Multivariate lattice deformation: A spatially explicit framework for assessing crop rotation impacts on soil nutrient dynamics

TL;DR

This paper introduces a multivariate lattice model to assess how crop rotations affect soil nutrient dynamics spatially and over time, capturing heterogeneity and interactions often overlooked by traditional methods.

Contribution

It presents a novel 4D tensor-based framework that integrates spatial, temporal, and multivariate nutrient data, enabling detailed analysis of crop rotation impacts on soil health.

Findings

Phosphorus depletion exceeds nitrogen in crop rotations.

Spatial autocorrelation confirms risk zones for nutrient depletion.

Significant differences detected by permutation tests.

Abstract

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.