Crop rotation systems are an important part of agricultural production for managing pests, diseases, and soil fertility. Recent interest in sustainable agriculture focuses on low input-use practices which require knowledge of the underlying dynamics of production and rotation systems. Polices to limit chemical application depending on proximity to waterways and flood management require field-level data and analysis. Additionally, supply elasticity estimates based on crop production as independent activities omit the dynamic effects of a cyclical rotation. We estimate a dynamic programming model of crop rotation which incorporates yield and cost inter-temporal effects in addition to field-specific factors including salinity and soil quality. Using an Optimal Matching algorithm from the Bioinformatics literature we determine empirically observed rotations using a geo-referenced panel dataset of 14,000 fields over 13 years. We estimate the production parameters which satisfy the Euler Equations of the field-level rotation problem and solve an empirically observed four-crop rotation.