Unraveling Nonlinear Thresholds and Spatiotemporal Heterogeneity in Agricultural Water–Energy–Food Coordination: Evidence from the Lower Yellow River Irrigation Districts

Irrigation districts are key operational units where water diversion, agricultural energy inputs, cultivated land use, and food production are directly coupled. However, existing water–energy–food nexus studies have mainly focused on provincial or basin scales, with limited attention to nonlinear associations and regional heterogeneity at the irrigation-district scale. This study examined the spatiotemporal evolution and associated factors of the agricultural water–energy–food (AWEF) coupling coordination degree (CCD) in 40 lower Yellow River irrigation districts from 2000 to 2020. An integrated framework combining the CCD model, XGBoost–SHAP, nonlinear fitting with bootstrap threshold analysis, and GTWR was used to identify leading associated factors, nonlinear transition points, and spatiotemporal heterogeneity. The AWEF CCD showed an overall upward trend from 2000 to 2020, with the mean value increasing from approximately 0.54 in 2000 to 0.77 in 2020. Spatially, the distribution gradually shifted from the lower-value classes of 0.48–0.55 and 0.55–0.62 in the early stage to the higher-value classes of 0.69–0.76 and 0.76–0.84 in the later stage. Population density (PD), nighttime light index (NLI), proportion of cultivated land (PCL) and proportion of water area (WP) were identified as the key associated factors. Their associations with CCD were not uniform across regions. Their relationships with CCD were nonlinear and region-specific: the SHAP contribution of PD changed from positive to negative across thresholds of 432.7–470.8 persons/km2, whereas NLI changed from negative to positive at 7.655–8.472; PCL shifted from positive to negative at 0.8157–0.8241, while WP changed from negative to positive at approximately 0.006–0.012. GTWR further revealed spatiotemporal heterogeneity in the local relationships between these factors and CCD. The local coefficients of PD remained negative throughout the study period, whereas those of NLI remained positive but were generally lower during 2010–2020 than during 2000–2009. The local relationships of PCL and WP with CCD varied across regions and stages, with both positive and negative coefficients observed.