Crop rotation impacts on soil nutrients are typically assessed using field-averaged or single-nutrient analyses that ignore spatial heterogeneity and multivariate interactions. We propose a multivariate lattice model treating soil as a 4D tensor (space, time, and N, P, K channels). Crop rotations are represented as force vectors, with soil buffering capacity ("stiffness") varying spatially with texture. Lateral nutrient movement is introduced via kernel smoothing. Cumulative impact is quantified by Euclidean distance in N-P-K space, with significance assessed via Cramer-von Mises permutation tests. Simulating a three-year corn-soybean-wheat rotation on a 20 x 20 heterogeneous grid shows mean stress of 0.63 after one cycle, with maximum 0.91 in sandy areas. Phosphorus depletion (17.9%) exceeds nitrogen (10.8%), dominating stress in 19% of cells - obscured by single-nutrient analyses. Continuous corn increases mean stress by 41%. Cramer-von Mises tests detect significant deviation (p <= 0.002), and Moran's I (0.29-0.30) confirms spatial autocorrelation. Our framework identifies risk zones and guides site-specific management, bridging geostatistics with mechanistic crop models.

翻译：轮作对土壤养分的影响通常通过田间平均或单一养分分析进行评估，这些方法忽略了空间异质性和多变量交互作用。我们提出了一种多元晶格模型，将土壤视为四维张量（空间、时间及氮、磷、钾通道）。轮作被表示为力矢量，土壤缓冲能力（“刚度”）随质地空间变化。通过核平滑引入养分横向迁移。累积影响通过氮-磷-钾空间中的欧氏距离量化，并借助克拉默-冯·米塞斯置换检验评估显著性。在20×20异质网格上模拟三年玉米-大豆-小麦轮作显示，一个周期后平均应力为0.63，沙质区域最大应力达0.91。磷耗竭（17.9%）超过氮（10.8%），在19%的网格中主导应力——该现象被单一养分分析所掩盖。连续玉米种植使平均应力增加41%。克拉默-冯·米塞斯检验检测到显著偏离（p ≤ 0.002），莫兰指数（0.29–0.30）证实空间自相关性。我们的框架可识别风险区域并指导场地特异性管理，架起了地质统计学与机理作物模型之间的桥梁。