Relative yield decomposition: A method for understanding the behaviour of complex crop models

Dynamic crop simulation models are widely used to investigate, through virtual experiments, the response of crop yield to changes in climate, management or crop genetic traits. In a search for widespread applicability, crop models include a large number of processes, sometimes to the detriment of their mathematical transparency. Simulated crop yield responses to variation in model inputs result from the integration over a long period (one or several years) of many different crop processes interacting at the model time-step, typically the day. Thus, by definition, yield explanatory factors are intricate and difficult to link efficiently to the crop processes. Ranking their relative contributions to the final yield output is for example almost impossible. In this work, we introduce a new approach to understand the response of crop yield Y by comparing two simulation runs (computing two yields Y"1 and Y"2) of the same model and by focussing on the relative yield: y = Y"1/Y"2. Providing that the mathematical formulation of the dynamic crop model verifies simple hypotheses held by most crop models, we show that it is possible to factorise the relative yield y into several terms. These terms can be (i) interpreted as the specific effects of the modelled crop processes on the crop yield, (ii) compared to rank the effects of the crop processes on the crop yield. Their definition involves using state variables of the model computed during the simulation runs. The method does not involve running the model numerous times, neither changing its formulation. It may require to output new variables that are not in the set of variables proposed by the released version of the model. We call our method the relative yield decomposition (RYD) method. We illustrate how the RYD provides insight in the analysis of complex crop models by applying it to two models: Yield-SAFE (agroforestry model) and STICS (crop model). The method allows to identify and quantify the importance of the main processes responsible for crop yield variations for different simulation configurations in the two models. The relative yield decomposition method is complementary to other model analysis methods like sensitivity analysis or multiple model simulations. We show that it could be applied to some widely used crop models (e.g. AQUACROP, CERES, CROPGRO, CROPSYST, EPIC, SIRIUS, SUCROS). The relative yield decomposition method appears as a powerful and generic tool to analyse the behaviour of complex crop models that can help to improve the formulation of the models, or even to study specific plant traits or crop processes when applied to a model accurate enough.