A Unified Framework for Uncertainty Quantification and Attribution in Agricultural Supply Mathematical Programming Models

Agricultural Supply Mathematical Programming (ASMP) models are widely used to evaluate agricultural, water, and environmental policies, yet their application remains overwhelmingly deterministic. While substantial advances have been made in model calibration, little attention has been devoted to understanding how uncertainty propagates through model inputs, calibration parameters, behavioral assumptions, and alternative model structures. This study develops a unified framework for uncertainty quantification and sensitivity attribution in ASMP models that integrates expectation formation from historical data, dependence-preserving multivariate sampling, Latin Hypercube Sampling, machine-learning emulation, and SHAP interaction decomposition. The framework simultaneously accounts for uncertainty in market conditions, production costs, technical coefficients, resource availability, calibration parameters, behavioral representations, and model structure. The framework is applied to two alternative ASMP paradigms—a Generalized Constant Elasticity of Substitution Mathematical Programming model (GCES-MP) and a Generalized Maximum Entropy Mathematical Programming model (GME-MP)—across three contrasting agricultural systems: the Duero Basin (Spain), the Nile Delta (Egypt), and the Piedmont Region (Italy). Results show that uncertainty propagation is strongly conditioned by model structure, which can be as influential as inputs and parameter uncertainties in determining model outcomes. Although both models reproduce identical benchmark equilibria, they generate substantially different uncertainty rankings, economic risk profiles, and adaptation responses under fixed and uncertain water availability conditions. Across all case studies, interaction effects (that is, when the effect of one uncertain factor depends on the values of others because of nonlinear production relationships and resource constraints) account for a substantial share of total variance, highlighting the importance of nonlinear uncertainty propagation in hydro-economic systems. The proposed framework provides a general approach for evaluating the robustness and reliability of ASMP-based policy analyses under deep economic, environmental, behavioral, and structural uncertainty.