Wu et al. (2026) C-Vine Copulas Function and Conditional Quantile Regression Coupling Model for Agricultural Drought Prediction Analysis

Identification

• Journal: Water Resources Management
• Year: 2026
• Date: 2026-01-01
• Authors: Chengguo Wu, Chengjie Ren, Juliang Jin, Yuliang Zhou, Boyu Nie, Xia Bai, Yi Cui, Fang Tong, Libing Zhang
• DOI: 10.1007/s11269-025-04456-4

Research Groups

• School of Civil Engineering, Hefei University of Technology, Hefei, China
• Institute of Water Resources and Environmental Systems Engineering, Hefei University of Technology, Hefei, China
• College of Civil Engineering, Anhui Jianzhu University, Hefei, China

Short Summary

This study develops a novel agricultural drought prediction model (CQRM) by coupling C-Vine Copulas and conditional quantile regression, which accounts for non-stationary drought indicators and optimizes conditional variable selection, demonstrating its reliability in Northern Anhui Province, China.

Objective

• To propose a Conditional Quantile Regression Model (CQRM) based on C-Vine Copulas function for agricultural drought prediction analysis, considering non-stationary drought indicators and optimizing the selection and combination structure of conditional variables.
• To verify the reliability of the proposed approach through its application in Northern Anhui Province, China.

Study Configuration

• Spatial Scale: Northern Anhui Province (NAP), China, covering an area of 39.2 thousand square kilometers, including 6 prefecture-level cities (Bozhou, Fuyang, Suzhou, Huaibei, Huainan, and Bengbu).
• Temporal Scale: Historical data from 1960 to 2014 (55 years).

Methodology and Data

• Models used:
  • Generalized Additive Models for Location, Scale and Shape (GAMLSS) for deriving time-variant drought indicators (SPIt, STIt, SSMIt).
  • C-Vine Copulas function for constructing optimal dependency structures between variables.
  • Conditional Quantile Regression Model (CQRM) for agricultural drought prediction.
  • Pearson correlation coefficient for selecting conditional variables.
  • Kendall correlation coefficient and Akaike Information Criterion (AIC) for C-Vine structure optimization.
  • Leave-one-out cross-validation for model establishment.
  • Root Mean Square Error (RMSE) and Nash Sutcliffe Efficiency (NSE) for evaluating prediction performance.
• Data sources:
  • Historical agricultural drought disaster loss statistics: Anhui Provincial Statistical Yearbook, Anhui Provincial Drought-resistance Plan.
  • Monthly precipitation and temperature data: Chinese Meteorological Data Service Centre.
  • Monthly soil moisture data (0.25° × 0.25° spatial grid resolution): Global Land Data Assimilation System (GLDAS).

Main Results

• Previous 1–3 monthly-scale drought indicators (SPIt, STIt, SSMIt) are generally identified as primary conditional variables for agricultural drought prediction.
• The response time of drought propagation to diverse conditional variables is shorter in summer and autumn (less than 1 month) compared to winter and spring (nearly 3 months).
• The overall correlation coefficient between 1–12 month-scale Standardized Precipitation Index (SPIt) and Standardized Soil Moisture Index (SSMIt) was the highest (average 0.6768), while the correlation between Standardized Temperature Index (STIt) and SSMIt was the lowest (average 0.2753).
• The meteorological-to-agricultural drought propagation time in Northern Anhui Province is approximately 1–3 months, with a maximum of 3 months in winter and a minimum of 1 month in summer.
• The proposed CQRM model demonstrated good consistency between predicted and observed agricultural drought indicators (SSMIt) for the period 1960–2014, with Root Mean Square Error (RMSE) below 0.61 and Nash Sutcliffe Efficiency (NSE) greater than 0.62.
• Prediction results were relatively better in spring and winter (RMSE < 0.52, NSE > 0.75) due to higher correlations between prediction and conditional variables.
• The study found that increasing the number of conditional variables does not always improve prediction accuracy; recognizing effective monthly conditional variables and constructing their optimal combination structure through correlation analysis is crucial and region/season-specific.

Contributions

• Proposed a novel agricultural drought prediction model (CQRM) that integrates C-Vine Copulas function and conditional quantile regression, explicitly addressing the non-stationary characteristics of drought indicators.
• Introduced the Generalized Additive Models for Location, Scale and Shape (GAMLSS) method to derive time-variant drought indicators, overcoming limitations of static drought indicators in previous models.
• Developed a systematic methodology for identifying optimal monthly conditional variables and their combination structures through correlation analysis, leading to enhanced prediction accuracy tailored to specific regions and seasons.
• Demonstrated that the optimal combination of conditional variables for drought prediction is dynamic and varies significantly across different seasons and geographical areas, providing a more nuanced and effective approach than uniform models.

Funding

• National Natural Science Foundation of China (Grant Nos. 52409001, 52209012, 52379006, 42271084)
• National Key Research and Development Program of China (Grant No. 2023YFC3206604–02)
• Anhui Provincial Natural Science Foundation of China (Grant Nos. 2408085ME135, 2208085US03, 2308085US06)

Citation

@article{Wu2026CVine,
  author = {Wu, Chengguo and Ren, Chengjie and Jin, Juliang and Zhou, Yuliang and Nie, Boyu and Bai, Xia and Cui, Yi and Tong, Fang and Zhang, Libing},
  title = {C-Vine Copulas Function and Conditional Quantile Regression Coupling Model for Agricultural Drought Prediction Analysis},
  journal = {Water Resources Management},
  year = {2026},
  doi = {10.1007/s11269-025-04456-4},
  url = {https://doi.org/10.1007/s11269-025-04456-4}
}