Zhang et al. (2026) Hidden markov models to analyze China’s total water resources states and transfer characteristics

Identification

• Journal: Theoretical and Applied Climatology
• Year: 2026
• Date: 2026-04-10
• Authors: Tao Zhang, Xiaojun Wang, Jianyun Zhang, Zhiyong Liu, Shamsuddin Shahid
• DOI: 10.1007/s00704-026-06210-1

Research Groups

• The National Key Laboratory of Water Disaster Prevention, Nanjing Hydraulic Research Institute, Nanjing, China
• Research Center for Climate Change, Ministry of Water Resources, Nanjing, China
• Yangtze Institute for Conservation and Development, Nanjing, China
• Center for Water Resources and Environment, School of Civil Engineering, Sun Yat-sen University, Guangzhou, China
• Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai, China
• National Center for Meteorology (NCM), Regional Climate Change Center (RCCC), Jeddah, Saudi Arabia

Short Summary

This study introduces a novel Hidden Markov Model (HMM) to analyze the hidden states and inter-annual transfer characteristics of China's total water resources, addressing limitations of traditional methods by accounting for temporal dependency. It identifies three hidden states ("Dry," "Flat," "Abundant") and their transition patterns across China's six major geographic regions, revealing an overall increase in water resources over the past 20 years, particularly in the north.

Objective

• To propose a novel water resources assessment method based on Hidden Markov Models (HMM) that accounts for temporal dependency and inter-annual continuity, overcoming limitations of traditional frequency distribution methods.
• To analyze the hidden states ("Dry," "Flat," "Abundant") of total water resources and their inter-annual transition patterns across China's six major geographic regions from 2001 to 2020.

Study Configuration

• Spatial Scale: China and its 6 major geographic regions (North China, Northeast China, East China, Central South China, Southwest China, Northwest China), including administrative regions (provinces, municipalities, autonomous regions).
• Temporal Scale: 20 years (2001–2020).

Methodology and Data

• Models used: Hidden Markov Model (HMM) (specifically Gaussian HMM), Polynomial fitting for temporal trend analysis, Gaussian Mixture Model (GMM) for comparative analysis.
• Data sources: China Water Resources Bulletins (2001–2020) from the Ministry of Water Resources of China, providing total regional water resources and precipitation data.

Main Results

• China's total water resources showed a consistent linear increase from 2001 to 2020, with an annual growth rate of 19.612 billion cubic meters per year.
• Northern regions (e.g., Beijing, Heilongjiang, Gansu) exhibited an upward trend in total water resources, while Yunnan and Xinjiang experienced a gradual decline.
• The HMM identified three hidden states: "Dry," "Flat," and "Abundant," with distinct classification standards and transition probabilities for China and its six major geographic regions.
• For China as a whole, the "Dry" state was 73.22% lower, "Flat" 5.65% higher, and "Abundant" 80.75% higher than the overall average total water resources.
• Most regions showed a tendency to transition to the "Flat" state. "Dry" states in North, Northeast, and Northwest China exhibited high self-persistence. "Flat" states in Central-South and Southwest China tended to switch to "Dry." "Abundant" states in Northwest and Southwest China had greater than 50% self-persistence, but Northeast China's "Abundant" often transitioned directly to "Dry."
• The predominant state in China was "Dry" and "Flat" during 2001–2010, shifting to "Flat" and "Abundant" during 2011–2020.
• The HMM outperformed the GMM in terms of log-likelihood (Score) across most regions (e.g., China scale: HMM Score -185.28 vs. GMM -188.39), demonstrating superior fitting capability by explicitly modeling temporal dependencies.
• A 3-state HMM configuration was determined to be optimal, balancing statistical robustness and physical interpretability, aligning with common hydrological quantiles.

Contributions

• Proposed a novel water resources assessment method using Hidden Markov Models (HMM) that explicitly accounts for temporal dependencies and inter-annual continuity in water resource dynamics, addressing limitations of traditional frequency distribution methods that assume data independence.
• Defined and quantified three hidden states ("Dry," "Flat," "Abundant") of total water resources and their inter-annual transition patterns across China's six major geographic regions, providing a more nuanced understanding beyond simple average values.
• Demonstrated the methodological advantage of HMM over Gaussian Mixture Models (GMM) in capturing the dynamic evolution of water resource systems, justifying the increased model complexity.
• Provided practical policy implications for water resource management, such as informing reservoir operations based on "Dry" state persistence and optimizing inter-regional water transfer projects using state transition matrices.
• Addressed the challenge of limited historical data by expanding the study area to geographical regions, using multiple administrative regions as independent samples to improve model robustness and stability.

Funding

• National Natural Science Foundation of China (No. 52121006)
• Young Top-Notch Talent Support Program of National High-level Talents Special Support Plan
• Research Project of Ministry of Natural Resources (No. 20210103)
• Research Project of Department of Natural Resources of Jiangsu Province (No. 2021003, No. 2022022)
• Research Project of Jiangsu Land and Resources Research Center (No. ZK202106, No. ZK22003)
• Six Talents Peak Project of Jiangsu Province (No. JNHB-068)
• 333 High-level Talents Cultivation Project of Jiangsu Province
• Research Project of Jiangsu Water Conservancy Research Institute (No. 2022019)
• Nanjing Hydraulic Research Institute 2024 Graduate Dissertation Development Fund (Yy524012)

Citation

@article{Zhang2026Hidden,
  author = {Zhang, Tao and Wang, Xiaojun and Zhang, Jianyun and Liu, Zhiyong and Shahid, Shamsuddin},
  title = {Hidden markov models to analyze China’s total water resources states and transfer characteristics},
  journal = {Theoretical and Applied Climatology},
  year = {2026},
  doi = {10.1007/s00704-026-06210-1},
  url = {https://doi.org/10.1007/s00704-026-06210-1}
}