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: Croplands play an important role in the carbon budget of many regions. However, the estimation of their carbon balance remains difficult due to diversity and complexity of the processes involved. We report the coupling of a one-dimensional soil water, heat, and CO2 flux model (SOILCO2), a pool concept of soil carbon turnover (RothC), and a crop growth module (SUCROS) to predict the net ecosystem exchange (NEE) of carbon. The coupled model, further referred to as AgroC, was extended with routines for managed grassland as well as for root exudation and root decay. In a first step, the coupled model was applied to two winter wheat sites and one upland grassland site in Germany. The model was calibrated based on soil water content, soil temperature, biometric, and soil respiration measurements for each site, and validated in terms of hourly NEE measured with the eddy covariance technique. The overall model performance of AgroC was sufficient with a model efficiency above 0.78 and a correlation coefficient above 0.91 for NEE. In a second step, AgroC was optimized with eddy covariance NEE measurements to examine the effect of different objective functions, constraints, and data-transformations on estimated NEE. It was found that NEE showed a distinct sensitivity to the choice of objective function and the inclusion of soil respiration data in the optimization process. In particular, both positive and negative day- and nighttime fluxes were found to be sensitive to the selected optimization strategy. Additional consideration of soil respiration measurements improved the simulation of small positive fluxes remarkably. Even though the model performance of the selected optimization strategies did not diverge substantially, the resulting cumulative NEE over simulation time period differed substantially. Therefore, it is concluded that data transformations, definitions of objective functions, and data sources have to be considered cautiously when a terrestrial ecosystem model is used to determine NEE by means of eddy covariance measurements. (C) 2017 Elsevier B.V. All rights reserved.