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<p>This study proposes an integrated mathematical modeling approach that combines water footprint, carbon footprint, chance-constrained programming (CCP), and fuzzy chance-constrained programming (FCCP) to support water resources management under uncertainty. The approach addresses stochastic and fuzzy uncertainties through discrete probabilities and fuzzy sets, enabling low-carbon and efficient water use by controlling the blue-water footprint rate (BFR), grey-water footprint rate (GFR), and carbon footprint intensity (CFI). It is applied to water resources allocation in the Hanjiang River Ecological Economic Belt (HREEB), China. Results show that: (i) optimal allocation prioritizes municipal users to maximize net benefits, while ensuring substantial agricultural water supply to safeguard food security; (ii) GFR is primarily influenced by allocations to non-agricultural users, while increased allocations to agricultural and municipal sectors are associated with higher BFR and lower CFI, respectively; and (iii) higher allowable risk of violating water supply capacity or lower credibility of footprint constraints leads to increased net benefits. These findings provide a quantitative basis for balancing economic gains, food security, and environmental sustainability in regional water resources management.</p>

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An integrated mathematical modeling approach for reducing water footprint rate and carbon footprint intensity of Hanjiang River Ecological Economic Belt in China

  • 期刊论文

  • 发表日期：

    2025年11月7日

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  • Zuo Zhang,
  • Yuze Du,
  • Yaru Lyu,
  • Chao Dai,
  • Yanpeng Cai

摘要

This study proposes an integrated mathematical modeling approach that combines water footprint, carbon footprint, chance-constrained programming (CCP), and fuzzy chance-constrained programming (FCCP) to support water resources management under uncertainty. The approach addresses stochastic and fuzzy uncertainties through discrete probabilities and fuzzy sets, enabling low-carbon and efficient water use by controlling the blue-water footprint rate (BFR), grey-water footprint rate (GFR), and carbon footprint intensity (CFI). It is applied to water resources allocation in the Hanjiang River Ecological Economic Belt (HREEB), China. Results show that: (i) optimal allocation prioritizes municipal users to maximize net benefits, while ensuring substantial agricultural water supply to safeguard food security; (ii) GFR is primarily influenced by allocations to non-agricultural users, while increased allocations to agricultural and municipal sectors are associated with higher BFR and lower CFI, respectively; and (iii) higher allowable risk of violating water supply capacity or lower credibility of footprint constraints leads to increased net benefits. These findings provide a quantitative basis for balancing economic gains, food security, and environmental sustainability in regional water resources management.