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<p>The determination of thresholds is a critical challenge in evaluating the regional gray water footprint (GWF). This study proposes a novel threshold identification model for the regional gray water footprint index (GWFI)—defined as the ratio of GWF to total regional water resources—using the classification and regression tree (CART) method. Unlike the traditional approach that presumes a uniform threshold of 1 for all regions, the CART-based model derives data-driven, region-specific thresholds. The model is applied to regional data from China, yielding the following key findings: (i) Regional Thresholds: region-specific thresholds are identified as 4.228 for North China, 2.295 for Northeast China, 1.784 for East China, 1.288 for Central China, 0.840 for South China, 0.846 for Southwest China, and 2.786 for Northwest China. (ii) Model Performance: CART proves to be an effective threshold identification model for GWFI, with area under curve (AUC) values of 0.589 (North China), 0.964 (Northeast China), 0.755 (East China), 0.852 (Central China), 0.778 (South China), 0.838 (Southwest China), and 0.830 (Northwest China). Compared to traditional methods, the CART-based approach demonstrates superior accuracy and effectiveness in threshold evaluation. (iii) Regional Limitations: The CART model is less suitable for North China due to the influence of water transfer projects, such as the South-to-North Water Diversion Project. This intervention disrupts the assumption that pollutants are diluted solely by local water resources. (iv) Regional Characteristics: Thresholds exhibit distinct regional variation, with lower values in water-rich areas and higher values in water-scarce regions.</p>

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Threshold of Regional Gray Water Footprint Based on CART Decision Tree

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • Yan Feng,
  • Fang Li,
  • Wu Hongiang

摘要

The determination of thresholds is a critical challenge in evaluating the regional gray water footprint (GWF). This study proposes a novel threshold identification model for the regional gray water footprint index (GWFI)—defined as the ratio of GWF to total regional water resources—using the classification and regression tree (CART) method. Unlike the traditional approach that presumes a uniform threshold of 1 for all regions, the CART-based model derives data-driven, region-specific thresholds. The model is applied to regional data from China, yielding the following key findings: (i) Regional Thresholds: region-specific thresholds are identified as 4.228 for North China, 2.295 for Northeast China, 1.784 for East China, 1.288 for Central China, 0.840 for South China, 0.846 for Southwest China, and 2.786 for Northwest China. (ii) Model Performance: CART proves to be an effective threshold identification model for GWFI, with area under curve (AUC) values of 0.589 (North China), 0.964 (Northeast China), 0.755 (East China), 0.852 (Central China), 0.778 (South China), 0.838 (Southwest China), and 0.830 (Northwest China). Compared to traditional methods, the CART-based approach demonstrates superior accuracy and effectiveness in threshold evaluation. (iii) Regional Limitations: The CART model is less suitable for North China due to the influence of water transfer projects, such as the South-to-North Water Diversion Project. This intervention disrupts the assumption that pollutants are diluted solely by local water resources. (iv) Regional Characteristics: Thresholds exhibit distinct regional variation, with lower values in water-rich areas and higher values in water-scarce regions.