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Mansouri, M., Dumont, B., Leemans, V., & Destain, M. - F. (2014). Bayesian methods for predicting LAI and soil water content. Precision Agric., 15(2), 184–201.
Abstract: LAI of winter wheat (Triticum aestivum L.) and soil water content of the topsoil (200 mm) and of the subsoil (500 mm) were considered as state variables of a dynamic soil-crop system. This system was assumed to progress according to a Bayesian probabilistic state space model, in which real values of LAI and soil water content were daily introduced in order to correct the model trajectory and reach better future evolution. The chosen crop model was mini STICS which can reduce the computing and execution times while ensuring the robustness of data processing and estimation. To predict simultaneously state variables and model parameters in this non-linear environment, three techniques were used: extended Kalman filtering (EKF), particle filtering (PF), and variational filtering (VF). The significantly improved performance of the VF method when compared to EKF and PF is demonstrated. The variational filter has a low computational complexity and the convergence speed of states and parameters estimation can be adjusted independently. Detailed case studies demonstrated that the root mean square error of the three estimated states (LAI and soil water content of two soil layers) was smaller and that the convergence of all considered parameters was ensured when using VF. Assimilating measurements in a crop model allows accurate prediction of LAI and soil water content at a local scale. As these biophysical properties are key parameters in the crop-plant system characterization, the system has the potential to be used in precision farming to aid farmers and decision makers in developing strategies for site-specific management of inputs, such as fertilizers and water irrigation.
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Ben Touhami, H., & Bellocchi, G. (2015). Bayesian calibration of the Pasture Simulation model (PaSim) to simulate European grasslands under water stress. Ecological Informatics, 30, 356–364.
Abstract: As modeling becomes a more widespread practice in the agro-environmental sciences, scientists need reliable tools to calibrate models against ever more complex and detailed data. We present a generic Bayesian computation framework for grassland simulation, which enables parameter estimation in the Bayesian formalism by using Monte Carlo approaches. We outline the underlying rationale, discuss the computational issues, and provide results from an application of the Pasture Simulation model (PaSim) to three European grasslands. The framework was suited to investigate the challenging problem of calibrating complex biophysical models to data from altered scenarios generated by precipitation reduction (water stress conditions). It was used to infer the parameters of manipulated grassland systems and to assess the gain in uncertainty reduction by updating parameter distributions using measurements of the output variables.
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Makowski, D. (2017). A simple Bayesian method for adjusting ensemble of crop model outputs to yield observations. Europ. J. Agron., 88, 76–83.
Abstract: Multi-model forecasting has drawn some attention in crop science for evaluating effect of climate change on crop yields. The principle is to run several individual process-based crop models under several climate scenarios in order to generate ensembles of output values. This paper describes a simple Bayesian method – called Bayes linear method- for updating ensemble of crop model outputs using yield observations. The principle is to summarize the ensemble of crop model outputs by its mean and variance, and then to adjust these two quantities to yield observations in order to reduce uncertainty. The adjusted mean and variance combine two sources of information, i.e., the ensemble of crop model outputs and the observations. Interestingly, with this method, observations collected under a given climate scenario can be used to adjust mean and variance of the model ensemble under a different scenario. Another advantage of the proposed method is that it does not rely on a separate calibration of each individual crop model. The uncertainty reduction resulting from the adjustment of an ensemble of crop models to observations was assessed in a numerical application. The implementation of the Bayes linear method systematically reduced uncertainty, but the results showed the effectiveness of this method varied in function of several factors, especially the accuracy of the yield observation, and the covariance between the crop model output and the observation. (C) 2015 Elsevier B.V. All rights reserved.
Keywords: Bayesian method; Climate change; Ensemble modelling; Uncertainty; Yield; Linear-Approach; Climate-Change; CO2
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