Crop models describe the growth and development of a crop interacting with soil, climate, and management techniques. They are constituted by a system of difference equations (mostly nonlinear) which describe the evolution over time of state variables, such as plant biomass, leaf area index (LAI), soil moisture, ...The main problem is that parameter estimation is not a straightforward regression problem, since crop models include many parameters (for example, 200 parameters in the STICS model), while the available field data are limited in time and space and present some noise.
Parameter estimation can be viewed as an optimal filtering problem, which consists of recursively updating the posterior distribution of the unobserved state given the sequence of observed data and the state evolution model. It has been addressed with several methods, such as the Kalman Filter (KF) which provides an optimal Bayesian solution but is limited by the non-universal Gaussian modeling assumptions. Amongst the methods overcoming these limitations, two methods have recently gained popularity: the Particle Filter (PF) and the variational filtering (VF). The objectives of the paper are to compare both methods (PF and VF) in parameters estimation and evaluating a crop model.
The PF approximates the probability distribution by a set of weighted samples. It has the flexibility to accommodate non-linear dynamics and multi-modal observation model but at the cost of more computation and storage requirement. While, VF is proposed for approximating intractable integrals in Bayesian statistics. By using a separable approximating distribution to lower bound the marginal likelihood, an analytical approximation to the posterior probability is provided by minimizing the Kullback-Leibler divergence.
The model for which the methods are tested is a part of the STICS model. The data are issued from experiments carried out on a silty soil in Belgium, with a wheat crop (Triticum aestivum L.) during 3 years. A wireless monitoring system completed by a micrometeorological station is used for measuring soil and climate characteristics. The plant characteristics (LAI and biomass) are regularly manually measured. The model equations are integrated to estimate two important response variables: the LAI and the soil moisture. Evaluation of the methods is performed by using RMSE, normalized deviation and model efficiency.
