## 2 Model Description  
Modelling of constructed wetlands is complex because of the large number of processes involved in pollution removal, the hydraulics in a porous medium with the diffusive flow, and the dead time. In addition, the pollution removal is influenced considerably by the hydraulics and environmental conditions. The last generation of models (process--based models) are rigorous but overly complex, with difficult estimation of its parameters [31; 32; 33]. In contrast, series/parallel connection of CSTRs is simple and capable of describing transport dead time, diffusion and reaction [31]. In [PERSON] (2005), a simple model is proposed for describing the disperse hydraulics and pollution removal dynamics in horizontal subsurface constructed wetlands [31]. The structure of the hydraulic model comprises three series CSTRs, followed by two parallel CSTRs, and a plug flow reactor. The parallel CSTRs involve no flow exchange. The kinetics is of the Monod type, and only depends on the concentration of the modelled pollutant. The outlet and inlet flows of the system are the same, and the liquid CSTR volumes are constant. The model was fitted to both experimental tracer data and current (no tracer) data. In [PERSON] (2007) and [PERSON] (2009), a simple modelling strategy is proposed for describing hydraulics and pollution removal dynamics corresponding to tracer data from vertical subsurface constructed wetlands [34; 35]. The model comprises three CSTRs, the first and second CSTRs are connected in series, whereas the second and third CSTRs are connected in parallel with flow exchange. The inlet flow is considered different from the outlet flow, and no model is considered for it. The liquid volumes of the parallel CSTRs are constant, whereas the liquid volume of the first CSTR is considered varying and is described by a first-order differential equation that is fitted to experimental data. The specific reaction rate is of the first order and it only depends on the concentration of the modelled pollutant. We use the global stability definition as follows. **Definition 1**. : _Consider the system \(dX/dt=f(X)\), where \(X=(x_{1},x_{2},\ldots,x_{n})\in\mathcal{R}^{n},f\colon\mathcal{R}^{n}\to \mathcal{R}^{n}\), \(X(t,t_{o},X_{o})\) denoted as \(X(t)\) is a solution to the system, and \(X_{0}\in\mathcal{R}^{n}\) is an initial value of \(X(t)\). Consider the compact set \(\Omega_{Q}\subset\mathcal{R}^{n}\). Define the distance between the solution \(X\) and the compact set \(\Omega_{Q}\) as:_  
\[\rho\big{(}X,\Omega_{Q}\big{)}=\underset{Y\in\Omega_{Q}}{inf}||X-Y||.\]  
If for all \(X_{0}\) satisfying \(X_{0}\in\mathcal{R}^{n}\), \(X_{0}\
otin\Omega_{Q}\) the property \(\underset{t\to\infty}{\lim}\rho\big{(}X,\Omega_{Q}\big{)}=0\) holds, then the compact set \(\Omega_{Q}\) is called a global convergence set of the system, and the system is called globally asymptotically stable. We consider a series/parallel CSTRs-based model for representing the hydraulics and pollution removal dynamics in subsurface constructed wetlands, resulting from a combination of the models proposed by [31; 34]. A single pollutant and a time-varying inflow pollutant concentration are considered. The CSTRs connection comprises three CSTRs, the first and second CSTRs are connected in series, whereas the second and third CSTRs are connected in parallel with flow exchange (Figure 1).