Temporal estimation of hydrodynamic parameter variability in stormwater constructed wetlands – The hysteresis effect during multi-rainfall events
Introduction
Stormwater runoff is a leading threat to surface water quality, due to the large variety of pollutants involved (Zgheib et al., 2012, Schmitt et al., 2015). Urban wet weather discharges are episodic, but recurrent. They may have long term effects on the receiving media and pose serious risks to the quality of the biotopes. The increase of impervious surfaces puts an even larger pressure on stormwater managers to apply the most efficient practices regarding treatment systems for the removal of both organic and heavy metal pollutants (Daly et al., 2012) for instance, so as to comply with the European Water Framework Directive (Commision Directive, 2008). Thus, many studies have been focused on the impact of urban discharges during rainy episodes and on the best practices for stormwater management. Among these practices, nature-based solutions such as stormwater constructed wetlands (SCWs) are widely studied.
SCWs are engineered systems implemented to manage flood peaks and to reproduce natural treatment processes by means of wetland vegetation, sand and gravel, and their microbial flora, within a monitored environment (Vymazal and Kropfelova, 2008). They are considered as a sustainable and promising option, whose performance, cost and resources utilization can complement or replace conventional water treatment (Tack et al., 2007, Arias and Brown, 2009). Stormwater is diverted to the system and, by flowing through the soil media, is subjected to physical and chemical treatment processes such as sedimentation, fine filtration, adsorption and biological uptake (Davis et al., 2009). Their significant efficiency in reducing the ecological impact of urban runoff has been proven in the field (Schmitt et al., 2015). Among SCW systems, planted filters with horizontal or vertical flow have long demonstrated their effectiveness in the treatment of stormwater (Albalawneh et al., 2016). The abilities of SCWs to improve water quality are widely recognized, and their efficiency in reducing suspended solids and micropollutants has been reported in several studies (Tang et al., 2009, Walaszek et al., 2018). Available guidelines and rules for the design of SCW are based on empirical rules of thumb (Brix and Arias, 2005) derived from experiments under specific conditions. These raise issues about customized design, implementation and operation of SCWs that are necessary to optimize potential treatment efficiency and to limit malfunctions. These may be clogging due to excessive loads of suspended solids, water stress of macrophytes and microorganisms due to extended dry periods, or inadequate SCWs sizing. The predictive ability of simulation tools is of great interest to evaluate the filtering characteristics of a SCW (Langergraber, 2011).
Langergraber (2008) provided a survey of existing simulation tools for SCWs ensuring that measured data from SCWs can be matched. Using the HYDRUS simulation tool when the hydraulic behavior of the system is well described, it was concluded that the influence of the hydraulic parameters of the filter material is much higher than that of the biokinetic model parameters. The van Genuchten-Mualem (vGM) model is still one of the most frequently used models for the prediction of hydraulic conductivities. However, the parameters of soil-water retention curves, which are the key functions required in variably saturated porous media involved in environmental and ecological modeling, are difficult to measure. The calibration of hydrodynamic parameters for subsurface SCWs is a sensitive process and remains a challenging task since unsaturated flow modeling involves highly non-linear equations. Several studies investigated how to predict these parameters from basic soil properties. Fournel et al. (2013) used HYDRUS to explore specific features of SCWs. They added a conceptual layer at the bottom of the wetland to mimic the local head loss resulting from seepage boundary condition. Morvannou et al. (2013) also described some characterization of the hydraulic properties of the system by means of direct laboratory methods and inverse modeling from in situ measurements.
An initial set of parameters can be produced by carrying out a hydrodynamic characterization of porous media. This set can be used in the inverse optimization module included in HYDRUS-1D. Implemented by Morvannou et al. (2013), such a calibration methodology reduces the risk of non-convergence of the model, since the values obtained are likely to be close to optimal values. As a deterministic inverse approach, a gradient method may be used but its well-known disadvantage is that it may fall in local minima. Maier et al. (2009) used a global optimization based on a stochastic search strategy in which hydraulic calibration was performed on the outflow rate measurement. Thus, soil hydraulic functions based on vGM coefficients and preferential flow characteristics in large pores at high saturation were obtained. For many actual problems, data cannot be known with certainty due to simple measurement errors.
The variations of soils characteristics including in particular the behavior of unsaturated soils, may greatly be influenced by hydrodynamic hystereses, defined as the dependency of capillary pressure saturation curves on the history of the flow. This phenomenon is generally due to several reasons cited by Feddes et al. (1988) such as swelling and shrinkage for fine grained clays which may result from wetting and drying or thermal effects (Nimmo, 2005). If after one of the two processes the other follows, a sequence of cycles of wetting or drying inner curves, called scanning curves, occurs, which is the case for SCWs receiving randomized stormwater. If the hysteresis phenomena, physically caused by the presence of entrapped air, are not accounted for in the analysis of the behavior of unsaturated soils, this may result in significant errors in the prediction of solute movement and contaminant concentrations (Kool and Parker, 1987). Consequently, primary wetting and draining branches of soil-water characteristics have to be considered in calibration process for both empirical (Gillham et al., 1976) and theoretical models (Mualem, 1984). Fig. 1 shows a typical example of hysteretic water retention in a soil. The outer drying and wetting curves correspond to the drying from the highest reproducible saturation degree to the residual water saturation and the wetting from the residual water content to the highest saturation degree, respectively.
The present study focuses on the long-term hydrodynamic characterization by implementing a numerical model of a vertical flow stormwater constructed wetland (VFSCW). The hydrodynamic modelling is carried out by implementing the Richards model by means of a mixed hybrid finite element method (MHFEM) adapted to the simulation of heterogeneous media (Younes et al., 1999), and the van Genuchten-Mualem (vGM) parametrization. Particular attention is given to the top boundary conditions – surface ponding or evaporation – for the purposes of modeling the sequences of rain-runoff events. MHFEM results after parameter estimation are compared to those of HYDRUS (Simunek et al., 2009). The monitoring of the VFSCW provides us information in terms of water exchanges, filtering abilities during feeding and drainage sub-periods, and ageing with time. Large datasets are needed to account for significant spatial and temporal variability in the vGM soil parameters hidden behind the hysteresis effect. As such datasets are usually not available, in part due to the randomness of the storm events, the paper presents a simple, robust and low-cost numerical method for the identification of the soil hydrodynamic properties. On the one hand, it relies on the automatic differentiation (AD) of the MHFEM code for sensitivity analysis and gradient-based data assimilation. On the other hand, a stochastic method is implemented to, eventually, determine a global optimum. The modeling efficiency, as defined by Moriasi et al. (2007), and a statistical analysis are then evaluated for the different parameter sets to demonstrate the hysteresis effect.
Section snippets
Governing equations
For unsaturated flow with an incompressible fluid through porous media, the hydrodynamic equation is obtained by associating the continuity equation with the Buckingham-Darcy’s law in which the hydraulic conductivity depends on the pressure head and the water content [–]:where t is the time variable [T], is the flow region here considered as a one dimensional unconfined aquifer, and are the specific storage [] and the degree of saturation [–],
Sensitivity analysis and temporal parameter estimation
The sensitivities of our MHFEM model to various vGM parameters of the first layer and the saturated hydraulic conductivity of the last layer were examined. To that end, a perturbation of was applied to the vGM parameters related to the first layer and to the hydraulic conductivity of the third layer.
Fig. 6-a represents the sensitivity of water pressure to vGM parameters for the 1st period of May. The parameters identified as having the greatest influence are: the saturated water content
Conclusions
This study discusses numerical approaches to investigate the temporal variability of vGM parameters in a VFSCW during multi-rainfall periods considering the hysteresis effect. The results show that the characteristics of the filter layer alter with time. This indicates that several issues such as water accumulation due to biomass and plants growth, presence of organic matter, and the relying of total suspended solids in this layer have to be considered or discussed within the modeling. The
Acknowledgement
Mohammad Moezzibadi was supported by the YEKAN Center Grant No. 139392351345000041.
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