Développement e méthodes de métamodelisation incluant des variables qualitatives pour évaluer un outil d'aide à la décision de dimensionnement de bande enherbée | Development of metamodeling methods considering qualitative variables to evaluate a decision-making tool of pesticide transfers

In France and more generally over Europe, significant amounts of pollutants are measured in surface water, partly due to the use of pesticides by agriculture. In the European Water Framework Directive, Europe is advocating the development of best management practices to reduce pesticide transfers to the river network once they are applied in the watershed. This includes implementing vegetative filter strips (VFS), that ensure the interception and the mitigation of contaminant transfers arising from fields. VFS are now mandatory along rivers in many countries, due to their recognized effectiveness to limit pesticide and sediment transfer by surface runoff (Asmussen et al., 1977; Dosskey, 2001). However, the general effectiveness of these buffers to reduce runoff transport of pesticides highly depends on pedologic characteristics, climatic conditions, and cultural practices. It is thus necessary to use mechanistic models that represent processes occurring on a vegetative filter strip, such as VFSMOD (Vegetative Filer Strip Modeling, Muñoz-Carpena et al., 1999). These models are relevant tools to design properly the buffers accounting for local conditions, although they are rarely used in France, since they are considered too complex for operational use (Carluer et al., 2017). In France, in order to help decision-makers use physically-based modelling, Irstea developed the modeling toolkit BUVARD (BUffer strip for runoff Attenuation and pesticides Retention Design tool). It consists of several steps including analyzing the watershed and its characteristics (soil, climate, cultural practices), and running dynamical models, in particular the mechanistic model VFSMOD adapted to French conditions (Muñoz-Carpena et al., 2018, Lauvernet and Muñoz-Carpena, 2018). At the end this toolkit delivers the optimal VFS width considering the needed filter efficiency (for example, 70% of runoff reduction). However, this very complete method assumes that the user provides detailed field knowledge and data (type of soil of the contributive area and of the VFS, rainfall rate, water table depth, slope, etc.), which are not easily available in many practical applications. Moreover, the variety of tools, which rely on several interfaces or several programming languages, makes it relatively difficult to take over the design procedure. We get to situations where the tool is used, without any uncertainty quantification nor sensitivity analysis, although they should be performed together with the tool's simulations (Saltelli et al., 2008). The next step in seeking to increase the operational scope of the modeling toolkit was to use metamodeling techniques. By reducing the computational cost of the modeling toolkit, the metamodel of BUVARD will make it possible to apply the tool on new watersheds with far fewer input parameters (6 against 70), and to determine the output uncertainty and sensitivity to input parameters in other climatic and agronomic conditions at low cost. Metamodeling is still rarely used in the water quality domain, since processes related to pesticide transfer are highly nonlinear. The VFS sizing tool BUVARD and the physical processes it represents (water and pesticide transfer at surface/subsurface) includes high non-linearities, due to the dependence on qualitative inputs (or categorical variables). Indeed, two major inputs, the typeof soil of the VFS and the type of rainfall event, have been defined in BUVARD for operational purposes, as substitute to functional inputs (rainfall hyetograph) and to correlated inputs that are the hydrodynamics properties of the soil (saturated hydraulic conductivity, porosity, and van Genuchten parameters). Qualitative inputs generate discontinuities in the model's response that many methods are unable to deal with, removing the smoothness of the model's output that is generally a necessary condition to build a metamodel (Zang and Notz, 2015). In this study, we adapted kriging to mixed variables (qualitative and quantitative), by testing several covariance kernels for a mixture of qualitative and quantitative inputs. Their performances are compared to a linear model and to a generalized additive model (GAM) that have been often used in water quality metamodeling. The methods are validated with the physically-based simulations conducted on a full factorial test design. It will be shown that the adapted kriging is very efficient and weakly dependent on the sampling size of the experimental design. These metamodels will then be used to perform uncertainty quantification and global sensitivity analysis of the VFS efficiency in a French watershed in the Beaujolais vineyard region. Polynomial Chaos Expansion do not allow to account for qualitative variables to our knowledge, but they have the advantage of being very efficient on complex models, and to compute Sobol indices directly from polynomial chaos expansions (Le Gratiet et al., 2017). We will compare the analysis from the PCE on each group of modality to the one performed with the kriging with an adapted covariance kernel. The final aim of this study is to give the users a complete tool accounting for uncertainty and sensitivity of the model outputs to design their vegetative filter strips. 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