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Wallach, D., Thorburn, P., Asseng, S., Challinor, A. J., Ewert, F., Jones, J. W., et al. (2016). Estimating model prediction error: Should you treat predictions as fixed or random. Env. Model. Softw., 84, 529–539.
Abstract: Crop models are important tools for impact assessment of climate change, as well as for exploring management options under current climate. It is essential to evaluate the uncertainty associated with predictions of these models. We compare two criteria of prediction error; MSEPfixed, which evaluates mean squared error of prediction for a model with fixed structure, parameters and inputs, and MSEPuncertain(X), which evaluates mean squared error averaged over the distributions of model structure, inputs and parameters. Comparison of model outputs with data can be used to estimate the former. The latter has a squared bias term, which can be estimated using hindcasts, and a model variance term, which can be estimated from a simulation experiment. The separate contributions to MSEPuncertain(X) can be estimated using a random effects ANOVA. It is argued that MSEPuncertain(X) is the more informative uncertainty criterion, because it is specific to each prediction situation.
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Murat, M., Malinowska, I., Hoffmann, H., & Baranowski, P. (2016). Statistical modelling of agrometeorological time series by exponential smoothing. International Agrophysics, 30(1), 57–65.
Abstract: Meteorological time series are used in modelling agrophysical processes of the soil-plant-atmosphere system which determine plant growth and yield. Additionally, longterm meteorological series are used in climate change scenarios. Such studies often require forecasting or projection of meteorological variables, eg the projection of occurrence of the extreme events. The aim of the article was to determine the most suitable exponential smoothing models to generate forecast using data on air temperature, wind speed, and precipitation time series in Jokioinen (Finland), Dikopshof (Germany), Lleida (Spain), and Lublin (Poland). These series exhibit regular additive seasonality or non-seasonality without any trend, which is confirmed by their autocorrelation functions and partial autocorrelation functions. The most suitable models were indicated by the smallest mean absolute error and the smallest root mean squared error.
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Refsgaard, J. C., Madsen, H., Andréassian, V., Arnbjerg-Nielsen, K., Davidson, T. A., Drews, M., et al. (2014). A framework for testing the ability of models to project climate change and its impacts. Clim. Change, 122(1-2), 271–282.
Abstract: Models used for climate change impact projections are typically not tested for simulation beyond current climate conditions. Since we have no data truly reflecting future conditions, a key challenge in this respect is to rigorously test models using proxies of future conditions. This paper presents a validation framework and guiding principles applicable across earth science disciplines for testing the capability of models to project future climate change and its impacts. Model test schemes comprising split-sample tests, differential split-sample tests and proxy site tests are discussed in relation to their application for projections by use of single models, ensemble modelling and space-time-substitution and in relation to use of different data from historical time series, paleo data and controlled experiments. We recommend that differential-split sample tests should be performed with best available proxy data in order to build further confidence in model projections.
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Dumont, B., Basso, B., Leemans, V., Bodson, B., Destain, J. - P., & Destain, M. - F. (2015). A comparison of within-season yield prediction algorithms based on crop model behaviour analysis. Agricultural and Forest Meteorology, 204, 10–21.
Abstract: The development of methodologies for predicting crop yield, in real-time and in response to different agro-climatic conditions, could help to improve the farm management decision process by providing an analysis of expected yields in relation to the costs of investment in particular practices. Based on the use of crop models, this paper compares the ability of two methodologies to predict wheat yield (Triticum aestivum L.), one based on stochastically generated climatic data and the other on mean climate data. It was shown that the numerical experimental yield distribution could be considered as a log-normal distribution. This function is representative of the overall model behaviour. The lack of statistical differences between the numerical realisations and the logistic curve showed in turn that the Generalised Central Limit Theorem (GCLT) was applicable to our case study. In addition, the predictions obtained using both climatic inputs were found to be similar at the inter and intra-annual time-steps, with the root mean square and normalised deviation values below an acceptable level of 10% in 90% of the climatic situations. The predictive observed lead-times were also similar for both approaches. Given (i) the mathematical formulation of crop models, (ii) the applicability of the CLT and GLTC to the climatic inputs and model outputs, respectively, and (iii) the equivalence of the predictive abilities, it could be concluded that the two methodologies were equally valid in terms of yield prediction. These observations indicated that the Convergence in Law Theorem was applicable in this case study. For purely predictive purposes, the findings favoured an algorithm based on a mean climate approach, which needed far less time (by 300-fold) to run and converge on same predictive lead time than the stochastic approach. (C) 2015 Elsevier B.V. All rights reserved.
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Dumont, B., Leemans, V., Ferrandis, S., Bodson, B., Destain, J. - P., & Destain, M. - F. (2014). Assessing the potential of an algorithm based on mean climatic data to predict wheat yield. Precision Agric., 15(3), 255–272.
Abstract: The real-time non-invasive determination of crop biomass and yield prediction is one of the major challenges in agriculture. An interesting approach lies in using process-based crop yield models in combination with real-time monitoring of the input climatic data of these models, but unknown future weather remains the main obstacle to reliable yield prediction. Since accurate weather forecasts can be made only a short time in advance, much information can be derived from analyzing past weather data. This paper presents a methodology that addresses the problem of unknown future weather by using a daily mean climatic database, based exclusively on available past measurements. It involves building climate matrix ensembles, combining different time ranges of projected mean climate data and real measured weather data originating from the historical database or from real-time measurements performed in the field. Used as an input for the STICS crop model, the datasets thus computed were used to perform statistical within-season biomass and yield prediction. This work demonstrated that a reliable predictive delay of 3-4 weeks could be obtained. In combination with a local micrometeorological station that monitors climate data in real-time, the approach also enabled us to (i) predict potential yield at the local level, (ii) detect stress occurrence and (iii) quantify yield loss (or gain) drawing on real monitored climatic conditions of the previous few days.
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