Dynamic Bayesian modeling and optimization of agricultural water–energy–food–carbon systems under resource constraints: Evidence from the North China Plain

The transition toward low-carbon cropland systems requires coordinated management of water, energy, food production, and carbon emissions. The North China Plain (NCP), one of China’s most intensively cultivated regions, faces particularly strong trade-offs among these objectives. This study developed a structurally coupled Dynamic Bayesian Network–Bayesian Neural Network (DBN–BNN) framework to assess the water–energy–food–carbon (WEFC) system across 492 counties from 2001 to 2020. The DBN represented temporal dependencies, while an approximate Bayesian neural network based on Monte Carlo dropout captured nonlinear responses and predictive uncertainty. The framework was used to evaluate WEFC coordination, identify dominant coordinating and de-coordinating factors, and derive county-specific management pathways through perturbation analysis. WEFC coordination followed a rise–fall–recovery pattern and showed pronounced spatial heterogeneity, with average scores ranging from 0.75 in Beijing to 1.21 in Shandong on a 0–3 scale. Groundwater conditions, irrigated area, and ecosystem water-use efficiency were the main factors underlying county-level differences. Under the integrated adjustment scenario, cropland carbon emissions decreased by 1.17 × 10 8 kg CO 2 -eq (8.1%), while grain production increased by 1.47 × 10 10 kg (9.8%) relative to 2020. The identified pathways were strongly location-specific: 110 counties were prioritized for water-use efficiency improvement, 184 showed favorable responses to irrigation restructuring, and 310 required groundwater recovery. In counties facing both irrigation and groundwater constraints, improvements depended on infrastructure rehabilitation, water-saving technologies, and surface-water substitution rather than additional groundwater abstraction. This study contributes to the WEFC nexus literature by introducing a hybrid probabilistic framework that captures nonlinear dynamics and uncertainty propagation, and by providing fine-scale, policy-relevant insights into adaptive water–energy management. The findings offer transferable implications for intensively cultivated regions worldwide facing similar resource–environment trade-offs.