Control of soil fertility from organic matter amendments and rotations

Sustainable agriculture requires that soil fertility be optimal so as to maintain current levels of food production whilst also maintaining environmental quality and even improving both together. Like inorganic fertiliser, organic amendments such as manure or compost can increase crop yield and could partly replace artificial nitrogen, but need a multi-year strategy, because yields may decrease when amendments cease. Other measures to manage arable land such grass and clover leys used in rotation can also enhance crop yield and mitigate certain drawbacks of continuous arable cropping such as soil degradation. Because i. chemical fertilisers may become restricted to reduce GHG emissions and improve water quality, ii. organic amendments can be in short supply, and iii. ley-arable rotations can decrease the prevalence of cash crops, we are seeking optimal means for improving the fertility of land that takes account of the dynamics of the yield-enhancing benefits of organic amendments and leys alongside annual applications of artificial fertiliser.

Using optimal control theory, we shall present a rational basis for combining applications of inorganic fertiliser and organic matter treatments of arable land to a sequence of crops grown in consecutive seasons that ensures maximum profit from crop production and improves soil fertility. Instead of a complex mechanistic approach, we use the empirical idea of a nutrient response curve, which is extended to include both the effects on yield of the nutrients themselves but also the long-lasting benefits of different types of organic matter management using ad hoc recurrence relations to model the carry-over of soil carbon and nitrogen from one season to the next.

Based on this methodology, we will present an analysis of an organic manuring long term experiment at Rothamsted, using, in particular, eight years winter wheat yield data that followed organic matter treatments in the previous stage of the experiment; these treatments ceased before the wheats were grown. Nonlinear regression allowed for the selection and the parameter identification of a single nutrient response curve valid for different organic treatments (farmyard manure, straw, ley). Preliminary results of our control theory suggest that growing wheat for four years in rotation with one year of leys can both reduce the use of nitrogen fertilisers and maximise the farmer's annual profit compared to using either farmyard manure or straw as alternative organic amendments together with inorganic nitrogen fertilisers. We aim to study the impact of such optimal economic strategies on greenhouse gas emissions and nitrate leaching to shed new light on greener farm management strategies and the economic landscape supporting sustainable farming scenarios. Our methodology generalises the well-known single year break-even ratio used in nitrogen fertiliser recommendations to a multi-year metric for interventions such as manure application that persist for several cropping years.