In order to assess the NBS efficiency under current and future climate conditions, a series of hydrological and groundwater simulations were performed. To this end, two models were selected: (1) the TUFLOW hydraulic model [
29] and (2) the MIKE-SHE (MIKE- Système Hydrologique Européen) hydrological model [
30,
31]. TUFLOW was selected due to its capabilities to handle very high resolutions (several meters) and MIKE-SHE has already been applied for the Spercheios River basin in several previous studies (see [
19] and references within). Each model suite is presented below, followed by a description of the datasets used for defining current and future climate. Unfortunately, the area of NBS deployment is not monitored and there are no measurements to extensively evaluate the TUFLOW setup. However, the results presented below are in good agreement with a study performed in the area in 2003 [
32].
3.1. Models Setup and Basic Equations
The TUFLOW hydraulic model is a suite of advanced numerical packages and supporting tools for simulating free-surface water flow for urban waterways, rivers, floodplains, estuaries and coastlines. The model is capable of solving all the necessary physical processes using 1D, 2D and 3D solutions. A fully hydrodynamic approach was adopted rather than a quasi approach as the full solution was stable and the simulations completed in reasonable computational time. There were therefore no clear benefits of a simpler quasi routing approach. A 10 m grid was selected, as offering an acceptable compromise between the need for resolution and model runtimes and a timestep of 8 s was used.
The hydraulic model was constructed using a digital terrain model (DTM) developed from a high-resolution dataset provided by the Greek Land Register (2018 dataset). The DTM was sourced from the Geospatial Data INSPIRE Geoportal of the “Hellenic Cadastre”. The DTM metadata and technical guidelines were based on EN ISO 19,115 and EN ISO 19,119 (Version 1.2). The data series of the DTM consists of a series of tiles (based on 1:5000 scale maps) with a 5 m grid resolution. The source is the “Large Scale Orthophotos” project. It is a homogenous systematic point grid that refers to terrain elevation and creates an Earth elevation model. The digital elevation model has been produced as part of the orthophotos creation from color aerial photos of the “Large Scale Orthophotos” (LSO) project, which was a part of the Big Project: “Data and Information Technology Infrastructure for a contemporary cadastre” that was implemented by the (former) CADASTRE S.A. (predecessor of the Legal Entity of Public Law “Hellenic Cadastre”) and it was cofunded by the European Union within the framework of the Operational Program “Information Society” of the 3rd Community Support Framework.
Care has been taken to exclude DTM features that unrealistically constrain/influence routing of flood flows. For example, local high or low spots, attributable to the filtering approach have been excluded (
Figure 3). The goal is to produce flood depths and flood extents before and after the NBS deployment in order to examine the effects of the intervention.
Land use from the CORINE 2018 database [
33] was employed to identify roughness values (
Figure 4). Roughness within the 2D broadscale model is defined in the materials layer and roughness categories were based on the CORINE Manning’s
n values (
Table 1). In addition, a normal depth boundary was applied to form the downstream boundary condition. The normal depth boundary is defined based on a typical slope and the flow through the boundary was calculated during model integration. For the final broadscale simulations slopes of 0.0041–0.0048 m/m were used. This slope is the average of the left and right bank slopes, orthogonal to the main river reach. The downstream boundary was located 3 km upstream of the confluence with the sea.
The basic TUFLOW scheme is based on a numerical solution of the 1D unsteady St Venant fluid flow equations (momentum and continuity) including the inertia terms. The 1D solution uses an explicit finite difference, second-order, Runge–Kutta solution technique [
34] for the 1D shallow water equations of continuity and momentum as given by the equations below. The equations contain the essential terms for modeling periodic long waves in estuaries and rivers, that is: wave propagation; advection of momentum (inertia terms) and bed friction (Manning’s equation).
where: (
u) is the depth and width averaged velocity, (
ζ) is the water level, (
t) is the time, (
x) is the distance, (
A) it the cross-sectional area, (
B) is the width of flow, (
k) is the energy loss coefficient, (
n) is the Manning’s
n, (
ft) is the form (Energy) loss coefficient, (
R) is the hydraulic radius and (
g) is the acceleration due to gravity.
Accordingly, in order to examine the impact of the deployed NBS on the groundwater resources the hydrological model MIKE-SHE was used. MIKE-SHE is a physically based distributed model that is able to simulate all hydrological processes within the land phase of the hydrological cycle in a river basin [
35]. This integrated modeling tool can simulate overland flow, unsaturated flow, vegetation-based evapotranspiration, groundwater flow and fully dynamic channel flow and can describe their hydraulic relationships [
30] MIKE-SHE is fully integrated with the one-dimension model MIKE Hydro River, which incorporates river hydraulics applications, flood analysis, ecology and water quality assessments and sediment transport analysis in rivers, flood plains, irrigation channels, reservoirs and other inland water bodies [
31].
The overland flow was simulated using the conceptual reservoir representation based on an empirical relation between flow depth and surface detention, together with the Manning equation describing the discharge under turbulent flow conditions [
32,
36]. The relationship between the depth (
y), the slope (
L), the surface storage at equilibrium (
De) and the detained surface storage prior to equilibrium (
D), is given by an empirical model:
where during the recession part of the hydrograph, when
D/De is greater than 1,
D/De is assumed to be equal to 1. The 2-layer water balance method was used for the simulation of the unsaturated zone and is based on a formulation presented in [
37]. The saturated zone simulation was achieved using the linear reservoir module, a concept firstly introduced by Zoch [
38,
39,
40]. A linear reservoir is one, whose storage is linearly related to the output by storage constant with the dimension time, also called a time constant, as
S =
kq, where (
S) is storage in the reservoir with dimensions length, (
k) is the time constant and (
q) is the outflow from the reservoir with dimensions length/time. The outflows from a linear reservoir with two outlets can also be calculated explicitly. In this case, storage is merely given as:
S =
kpqp =
koqo +
hthresh, where (
kp) is the time constant for the percolation outlet, (
qp) is percolation, (
ko) is the time constant for the overflow outlet, (
qo) is the outflow from the overflow outlet and (
hthresh) is the threshold value for the overflow outlet. (
qp) and (
qo) at the time (
t +
dt) can be expressed as:
where
I is the inflow to the reservoir and constant in time.
The necessary information for the model set-up concerns the topography, climatological forcing (precipitation rate, reference evapotranspiration and air temperature), land-use distribution, hydrographic network (river network, cross-sections, hydraulic structures, boundary conditions and hydrodynamic parameters), surface runoff parameters (overland flow), unsaturated zones parameters (soil map) and saturated subsurface flow parameters (linear reservoir method). The eastern part of the Spercheios river basin is structured by alluvial deposits. In this porous media, the groundwater body consists of successive permeable and impermeable soil layers forming successive unconfined and confined aquifers.
The grid spacing for the simulations was set to 400 m. The topography of the Spercheios river basin was defined from the 50 m × 50 m digital elevation model (DEM) of the area, after resampling (
Figure 5). Land use is connected to vegetation distribution and therefore the actual evapotranspiration was derived for the CORINE 2018 dataset. For each land use category the time-varying values of the leaf area index (LAI), root depth and crop coefficient (Kc) were assigned in the vegetation property file based on bibliography (for more details see [
41]). Reference evapotranspiration was calculated based on the Hargreaves empirical approach [
42]. Model performance for the area has already been established in [
41] and meet the criteria proposed by [
43] during calibration and validation (Nash–Sutcliffe coefficient of efficiency > 0.50, RMSE observations standard deviation ratio < 0.70, and percent bias ± 25% for streamflow) in selected cases where river discharge measurements were available.
The implemented NBS was included in the model by altering the topography (cross-sections) upstream of the existing hybrid solution in the Spercheios River basin. After the NBS deployment, the elevation in the said area upstream was 7 m lower (from about 11.0 to 4.0 m.a.s.l. and up to 140 m wide). The area affected by the interventions was about 600 m upstream of the hybrid solution.