Application of an interacting particle filter to improve nitrogen nutrition index predictions for winter wheat

Dynamic crop models predict several state variables at a daily time step and thus provide useful information for optimizing agricultural techniques. But the prediction errors of these models are often large due to uncertainties in parameters, initial state values, and equations. Monte Carlo sequential methods, like the interacting particle filter [Del Moral, 1996. Nonlinear filtering: interacting particle solution. Markov Process. Relat. Fields 2, 555–580], can be used to update the state variable values predicted by nonlinear dynamic models from a set of measurements and thus reduce the prediction errors. An interesting feature of these methods is that they do not require a linearization of the original nonlinear model. Up to now, these methods have never been applied to complex dynamic crop models. In this paper, the interacting particle filter was used to update the Azodyn model, a dynamic winter wheat crop model, at 10 or 11 dates, from biomass and nitrogen uptake measurements, and to predict a variable of practical interest, the nitrogen nutrition index. We showed that the implementation of this method can reduce the root mean squared error by 66.7–79.7% for the nitrogen nutrition index, but that the filter is highly sensitive to the assumptions made about the probability distribution of the model errors. We also showed that the particle filter gives stable results with 10,000 Monte Carlo simulations and that this number of simulations can be performed in a very reasonable calculation time.