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Benchmark data set for wheat growth models: field experiments and AgMIP multi-model simulations

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Abstract

The data set includes a current representative management treatment from detailed, quality-tested sentinel field experiments with wheat from four contrasting environments including Australia, The Netherlands, India and Argentina. Measurements include local daily climate data (solar radiation, maximum and minimum temperature, precipitation, surface wind, dew point temperature, relative humidity, and vapor pressure), soil characteristics, frequent growth, nitrogen in crop and soil, crop and soil water and yield components. Simulations include results from 27 wheat models and a sensitivity analysis with 26 models and 30 years (1981-2010) for each location, for elevated atmospheric CO2 and temperature changes, a heat stress sensitivity analysis at anthesis, and a sensitivity analysis with soil and crop management variations and a Global Climate Model end-century scenario.

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... Late century downscaled weather data were derived from the UKMO HadCM3 realization of the A2 IPCC scenario (high emissions, 734 ppm CO 2 at 2085), and compared with baseline (360 ppm CO 2 ). The dataset in Asseng et al. (2013Asseng et al. ( , 2016 also includes results from model sensitivity analyses to changes in temperatures and CO 2 concentrations. We chose here to focus on the outputs of calibrated models run in the four sites, to analyze their behaviour under baseline and late century scenarios. ...
... This dataset includes, for each site and each scenario, the annual simulations' results of the 27 models. Available outputs are grain yield (kg ha À1 ), and 38 intermediate outputs (see some examples in Table 1, and the exhaustive list in the datafiles of Asseng et al., 2016). ...
... These groups were composed by 20 and 7 models in baseline, and by 22 and 5 models in late century scenario (Fig. 7). GLAM-wheat, MONICA, EPIC-Wheat and AquaCrop were grouped together in Asseng et al. (2013Asseng et al. ( , 2016. Right: Significant and of the right sign, Wrong: significant and of the opposite sign, NS ¼ not significant, NA ¼ not available as missing data, LC ¼ late century scenario, BA ¼ baseline. ...
Article
Crop models are reference tools that can be used to evaluate the performances of cropping systems under current and future agro-climatic scenarios. A recent trend is the adoption of multi-model ensembles, as crop model responses vary across pedoclimatic contexts. We present the web application MOBEDIS, aimed at investigating the causes of differences in crop models’ behaviour. MOBEDIS combines non-parametric statistical methods (Spearman correlation, Random Forest, Hierarchical clustering, Mantel statistics) to analyze and cluster crop models according to the relationship between final outputs (e.g., yield) and a set of intermediate outputs related to plant processes. We applied MOBEDIS in three case studies to (1) discuss its capability to facilitate the understanding of the behaviour of two crop models in a simulation experiment, and (2) prove its applicability for model ensemble studies. MOBEDIS is freely available and ready-to-use for understanding single model responses and identifying groups of crop models sharing similar behaviour.
... Phase 2a (Asseng et al 2015a(Asseng et al , 2015b Protocol-based multi-model analysis of temperature response at Hot Serial Cereals artificial heating experiment in Arizona and temperature responses in Mexico. ...
... Phase 2b (Asseng et al 2015a, 2015b, Liu et al 2016 Intercomparison of temperature responses across 30 sites selected as a representative network of well-watered wheat production regions around the world. ...
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Integrated assessment models (IAMs) hold great potential to assess how future agricultural systems will be shaped by socioeconomic development, technological innovation, and changing climate conditions. By coupling with climate and crop model emulators, IAMs have the potential to resolve important agricultural feedback loops and identify unintended consequences of socioeconomic development for agricultural systems. Here we propose a framework to develop robust representation of agricultural system responses within IAMs, linking downstream applications with model development and the coordinated evaluation of key climate responses from local to global scales. We survey the strengths and weaknesses of protocol-based assessments linked to the Agricultural Model Intercomparison and Improvement Project (AgMIP), each utilizing multiple sites and models to evaluate crop response to core climate changes including shifts in carbon dioxide concentration, temperature, and water availability, with some studies further exploring how climate responses are affected by nitrogen levels and adaptation in farm systems. Site-based studies with carefully calibrated models encompass the largest number of activities; however they are limited in their ability to capture the full range of global agricultural system diversity. Representative site networks provide more targeted response information than broadly-sampled networks, with limitations stemming from difficulties in covering the diversity of farming systems. Global gridded crop models provide comprehensive coverage, although with large challenges for calibration and quality control of inputs. Diversity in climate responses underscores that crop model emulators must distinguish between regions and farming system while recognizing model uncertainty. Finally, to bridge the gap between bottom-up and top-down approaches we recommend the deployment of a hybrid climate response system employing a representative network of sites to bias-correct comprehensive gridded simulations, opening the door to accelerated development and a broad range of applications.
... Open sharing of data and model parameterisations for crops/ systems modelling would be very useful to further interpret simulation results and model improvement. All the data used in this study will be available and published in a data paper, analog to other AgMIP studies (Asseng et al. 2016;. ...
Article
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To better understand how climate change might influence global canola production, scientists from six countries have completed the first inter-comparison of eight crop models for simulating growth and seed yield of canola, based on experimental data from six sites across five countries. A sensitivity analysis was conducted with a combination of five levels of atmospheric CO2 concentrations, seven temperature changes, five precipitation changes, together with five nitrogen application rates. Our results were in several aspects different from those of previous model inter-comparison studies for wheat, maize, rice, and potato crops. A partial model calibration only on phenology led to very poor simulation of aboveground biomass and seed yield of canola, even from the ensemble median or mean. A full calibration with additional data of leaf area index, biomass, and yield from one treatment at each site reduced simulation error of seed yield from 43.8 to 18.0%, but the uncertainty in simulation results remained large. Such calibration (with data from one treatment) was not able to constrain model parameters to reduce simulation uncertainty across the wide range of environments. Using a multi-model ensemble mean or median reduced the uncertainty of yield simulations, but the simulation error remained much larger than observation errors, indicating no guarantee that the ensemble mean/median would predict the correct responses. Using multi-model ensemble median, canola yield was projected to decline with rising temperature (2.5–5.7% per °C), but to increase with increasing CO2 concentration (4.6–8.3% per 100-ppm), rainfall (2.1–6.1% per 10% increase), and nitrogen rates (1.3–6.0% per 10% increase) depending on locations. Due to the large uncertainty, these results need to be treated with caution. We further discuss the need to collect new data to improve modelling of several key physiological processes of canola for increased confidence in future climate impact assessments.
... Phase 2a (Asseng et al 2015a(Asseng et al , 2015b Protocol-based multi-model analysis of temperature response at Hot Serial Cereals artificial heating experiment in Arizona and temperature responses in Mexico. ...
Article
Full-text available
Integrated assessment models (IAMs) hold great potential to assess how future agricultural systems will be shaped by socioeconomic development, technological innovation, and changing climate conditions. By coupling with climate and crop model emulators, IAMs have the potential to resolve important agricultural feedback loops and identify unintended consequences of socioeconomic development for agricultural systems. Here we propose a framework to develop robust representation of agricultural system responses within IAMs, linking downstream applications with model development and the coordinated evaluation of key climate responses from local to global scales. We survey the strengths and weaknesses of protocol-based assessments linked to the Agricultural Model Intercomparison and Improvement Project (AgMIP), each utilizing multiple sites and models to evaluate crop response to core climate changes including shifts in carbon dioxide concentration, temperature, and water availability, with some studies further exploring how climate responses are affected by nitrogen levels and adaptation in farm systems. Site-based studies with carefully calibrated models encompass the largest number of activities; however they are limited in their ability to capture the full range of global agricultural system diversity. Representative site networks provide more targeted response information than broadly-sampled networks, with limitations stemming from difficulties in covering the diversity of farming systems. Global gridded crop models provide comprehensive coverage, although with large challenges for calibration and quality control of inputs. Diversity in climate responses underscores that crop model emulators must distinguish between regions and farming system while recognizing model uncertainty. Finally, to bridge the gap between bottom-up and top-down approaches we recommend the deployment of a hybrid climate response system employing a representative network of sites to bias-correct comprehensive gridded simulations, opening the door to accelerated development and a broad range of applications.
... (iii) Modernize data storage and interoperability. Collaboration across researchers in crop modeling in global or regional projects, including the Agricultural Model Inter-comparison Project (AgMIP), has helped the crop modeling community to identify high-value datasets (Asseng et al., 2015;Raymundo et al., 2018), resulting in improved models with greater applicability for breeding under future climates, for example for heat stress response on wheat (Asseng et al., , 2019b, or CO 2 response on maize (Durand et al., 2018). ...
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Crop improvement efforts aiming at increasing crop production (quantity, quality) and adapting to climate change have been subject of active research over the past years. But, the question remains ‘to what extent can breeding gains be achieved under a changing climate, at a pace sufficient to usefully contribute to climate adaptation, mitigation and food security?’. Here, we address this question by critically reviewing how model‐based approaches can be used to assist breeding activities, with particular focus on all CGIAR (formerly the Consultative Group on International Agricultural Research but now known simply as CGIAR) breeding programs. Crop modeling can underpin breeding efforts in many different ways, including assessing genotypic adaptability and stability, characterizing and identifying target breeding environments, identifying tradeoffs among traits for such environments, and making predictions of the likely breeding value of the genotypes. Crop modeling science within the CGIAR has contributed to all of these. However, much progress remains to be done if modeling is to effectively contribute to more targeted and impactful breeding programs under changing climates. In a period in which CGIAR breeding programs are undergoing a major modernization process, crop modelers will need to be part of crop improvement teams, with a common understanding of breeding pipelines and model capabilities and limitations, and common data standards and protocols, to ensure they follow and deliver according to clearly defined breeding products. This will, in turn, enable more rapid and better‐targeted crop modeling activities, thus directly contributing to accelerated and more impactful breeding efforts.
... In the following, we exemplify the ongoing model improvement efforts by presenting major outputs from five interconnected papers documenting the scientific work (Asseng et al., 2015a;Wang et al., 2017a), as well as the associated data (Asseng et al., 2015b;Martre et al., 2017a,b). ...
Article
Climate change implies higher frequency and magnitude of agroclimatic extremes threatening plant production and the provision of other ecosystem services. This review is motivated by a mismatch between advances made regarding deeper understanding of abiotic stress physiology and its incorporation into ecophysiological models in order to more accurately quantifying the impacts of extreme events at crop system or higher aggregation levels. Adverse agroclimatic extremes considered most detrimental to crop production include drought, heat, heavy rains/hail and storm, flooding and frost, and, in particular, combinations of them. Our core question is: How have and could empirical data be exploited to improve the capability of widely used crop simulation models in assessing crop impacts of key agroclimatic extremes for the globally most important grain crops? To date there is no comprehensive review synthesizing available knowledge for a broad range of extremes, grain crops and crop models as a basis for identifying research gaps and prospects. To address these issues, we selected eight major grain crops and performed three systematic reviews using SCOPUS for period 1995-2016. Furthermore, we amended/complemented the reviews manually and performed an in-depth analysis using a sub-sample of papers. Results show that by far the majority of empirical studies (1631 out of 1772) concentrate on the three agroclimatic extremes drought, heat and heavy rain and on the three major staples wheat, maize and rice (1259 out of 1772); the concentration on just a few has increased over time. With respect to modelling studies two model families, i.e. CERES-DSSAT and APSIM, are clearly dominating for wheat and maize; for rice, ORYZA2000 and CERES-Rice predominate and are equally strong. For crops other than maize and wheat the number of studies is small. Empirical and modelling papers don't differ much in the proportions the various extreme events are dealt with-drought and heat stress together account for approx. 80% of the studies. There has been a dramatic increase in the number of papers, especially after 2010. As a way forward, we suggest to have very targeted and well-designed experiments on the specific crop impacts of a given extreme as well as of combinations of them. This in particular refers to extremes addressed with insufficient specificity (e.g. drought) or being under-researched in relation to their economic importance (heavy rains/storm and flooding). Furthermore, we strongly recommend extending research to crops other than wheat, maize and rice.
... Nevertheless, the need for improved model structures, i.e. improved representation of biomass production, soil temperature and soil water content, to reduce uncertainty is shown by a multi-model intercomparison project for grassland models (Houska et al., 2017;Ma et al., 2014;Sándor et al., 2016aSándor et al., , 2016b and by the vast number of model intercomparison studies on wheat (Asseng et al., 2014;Kollas et al., 2015;Rosenzweig et al., 2013Rosenzweig et al., , 2014Rötter et al., 2012). Moreover, the utilization of benchmark datasets for growth models as presented by Asseng et al. (2015) is helpful to identify uncertainties. ...
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Elevated CO2 (eCO2) reduces transpiration at the leaf level by inducing stomatal closure. However, this water saving effect might be offset at the canopy level by increased leaf area as a consequence of eCO2 fertilization. To investigate this bi-directional effect, we coupled a plant growth and a soil hydrological model. The model performance and the uncertainty in model parameters were checked using a 13 year data set of a Free Air Carbon dioxide Enrichment (FACE) experiment on grassland in Germany. We found a good agreement of simulated and observed data for soil moisture and total above-ground dry biomass (TAB) under ambient CO2 (∼395 ppm) and eCO2 (∼480 ppm). Optima for soil and plant growth model parameters were identified, which can be used in future studies. Our study presents a robust modelling approach for the investigation of effects of eCO2 on grassland biomass and water dynamics. We show an offset of the stomatal water saving effect at the canopy level because of a significant increase in TAB (6.5%, p < 0.001) leading to an increase in transpiration by +3.0 ± 6.0 mm, though insignificant (p = 0.1). However, the increased water loss through transpiration was counteracted by a significant decrease in soil evaporation (−2.1 ± 1.7 mm, p < 0.01) as a consequence of higher TAB. Hence, evapotranspiration was not affected by the increased eCO2 (+0.9 ± 4.9 mm, p = 0.5). This in turn led to a significantly better performance of the water use efficiency by 5.2% (p < 0.001). Our results indicate that mown, temperate grasslands can benefit from an increasing biomass production while maintaining water consumption at the +20% increase of eCO2 studied.
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CONTEXT Process-based greenhouse climate models are valuable tools for the analysis and design of greenhouse systems. A growing number of greenhouse models are published in recent years, making it difficult to identify which components are shared across models, which are new developments, and what are the objectives, strengths and weaknesses of each model. OBJECTIVE We present an overview of the current state of greenhouse modelling by analyzing studies published between 2018 and 2020. This analysis helps identify the key processes considered in process-based greenhouse models, and the common approaches used to model them. Moreover, we outline how greenhouse models differ in terms of their objectives, complexity, accuracy, and transparency. METHODS We describe a general structure of process-based greenhouse climate models, including a range of common approaches for describing the various model components. We analyze recently published models with respect to this structure, as well as their intended purposes, greenhouse systems they represent, equipment included, and crops considered. We present a model inheritance chart, outlining the origins of contemporary models, and showing which were built on previous works. We compare model validation studies and show the various types of datasets and metrics used for validation. RESULTS AND CONCLUSIONS The analysis highlights the range of objectives and approaches prevalent in greenhouse modelling, and shows that despite the large variation in model design and complexity, considerable overlap exists. Some possible reasons for the abundance of models include a lack of transparency and code availability; a belief that model development is in itself a valuable research goal; a preference for simple models in control-oriented studies; and a difference in the time scales considered. Approaches to model validation vary considerably, making it difficult to compare models or assess if they serve their intended purposes. We suggest that increased transparency and availability of source code will promote model reuse and extension, and that shared datasets and evaluation benchmarks will facilitate model evaluation and comparison. SIGNIFICANCE This study highlights several issues that should be considered in greenhouse model selection and development. Developers of new models can use the decomposition provided in order to present their models and facilitate extension and reuse. Developers are encouraged to reflect on and explicitly state their model's range of suitability, complexity, validity, and transparency. Lastly, we highlight several steps that could be taken by the greenhouse modelling community in order to advance the field as a whole.
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A recent innovation in assessment of climate change impact on agricultural production has been to use crop multi model ensembles (MMEs). These studies usually find large variability between individual models but that the ensemble mean (e‐mean) and median (e‐median) often seem to predict quite well. However few studies have specifically been concerned with the predictive quality of those ensemble predictors. We ask what is the predictive quality of e‐mean and e‐median, and how does that depend on the ensemble characteristics. Our empirical results are based on five MME studies applied to wheat, using different data sets but the same 25 crop models. We show that the ensemble predictors have quite high skill and are better than most and sometimes all individual models for most groups of environments and most response variables. Mean squared error of e‐mean decreases monotonically with the size of the ensemble if models are added at random, but has a minimum at usually 2‐6 models if best‐fit models are added first. Our theoretical results describe the ensemble using four parameters; average bias, model effect variance, environment effect variance and interaction variance. We show analytically that mean squared error of prediction (MSEP) of e‐mean will always be smaller than MSEP averaged over models, and will be less than MSEP of the best model if squared bias is less than the interaction variance. If models are added to the ensemble at random, MSEP of e‐mean will decrease as the inverse of ensemble size, with a minimum equal to squared bias plus interaction variance. This minimum value is not necessarily small, and so it is important to evaluate the predictive quality of e‐mean for each target population of environments. These results provide new information on the advantages of ensemble predictors, but also show their limitations. This article is protected by copyright. All rights reserved.
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Crop models are widely used in agricultural impact studies. However, many studies have reported large uncertainties from single-model-based simulation analyses, suggesting the need for multi-model simulation capabilities. In this study, the APSIM-Nwheat model was integrated into the Decision Support System for Agro-technology (DSSAT), which already includes two wheat models, to create multi-model simulation capabilities for wheat cropping systems analysis. The new model in DSSAT (DSSAT-Nwheat) was evaluated using more than 1000 observations from field experiments of 65 treatments, which included a wide range of nitrogen fertilizer applications, water supply (irrigation and rainout shelter), planting dates, elevated atmospheric CO2 concentrations, temperature variations, cultivars, and soil types in diverse climatic regions that represented the main wheat growing areas of the world. DSSAT-Nwheat reproduced the observed grain yields well with an overall root mean square deviation (RMSD) of 0.89 t/ha (13%). Nitrogen applications, water supply, and planting dates had large effects on observed biomass and grain yields, and the model reproduced these crop responses well. Crop total biomass and nitrogen uptake were reproduced well despite relatively poor simulations of observed leaf area measurements during the growing season. The low sensitivity of biomass simulations to poor simulations of leaf area index (LAI) were due to little changes in intercepted solar radiation at LAI >3 and water and nitrogen stress often limiting photosynthesis and growth rather than light interception at low LAI. The responses of DSSAT-Nwheat to temperature variations and elevated atmospheric CO2 concentrations were close to observed responses. When compared with the two other DSSAT-wheat models (CERES and CROPSIM), these responses were similar, except for the responses to hot environments, due to different approaches in modeling heat stress effects. The comprehensive evaluation of the DSSAT-Nwheat model with field measurements, including a comparison with two other DSSAT-wheat models, created a multi-model simulation platform that allows the quantification of model uncertainties in wheat impact assessments.
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APSIM-wheat is a crop system simulation model, consisting of modules that incorporate aspects of soil water, nitrogen (N), residues, and crop development. The model was used to simulate above- and belowground growth, grain yield, water and N uptake, and soil water and soil N in wheat crops in Western Australia. Model outputs were compared with detailed field experiments from four rainfall zones, three soil types, and five wheat genotypes. The field experiments covered 10 seasons, with variations in sowing date, plant density, N fertiliser, deep ripping and irrigation. The overall APSIM model predictions of shoot growth, root depth, water and N uptake, soil water, soil N, drainage and nitrate leaching were found to be acceptable. Grain yields were well predicted with a coefficient of determination r2(1:1)=0.77, despite some underestimation during severe terminal droughts. Yields tended to be underestimated during terminal droughts due to insufficient pre-anthesis stored carbohydrates being remobilised to the grain. Simulation of grain protein, and depth to the perched water table showed limited accuracy when compared with field measurements. In particular, grain protein tended to be overpredicted at high protein levels and underpredicted at low levels. However, specific simulation studies to predict biomass, yield, drainage and nitrate leaching are now possible for wheat crops on the tested soil types and rainfall zones in Western Australia.
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Projections of climate change impacts on crop yields are inherently uncertain. Uncertainty is often quantified when projecting future greenhouse gas emissions and their influence on climate. However, multi-model uncertainty analysis of crop responses to climate change is rare because systematic and objective comparisons among process-based crop simulation models are difficult. Here we present the largest standardized model intercomparison for climate change impacts so far. We found that individual crop models are able to simulate measured wheat grain yields accurately under a range of environments, particularly if the input information is sufficient. However, simulated climate change impacts vary across models owing to differences in model structures and parameter values. A greater proportion of the uncertainty in climate change impact projections was due to variations among crop models than to variations among downscaled general circulation models. Uncertainties in simulated impacts increased with CO 2 concentrations and associated warming. These impact uncertainties can be reduced by improving temperature and CO 2 relationships in models and better quantified through use of multi-model ensembles. Less uncertainty in describing how climate change may affect agricultural productivity will aid adaptation strategy development andpolicymaking.
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Crop models of crop growth are increasingly used to quantify the impact of global changes due to climate or crop management. Therefore, accuracy of simulation results is a major concern. Studies with ensembles of crop models can give valuable information about model accuracy and uncertainty, but such studies are difficult to organize and have only recently begun. We report on the largest ensemble study to date, of 27 wheat models tested in four contrasting locations for their accuracy in simulating multiple crop growth and yield variables. The relative error averaged over models was 24-38% for the different end-of-season variables including grain yield (GY) and grain protein concentration (GPC). There was little relation between error of a model for GY or GPC and error for in-season variables. Thus, most models did not arrive at accurate simulations of GY and GPC by accurately simulating preceding growth dynamics. Ensemble simulations, taking either the mean (e-mean) or median (e-median) of simulated values, gave better estimates than any individual model when all variables were considered. Compared to individual models, e-median ranked first in simulating measured GY and third in GPC. The error of e-mean and e-median declined with an increasing number of ensemble members, with little decrease beyond 10 models. We conclude that multimodel ensembles can be used to create new estimators with improved accuracy and consistency in simulating growth dynamics. We argue that these results are applicable to other crop species, and hypothesize that they apply more generally to ecological system models. This article is protected by copyright. All rights reserved.
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Increasing use of regionally and globally oriented impacts studies, coordinated across international modelling groups, promises to bring about a new era in climate impacts research. Coordinated cycles of model improvement and projection are needed to make the most of this potential.
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Projections of climate change impacts on crop yields are inherently uncertain. Uncertainty is often quantified when projecting future greenhouse gas emissions and their influence on climate. However, multi-model uncertainty analysis of crop responses to climate change is rare because systematic and objective comparisons among process-based crop simulation models are difficult. Here we present the largest standardized model intercomparison for climate change impacts so far. We found that individual crop models are able to simulate measured wheat grain yields accurately under a range of environments, particularly if the input information is sufficient. However, simulated climate change impacts vary across models owing to differences in model structures and parameter values. A greater proportion of the uncertainty in climate change impact projections was due to variations among crop models than to variations among downscaled general circulation models. Uncertainties in simulated impacts increased with CO2 concentrations and associated warming. These impact uncertainties can be reduced by improving temperature and CO2 relationships in models and better quantified through use of multi-model ensembles. Less uncertainty in describing how climate change may affect agricultural productivity will aid adaptation strategy development and policy making.
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A simulation model for winter wheat growth, crop nitrogen dynamics and soil nitrogen supply was tested against experimental data. When simulations of dry matter production agreed with measurements, nitrogen uptake was simulated accurately. The total amount of soil mineral nitrogen as well as the distribution of mineral nitrogen over the various soil layers were generally simulated well, except for experiments in which fertilizer was applied late in spring. In these experiments, applied nitrogen disappeared because it could not be accounted for by the model. Some explanations for this disappearance are briefly discussed.
Evaluation of Soil Water Status, Plant Growth and Canopy Environment in Relation to Variable Water Supply to Wheat
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Comparing Ceres-Wheat and Sucros2 in the Argentinean Cereal Region
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Travasso, M.I., M.R. Rodriguez and M.O. Grondona. 1995. "Comparing Ceres-Wheat and Sucros2 in the Argentinean Cereal Region." Pp. 366-69 in International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand, edited by A. Zerger and R. M. Argent. The University of Newcastle, Australia: Modelling and Simulation Society of Australia Inc.
The University of Newcastle, Australia: Modelling and Simulation Society of Australia Inc
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Argent. The University of Newcastle, Australia: Modelling and Simulation Society of Australia Inc.
Performance of the Apsim-Wheat Model in Western Australia
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Asseng, S., B. A. Keating, I. R. P. Fillery, P. J. Gregory, J. W. Bowden, N. C. Turner, J. A. Palta and D. G. Abrecht. 1998. "Performance of the Apsim-Wheat Model in Western Australia." Field Crops Research 57(2):163-79. http://dx.doi.org/10.1016/S0378-4290(97)00117-2.