Batool et al. (2026) Development of co-integrated standardized procedure for the joint monitoring, forecasting and probabilistic characterization of climate extremes under global climate models

Identification

• Journal: Theoretical and Applied Climatology
• Year: 2026
• Date: 2026-02-27
• Authors: Aamina Batool, Mahrukh Yousaf, Muhammad Shakeel, Amina Magdich, Reem Alreshidi, Zulfiqar Ali, Veysi Kartal
• DOI: 10.1007/s00704-026-06089-y

Research Groups

• College of Statistical and Actuarial Sciences, University of the Punjab, Lahore, Pakistan
• Department of Computer Science, Applied College, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia
• Department of Physics, College of Science, Northern Border University, Arar, Saudi Arabia
• Civil Engineering, Engineering Faculty, Siirt University, Siirt, Turkey

Short Summary

This research develops the Adaptive Joint Standardized Drought and Heatwave Index (AJSDHI) for joint monitoring, forecasting, and probabilistic characterization of climate extremes using multi-model ensembles from CMIP6 GCMs. The study finds K-Component Gaussian Mixture Distribution (K-CGMD) to be the most suitable fitting approach and shows that machine learning models (ELM, MLP) generally outperform ARIMA for forecasting, with moderate wet and cold events having higher long-term probabilities than moderate dry and hot events in the Tibetan Plateau.

Objective

• To develop the Adaptive Joint Standardized Drought and Heatwave Index (AJSDHI) for co-integrated monitoring, forecasting, and probabilistic characterization of climate extremes.
• To employ K-Component Gaussian Mixture Distribution (K-CGMD) models for probabilistic monitoring and dry/hot spell characterization.
• To assess the long-term probability of various climate extreme classes using Steady-State Probabilities (SSPs) of the Markov chain.

Study Configuration

• Spatial Scale: Thirty-two selected locations across the Tibetan Plateau (25° to 40°N latitude and 74° to 104°E longitude, covering 2.5 million square kilometers), with data re-gridded to a 0.5° × 0.5° resolution.
• Temporal Scale: Monthly precipitation and temperature data from 1961 to 2014 for observations and CMIP6 model simulations, with projections for the 21st century.

Methodology and Data

• Models used:
  • Adaptive Joint Standardized Drought and Heatwave Index (AJSDHI)
  • Weighted Aggregation (WA) scheme for multi-model ensemble
  • K-Component Gaussian Mixture Distribution (K-CGMD) for distribution fitting
  • Bivariate probabilistic distribution approach
  • Markov chain for Steady-State Probabilities (SSPs)
  • Forecasting algorithms: Autoregressive Integrated Moving Average (ARIMA), Extreme Learning Machine (ELM), Multilayer Perceptron (MLP)
• Data sources:
  • Monthly precipitation and temperature observations (CN05.1 dataset)
  • Eighteen Global Climate Models (GCMs) from the Coupled Model Intercomparison Project phase 6 (CMIP6)

Main Results

• K-Component Gaussian Mixture Distribution (K-CGMD) consistently demonstrated the smallest Bayesian Information Criterion (BIC) values across all selected locations, indicating its superior suitability for fitting ensemble precipitation and temperature data compared to univariate distributions.
• Markov chain analysis revealed that the "Normal" climate class consistently exhibits the highest steady-state probabilities (ranging from approximately 0.67 to 0.68) across all 32 locations.
• The long-term probabilities of moderate wet and cold events were found to be considerably higher than those of moderate dry and hot events across most locations in the Tibetan Plateau.
• In forecasting, Extreme Learning Machine (ELM) and Multilayer Perceptron (MLP) generally outperformed Autoregressive Integrated Moving Average (ARIMA) in terms of Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), particularly in capturing complex nonlinear drought dynamics. ELM showed a significant performance advantage over both ARIMA and MLP in terms of RMSE.

Contributions

• Development of the novel Adaptive Joint Standardized Drought and Heatwave Index (AJSDHI) for co-integrated monitoring, forecasting, and probabilistic characterization of compound climate extremes.
• Integration of a Weighted Aggregation (WA) scheme for multi-model ensemble of GCMs to enhance accuracy and reduce bias in climate projections.
• Application of K-Component Gaussian Mixture Distribution (K-CGMD) for robust distribution fitting of multi-modal climate data, addressing limitations of traditional single-distribution approaches.
• Utilization of Markov chain Steady-State Probabilities (SSPs) for a comprehensive long-term probabilistic assessment of joint extreme events.
• Comparative evaluation of machine learning (ELM, MLP) and statistical (ARIMA) models for forecasting joint drought and heatwave behavior, providing insights into their suitability for different data characteristics.

Funding

• Princess Nourahbint Abdulrahman University Researchers Supporting Project number (PNURSP2026R848), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

Citation

@article{Batool2026Development,
  author = {Batool, Aamina and Yousaf, Mahrukh and Shakeel, Muhammad and Magdich, Amina and Alreshidi, Reem and Ali, Zulfiqar and Kartal, Veysi},
  title = {Development of co-integrated standardized procedure for the joint monitoring, forecasting and probabilistic characterization of climate extremes under global climate models},
  journal = {Theoretical and Applied Climatology},
  year = {2026},
  doi = {10.1007/s00704-026-06089-y},
  url = {https://doi.org/10.1007/s00704-026-06089-y}
}