Abstract:
The cropland water–land balance relationship is a fundamental support and key regulatory mechanism for maintaining cropland productivity, ecological stability, and sustainable land use. Investigating this relationship is of great practical significance for supporting the principle of “determining land use by water availability”, optimizing cropland spatial layout and crop planting structure, and promoting the sustainable utilization of water and land resources. Taking the five major agricultural regions in northern China as the study area, this study used monthly gridded meteorological data, crop planting structure data, and gross primary productivity (GPP) data from 2001 to 2022. The full-growing-season crop water requirements of winter wheat, spring maize, and summer maize were estimated using the FAO-56 crop coefficient method. A dekadal Crop Water Deficit and Surplus Index (CWDI) and its standardized form, the Standardized Crop Water Deficit and Surplus Index (SCWDI), were then constructed. By integrating run theory, empirical orthogonal function (EOF) analysis, correlation analysis, and a Copula–Bayesian conditional probability model, this study systematically identified the spatiotemporal evolution of cropland water–land balance relationships, crop critical water-demand periods, and productivity loss risks under drought stress in northern China.The results showed that: (1) The multi-year mean full-growing-season water requirements of winter wheat and maize in the study area were 500 mm and 594 mm, respectively, with 627 mm for spring maize and 536 mm for summer maize. Crop water requirements showed significant regional differences. For winter wheat, the water requirement followed the order Huang–Huai–Hai Plain (521 mm) > Loess Plateau (514 mm) > Gansu–Xinjiang Region (467 mm), while spring maize had the highest water requirement in the Gansu–Xinjiang Region (662 mm). (2) The average drought-event frequency in the study area ranged from 0.4 to 2.0 events per year. The Gansu–Xinjiang Region was characterized by a high proportion of extreme drought events, long duration, and high intensity, indicating a cumulative drought pattern, whereas the Huang–Huai–Hai Plain was dominated by high-frequency but short-duration drought events. (3) EOF decomposition showed that the first five modes cumulatively explained 73.3% of the total variance, with EOF1 and EOF2 accounting for 28.6% and 20.0%, respectively, indicating that interannual dry–wet variations of cropland in northern China exhibited both region-wide consistency and regional heterogeneity. (4) Correlation analysis between SCWDI and standardized GPP (SGPP) showed that the identified key months were July for spring maize and summer maize, and May for winter wheat. After considering the cumulative effect, the critical water-demand stages of spring maize, summer maize, and winter wheat corresponded to May–June, June, and March–April, respectively. (5) The SCWDI–SGPP dependence structures of spring maize and summer maize were best fitted by the Gaussian Copula, while the Frank Copula performed best for winter wheat. Under extreme drought conditions, the average probabilities of productivity loss for spring maize, summer maize, and winter wheat were approximately 63%, 80%, and 44%, respectively. The north-central Huang–Huai–Hai Plain and the Loess Plateau were identified as key regions where drought stress was more likely to be transformed into productivity loss. This study develops an integrated analytical framework linking crop water requirement, water deficit and surplus, drought events, and productivity loss risk, providing a scientific basis for cropland layout optimization, crop structure adjustment, and agricultural drought risk prevention and control in northern China.