GP model performs better in spatial prediction, achieving a MAE of 24.33. The model’s predictive performance significantly improves when the Matérn covariance function is combined with a square root transformation of the data.