Abstract: An environmental dynamic system is usually modeled as a nonlinear system described by a set of nonlinear ODEs. A central challenge in computational modeling of environmental systems is the determination of the model parameters. In these cases, estimating these variables or parameters from other easily obtained measurements can be extremely useful. This work addresses the problem of monitoring and modeling a leaf area index and soil moisture model (LSM) using state estimation. The performances of various conventional and state-of-the-art state estimation techniques are compared when they are utilized to achieve this objective. These techniques include the extended Kalman filter (EKF), particle filter (PF), and the more recently developed technique variational filter (VF). Specifically, two comparative studies are performed. In the first comparative study, the state variables (the leaf-area index LAI, the volumetric water content of the soil layer 1, HUR1 and the volumetric water content of the soil layer 2, HUR2) are estimated from noisy measurements of these variables, and the various estimation techniques are compared by computing the estimation root mean square error (RMSE) with respect to the noise-free data. In the second comparative study, the state variables as well as the model parameters are simultaneously estimated. In this case, in addition to comparing the performances of the various state estimation techniques, the effect of number of estimated model parameters on the accuracy and convergence of these techniques are also assessed. The results of both comparative studies show that the PF provides a higher accuracy than the EKF, which is due to the limited ability of the EKF to handle highly nonlinear processes. The results also show that the VF provides a significant improvement over the PF because, unlike the PF which depends on the choice of sampling distribution used to estimate the posterior distribution, the VF yields an optimum choice of the sampling distribution, which also accounts for the observed data. The results of the second comparative study show that, for all techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. However, the VF can still provide both convergence as well as accuracy related advantages over other estimation methods. (C) 2013 Elsevier B.V. All rights reserved.

Abstract: This paper is part review and part opinion piece; it has three parts of increasing novelty and speculation in approach. The first presents an overview of how some of the major crop simulation models approach the issue of simulating the responses of crops to changing climatic and weather variables, mainly atmospheric CO2 concentration and increased and/or varying temperatures. It illustrates an important principle in models of a single cause having alternative effects and vice versa. The second part suggests some features, mostly missing in current crop models, that need to be included in the future, focussing on extreme events such as high temperature or extreme drought. The final opinion part is speculative but novel. It describes an approach to deconstruct resource use efficiencies into their constituent identities or elements based on the Kaya-Porter identity, each of which can be examined for responses to climate and climatic change. We give no promise that the final part is correct’, but we hope it can be a stimulation to thought, hypothesis and experiment, and perhaps a new modelling approach.