Hydrological performance of lined permeable pavements in Norway

Lined permeable pavements (LPPs) are types of sustainable urban stormwater systems (SUDs) that are suitable for locations with low in ﬁ ltration capacity or shallow groundwater levels. This study evaluated the hydrological performance of an LPP system in Norway using common detention indicators and ﬂ ow duration curves (FDCs). Two hydrological models, the Storm Water Management Model (SWMM)-LID module and a reservoir model, were applied to simulate continuous out ﬂ ows from the LPP system to plot the FDCs. The sensitivity of the parameters of the SWMM-LID module was assessed using the generalized likelihood uncertainty estimation methodology. The LPP system was found to detain the ﬂ ow effectively based on the median values of the detention indicators (peak reduction ¼ 89%, peak delay ¼ 40 min, centroid delay ¼ 45 min, T50-delay ¼ 86 min). However, these indicators are found to be sensitive to the amount of precipitation and initial conditions. The reservoir model developed in this study was found to yield more accurate simulations (higher NSE) than the SWMM-LID module, and it can be considered a suitable design tool for LPP systems. The FDC offers an informative method to demonstrate the hydrological performance of LPP systems for stormwater engineers and decision-makers. (cid:129) The study evaluates the hydrological performance of a lined permeable pavement system using detention indicators and ﬂ ow duration curves (FDCs). (cid:129) A simple reservoir model was developed to predict the hydrological performance of permeable pavement. (cid:129) FDCs are very useful and practical tools to demonstrate the hydrological performance of permeable pavement.


INTRODUCTION
Permeable pavements (PPs) are a type of sustainable urban stormwater systems (SUDs) that can substitute normal pavements and provide valuable environmental services. PPs reduce the amounts of stormwater runoff through soil infiltration (Winston et al. 2018) and enhance the quality of the treated runoff (Pilon et al. 2019). In addition, PPs reduce the heat island impact through evaporative cooling and reduce the amount and time of standing water that may cause odor and health issues (Kuruppu et al. 2019).
PPs can either be drained or undrained. Undrained PPs infiltrate the water from the surface to the native soil and can be suitable for sites with deep groundwater levels and good infiltration conditions. On the other hand, drained PPs are equipped with an underdrain pipe connected to the downstream stormwater drainage system. Furthermore, the bottom of drained PPs can either be permeable or impermeable, depending on the local site conditions. Drained PPs with an impermeable liner are lined PPs (LPPs). They are more suitable for sites with low infiltration capacity or shallow groundwater levels (Zhang & Chui 2020).
For LPP systems, the permanent reduction of flow is limited to evaporation. Brown & Borst (2015) quantified the evaporation from several LPP systems and found it to account only for 2.4-7.6% of the annual water budget. Therefore, the hydrological benefits of LPPs are primarily expected through runoff detention, which can be expressed by several indicators such as peak flow reduction, per event volume reduction, peak delay, and centroid delay. Numerous studies have investigated the hydrological benefits of PPs in the last decades (see Drake et al. (2013) for review). However, only a few studies were found to investigate the performance of LPP systems (Pratt et al. 1995;Abbott & Comino-Mateos 2003;Støvring et al. 2018). Abbott & Comino-Mateos (2003) analyzed 20 rainfall-runoff events collected from an LPP site. They found the LPP to reduce rainfall peaks significantly; a rainfall with 12 mm/h intensity was found to produce a runoff with a peak of 0.37 mm/h. Similarly, Støvring et al. (2018) investigated the hydraulic performance of several LPP plots with different layers and equal surface areas (25 m 2 each). During a period of 12 months, they observed a total of 22 rainfall-runoff events with return periods up to 2 years. They reported peak delay values ranging from 0:39 to 3:16 h and per event volume reduction of 27-69%, demonstrating good detention capabilities of LPP systems.
It can be noted that commonly reported detention indicators in PP literature, such as peak delay and peak reduction, exhibit a wide range of values even within the same PP site. For instance, Støvring et al. (2018) found the peak delay of one LPP to vary between 0:05 hr and 4:02, while Winston et al. (2018) reported a peak reduction range of 0-100% from one PP site. These indicators are inherently sensitive to PP initial conditions (Fassman & Blackbourn 2010) and rainfall characteristics (Støvring et al. 2018). In the general SUD literature, many studies have suggested moving toward more robust approaches that can unambiguously demonstrate the detention performance of SUD measures. Stovin et al. (2017) discussed the issues regarding detention indicators in green roof studies and recommended two alternative approaches based on long-term simulations. The first approach is based on plotting the cumulative density function of detention indicators across a wide range of rainfall events, while the second approach simulates design rainfall events with different amounts and varying initial conditions to produce detention charts. Lucas & Sample (2015) modified the flow duration curve (FDC) to represent the relation between runoff values and durations when these runoff values are exceeded. They applied FDCs to evaluate different scenarios of SUD implementation in a catchment. Similarly, Hernes et al. (2020) applied FDCs to investigate the performance of different SUD scenarios, and they concluded the suitability of FDC as a practical measure to evaluate the hydrological performance of SUDs. Using the FDC to evaluate the performance of PP was found to be limited to few studies in the literature (Fassman & Blackbourn 2010;Brown et al. 2012;Winston et al. 2018), and no study was found to apply the FDC for LPP systems.
The derivation of FDCs requires long time series of observations. For instance, Fassman & Blackbourn (2010) utilized 2 years of measurements to derive FDCs for a PP site, while Brown et al. (2012) used 17 months of data to plot the FDC of PP parking lot. Alternatively, a calibrated hydrological model can be applied to simulate long time series, which is beneficial when observations are limited. Several hydrological models are applied to simulate PP systems in the literature. The most common model perhaps is the Storm Water Management Model (SWMM) (Rossman 2010).
The SWMM-LID module, hereafter referred to as the SWMM-PP model, is a simplified physically based model. It has been applied in many PP studies (Kim et al. 2015;Chui et al. 2016;Xie et al. 2017;Randall et al. 2020). Most of the studies applied the SWMM-PP model of PP using parameters selected from the SWMM manual without calibration, and only a few studies were found to evaluate the accuracy of SWMM-PP models with measured data. Randall et al. (2020) investigated the accuracy of the SWMM-PP model using 18 rainfall-runoff events. They found the SWMM-PP model to yield simulation with reasonable accuracy for single-peak events and to perform poorly for events with multiple peaks. Liu & Chui (2017) found the SWMM-PP model to yield accurate simulations with Nash-Sutcliffe efficiency (NSE) values above 0.9 for validation events. Likewise, Palla & Gnecco (2015) calibrated a SWMM-PP model with data of one artificial rainfall event and found the model to produce simulations with high accuracy (NSE values above 0.75).
One issue in the SWMM-PP model is the high number of parameters (15 parameters) that need careful selection through measurements and calibration. One way to reduce the number of parameters that need adjustments is through a parameter sensitivity analysis. Such an analysis is made before calibration to select the most influential parameters for calibration/measurement while assigning standard values of the insensitive ones. However, only one study was found to investigate the sensitivity of the SWMM-PP model for long-term simulation (Randall et al. 2020). Hence, there is a need to investigate the sensitivity of SWMM-PP parameters for event-based simulations. Alternative to SWMM-PP, models with a fewer number of parameters can be applied. Conceptual reservoir models are popular in modeling green roofs (Vesuviano et al. 2014). However, no study was found to investigate its applicability for LPP systems.
This study attempted to address some of the mentioned limitations, specifically by: 1. Evaluating the hydrological performance of an LPP system using different detention indicators and FDCs. 2. Evaluating the sensitivity of the SWMM-PP model parameters for event-based simulations. 3. Investigating the suitability of a simple reservoir model for LPPs. 4. Comparing the performances of the SWMM-PP model and the reservoir model.

Site description and data collection
The site is an active parking lot near Trondheim city in Norway. It was constructed in 2019, and the data collection started in December 2019. The site includes three plots of LPPs with different properties and two undrained pavements. Each LPP has a surface area of 100 m 2 (12.5 m widthÂ8 m length). Precipitation data were collected on-site using a heated tipping bucket rain gauge. The outflows from the three LPP systems were measured using a V-NOTCH weir. The water levels above the weir were measured using an ultrasonic distance sensor. These water levels were converted into flows using a calibrated rating curve. During the measurement period, 5 months were dominated by snowfalls and accumulations (January 2020-May 2020). Additionally, frequent malfunctions occurred for the precipitation gauge during June, July, and August, but the quality of measurement improved between August and December. This study has focused on measurements from one of the plots (plot 4). Plot 4 comprises an interlocking pavement layer with 80 mm thickness. About 10 mm distances were made between the interlocks to allow for water to infiltrate. A bedding layer with 30 mm thickness was placed beneath the pavement layer with a particle grading ranged between 2 and 11 mm. The base layer thickness is 100 mm with course materials (grading 4-32 mm), while the sub-base layer thickness is 250 mm (grading 20-120 mm). An impermeable liner (geotextile) was placed at the boundaries of the LPP to prohibit infiltration to the native soil. A drainage pipe with a diameter of 100 mm was placed at the bottom of the sub-base layer.

Detention metrics used in the study
During the valid measurement period between August and December 2020, 11 rainfall-runoff events were observed and considered for analysis (Table 1). Four detention metrics were calculated for each of these events: peak reduction (PR), peak delay (Pd), centroid delay (Cd), and T50 delay. The PR measures the attenuation of the peak of precipitation events, while the other three indicators measure the delay of the permeable pavement drainage outflow. The following equations were used to determine the four metrics (Equations (1)-(4)).
T50 delay ¼ t R 50% of rain volume À t P 50% of rain volume (4) P max is the peak of the rain during the rainfall-runoff event in (mm/min). R max is the peak of the PP drainage outflow during the rainfall-runoff event (mm/min). t Pmax is the time from the start of the rainfall event to the peak of the rain (min). t Rmax is the time from the start of the rainfall event to the peak of the PP drainage outflow (min). t P centroid is the time from the start of the rainfall event to the centroid of the rainfall hyetograph (min). t R centroid is the time from the start of the rainfall event to the centroid of the PP drainage outflow hydrograph (min). t P 50% of rain volume is the time from the start of the rainfall event to the time in which 50% of the rain amount has passed (min). t R 50% of rain volume is the time from the start of the rainfall event to the time in which the accumulative volume of the PP drainage outflow reaches 50% of the rain amount (min).

Hydrological models
The SWMM-PP model is a simplified physically based model. It can be also classified as a hybrid model as it combines physical-based equations (Darcy law for water percolation) and empirical power formula for underdrain flow calculations (Rossman 2010). SWMM-PP conceptualizes the PP system as three layers: surface, soil, and storage layers. The water infiltrates from the surface to the soil layer (the bedding layer in the pavement) based on the permeability of the pavement layer. Water movement through the soil layer is modeled using the Darcy law.
Water is stored permanently in the soil layer until the soil moisture content exceeds the soil field capacity. The water percolates to the storage layer after the filed capacity of the soil layer is exceeded, while the underdrain flow is determined using a power-law empirical equation that is a function of the water depth above the drainage pipe. More details about SWMM-PP equations are illustrated in the Supplementary Material. The reservoir model ( Figure 1) represents the LPP by two layers: soil and storage. Precipitation falls into the soil layer and fills the available storage (S1-S0). Water starts to infiltrate (INF) to the storage layer when the permanent storage of the soil layer (S1) is exceeded. The storage layer is represented by a reservoir model with two outlets: the lower outlet simulates the low flows, and the upper outlet models the high flows. The flow from the  Uncorrected Proof upper outlet starts after the storage depth (St) exceeds a certain threshold value (Fth). The flow through the outlet is controlled by parameters k1 and k2, and the value of k1 which is assigned for the lower outlet is much smaller than the value of k2. The equations of the reservoir models are presented as follows (Equations (5)-(9)). S1 t ¼ S1 tÀ1 þ P t À AET1 t (5) The actual evapotranspiration (AET) was determined from the two tanks as a function of the potential evapotranspiration (PET) (Equations (10) and (11)). PET is the maximum evapotranspiration considering the climatological variables. In this study, the Oudin formula (Oudin et al. 2005) was selected to estimate the PET following the recommendation of the study of Johannessen et al. (2017).
In the Oudin formula, the PET is calculated from the latitude of the site and the Julian day (Equation (12)).
T mean is the mean daily temperature (°C). The extra-terrestrial radiation Ra is calculated from the Julian day and the latitude (MJ/m 2 ), 1=lr % 0:408 where λ is the latent heat of vaporization (MJ/kg 1 ), and r is the volumetric mass of water (kg/m 3 ).

Sensitivity analysis of SWMM parameters
The number of parameters in the SWMM-PP model that needs careful selection is 15 beside the depths of the different pavement layers, while only five parameters are required for the reservoir model. Table 2 presents the models' parameters. Before the calibration of the SWMM-PP model, a sensitivity analysis was conducted using the generalized likelihood uncertainty estimation (GLUE) methodology (Beven & Binley 1992). The steps followed to conduct the GLUE methodology were based on the study of Krebs et al. (2016). In this study, 70,000 parameter sets were randomly selected from the parameter ranges presented in Table 2, assuming a uniform prior distribution of each parameter. These ranges were initially selected based on the recommendation of the SWMM-PP manual. Each parameter set was used to simulate a selected rainfall-runoff event, and the NSE (Nash & Sutcliffe 1970) was determined and stored. A threshold value (NSE ¼ 0.65) was selected to separate behavioral and non-behavioral parameters. The behavioral parameters were selected to form posterior distribution for each model parameter. The Kolmogorov-Smirnov (KS) (Darling 1957) test was conducted to measure the difference between each parameter's prior and posterior distributions (Beven & Binley 1992;Krebs et al. 2016). The parameter is considered sensitive if the difference between the prior and posterior distributions is statistically significant based on the KS test. Event 9 was selected for the sensitivity analysis of the SWMM model parameter. This event was selected due to the long antecedent dry weather period (15 days), which allows to set the initial saturation to zero.

Model calibration
Five events were chosen for models' calibration based on the quality of the measurements. For the SWMM-PP model, the sensitive parameters were selected for calibration, while the insensitive ones were fixed to their default values, following the SWMM-PP manual. The differential evolution algorithm (DE) was used to calibrate the two models (Storn & Price 1997). The algorithm generates populations of candidate solutions by varying model parameters within given ranges. Each population has several solutions equal to the number of model parameters multiplied by two. At each iteration, a new population is evolved from the previous one in a way that each solution of the new population is either better-off or remains the same. The algorithm was applied to optimize model parameters for each of the five events with 1,500 iterations. The best solution for each iteration was stored. The optimized 1,500 parameter sets of each of the five events were compared to find a common parameter set that produces reasonable simulations for all five events. In this study, a 'reasonable' or 'acceptable' simulation was defined based on the NSE value (NSE.0.5), as commonly applied in the literature (Rosa et al. 2015;Johannessen et al. 2019).
A reservoir model with one outlet was used to calibrate the k1 and k2 values for the reservoir model. An event with a high amount of precipitation was used to find the optimal value of k2, while the value of k1 was optimized using the event with a low amount of precipitation. The threshold value was selected as the maximum water level in the storage tank (St) during the simulation of the low event. The maximum holding capacity (S1) was selected as 10% of soil layer depth following the calibration result of the SWMM model. Finally, these parameters were fixed, and each event was calibrated to find the optimal initial contents.

Continuous simulations
Precipitation and temperature data of 2017, with a one-minute time step, from the Risvollan station in the Trondheim city was used in the two calibrated models to generate 1 year of continuous outflow of the LPP from each model. In addition, a catchment with 100% impervious surface and the same area as the LPP site (8 m * 12.5 m) was modeled in the SWMM using the same climatic data to generate continuous outflow of an impermeable pavement. The distance from the Risvollan station and the LPP site is about 20 km. In the Risvollan station, climatic variables are collected and processed for a green roof site (Johannessen et al. 2018). Periods from 1st October to 31st March were excluded to avoid snow accumulation periods. Evapotranspiration was excluded from the eventbased calibration but included in the continuous simulations. PET, calculated from the Oudin formula, was supplied to the SWMM model as an input file. It should be noted that, unlike the reservoir model, the SWMM-PP model does not account for reduced evapotranspiration due to the soil moisture deficit.

Derivation of FDCs
Simulated outflows from the two models were used to derive FDCs. The derivation of FDCs was similar to the study of Hernes et al. (2020). Firstly, outflow values were ranked from highest to lowest. Secondly, the probability Uncorrected Proof of exceedance (Pe q ) for each outflow value (q) was calculated, based on the value's rank, using Equation (13). Lastly, the probability of exceedance for each outflow value was converted into the duration of outflow above the outflow value D above q , using Equation (14).

RESULTS AND DISCUSSION
Hydrological performance of the lined permeable pavement During the measurement period, 11 events were considered valid for analysis. For each event, peak delay, PR, centroid delay, and T50-delay were determined. Figure 2 shows an example of these indicators determined for one event, while Table 2 summarizes the indicators values for the 11 events. The median value of the PR was 89% ranging from 44.65 to 99.97%. The delay indicators' median values were 40, 45 and 86 min for the peak delay, centroid delay, and T50-delay, respectively. The median values demonstrate the good detention performance of the LPP system, which confirmed the finding of previous studies (Pratt et al. 1995;Abbott & Comino-Mateos 2003;Støvring et al. 2018). However, it can be noted that these indicators are dependent on the initial condition and the volume of rainfall events. The lowest values of the indicators were found for Event 3, which has a high precipitation amount (8.8 mm). In addition, the LPP system was believed to be wet because of the previous event (Event 2), which occurred 1 day before Event 3. On the other hand, high PR and delay indicators were obtained for Event 8, which only has a precipitation amount of 2.53 mm. It is relatively unambiguous to determine the PR indicator within the defined time frames for the rainfall-runoff events. In contrast, several issues regarding some delay indicators were encountered. For instance, it is unclear how to determine the value of peak delay when the rainfall event has multiple peaks with the same magnitude. This can be illustrated in Figure 3, which presents a rainfall event (Event 11) with two peaks with the same value. On the other hand, to determine T50 delay, at least 50% of the rainfall should be converted to runoff within the given time frame. However, for small precipitation events and dry initial conditions, most of the water will be retained, and the amount of runoff will not reach 50% of the amount of precipitation (Events 1, 5, 10 and 11).
Figure 2 | Detention performance of the lined permeable pavement (plot 4) during Event 9 (October 8, 2020) using four detention metrics, which are PR (peak reduction), Pd (peak delay), Cd (centroid delay) and T50 delay. In the left figure, the blue two-sided arrow represents the value of Cd, the black two-sided arrow represents the value of Pd, and the red two-sided arrow shows the value of PR. The value of T50 delay is the difference between the accumulative curves in the right figure along the red dash line. 7 Uncorrected Proof Sensitivity analysis and model calibration 5,000 parameter sets were found to be behavioral, based on the NSE values, which account for 7% of the total parameter sets. The cumulative distribution plots of the SWMM-PP parameters are presented in Figure 4, and the statistic D-value and the p-value from the KS-test are shown in Table 2. Based on the KS test, only three  Uncorrected Proof parameters of the SWMM-PP parameters are considered insensitive (p.0.05). These are the void fraction of the pavement layer, the impermeable fraction of the pavement layer, and the soil layer's suction head.

Blue
The latter agrees with similar studies that found the suction head parameter to be insensitive in SWMM-LID modules (Krebs et al. 2016;Randall et al. 2020). The most sensitive parameters were found to be the hydraulic conductivity slope, the field capacity and the porosity of the soil layer. Similarly, Krebs et al. (2016) found all soil parameters of the SWMM-green roof model, except the suction head, to be sensitive.
The parameters of the soil layers were the most influential, followed by the parameters of the storage layers. The soil layer was considered in the SWMM-PP model to represent the bedding layer beneath the pavement interlocks. In other PP types without bedding layer (e.g. Zhang & Guo 2015), the soil layer can be eliminated from the SWMM-PP model, which reduces significantly the number of calibrated parameters and is expected to increase the sensitivity of the storage and drain parameters of the SWMM-PP model.

Model evaluations and comparisons
For the SWMM-PP model, the most optimal parameter set (highest NSE value) differed between the five selected events. Efforts were made to find a common parameter set that gives reasonable results for the five events. This was an iterative process by exploring the 1,500 parameter sets identified by the DE algorithm for each event. Uncorrected Proof Eventually, a common parameter set was found to yield simulation with reasonable accuracy (NSE.0.5) for the five selected events (Table 2). For the reservoir model, Event 9 was selected to find the optimal value of k2, which was found to be 0.04. The value of k2 was validated on Event 2 and found to produce a result with reasonable accuracy. Event 7 was selected to optimize the value of k1, which was validated on Event 10 and was found to equal 0.004. The maximum water level at the storage layer (St) for Event 7 was selected as the value of the flow threshold parameter (Fth). The value of S1 was taken as 10% of the soil layer, following the calibration of the SWMM-PP model. The results of the two models are illustrated in Figure 5 and Table 3.
In general, the reservoir model yielded slightly more accurate simulations (average NSE ¼ 0.74) than the SWMM-PP model (average NSE ¼ 0.69). The reservoir model was found to perform better (higher NSE) than the SWMM-PP model in three events (Events 7, 9, and 10), while the SWMM-PP performed slightly better in two events (Events 2 and 3). In addition, it should be emphasized that the calibration of the reservoir model, with the aim of finding a common parameter set for the five events, was much easier and faster than the SWMM-PP model calibration.

Continuous simulations and FDCs
The FDCs are presented in Figure 6. The two models produced similar permeable pavement outflows. However, it can be noted that the SWMM-PP model outflows were lower than those predicted by the reservoir model, especially during low flows. This was expected, as the SWMM model does not account for the soil moisture deficit when determining the actual evapotranspiration (Peng & Stovin 2017). In contrast, the reservoir model accounts for the soil moisture deficit (Equation (10)), which is more realistic.
The FDCs could unambiguously demonstrate the hydrological performance of LPP and provide valuable information for stormwater engineers and decision-makers. For instance, suppose that a value of 0.1 mm/min/area is a critical value that causes combined sewer overflow in this location, which can result in severe damages and  Figure 6 | FDCs of the normal pavement and the permeable pavement using the two models.
Blue-Green Systems Vol 3 No 1, 10 Uncorrected Proof health issues. The LPP could reduce the duration of flow above this critical value from 11 h to only 3 h. Additionally, the LPP reduced the maximum outflow per unit area from nearly 0.5 mm/min to less than 0.2 mm/min.