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Bannink, A., van Lingen, H. J., Ellis, J. L., France, J., & Dijkstra, J. (2016). The contribution of mathematical modeling to understanding dynamic aspects of rumen metabolism. Frontiers in Microbiology, 7, 1820.
Abstract: All mechanistic rumen models cover the main drivers of variation in rumen function, which are feed intake, the differences between feedstuffs and feeds in their intrinsic rumen degradation characteristics, and fractional outflow rate of fluid and particulate matter. Dynamic modeling approaches are best suited to the prediction of more nuanced responses in rumen metabolism, and represent the dynamics of the interactions between substrates and micro-organisms and inter-microbial interactions. The concepts of dynamics are discussed for the case of rumen starch digestion as influenced by starch intake rate and frequency of feed intake, and for the case of fermentation of fiber in the large intestine. Adding representations of new functional classes of micro-organisms (i.e., with new characteristics from the perspective of whole rumen function) in rumen models only delivers new insights if complemented by the dynamics of their interactions with other functional classes. Rumen fermentation conditions have to be represented due to their profound impact on the dynamics of substrate degradation and microbial metabolism. Although the importance of rumen pH is generally acknowledged, more emphasis is needed on predicting its variation as well as variation in the processes that underlie rumen fluid dynamics. The rumen wall has an important role in adapting to rapid changes in the rumen environment, clearing of volatile fatty acids (VFA), and maintaining rumen pH within limits. Dynamics of rumen wall epithelia and their role in VFA absorption needs to be better represented in models that aim to predict rumen responses across nutritional or physiological states. For a detailed prediction of rumen N balance there is merit in a dynamic modeling approach compared to the static approaches adopted in current protein evaluation systems. Improvement is needed on previous attempts to predict rumen VFA profiles, and this should be pursued by introducing factors that relate more to microbial metabolism. For rumen model construction, data on rumen microbiomes are preferably coupled with knowledge consolidated in rumen models instead of relying on correlations with rather general aspects of treatment or animal. This helps to prevent the disregard of basic principles and underlying mechanisms of whole rumen function.
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Mansouri, M., Dumont, B., & Destain, M. - F. (2013). Modeling and prediction of nonlinear environmental system using Bayesian methods. Computers and Electronics in Agriculture, 92, 16–31.
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.
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Crout, N. M. J., Craigon, J., Cox, G. M., Jao, Y., Tarsitano, D., Wood, A. T. A., et al. (2014). An objective approach to model reduction: Application to the Sirius wheat model. Agricultural and Forest Meteorology, 189-190(100), 211–219.
Abstract: An existing simulation model of wheat growth and development, Sirius, was evaluated through a systematic model reduction procedure. The model was automatically manipulated under software control to replace variables within the model structure with constants, individually and in combination. Predictions of the resultant models were compared to growth analysis observations of total biomass, grain yield, and canopy leaf area derived from 9 trials conducted in the UK and New Zealand under optimal, nitrogen limiting and drought conditions. Model performance in predicting these observations was compared in order to evaluate whether individual model variables contributed positively to the overall prediction. Of the 1 1 1 model variables considered 16 were identified as potentially redundant. Areas of the model where there was evidence of redundancy were: (a) translocation of biomass carbon to grain; (b) nitrogen physiology; (c) adjustment of air temperature for various modelled processes; (d) allowance for diurnal variation in temperature; (e) vernalisation (f) soil nitrogen mineralisation (g) soil surface evaporation. It is not suggested that these are not important processes in real crops, rather, that their representation in the model cannot be justified in the context of the analysis. The approach described is analogous to a detailed model inter-comparison although it would be better described as a model intra-comparison as it is based on the comparison of many simplified forms of the same model. The approach provides automation to increase the efficiency of the evaluation and a systematic means of increasing the rigour of the evaluation.
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Schmitz, C., Lotze-Campen, H., Gerten, D., Dietrich, J. P., Bodirsky, B., Biewald, A., et al. (2013). Blue water scarcity and the economic impacts of future agricultural trade and demand. Water Resource Research, 49(6), 3601–3617.
Abstract: An increasing demand for agricultural goods affects the pressure on global water resources over the coming decades. In order to quantify these effects, we have developed a new agroeconomic water scarcity indicator, considering explicitly economic processes in the agricultural system. The indicator is based on the water shadow price generated by an economic land use model linked to a global vegetation-hydrology model. Irrigation efficiency is implemented as a dynamic input depending on the level of economic development. We are able to simulate the heterogeneous distribution of water supply and agricultural water demand for irrigation through the spatially explicit representation of agricultural production. This allows in identifying regional hot spots of blue water scarcity and explicit shadow prices for water. We generate scenarios based on moderate policies regarding future trade liberalization and the control of livestock-based consumption, dependent on different population and gross domestic product (GDP) projections. Results indicate increased water scarcity in the future, especially in South Asia, the Middle East, and north Africa. In general, water shadow prices decrease with increasing liberalization, foremost in South Asia, Southeast Asia, and the Middle East. Policies to reduce livestock consumption in developed countries not only lower the domestic pressure on water but also alleviate water scarcity to a large extent in developing countries. It is shown that one of the two policy options would be insufficient for most regions to retain water scarcity in 2045 on levels comparable to 2005.
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Schönhart, M., Mitter, H., Schmid, E., Heinrich, G., & Gobiet, A. (2014). Integrated analysis of climate change impacts and adaptation measures in Austrian agriculture. German Journal of Agricultural Economics, 63(3), 156–176.
Abstract: An integrated modelling framework (IMF) has been developed and applied to analyse climate change impacts and the effectiveness of adaptation measures in Austrian agriculture. The IMF couples the crop rotation model CropRota, the bio-physical process model EPIC and the bottom-up economic land use model PASMA at regional level (NUTS-3) considering agri-environmental indicators. Four contrasting regional climate model (RCM) simulations represent climate change until 2050. The RCM simulations are applied to a baseline and three adaptation and policy scenarios. Climate change increases crop productivity on national average in the IMF. Changes in average gross margins at national level range from 0% to + 5% between the baseline and the three adaptation and policy scenarios. The impacts at NUTS-3 level range from -5% to + 7% between the baseline and the three adaptation and policy scenarios. Adaptation measures such as planting of winter cover crops, reduced tillage and irrigation are effective in reducing yield losses, increasing revenues, or in improving environmental states under climate change. Future research should account for extreme weather events in order to analyse whether average productivity gains at the aggregated level suffice to cover costs from expected higher climate variability.
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