Dynamic phosphorus and nitrogen yield response model for economic optimisation

This paper provides an approach for modelling joint impact of two main nutrients in crop production for situations where there are available separate datasets for nitrogen and phosphorus fertiliser field experiments. Developing yield response models for Finnish spring barley crops (Hordeum vulgare L.) for clay and coarse soils and applying the models for dynamic economic analysis demonstrate the modelling approach. Model selection is based on iterative elimination from a wide diversity of plausible model formulations. Nonlinear weighted least squares method was utilised in estimation of the yield response models and dynamic programming was utilised in economic analysis. Our results suggest that fertiliser recommendations can be insufficient if soil phosphorus dynamics are ignored. Further, the optimal fertilisation rates for nitrogen and phosphorus, as well as the economic alternative costs of agri-environmental programmes depend on the soil texture of production area. Therefore, the efficiency of such programmes could be improved by targeting different fertilisation limits for different soil textures. In addition, uncertainty analysis revealed that the parameter uncertainty had a greater effect on the model output than the structural uncertainty. Further, the interaction of nitrogen and phosphorus fertilisers appeared to be a factor of relatively minor importance. The modelling approach and the model structure can be extended to other geographical areas, given that adequate datasets are available. This paper provides an approach for modelling joint impact of two main nutrients in crop production for situations where there are available separate datasets for nitrogen and phosphorus fertiliser field experiments. Developing yield response models for Finnish spring barley crops (Hordeum vulgare L.) for clay and coarse soils and applying the models for dynamic economic analysis demonstrate the modelling approach. Model selection is based on iterative elimination from a wide diversity of plausible model formulations. Nonlinear weighted least squares method was utilised in estimation of the yield response models and dynamic programming was utilised in economic analysis. Our results suggest that fertiliser recommendations can be insufficient if soil phosphorus dynamics are ignored. Further, the optimal fertilisation rates for nitrogen and phosphorus, as well as the economic alternative costs of agri-environmental programmes depend on the soil texture of production area. Therefore, the efficiency of such programmes could be improved by targeting different fertilisation limits for different soil textures. In addition, uncertainty analysis revealed that the parameter uncertainty had a greater effect on the model output than the structural uncertainty. Further, the interaction of nitrogen and phosphorus fertilisers appeared to be a factor of relatively minor importance. The modelling approach and the model structure can be extended to other geographical areas, given that adequate datasets are available.