Khan et al. (2026) Integrating Standardized Climate Indicators Using Triple and Scaled Triple Collocation to Develop an Agricultural Productivity Stress Index

Identification

• Journal: Water Resources Management
• Year: 2026
• Date: 2026-01-01
• Authors: Muhammad Asim Khan, Jianyi Lin, Mohammed M. A. Almazah, Ijaz Hussain, Hanen Louati, Mhassen E. E. Dalam
• DOI: 10.1007/s11269-025-04426-w

Research Groups

• Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
• State Key Laboratory for Ecological Security of Regions and Cities, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen, China
• Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil, Saudi Arabia
• Mathematics Department, Faculty of Science, Northern Border University, Arar, Saudi Arabia

Short Summary

This study introduces the Agricultural Productivity Stress Index (APSI), a new composite metric integrating Photosynthetically Active Radiation (PAR), Wind Direction at 10 m (WD10), and the Warm Spell Duration Index (WSDI), objectively merged using Triple Collocation (TC) and Scaled Triple Collocation (STC) without ground-truth data. The findings demonstrate that STC generally improves APSI estimation by reducing error variances and strengthening correlations, particularly for WD10 and PAR, offering a robust tool for assessing climate stress on agriculture.

Objective

• To develop a new composite metric, the Agricultural Productivity Stress Index (APSI), by integrating standardized climate indicators (All Sky Surface Photosynthetically Active Radiation total (PAR), Wind Direction at 10 m (WD10), and Warm Spell Duration Index (WSDI)) using Triple Collocation (TC) and Scaled Triple Collocation (STC) methods to better capture agroclimatic stress and its implications for crop productivity.

Study Configuration

• Spatial Scale: Six major agricultural cities in Pakistan: Multan, Faisalabad, Layyah, Rahim Yar Khan, Quetta, and Sukkur.
• Temporal Scale: Long-term climate data spanning 32 years, from 1991 to 2022.

Methodology and Data

• Models used:
  • Triple Collocation (TC)
  • Scaled Triple Collocation (STC)
  • Z-score standardization
  • Least-Squares Optimal Merging method for weighting indicators
  • Correlation Analysis
  • Error Variance Analysis
  • Nash-Sutcliffe Efficiency (NSE)
  • Taylor Diagram
  • Mann-Kendall test for trend detection
  • Sen’s Slope estimation for trend magnitude
• Data sources:
  • NASA POWER MERRA-2 reanalysis datasets for climate variables.
  • All Sky Surface Photosynthetically Active Radiation total (PAR) (energy flux).
  • Wind Direction at 10 m (WD10) (degrees).
  • Warm Spell Duration Index (WSDI) computed from daily maximum temperature data.

Main Results

• STC generally improved APSI estimation compared to TC, demonstrating reduced error variances, strengthened correlations, and enhanced Nash-Sutcliffe Efficiency (NSE) values.
• STC significantly enhanced the performance of WD10, showing substantial increases in correlation (e.g., Rahim Yar Khan: r = 0.880; Faisalabad NSE: from -0.190 to 0.402) and reductions in error variance (e.g., Faisalabad: from 1.153 to 0.580).
• PAR performance remained robust and consistent under STC, maintaining strong correlations (e.g., Sukkur: r = 0.909) and stable error variances across locations.
• WSDI showed less consistent improvements under STC, with only slight and location-dependent gains in correlation and NSE, and variable error variance reductions.
• Trend analysis (Mann-Kendall test and Sen’s Slope) revealed:
  • Statistically significant declining trends in PAR across most study locations (e.g., Faisalabad: Z = -0.6216, p < 0.0001; slope = -0.0358).
  • Significant decreasing trends in WD10 in several regions (e.g., Rahimyar Khan: Z = -0.4560, p < 0.0001; slope = -0.0274).
  • A statistically significant upward trend in WSDI in Quetta (Z = 0.1952, p = 0.0272; slope = 0.0080), indicating increased heat exposure.
• Both TC and STC-based APSI showed significant declining trends across most sites, with STC providing a smoother and potentially more robust signal (e.g., Rahimyar Khan TC slope = -0.0510 vs. STC slope = -0.0289).
• Taylor diagrams confirmed STC's ability to produce more consistent and dependable APSI outputs with lower errors for PAR and WD10 compared to TC.

Contributions

• Introduces a novel composite Agricultural Productivity Stress Index (APSI) by integrating three key climate indicators (PAR, WD10, WSDI) to provide a holistic view of agroclimatic stress.
• Applies and rigorously evaluates Triple Collocation (TC) and Scaled Triple Collocation (STC) methods for objectively merging climate indicators without requiring ground-truth reference data, demonstrating STC's superior performance for specific variables.
• Provides a robust, flexible, and information-driven framework for assessing agricultural stress related to climate variability, offering valuable insights for climate-smart agriculture, policy formulation, and adaptation strategies in climate-vulnerable regions.
• Quantifies long-term trends (1991–2022) of key climate stressors and the composite APSI in major agricultural regions of Pakistan, highlighting regional vulnerabilities to declining solar radiation, altered wind patterns, and increasing heat stress.

Funding

• King Khalid University, Large Research Project (grant number RGP. 2/145/46)
• Northern Border University, Arar, Saudi Arabia (project number NBU-FFR-2026-2920-02)

Citation

@article{Khan2026Integrating,
  author = {Khan, Muhammad Asim and Lin, Jianyi and Almazah, Mohammed M. A. and Hussain, Ijaz and Louati, Hanen and Dalam, Mhassen E. E.},
  title = {Integrating Standardized Climate Indicators Using Triple and Scaled Triple Collocation to Develop an Agricultural Productivity Stress Index},
  journal = {Water Resources Management},
  year = {2026},
  doi = {10.1007/s11269-025-04426-w},
  url = {https://doi.org/10.1007/s11269-025-04426-w}
}