Liu et al. (2025) Understanding copula-based multivariate standardized drought indices for characterizing meteorological, hydrological and agricultural droughts across global land areas

Identification

• Journal: Agricultural Water Management
• Year: 2025
• Date: 2025-10-06
• Authors: Y.R. Liu, Tingting Hu, Qiting Zuo, Lei Yu, Jiawen Yang
• DOI: 10.1016/j.agwat.2025.109864

Research Groups

• School of Water Conservancy and Transportation, Zhengzhou University, Zhengzhou, Henan, China
• School of Environmental and Municipal Engineering, North China University of Water Resources and Hydropower, China

Short Summary

This study systematically evaluates the Copula-based Multivariate Standardized Drought Index (CMSDI) for characterizing meteorological, hydrological, and agricultural droughts across global land areas, demonstrating its applicability and reliability in monitoring diverse composite drought conditions using bivariate and vine copulas.

Objective

• To comprehensively evaluate copula-based multivariate drought indices (CMSDIs) for characterizing composite meteorological, hydrological, and agricultural droughts across global land areas.

Study Configuration

• Spatial Scale: Global land areas (excluding Antarctica and Greenland), with data interpolated to a 1 degree x 1 degree spatial resolution.
• Temporal Scale: Reference period from 1948 to 2014, with monthly data aggregated over 1-month, 3-month, 6-month, 12-month, and 24-month accumulation periods.

Methodology and Data

• Models used:
  • Univariate Standardized Drought Indices (USDIs): Standardized Precipitation Index (SPI), Standardized Evapotranspiration Index (SEI), Standardized Runoff Index (SRI), Standardized Soil Moisture Index (SSI).
  • Copula models: Bivariate copulas (Gaussian, Clayton, Frank, Gumbel, Joe), Vine copulas (C-vines, D-vines, R-vines).
  • Land surface models (for GLDAS data): Noah, Catchment (CLSM), Variable Infiltration Capacity (VIC) models (ensemble mean).
• Data sources:
  • Monthly precipitation and potential evapotranspiration (PET): Climatic Research Unit gridded Time Series (CRU TS4.08).
  • Monthly runoff and soil moisture: National Oceanic and Atmospheric Administration Global Land Data Assimilation System (NOAA GLDAS) versions 2.0.

Main Results

• Copula-based Multivariate Standardized Drought Indices (CMSDIs) are applicable and reliable for monitoring and detecting diverse composite drought conditions across global land areas.
• Vine copula models demonstrate superior effectiveness in modeling the dependence structure of high-dimensional drought indices, confirming the propagation pathways from meteorological to hydrological, and then to agricultural droughts.
• The fitting performance of CMSDIs exhibits significant spatial and seasonal heterogeneity, which is closely related to the correlations between the constructed marginal univariate drought indices (USDIs).
• Gaussian and Frank copula functions are generally more suitable for constructing bivariate dependence structures, while for three- and four-variate indices, independence and Frank copulas are also prominent.
• The dominant pair-copula structure for three-dimensional CMSDIPRS is SPI-SRI-SSI (69.4% to 86.7%), indicating the meteorological-hydrological-agricultural drought propagation pathway. For four-dimensional CMSDIPERS, SPI-SRI-SSI-SEI and SEI-SPI-SRI-SSI structures are of equal importance.
• CMSDIs that do not consider potential evapotranspiration (SEI) show significant drying trends in eastern Asia and central Africa, and significant wetting trends in central Asia, western Australia, and North America.
• CMSDIs integrated with potential evapotranspiration (SEI) exhibit a consistent global drying trend due to increased atmospheric evaporative demand, particularly in eastern Asia and Africa.
• CMSDIs are positively correlated with USDIs and other CMSDIs, with higher correlation coefficients observed at longer accumulation periods due to the lag effect in hydrological processes.
• Sensitivity analysis (Fbench) indicates that in most regions, the two USDI marginal functions exhibit equivalent similarity to their respective CMSDIs, but deviations occur in arid/cold regions. Globally, the sensitivity of CMSDIPRS is SRI > SSI > SPI, and for CMSDIPERS is SRI > SSI ≈ SPI > SEI.

Contributions

• Provides a comprehensive, global-scale evaluation of copula-based multivariate drought indices (CMSDIs) for characterizing meteorological, hydrological, and agricultural droughts, addressing a gap in large-scale applicability assessment.
• Demonstrates the effectiveness and flexibility of vine copula models for constructing high-dimensional (three- and four-dimensional) drought indices, decomposing complex multivariate relationships into tractable pair-copula constructions.
• Offers critical foundational insights into the propagation pathways of meteorological-hydrological-agricultural droughts, enhancing the understanding of composite drought dynamics.
• Highlights the crucial role of increased atmospheric evaporative demand in exacerbating global drying trends, particularly in eastern Asia and Africa, when integrated into composite drought indices.
• Improves composite drought monitoring and early warning systems, providing a robust framework for optimizing agricultural water management strategies such as irrigation scheduling and water allocation planning under climate change.

Funding

• National Key R&D Program of China (2023YFC3205600)

Citation

@article{Liu2025Understanding,
  author = {Liu, Y.R. and Hu, Tingting and Zuo, Qiting and Yu, Lei and Yang, Jiawen},
  title = {Understanding copula-based multivariate standardized drought indices for characterizing meteorological, hydrological and agricultural droughts across global land areas},
  journal = {Agricultural Water Management},
  year = {2025},
  doi = {10.1016/j.agwat.2025.109864},
  url = {https://doi.org/10.1016/j.agwat.2025.109864}
}