Abstract

In this study, water depth measurements were collected in storm water infrastructure during rain events using a pressure based water level sensor. Irregularities within the measured water level datasets required data smoothing to prepare the observed data for calibration. A rainfall–runoff model was created using a proprietary version of the U.S. Environmental Protection Agency’s Storm Water Management Model, PCSWMM, to predict the performance of recently implemented green stormwater infrastructure with respect to runoff at the site. The PCSWMM model calibration was accomplished by comparing water level data collected on site to the PCSWMM output data produced by the uncalibrated model. Nash–Sutcliffe efficiency was used to assess the performance of the calibration procedure. Sensitivity analyses of the estimated parameters were performed to assess the impacts of the model parameters on overall model output. The overarching objective of the study was to demonstrate the value of inexpensive and readily available real-time pressure based water level sensor data to calibrate a PCSWMM model.

1 Introduction

Non-point source pollution, such as stormwater runoff resulting from local and global increases in impervious surfaces, threatens to erase much of the progress achieved by the Clean Water Act (Dietz and Clausen 2007). Pollutants found in runoff, such as nutrients from fertilizers, can cause a harmful chain reaction in the aquatic ecosystem leading to contaminated source water and ecosystem damage, as observed in the western portion of Lake Erie in recent years (Urry et al. 2014). Mitigating stormwater contamination that contributes to eutrophication in natural waters is critical (Ding et al. 2015). Eutrophication creates abundant growth in aquatic plants and algae blooms which lead to the depletion of oxygen in water (Behbahani et al. 2013). On 2014-08-01 a harmful algal bloom (HAB) occurred near the drinking water intake for the city of Toledo causing a regional water crisis. Due to the resulting public health concerns and the global attention drawn by this event, various organizations and researchers have taken preventative action.

In response to the event, the University of Toledo authorized the construction of various forms of green stormwater infrastructure (GSI) to moderate the quantity and improve the quality of stormwater runoff (Jaffe 2010). The Civil and Environmental Engineering Department at the University of Toledo facilitated the construction of a tree filter to conduct research in order to determine the potential benefits of GSI. A simulation model was created, using the U.S. Environmental Protection Agency’s (USEPA) Stormwater Management Model 5 (SWMM) to predict the influence of the tree filter on runoff leaving the parking lot. SWMM has been widely used to simulate the quantity and quality of urban storm water runoff and to model runoff mitigation through structural storm water best management practices, such as tree filters (Tsihrintzis and Hamid 1997).

SWMM model calibration is recommended for achieving the best and most accurate results (Tsihrintzis and Hamid 1997). Calibration can be done by comparing independently measured real time data (with sensors) to the output data produced by the un-calibrated model (Rossman et al. 2004). Suitable calibration methods include trial and error, which consists of adjusting model parameters manually and evaluating the best fit based on selected statistical criteria or graphical comparisons. This method is time consuming and relies on the researcher’s experience and discretion (Mbonimpa et al. 2015). Parameter estimation (PEST) calibration is based on an inverse modeling procedure, which adjusts the parameters of parameterized models until the best fit for both modeled outputs and field measured data is optimized by minimizing the sum of squared weighted residuals (Doherty et al. 2010). Using a proprietary spatial decision support system for SWMM, for example PCSWMM, model calibration can be conducted by comparing a time series of data measured independently, using deployed sensors, to the model output time series data produced by the uncalibrated model (Rossman et al. 2004). The calibration method selection can depend on sensor application and the desired accuracy of the measurements (Kinsey et al. 2006). The model calibration process can be limited by the accuracy and extent of the field data collected.

Previous researchers have used flow data for calibration (Gülbaz and Kazezyılmaz-Alhan 2012; Khader and Montalto 2009). Although the use of flow data to calibrate SWMM has produced successful models, flow meters are expensive and somewhat difficult to use. For example, area–velocity flow meters, which must be installed within the pipeline, require an external part such as a pipe band to properly mount the product (Greyline 2013). This proves to be difficult to do in a retrofit of stormwater pipes. In addition, area–velocity flow meters for the study site would cost between $3500 and $5000 (Hach 2015; Greyline 2013). In this study, real time depth data from traditional stormwater infrastructure (i.e. catchbasins) were used for model calibration rather than area–velocity flow meters.

With the advent and widespread use of digital data loggers in recent years, the ability to collect and store real time data in remote and varied locations has grown significantly (Sophocleous and Perry 1984). There are many applications for inexpensive and accurate water level sensors in chemical, engineering, power generation, hydrology and environmental studies (Ross 1983). Liquid level in a storage unit is one of the important variables to be measured and controlled in many industrial processes (Lipták 1998). Depth sensors have proven to be more cost effective and easier to install than flow meters. In this study, PCSWMM model calibration was completed using the sensitivity based radio tuning calibration (SRTC) tool to compare time series data of water level loggers in a storage node with time series data generated by the uncalibrated model. Depth sensors, such as the HOBO U20 and U20L water level loggers by Onset used in this study, require only a non-stretchable wire for mounting and cost between $300 and $500 (Onset 2014).

2 Methodology

2.1 Site Description

This research was performed at the University of Toledo located in the Ottawa River–Ten Mile Creek watershed in the Maumee area of concern (AOC). The location is shown in Figure 1. In 1972, the binational Great Lakes Water Quality Agreement (under section 118 of the Clean Water Act) between the United States and Canada was established as part of an effort to restore and protect the Great Lakes. The Maumee AOC is included in the watershed of the Western Lake Erie basin. This AOC was initially designated due principally to the detrimental effects of agricultural runoff; however, further study has revealed significant impacts from contaminated industrial sites, urbanization, combined sewer overflows and landfill leachate.

Figure 1 University of Toledo location in the Ottawa River–Ten Mile Creek watershed.

In 2014, a tree filter was installed adjacent to the Ottawa River, which passes through the University of Toledo campus and is a tributary of the Western Lake Erie basin. Details of the construction are shown in Figure 2. The precast structure (5 ft × 7 ft, 1.5 m × 2.1 m, footprint) includes an inlet storage node (still well), a weir wall, engineered filtration media, a native deciduous tree, an overflow pipe, and an underdrain. The contributing watershed consists of about 3200 m² (0.86 acres) of 100% impervious parking lot. The runoff that is generated is collected in four catchbasins and directed into the tree filter through a series of stormwater conduits. Real time water level and weather data were collected from a nearby weather station (Onset HOBO U30).

2.2 SWMM Model

The SWMM model of the site consists of 5 subcatchments, 6 storage nodes, 7 conduits, 2 outfalls and 1 weir in the tree filter. The model is shown in Figure 3. Green stormwater infrastructure (GSI) attempts to restore the pre-development hydrologic budget of a site and to capture stormwater pollutants through infiltration, evaporation and sedimentation of runoff. Many municipalities and government agencies that are tasked with the protection of receiving waters promote the implementation of GSI. In addition, numerous guidance documents for the planning, design, implementation and maintenance of GSI exist. In this study, a PCSWMM model was generated, calibrated and validated and then used to evaluate the long term performance (one full year) of the installed tree filter. Performance of the tree filter was estimated by comparing the SWMM model results before its installation to the results after implementation at the site.

Figure 3 Schematic of SWMM model for tree filter site.

The tree filter was modeled as a separate inline subcatchment to allow the implementation of LID controls to better represent the actual treatment process of the tree filter. The design details are provided in Table 1. Flow from the other four subcatchments was routed through the tree filter to the outfall through a collection pipe. An overflow is represented in the model by flows beyond the capacity of the tree filter that are diverted directly to the outfall.

Table 1 Tree filter subcatchment parameters in PCSWMM.

Parameter	Definition	Value
Area (acre)	Area of subcatchment	0.001
Width (ft)	Characteristic width of overland flow path for sheet flow runoff	5
Slope (%)	Average percentage slope of subcatchment	0.5
Imperviousness	Percentage of land area which is considered directly connected to impervious area	0
NImperv	Manning’s n for overland flow over the impervious portion of subcatchment	0.011
Nperv	Manning’s n for overland flow over the pervious portion of subcatchment	0.15
Zero Imperv	Percentage of the impervious area with no depression storage	0
Percent Routed (%)	Percentage of runoff routed between subareas	100

The water quantity and quality associated with urban storm water runoff can be modeled using bioretention LID (low impact development) controls. The low impact development can be added to the catchments of PCSWMM model as LID controls. LID controls may include any combination of layers: surface, pavement, soil, storage and underdrain system. Table 2 shows the properties of the tree filter as LID with different layers.

Table 2 Layers used to model tree filter as LID control.

	Parameters	Definition	Value
Surface	Berm height (in.)	Maximum depth at which water can pond above the surface before overflow occurs	12
	Vegetation volume (fraction)	The fraction of the volume within the storage depth filled with vegetation	0.1
	Surface roughness (Manning’s n)	Manning’s n for overland flow over porous pavement surface or a vegetative swale	0.07
	Surface slope (%)	Slope of porous pavement surface or vegetative swale	1
Soil	Thickness (in.)	The thickness of the soil layer	48
	Porosity (volume fraction)	The volume of pore space relative to total volume of soil	0.43
	Conductivity slope	The saturated hydraulic conducitivity value for the type of soil used in the soil layer	5
	Suction head	The average value of soil capillary suction along the wetting front	1.93
Storage	Thickness (in.)	The thickness of the storage layer	24
	Seepage rate (in./h)	The maximum allowable rate at which water infiltrates into the native soil below the layer	9.27
	Void ratio (void/solid)	The volume of void space relative to the volume of solids	0.45
Underdrain	Drain coefficient (in./h)	Coefficient C determines the rate of flow through the underdrain as a function of height of stored water above the drain height	0.5
	Drain exponent	Exponent n that determines the rate of flow through the underdrain	0.43
	Drain offset height (in.)	Height of any underdrain piping above the bottom of a storage layer	12

2.3 Water Level Sensor

Monitoring systems with sensors are more practical than manual measurements because they provide remote access to data through the network and give more accurate results. The sensors are more accurate because they collect more data more frequently (real-time) than is possibly by manual measurement. Four types of measuring sensors can be used to determine the water level: pressure sensors, float gauges, bubble gauges and non-contact radar gauges (Lo et al. 2015). Pressure based water depth sensors were used in this research (Onset HOBO U20; shown in Figure 4). Installation required a non-stretchable wire for mounting in the storage nodes (i.e. catchbasins). The accuracy of the water level sensor is 0.5 cm (0.016 ft) with a response time <1 s. These sensors can measure water level data in an operational range of approximately 0 to 4 m (up to 13.12 ft) of fresh water. They have a raw pressure accuracy of ±0.43 kPa (0.062 psi) and can detect up to 0.014 kPa (0.002 psi) or a 0.14 cm (0.004 ft) change in water level (HOBO water level manual).

Figure 4 Photo of wireless real-time water level sensor deployed in the tree filter.

The sensors were individually calibrated and connected to loggers that collected data every 1 min (Onset 2014). In this study, the sensor was deployed in the still well of the tree filter to obtain observed data for calibrating the tree filter model (Fattoruso et al. 2015). Loggers use an absolute pressure sensor to record values in kilopascals. These pressure values can be converted into water depths using the fluid statics equation for pressure (Equation 1; Stern 2013). To properly convert the absolute pressure readings into water level data, the atmospheric pressure was recorded by the weather station every minute. The equation for converting pressure to water depth is:

(1)

where:

P	=	pressure (Pa),
h	=	depth (m),
g	=	acceleration due to gravity (m/s2), and
ρ	=	density of water (kg/m3).

2.4 Water Level Data Collection and Analysis

Both laboratory and field data were collected to test the accuracy of the water level sensor data. Preliminary field experiments indicated that there were some anomalous water level measurements. Turbulence was assumed to be the cause of noise and outliers in the water level data collected in the field since turbulence can impact the pressure recorded by the water level sensor. Therefore, experiments to verify the effects of turbulence were conducted. In the laboratory. A Phipps & Bird PB-700 jar tester was used to create turbulence via mixing and to imitate the movement of stormwater in stormwater infrastructure during a rain event. Two 2 L containers were filled with water (14.60 cm depth). One container served as the control (no mixing). The speed of mixing in the other container was increased by ~100 rpm every 1 min for 3 min and then reduced at the same rate back to 0. The barometric pressure was measured in the laboratory for the conversion of pressure to water depth. The sensors recorded data every 1 s for 7 min. The apparatus is shown in Figure 5. Data collected from the control and the experimental samples were compared. The experiments were repeated in triplicate.

Figure 5 Apparatus used for laboratory based turbulence experiments.

In field experiments, water level sensors were deployed in the catchbasins and the tree filter still well in 2015. The loggers were launched and set up for data collection. Setup consisted of securing the water level sensors with non-stretchable cable to reduce the amount of bouncing caused by the moving water. The cable was long enough to allow the water level sensors to touch the bottom of the catch basin. In 2015, data was collected for 7 d. During launching, the loggers were set to record data at 1 min intervals. The weather station data was downloaded using HOBOlink. The barometric pressure readings taken by the weather station were saved individually as a semicolon delimited file. The catchbasin loggers were read using HOBO software. This allowed the use of the weather station file by the Pro Barometric Data Assistant for the conversion from pressure to depth. When the conversion was complete, the data were imported into Microsoft Excel. The data collected from both laboratory and field experiments were reviewed for outliers and processed by data smoothing.

2.5 Data Smoothing

It is critical to identify which data points in a time series of data are outliers and to determine how to accommodate them. In some cases, these data may be replaced with reasonable values or eliminated entirely. An outlier may result from noise in the signal or from an environmental anomaly (Basu and Meckesheimer 2007). Our laboratory studies implicated turbulence as a possible contributor to the creation of outliers. Our objective was to remove the outliers that were anomalous, regardless of the reason, and to replace them with reasonable values. To remove inaccurate data in this study, a data manipulation technique was applied for data smoothing. Following the methods explained by Leys et al. (2013), an algorithm was written to use median absolute deviation (MAD) to detect outliers. This approach requires the use of the median value of a neighbourhood of data points (a sliding window) to determine whether a particular data point is an outlier (Rosenmai 2013). A sliding window is chosen, thereby partitioning the data into intervals (e.g. 20 min of data). These intervals separate the data into sets based on the determination of where normal distributions occur. This will vary according to the size of the data set, the frequency of sample (data) collection, and the type of data being collected.

First, the median is found for each set and the absolute deviation from the median is calculated for each number in each set (Equation 2). Then all deviations are put in a list. In the determination of MAD, the median is found for the list of absolute deviations and multiplied by the upper quartile of the entire data set (Equation 3). A Z-score is then calculated for each individual point in the entire data set (Equation 4). This Z-score, along with the threshold, determines whether the point is an outlier or not. The Z-score is a determination of how far the individual number deviates from the mean of the whole set. The threshold was set as 2.5 for field data and 2 for laboratory data (Leys et al. 2013). Any number with a Z-score less than the threshold is included in the new dataset. The new data set is output as an Excel file with its corresponding date and time (Leys et al. 2013).

(2)

where:

ADM	=	absolute deviation from the median,
n	=	individual data point, and
med	=	median.

(3)

where:

MAD	=	median absolute deviation of the data, and
Q(0.75)	=	upper quartile of data set

(4)

The algorithm was run using water level data obtained from the laboratory experiments and from the field experiment data collection in the catchbasin and the still well of the tree filter. After smoothing, the datasets can be imported into PCSWMM as observed input data for model calibration.

2.6 Model Calibration and Validation

In order to evaluate the performance of the tree filter, calibration was carried out using observed data from a weather station and smoothed data from water level data loggers. This included an entire year (2015) of precipitation and water level data. The first step in calibrating the model (after obtaining the precipitation and water level data) was to select parameters for calibration and estimate the uncertainty of these parameters. The subcatchment parameters used to model surface runoff are estimated with varying degrees of uncertainty. The modeler then performs a sensitivity analysis to guide how adjustments to specific parameters impact the model results.

Some parameters, such as slope and subcatchment width, are hard to measure with certainty so these parameters are good candidates for calibration (James 2003). The subcatchment width is calculated by length of overland flow divided by the subcatchment area. NImperv for the runoff of subcatchments is dependent on the surface texture and is defined by the Manning’s roughness value. Depression storage is the ability of land area to hold water. Each depression is represented by geometric properties such as depth, surface area and volume (Ullah and Dickinson 1979). In the tree filter PCSWMM model, the width, slope, NImperv, and depression storage parameters were assigned uncertainty percentages ≤100 %. If the uncertainty is small, 5% to 50% should be assigned as the uncertainty. If any estimate can be made at all, 50% to100% could be assumed as a starting point for uncertainty (James 2003). These uncertainty values depend on the source and accuracy of the data used to build the model.

The calibration of the SWMM model was carried out using the sensitivity based radio tuning calibration (SRTC) tool that is offered in PCSWMM. The SRTC tool allows the user to have computed, observed and calibrated data in one graph (Finney and Gharabaghi 2011). The SRTC tool works by designating uncertainty percent rankings for each parameter of interest. For efficient calibration, estimates of the model parameters should be as close as possible to the true value. The aim of uncertainty analysis is to rank the contributions of individual parameters and input functions to each of the sources of uncertainty (James 2003). Clicking the SRTC tool causes PCSWMM to run the model twice for each parameter of interest, one scenario where subcatchment parameters are minimized and one scenario where subcatchment parameters are maximized. Figure 6 shows one calibration using the STRC tool. Subcatchment parameters were modified in the light of the results of the calibration procedure.

Figure 6 One calibration event using the STRC tool in PCSWMM with change in radio tuning to obtain the best match.

By choosing the SRTC function and selecting calibrate to observed location with parallel running simultaneously, calibrated model results can be displayed. Radio sliders located at the bottom of the window in the PCSWMM calibrated graph allow the user to change the uncertainty value of parameters within the predefined range in order to better match the time series plots. However, discrepancies always occur between observed data and model output due to, among other reasons, inaccurate measurement and imperfect parameterization (Wan and James 2002).

Calibration for the tree filter model was performed using data collected during a series of rain events in 2015. Limited available rain gauge data (due to equipment failure) may have precluded more adequate calibration and validation results. Two example calibration rain events and their duration, intensity and total rainfall amount are given in Table 3. In most hydrologic models, the model outputs are time series, either single site or multiple sites depending on the chosen model. The general guideline for a successfully calibrated model is that the model results closely resemble the observed historical data (Boon et al. 2012). There were various sizes of rain events within this time period. Calibration was completed based on events, including events 1 and 2, by comparing observed (water level logger) data with model data.

Table 3 Sample precipitation events used for model calibration and validation.

Events	Start Date	End Date	Rainfall (cm)	Duration (h)
Event 1	4/21/2016	4/24/2016	3.68	82.0
Event 2	11/02/2015	11/06/2015	1.01	91.8
Event 3	7/11/2015	7/17/2015	1.75	114.5

There are several methods that quantify model performance in calibration. Those used in this study included the integral square error, Nash–Sutcliffe efficiency, the coefficient of determination, simple least squares, and root square mean error. The integral square error rating (ISE), commonly used to compare the performance of many systems, can vary from excellent (<3) to poor (>25); it is given in Equation 5. Nash–Sutcliffe efficiency (NSE) indicates how well simulated data match observed data. It can range between −∞ and 1, and values between 0.0 and 1.0 are usually considered acceptable (Moriasi et al. 2007), with NSE = 1 indicating a perfect fit (Equation 6). The coefficient of determination R² is a key output of regression analysis, and an R² value of 1 indicates that the regression line perfectly fits the data (Equation 7). Similarly, the root mean square error (RMSE) can be used to estimate the differences between those values predicted by a model and the observed values (Equation 8). An RMSE value approaching zero is more desirable (Moriasi et al. 2007).

	(5)
	(6)
	(7)
	(8)

Calibration of the PCSWMM model that we developed was carried out by focusing on a series of rain events in the years 2015 and 2016. There were rain events of various durations within this period (82 h to 7 d). Since the goal was to calibrate a model for a continuous simulation of months (rather than individual events), precipitation data for calibration were multiple days in duration. During the summer months (the dry season), there were several smaller rain events that produced lower peak flows. Following calibration, the model was validated using input data from other rain events. The precipitation dataset is divided and partly used for calibration and partly used for validation (Kinsey et al. 2006). This verification process determined whether or not the parameter changes made through the SRTC tool had the desired effects on the accuracy of the model. The split sample validation test was used to calibrate and validate the model using the data collected on site and to identify if the parameters are valid for a time period outside of the calibration period.

A sensitivity analysis was also performed on each physical model parameter and its performance to determine the parameter’s influence on the model output based on simulations under various conditions (Edouard et al. 2016). The impact of slope, flow width, flow length and imperviousness were all considered for their effect on the model output.

3 Results and Discussion

3.1 Data Collection and Smoothing

Laboratory experiments verified the influence of turbulence on the logger depth data. The variation in the control data (standard deviation ±0.091 cm) was significantly smaller than the simulation data (standard deviation ±0.457 cm), indicating more variability in the water depth data collected during turbulence. The data set from the moving water varied between 10.79 cm and 12.98 cm (2.19 cm difference between the highest and lowest values) while the data from the control sensor only varied between 12.77 cm and 13.32 cm (0.55 cm difference between the highest and lowest values). The two sets of results are shown in Figure 7. When the mixer was at maximum speed (300 rpm), the depth data was lowest (at between 180 and 240 seconds). The cause is likely the vortex created by the turbulence moving the water surface and therefore reducing the pressure on the data logger.

Figure 7 Laboratory data indicating the effect of turbulence (due to stirring) on water level sensor data accuracy.

Outliers were removed from all data sets using the MAD-based smoothing approach. The field data from 2015, consisting of 10 174 data points, contained 954 outliers. The standard deviation of the field data from 2015 was ±0.61 cm before outlier removal and ±0.38 cm after. The differences between the maximum and minimum points for the field data changed from 43.16 cm to 9.63 cm (2014 data) and from 7.65 cm to 4.08 cm (2015 data). The two data sets are shown in Figure 8. The MAD algorithm caused the greatest reduction in deviation in the field data sets.

Figure 8 Time series of water level logger data, original and smoothed using MAD, collected in the tree filter still well in 2015-07.

3.2 Model Calibration and Validation

Any modeling exercise should aim to minimize the associated errors. Common errors that can occur within modeling are random or systematic errors in the input data, including errors due to non-optimal data values and errors because of incomplete or biased model structure (van der Sterren et al. 2014). Moreover, water level sensors provide realization of measurement process subject to normalized error, which is assumed in Equation 9:

(9)

where:

h	=	height of measurement,
ε	=	error from sensor, and
h(t)	=	true value of height (Boon et al. 2012).

In the tree filter PCSWMM model, the flow width, flow length, pervious roughness and slope subcatchment parameters were assigned uncertainty percentages. Table 4 shows the parameters of the subcatchment before and after calibration, which shows how the parameters were modified during calibration.

Table 4 Subcatchment parameters before and after calibration.

Parameter (subcatchment)	Parameter before calibration	Parameter after calibration
Area (acre)	0.185	0.185
Width (ft)	84.79	42.40
Flow length (ft)	0.750	1.170
Imperviousness (%)	100	100
Slope (%)	0.011	0.006
Impervious roughness	0.150	0.150
Pervious roughness	0.075	0.148
Impervious surface storage (in.)	0.150	0.150

In this study, modeled and observed data were computed. Table 5 shows the error functions in two calibration events and their acceptable ranges. Model calibration was followed by a verification analysis. The split sample validation test was used to calibrate and validate the model using the data collected on site. A split sample validation was used to identify if the parameters hold for a time period outside the calibration period. The hydrological validation range was done in the still well of the tree filter in different rain events from 2015-07-11 to 2015-07-17. The verification process determines whether or not the parameter changes made through the SRTC tool had the desired effects on the model. The calibration events and validation event results provided here represent a simulation of between 80 h and 115 h. Note that the length of the validation period will affect the performance results.

Table 5 Calibration and validation errors with their acceptable ranges.

Name of error	Rate of acceptance	Error calibration Event 1	Error calibration Event 2	Error calibration Event 3
ISE	Excellent < 3	Excellent	Excellent	Excellent
NSE	Closer to 1	0.9	0.93	0.475
R2	Closer to 1	0.94	94	0.801
RMSE	0<RMSE<1	0.06	0.2	0.001

3.3 PCSWMM figures

The observed data, collected by water level sensors in storage nodes, were compared to the results from the PCSWMM model. The HOBO level logger data is shown in meters and, after smoothing data with the MAD algorithm, these rainfall data were used as the input file for the calibration process. Figure 9 is a plot of observed data versus PCSWMM model data in the calibration period (2016-04). The model data has a higher peak depth and slightly less lag time than the observed data. The difference in measured depth data and PCSWMM model results may be associated with the input model parameters such as surface roughness, subcatchment slope, flow length, and underestimated surface storage on the parking lot.

Figure 9 PCSWMM model compared to sensor (observed) data.

The calibration of the PCSWMM model was carried out using the Sensitivity Based Radio Tuning Calibration (SRTC) tool, that is offered in PCSWMM. Figure 10 displays calibrated and uncalibrated model outputs in one graph for the 2016-04 data. The calibrated outputs were generated using the observed (field) data. Overall, the simulated depth data matches closely with the observed depth with a few exceptions. The overall curve after calibration is still shifted slightly to the right, indicating a slight lag time in the contributing subcatchments that is not predicted by the uncalibrated model.

Figure 10 Calibrated data compared to the uncalibrated data.

For this specific model, slope, flow length and flow width had negligible impact on the output. The results indicated that imperviousness is more sensitive than other parameters, based on changes in the output results, while other parameters stay constant. There was a small variability in output data based on a wide range of imperviousness in the subcatchment with an overall percentage of change in output depth (water level) of ≤3%.

3.5 Tree Filter Performance

The calibrated model is used to estimate the performance of the tree filter. Tree filter performance indicators include flow diversion (stormwater infiltrated rather than released) and flow treatment (filtered before release). With the calibrated model, performance predictions can be made for future rain events or estimates can be made based on past precipitation events. Table 5 above summarizes calibrated model results for 1 y simulation in 2015 after importing rain data to the calibrated model and running the long-term simulation. The tree filter area represents <0.3% of the contributing watershed area. During 2015, approximately 144 000 L untreated stormwater were infiltrated by the tree filter (not released to the river), and another 340 000 L were cleaned by the tree filter before release through the outfall. In total this represented ~24% of the total runoff from the subcatchment during 2015, which is encouraging for an undersized system (single tree filter treating significant portion of the parking lot). The exact amount captured and cleaned by the tree filter during a precipitation event as well as the amount that can be infiltrated (diverted) depends on the amount and intensity of precipitation as well as the initial conditions, including soil moisture.

4 Conclusions

The goal of this study was to demonstrate that an affordable, widely available and easy to install pressure-based water level sensors can be used to calibrate a SWMM model. Field data was collected and smoothed using median absolute deviation (MAD) for the detection and elimination of outliers. These smoothed data were chosen as input values for observed data in PCSWMM for calibration using the SRTC tool. The relative error from calibration shows good agreement between the observed data and calibrated model results (Nash–Sutcliffe efficiency between 0.85 and 0.92). The calibrated model may then be used to provide more accurate stormwater flow information including assessment of current or predictions of future performance of green stormwater infrastructure. This approach for SWMM model calibration may be more broadly applied to other more complicated SWMM models and can be further proven if flow measurement is conducted simultaneously.

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