Modeling and Prediction of Time-Varying Environmental Data Using Advanced Bayesian Methods

Modeling and Prediction of Time-Varying Environmental Data Using Advanced Bayesian Methods

Majdi Mansouri (Université de Liège, Belgium), Benjamin Dumont (Université de Liège, Belgium) and Marie-France Destain (Université de Liège, Belgium)
Copyright: © 2014 |Pages: 26
DOI: 10.4018/978-1-4666-4785-5.ch007
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Abstract

The problem of state/parameter estimation represents a key issue in crop models, which are nonlinear, non-Gaussian, and include a large number of parameters. The prediction errors are often important due to uncertainties in the equations, the input variables, and the parameters. The measurements needed to run the model and to perform calibration and validation are sometimes not numerous or known with some uncertainty. In these cases, estimating the state variables and/or parameters from easily obtained measurements can be extremely useful. In this chapter, the authors address the problem of modeling and prediction of time-varying Leaf area index and Soil Moisture (LSM) to better handle nonlinear and non-Gaussian processes without a priori state information. The performances of various conventional and state-of-the-art estimation techniques are compared when they are utilized to achieve this objective. These techniques include the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Particle Filter (PF), and the more recently developed technique Variational Bayesian Filter (VF). The original data was issued from experiments carried out on silty soil in Belgium with a wheat crop during two consecutive years, the seasons 2008-09 and 2009-10.
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1. Introduction

Parameter and states estimation in nonlinear environmental systems is an important issue in diagnosis, measurement and modeling. However, due to the difficulty of, or cost associated with, obtaining these measurements, state and/or parameter estimators are often used to overcome this problem. Crop models such as EPIC (Williams et al., 1989), WOFOST (Diepen et al., 1989), DAISY (Hansen et al., 1990), STICS (Brisson et al., 1998), and SALUS (Basso and Ritchie, 2005) are dynamic non-linear models that describe the growth and development of a crop interacting with environmental factors (soil and climate) and agricultural practices (crop species, tillage type, fertilizer amount, etc.). They are developed to predict crop yield and quality or to optimize the farming practices in order to satisfy environmental objectives, as the reduction of nitrogen lixiviation. More recently, crop models are used to simulate the effects of climate changes on the agricultural production. Nevertheless, the prediction errors of these models may be important due to uncertainties in the estimates of initial values of the states, in input data, in the parameters, and in the equations. The measurements needed to run the model are sometimes not numerous, whereas the field spatial variability and the climatic temporal fluctuations over the field may be high. The degree of accuracy is therefore difficult to estimate, apart from numerous repetitions of measurements. For these reasons, the problem of state/parameter estimation represents a key issue in such nonlinear and non-Gaussian crop models including a large number of parameters, while measurement noise exists in the data.

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