EHSMu: a New Ecohydrological Streamflow Model to Estimate Runoff in Urban Areas

The EHSMu model is based on a simple schematization of physical elements within an urban catchment and on several hypotheses regarding water fluxes. Urban areas are described as a lumped ensemble of impervious (roads, roofs) and pervious (gardens, parks) surfaces. When rain falls over impermeable surfaces, it is supposed to be directly transferred towards the drainage system, in a time depending on the catchment area and drainage network geometry and materials (Al-Janabi et al. 2019). The rain falling over permeable areas drives soil moisture dynamics, which frame evapotranspiration rates, excess runoff generation and leakage occurrences. The latter are supposed to partially feed deep aquifers, thus introducing a new element to the water balance.

The hydrological scheme of the urban basin, implemented in EHSMu and presented in Fig. 1, is defined as the combination of three interconnected elements: a soil bucket below the permeable area and two linear reservoirs, named fast and slow reservoir respectively. The fast reservoir collects both the runoff from impermeable areas (Q_imp) and runoff generated by the saturation excess in the permeable areas (Q_exc). The slow reservoir receives as input a fraction c₁ of the percolation leakage L originated from the soil bucket below the permeable area, while the component (1 − c₁)L infiltrates the aquifer. The total outflow runoff Q_out is defined as the combination of the fluxes deriving from the fast and slow reservoir.

The Charlotte metropolitan area (North Carolina, US) was chosen as a case study. In particular, Little Sugar Creek (#507; 111 km²) and Little Hope (#470; 7 km²) were selected to investigate the applicability of the EHSMu on two basins with different extensions (Fig. 2). Land use and cover data have been derived from high-resolution (30 m) gridded datasets, available from the American National Land Cover Dataset NLCD. The investigated basins are highly urbanized, with almost 30% of the area covered with medium or high intensity urbanization (Fig. 2b).

Rainfall data were obtained exploiting a network of 72 tipping-bucket type rain gauges, maintained by the United States Geological Survey (USGS), which covers the Charlotte metropolitan area and provides data with a 15-min temporal resolution. Eight stations from the mentioned network (Fig. 2a, red dots) were selected, choosing the ones that have a higher spatial influence and can provide a continuous data set. Streamflow data, measured at the hydrological outlet of each sub-catchment (Fig. 2a, blue square), can be accessed through the USGS website and can be downloaded with a temporal resolution of 15 min. A 15-year time series, from 1st January 2001 to 1st October 2015, was selected for both rainfall and streamflow data and aggregated to an hourly time step to feed the model.

Potential evapotranspiration was estimated with the Thornthwaite equation (Thornthwaite 1948), using monthly average temperature T_i, downloaded from the Global Historical Climate Network (GHCN) (Menne et al. 2012) at daily scale. The weather station located at the Charlotte airport was chosen to obtain the temperature data needed to estimate the potential evapotranspiration rate.

The input time series were divided into two periods: the first one used for calibration and the second one for validation. For the smallest basin, #470, the first 40% of the time series was used as the validation period and the remaining 60% as the calibration time series. This peculiar fractioning of hydrologic dataset into calibration and validation periods was motivated by the presence of a period of missing data in runoff records for the basin #470. Since these gaps are approximately after 40% of the considered period, the longer period was used for calibration purposes and the shorter one for validation.

EHSMu requires a set of 8 parameters to represent the hydrological behaviour of the catchment: the active soil depth nZr, the soil moisture triggering the leakage s_l and the hygroscopic point s₀, the crop coefficient K_c, the slow and fast reservoir constants K_s and K_f, the percentage of impervious surface c₀ and the fraction of leakage that contributes to the total runoff c₁. For each parameter a range of possible values was defined, based on literature and on a priori knowledge. The active soil depth nZr is quite difficult to identify without detailed information from pedological profiles and for this reason a large range is assumed for this parameter, which can vary between 1 mm and 1000 mm. The term s_l strongly depends on the soil characteristics and it is assumed to be between 0.3 and 0.95, while the hygroscopic point s₀ is limited between 0 and s_l. The crop coefficient K_c represents the potential capacity of the plants to sustain the evapotranspiration processes, under optimal weather conditions, ensuring no water stress for the vegetation. This coefficient is assumed to be equal to 1 for standard grass (Allen et al. 1998) and it is generally lower for vegetation with a Crassulacean acid metabolism, such as sedum, and higher for plants that require more water for survival (Farg et al. 2012; Guerra et al. 2016). The crop coefficient is assumed to vary between 0 and 2.5. The reservoir constants K_s and K_f represent the inverse of the residence time, which in the case of fast reservoir can be considered a proxy of the basin concentration time. The residence time in the slow and fast reservoir is assumed to range from 1 h to 240 h and 10 h, respectively. The fraction of imperviousness c₀ varies between 0, if there is no urbanization, and 1, a condition in which all the surfaces are impermeable. The coefficient c₁ changes from 0, if the all the percolated water contributes to the aquifer recharge, to 1, if all the soil bucket leakages supply the slow reservoir.

To calibrate the model, different parameter sets θ[nZr, s_l, s₀, K_c, K_s, K_f, c₀, c₁] were randomly generated through a Monte Carlo simulation, selecting the parameters from the previously described ranges. Among the different sets, only the first 20,000 with a Nash-Sutcliffe efficiency NSE (Nash and Sutcliffe 1970) higher than zero in the calibration period have been retained and considered behavioural (Beven and Binley 1992). NSE is defined as:where Q_outiand Q_obsi are simulated and observed runoff at i-th time step, while \( \overline{Q_{obs}} \) is the average of the observed runoff and N is the total number of time steps. NSE can vary between −inf and 1, where 1 indicates the perfect model representation of the observations. Considering only the simulations with NSE > 0 ensures that only sets of parameters that lead to a high model performance are analysed.

Through the Monte Carlo behavioural calibration, it was possible to obtain a set of parameters that ensure the highest performance in terms of NSE. For the investigated basins the maximum NSE during the calibration period (NSE = 0.72 in both cases) was achieved for the following parameter sets:and

However, as often reported in hydrologic literature, equifinality conditions are present (Beven and Freer 2001; Foulon and Rousseau 2018), implying that similar model performance (e.g. in terms of NSE) can be achieved by using different sets of parameters. To deal with this source of parametric uncertainty, out of the 20,000 behavioural Monte Carlo simulations, the best 5%, corresponding to the 1000 simulations with the highest NSE, were retained and used with two aims. The first was to identify a reference set, taking into account the parameters’ a posteriori distribution. At the same time, we used this restricted parameter ensemble to provide model output with parametric uncertainties.

Each model parameter cumulative probability distribution and the correspondent cumulative distribution weighted on the model performance NSE have been plotted in Fig. 3. The terms nZr, s_l and s₀ were combined in one factor, nZr(s_l − s₀), which represents the amount of water that can be stored in the soil bucket. The analysis of Fig. 3 reveals that parameter cumulative distributions are quite different for the two considered basins. Once the influence of NSE is considered, the cumulative distribution weighted on the model performance (orange) departs from the unweighted one (red) if the model has relatively higher performances for some parameter ranges. Otherwise, the two cumulative distributions are close to each other, as is the case for the fast reservoir constant K_f.

The model parameter probability distribution was derived from the cumulative distribution weighted on NSE: reference parameter sets were chosen considering their modal values. The following reference sets were selected for the investigated basins:

and

Using the model outputs associated with the 5%-best behavioural simulations, uncertainty bounds were evaluated and used to define an envelope of the 5%-best model outputs. Fig. 4 illustrates, for both basins during calibration and validation periods, an example rainfall event (blue) and corresponding observed streamflow (red), simulated streamflow (black), obtained from the reference parameter set, and the 5%-best simulation model output envelope (green shadow). The plots highlight that most of the observed streamflow falls within the envelope of the 5%-best simulation model outputs: in particular 94% (#470) and 96% (#507) of the observed streamflow used for calibration is inside this envelope. For the validation period, 91% and 96% of the observations are contained in the 5%-best simulation interval, respectively. Different envelopes, built from the 2.5%- and 7.5%-best simulations, have been investigated, confirming the increase in the percentage of points falling within the envelopes as the percentage of simulations rises.

Simulated outflow results have also been compared with the one obtainable from the ecohydrological streamflow model EHSM proposed by Viola et al. (2014), where aquifer recharge processes are not considered and the entire leakage derived from the soil bucket feeds the slow reservoir. The percentage of points that fall inside the envelopes is almost the same for both models, highlighting the good reliability of EHSMu. Moreover, EHSMu shows a higher model performance in terms of NSE than EHSM: during the calibration period for EHSM, the maximum NSE is equal to 0.61 and 0.64 for #470 and #507 respectively, while using EHSMu the best simulation led to 0.72. The higher performance obtained with EHSMu underlines the importance of evaluating the aquifer recharge as a fundamental component in the water balance for urban catchments.

EHSMu gives as outputs the runoff at the basin outlet, the actual evapotranspiration and the aquifer recharge at hourly time scale. We aggregated the water balance components over long time intervals to compare flux magnitude among calibration and validation periods and between the basins. Fig. 5 shows the water balance over the calibration and validation period for the investigated basins, highlighting evapotranspiration, slow and fast streamflow and aquifer recharge as a percentage of the cumulated rainfall. Evapotranspiration corresponds to about 45% in all considered scenarios, 15% is composed of aquifer recharge and the runoff at the basin outlet is 40%, divided in 10% slow streamflow and 30% fast streamflow.

Water balance during the calibration period for basin #507 is slightly different, since it presents a lower (40% instead of 45%) total evapotranspiration and consequently a higher aquifer recharge. This is probably due to the statistical properties of rainfall: for the basin #507, in the calibration period there are less but more intense rainfall events than in the validation period. This implies higher leakages from the soil bucket, with a consequent increase of the aquifer recharge and slow streamflow components and at the same time less evapotranspiration.

In this section, we analyse and discuss the potential impact of land use and land cover changes on the water balance of the Charlotte metropolitan area. The reference parameter sets have been used as zero scenario and variations of the imperviousness and crop coefficients are investigated.

The presence of houses, roads and car parks within an urban catchment is represented by the EHSMu with the imperviousness coefficient c₀, which was chosen as equal to 0.29 for #470 and to 0.30 for #507 in the reference parameter sets θ₄₇₀ and θ₅₀₇. These values are a good representative of the actual land use scenario presented in Fig. 2b, where about 30% of the surface presents a medium- or high-intensity development. To estimate the impact of land use changes on the urban basin water balance, a sensitivity analysis of c₀ was performed.

Figure 6a illustrates the percentages of each component of the water balance, as discussed in Section 3.3, estimated using the following reference parameter sets where c₀ varies from 0 to 1: and

In Fig. 6a, the blue dashed line indicates the zero scenario. Values higher than 0.3 represent a potential future scenario, where the urbanization and the presence of high-density buildings are increased. For these scenarios, a higher percentage of fast runoff is expected, with a corresponding decrease of evapotranspiration and aquifer recharge. Results highlight how aquifer recharge, slow streamflow and evapotranspiration processes linearly decrease with higher values of the imperviousness fraction. Aquifer recharge is slightly higher in the larger basin (#507), where it could constitute 20–25% of the water balance, in the case of a no impervious surface: this can be due to the lower c₁coefficient, which defines the percentage of leakage that feeds the slow linear reservoir.

The potential impact of vegetation coverage changes is evaluated by investigating different values of the crop coefficient K_c. Fig. 6b investigates the potential impact on the water balance of possible future variations of the vegetation type, represented through a perturbation of K_c:and

Lower values of K_c represent vegetation with a low evapotranspiration rate, such as cacti and succulent plants. In this scenario, evapotranspiration decreases with a corresponding increase in aquifer recharge and slow streamflow. Fast streamflow, instead, is not affected by crop coefficient and variations in the total outflow are caused only by increase in the slow runoff component. This is clearly observable in all the cases investigated in Fig. 6a: slow streamflow generally varies from being more than 20% of the total water balance, when K_c = 0, to 7–8%, for K_c = 2.5. Aquifer recharge is also strongly influenced by the crop coefficient, varying between 35% to 10% for catchment #470, and from 40% to 15% for the larger basin.