Metamodeling methods that incorporate qualitative variables for improved design of vegetative filter strips
Introduction
In recent decades, water quality degradation has become an increasing concern for society, considering its major effects on natural ecosystems and human health. In France and more generally over Europe1, significant amounts of pollutant are measured in surface water, due in part to the use of pesticides in agriculture [10]. The European Water Framework Directive advocates the development of best management practices (BMPs) to reduce pesticide transfers from the watershed to the river network. This includes implementing vegetative filter strips (VFSs, also called buffer strips or grass strips), which ensure the interception and mitigation of contaminant transfers from farm fields. VFSs are now mandatory along rivers in many countries2, due to their recognized effectiveness in limiting surface runoff transfers of pesticides and sediments (e.g., [34]). However, directives of this nature are regularly subject to questioning and discussion at European and national levels. For example in France, depending on the region, some rivers are classified to be protected by a VFS of 5 m length while others are not. More recently, it has been decided that an area free of pesticide treatment, of 5 m to 50 m in length depending on the chemical, should be implemented on or downslope of agricultural fields3. However, these regulations leave ditches and unclassified watercourses unprotected, and yet these small-scale hydrographic networks are usually the most impacted by pesticides emanating from watersheds, as they are highly exposed to drift and runoff. Whatever the regulation, scientific studies have shown that the general effectiveness of VFSs to act as a buffer can vary from 0% to 99%, depending on their design (position on the hillslope and size), and that the design of VFSs should account for agronomic conditions, soil characteristics, and climate [8], [21], [27]. In this context, [4] developed BUVARD (BUffer Vegetative strip for runoff Attenuation and pesticide Retention Design tool) to design site-specific VFSs over France by simulating their efficiency in controlling surface runoff pollution as a function of local field characteristics. The BUVARD modeling toolkit combines several dynamical models (for rainfall and surface runoff entering the filter and for processes occurring within the filter) with the benchmark numerical model VFSMOD, or Vegetative Filter Strip Modeling System [23], [24], [26], [27]. The method is similar to the design procedure for VFSs described in [26], but has been adapted to French conditions, in terms of input parameters and forcings given to VFSMOD. Considering local knowledge on climate, soil, cultivation practices, and water table depth, the model is run on a set of rainfall events, for several VFS lengths, and the length giving the targeted efficiency is selected for the user, including an associated uncertainty. This comprehensive method assumes that the user provides detailed field knowledge and data (such as hydrology and soil properties) that are not readily available in many practical applications, making the design procedure relatively difficult to follow.
Similar methods have been proposed for applications in the United States that present the same limits for operational purposes. A typical way to make the methodolgy more operational is to use a subset of the model simulations or to reduce the set with simple methods [9]. developed simple relationships for sediment-bound and dissolved pollutants based on simulations of VFSMOD [4]. conducted a set of virtual scenarios with BUVARD, among which the users have to choose the most relevant considering their own situation [45]., based on VFSMOD simulations, built some regressions on runoff and sediment VFS efficiency to include them in the watershed scale model SWAT. However, these regression equations involve only runoff loading and the saturated hydraulic conductivity, and thus do not properly represent the physically coupled processes occurring in a VFS as described in VFSMOD. Except for [4], these sizing methods did not take into account the presence of a shallow water table below the filter, although the water table can have a large impact on VFS efficiency with regards to water and pesticides infiltration [14], [23], [24]. However, in [4], while the large number of scenarios covers a wide range of conditions, it is not possible to extrapolate to scenarios that were not simulated by the original BUVARD toolkit. Moreover, these methods do not provide uncertainty quantification, which is essential for proper use of a model for risk assessment and/or decision-making for water quality [16], [28], [41].
The present study aims at enabling BUVARD to be used under new climatic and agronomic conditions at a reduced computational cost with metamodeling methods (or surrogate modeling, or model reduction) that allow uncertainty to be addressed. Metamodeling is still rarely used in the water quality domain, where processes related to pesticide transfer are highly nonlinear and interacting, and lead to complex models that combine empirical and mechanistic approaches [17], [18], [38]. Interest in metamodeling is, on the other hand, on the increase in costly environmental applications, such as calibration, data assimilation, and sensitivity analysis [33], and in operational projects with real-time decision-making [13]. Many studies use the term metamodel to refer to a simplified model of a complex physical model, built from first principles but not based on statistical methods of automatic learning. These deterministic approaches are not considered in this paper, which focuses on statistical metamodeling [47]. use a high-order polynomial chaos expansion of a flow and pesticide transport model to decrease the computational cost of Markov chain Monte Carlo calibration. The metamodel is built on reduced intervals that are obtained in a previous step by a first-order approximation method on the original model. They showed that the combined method is 70 times more efficient in time than the standard MCMC method for calibration, and that it yields accurate mean estimated values and confidence intervals. Tiktak et al. [42] used metamodeling to develop groundwater indicators for assessing groundwater pollution risks. The method is based on analytical expression built on simulations crossing geographical zones with regression techniques. Piñeros Garcet et al. [30] studied two metamodeling techniques applied to a nitrate leaching model: multidimensional kriging and radial based neural networks. They used the best method (kriging) to assess the probability of annual nitrate leaching concentration exceeding the legal threshold. At the European scale, [44] tested eight methods for surrogating another biogeochemical model, from parametric (linear model) to non-parametric approaches. They found that random forest was the most efficient method for N2O predictions, and support-vector machine for N leaching prediction.
The techniques surveyed above are shown to be particularly efficient for soil infiltration and groundwater processes that are slow and regular, since the deep soil that water travels through absorbs physical oscillations from rainfall. Surface processes such as runoff pesticide transfers can occur with two different types of runoff (saturation excess or infiltration excess) and depend directly on the rainfall oscillations and the soil characteristics but also on the treatment date before the rainfall event, the pollutant chemical properties, and other factors. The effects of these different phenomena are complex and difficult to model. This may explain why very few studies have proposed surrogate modeling of water and pesticide transfers taking into account surface and subsurface interactions Adriaanse et al. [1]. generated a metamodel based on regression to determine the peak concentration of pesticides in the FOCUS surface water scenarios used in the European Union registration procedures. Regression is defined as a function of the mass concentration in the runoff water leaving the treated agricultural fields, and is based on strong simplification assumptions concerning pesticide reaction processes. In short, the methods most commonly used in water quality metamodeling are Gaussian processes (or kriging, [32]) and regression. But in all these applications, the surrogate is built on quantitative variables only. However, the VFS sizing tool, BUVARD, and the physical processes it represents (water and pesticide transfer at the surface/subsurface interface) include some complex characteristics, including nonlinearities, due to the dependence on qualitative inputs (or categorical variables). Indeed, two major inputs, the type of soil of the VFS and the type of rainfall event, have been defined in BUVARD for operational purposes as substitutes for functional inputs (rainfall hyetograph) and for correlated inputs that are the hydrodynamic properties of the soil (such as saturated hydraulic conductivity, porosity, and retention curve parameters). Qualitative inputs generate discontinuities in the model response that many methods are unable to deal with, removing the smoothness of the model output, which is generally a necessary condition for building a metamodel. Yet, there is a clear need to include these disruptive qualitative inputs [19], [48]. Recently, kriging has been extended to take into account categorical inputs [7]. proposed several kernels to account for categorical variables and tested these methods successfully on very simple models, based on qualitative variables only, and [37] presented a kriging-based approach with mixed categorical and continuous inputs, not limited by a large amount of qualitative values.
The objectives of this work are both methodological and operational in scope. From a methodological point, we will first test the hypothesis that kriging can be adapted to the complexity of the data involved in BUVARD, according to [7] and [37]. Kriging on mixed variables will be compared to regression (which has already shown efficiency in water quality modeling), additive modeling (which is based on non parametric statistics), and kriging on quantitative variables only (one metamodel per qualitative level). The aim is not to provide a comprehensive review of metamodel performances but to evaluate the ability of kriging to take into account a mix of qualitative and quantitative variables and to provide high prediction performances. From an operational perspective through several applications in the context of risk analysis and management, we will then show that metamodeling is an interesting tool for addressing current operational issues of optimal vegetative filter strip design.
Section snippets
Modeling toolkit description
Vegetative filter strips, when properly designed and implemented, reduce surface runoff from upslope fields by improving soil infiltration, and thus slowing down pesticide transfer due to water runoff from the plot to the downslope water body (see Fig. 1a). While they are also effective for sediment and pesticide trapping, this study focuses on hydrological processes, assuming that surface runoff is the main process driving pesticide transfer in a VFS [4]. BUVARD is a set of coupled models
Metamodel output and inputs
The metamodel will be built on an area based on the experimental catchment Yzeron [22], which is included in the climatic zone 2 (see Fig. 2). The target output is not the optimal VFS size but the runoff delivery ratio, RDR, an index representing the efficiency of the VFS in reducing surface runoff, relative to rainfall volume, and that is directly a VFSMOD output [26]:
The very last step in BUVARD consists in getting the “optimal” VFS
Using kriging as a tool for uncertainty quantification
In this section, the analyses are obtained on the kriging model adjusted from the 100-point maximin LHS. Fig. 6 shows a sensitivity study of the runoff delivery ratio to the 5 quantitative inputs (CN, Slope, Length, WTD, VL). Each boxplot corresponds to the distribution of RDR according to the variation of one quantitative input on its definition range, while the four others are kept fixed to their mean value defined in Table 4.
CN is particularly noticeable from this analysis, generally
Conclusions
In this paper we are concerned with designing vegetative filter strips to reduce river water pollution as a consequence of pesticide runoff from upslope fields. Although VFS characteristics can be computed directly with the available BUVARD framework, in practice this modeling tool is difficult to handle for users. We introduce model reduction techniques to reduce BUVARD complexity and help users design VFSs in a simplified metamodeling context. Relevant information is summed up into a few
CRediT authorship contribution statement
Claire Lauvernet: Investigation, Methodology, Software, Writing - original draft, Writing - review & editing. Céline Helbert: Investigation, Methodology, Software, Writing - original draft, Writing - review & editing, Investigation, Methodology, Software, Writing - original draft, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors would like to thank Esperan Panodou for his help on the mixgp package, Robert Faivre and Nicolas Forquet for fruitful discussions on metamodeling issues, Rafael Muñoz-Carpena for his invaluable advice on how to improve the latest version of the paper, Clotaire Catalogne, Nadia Carluer, and Guy Le Hénaff for discussions about the BUVARD tool and VFS sizing and Benjamin Renard for the stimulating debates on non-linearities. This work is part of the BUVARD_MM project which was
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