Quantifying the insurance value of Managed Aquifer Recharge under hydro-economic uncertainty: A probabilistic modeling framework

Managed Aquifer Recharge (MAR) can generate significant insurance value by storing water resources during periods of surplus and delivering them during drought, thereby mitigating the economic losses that would otherwise occur. Existing economic assessments typically report deterministic insurance values, providing limited insight into how hydrological and economic uncertainty propagates through agricultural systems and affects the economic performance of MAR. This paper develops a probabilistic behavioral economic framework that combines Positive Mathematical Programming (PMP), an equilibrium-constrained Generalized Maximum Entropy (GME) calibration, Latin Hypercube Sampling, Gaussian copulas preserving crop-specific price–yield dependence, and SHAP-based global sensitivity analysis to quantify the insurance value of MAR under uncertainty. The framework is illustrated for three MAR systems using Alternative Water Resources in Llobregat (Spain), Comporta (Portugal), and Texel Island (the Netherlands). Across the three demo sites, the resulting probability distributions remain positively skewed, with median insurance values ranging from 0.04–0.34 EUR/m³ in Llobregat, −0.20–0.01 EUR/m³ in Comporta, and 3.74–4.24 EUR/m³ in Texel. The highest 10% of realizations exceed 0.78–1.08 EUR/m³, 0.10–0.31 EUR/m³, and 7.81–8.31 EUR/m³, respectively, demonstrating that MAR derives its greatest economic value under relatively rare but severe hydro-economic conditions. MAR recovers operation and maintenance costs across most realizations in Llobregat and Texel, whereas in Comporta the agricultural insurance value alone may be insufficient, highlighting the need for complementary cost-recovery mechanisms and ecosystem-service benefits. SHAP analysis identifies conventional water availability as the dominant source of uncertainty, followed by commodity prices and crop yields. The proposed framework provides a transparent and transferable methodology for probabilistic economic evaluation of MAR and other water management interventions under uncertainty.