Multiobjective optimization of low impact development stormwater controls

Accepted Manuscript Research papers Multiobjective Optimization of Low Impact Development Stormwater Controls Kyle Eckart, Zach McPhee, Tirupati Bolisetti PII: DOI: Reference:

S0022-1694(18)30321-4 https://doi.org/10.1016/j.jhydrol.2018.04.068 HYDROL 22771

To appear in:

Journal of Hydrology

Received Date: Revised Date: Accepted Date:

29 November 2017 25 April 2018 26 April 2018

Please cite this article as: Eckart, K., McPhee, Z., Bolisetti, T., Multiobjective Optimization of Low Impact Development Stormwater Controls, Journal of Hydrology (2018), doi: https://doi.org/10.1016/j.jhydrol. 2018.04.068

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Multiobjective Optimization of Low Impact Development Stormwater Controls Kyle Eckart, Zach McPhee, and Tirupati Bolisetti* Dept. of Civil and Environmental Engineering, University of Windsor, Windsor, ON, Canada, N9B3P4

Kyle Eckart Dept. of Civil and Environmental Engineering, University of Windsor, Windsor, ON, Canada, N9B3P4 Phone: 519-253-3000 x2548 [email protected] Zach McPhee Dept. of Civil and Environmental Engineering, University of Windsor, Windsor, ON, Canada, N9B3P4 Phone: 519-253-3000 x2548 [email protected]

Corresponding author: Tirupati Bolisetti* Dept. of Civil and Environmental Engineering, University of Windsor, Windsor, ON, Canada, N9B3P4 Phone: 519-253-3000 x2548 [email protected]

This work was partially supported by the NSERC Canada under Grant number xxxx and the University of Windsor awarded to senior author. The first and second authors were supported through university scholarships as well as Ontario Graduate Scholarship.

Multiobjective Optimization of Low Impact Development Stormwater Controls Kyle Eckart, Zach McPhee, and Tirupati Bolisetti* Dept. of Civil and Environmental Engineering, University of Windsor, Windsor, ON, Canada, N9B3P4

Abstract Green infrastructure such as Low Impact Development (LID) controls are being employed to manage the urban stormwater and restore the predevelopment hydrological conditions besides improving the stormwater runoff water quality. Since runoff generation and infiltration processes are nonlinear, there is a need for identifying optimal combination of LID controls. A coupled optimization-simulation model was developed by linking the U.S. EPA Stormwater Management Model (SWMM) to the Borg Multiobjective Evolutionary Algorithm (Borg MOEA). The coupled model is capable of performing multiobjective optimization which uses SWMM simulations as a tool to evaluate potential solutions to the optimization problem. The optimization-simulation tool was used to evaluate low impact development (LID) stormwater controls. A SWMM model was developed, calibrated, and validated for a sewershed in Windsor, Ontario and LID stormwater controls were tested for three different return periods. LID implementation strategies were optimized using the optimization-simulation model for five different implementation scenarios for each of the three storm events with the objectives of minimizing peak flow in the stormsewers, reducing total runoff, and minimizing cost. For the sewershed in Windsor, Ontario, the peak run off and total volume of the runoff were found to reduce by 13% and 29%, respectively.

Keywords Stormwater management, Low Impact Development, LID, SuDS, LIUDD, WSUD, Green Infrastructure, Sustainability, LID Implementation, Multi-Objective Optimization (MOO)

1 Introduction Urbanization drastically changes hydrological patterns and flow regimes. These changes often include increased peak flows, reduced times of concentration, redistribution of the water balance and flashier flows in urban streams and rivers (Chui et al. 2016; Konrad and Booth 2005; Li et al. 2017; Paule-Mercado et al. 2017; Todeschini 2016; WEF 2012). Urban areas can become prone to flooding and ecological degradation from accelerated stormwater runoff (Jennings et al. 2012; McGrane 2016). Ecosystem damage and property damage from flooding, often end up exceeding the cost of stormwater management (Visitacion et al. 2009). Rapid urbanization and climate change are expected to further increase the risk of flooding and drainage disasters in urban drainage systems (Duan, et al. 2016; Stovin et al. 2012; Visitacion, Booth, and Steinemann 2009; Wang et al. 2016). One way to combat this is the use of low impact development (LID), which is an emerging approach to stormwater management that is being utilized to reduce the impacts of urbanization and climate change on urban watersheds. Some of the commonly used LID controls include rain barrels, rain gardens, bioretention ponds, and porous pavements. The philosophy behind the LID approach is to attempt to replicate the hydrology of the pre-development watershed. LID uses distributed stormwater controls (source controls) and incorporates natural hydrologic features, in order to detain water, which in turn facilitates infiltration, and evapotranspiration. By doing so, LID can reduce flooding and improve ecological conditions (Damodaram et al. 2010; Shuster et al. 2008; van Roon 2005, 2007; van Roon and Knight-Lenihan 2004). LID has often been implemented as a retrofit designed to ease the stress on urban stormwater infrastructure as well as provide some resiliency to the impacts of climate change (Ahiablame et al. 2012; Jia et

al. 2012; Liu et al. 2015). The detailed investigations on the performance of the individual LID controls were performed, for example on permeable pavements (Brunetti et al. 2016; Huang et al. 2016) and bioretention units (Hathaway et al. 2014). Where there are a number of subcatchments within a catchment it can be difficult to determine which LID controls to place in each subcatchment, or if any at all (Cano and Barkdoll 2017). The selection and placement of LID controls, such as number, locations, and combinations of controls can be abundant due to varying features. The number of possible combinations may not be feasible to analyze, particularly at a large scale. Determining the optimal placement and selection of controls is required to achieve maximum runoff reductions at the minimum costs (Liu et al. 2016). The cost effectiveness of the LIDs from the point of view of life cycle assessment was investigated by Chui et al. (2016) and Wang et al. (2016). Two tools that stormwater professionals can utilize to help them implement LID controls are simulation and optimization. Computer modeling is a powerful tool for the design and optimization of sewer systems (Ahmed et al. 2017; Akhter and Hewa 2016; Freni et al. 2010; Palanisamy and Chui 2015; Palla and Gnecco 2015; Wang et al. 2016; Xu et al. 2017; Zahmatkesh et al. 2015). Several models now include methods for simulating LID controls, the most commonly used model for research is the U.S. Environmental Protection Agency's Stormwater Management Model (SWMM) (Rossman 2010). To expediently assess and compare LID scenarios in a watershed, optimization tools are extremely useful. Optimization tools have greatly improved and now allow for more accurate and less complex methods. Most often single objective optimization has been used; however, single objective optimization requires some objectives to be constrained to a target range or weighted a-priori. When attempting

to optimize multiple objectives without making preference decisions prior to optimization, multiobjective optimization is stronger. One of the most common sets of multiobjective optimization tools used with LID controls are genetic algorithms. Genetic or evolutionary algorithms can be used to optimize multiple objectives and are easily linked with simulation models such as SWMM (Baek et al. 2015; Duan et al. 2016; Jung et al. 2016; Karamouz and Nazif 2013) and Soil and Water Assessment Tool (SWAT) (Kaini et al., 2008; Neitsch et al., 2011). There are several genetic algorithms available to be used in multiobjective optimization and several improvements have been made over time. For this study the genetic algorithm of choice is the Borg Multi-Objective Evolutionary Algorithm (MOEA) (Hadka and Reed 2013). Coupling a multi-objective optimization model with SWMM is being explored more recently for analyzing LID scenarios. Duan et al. (2016) studied the multi-objective optimal design of detention tanks and LID devices. They used SWMM for the numerical simulation and applied the modified Particle Swarm Optimization (NPSO) scheme to solve the multi-objective optimization problem. Baek et al. (2015) combined SWMM with MATLAB and used the pattern search algorithm to optimize LID sizes. Jung et al. (2016) developed an optimization model using the Harmony Search (HS) algorithm coupled with SWMM to determine the optimal design of permeable pavement. Liu et al (2016) have coupled their own LID simulator, L-THIA-LID 2.1 with AMALGAM, an optimization algorithm developed by Vrugt and Robinson (2007). The ability to optimize multiple objectives is useful for the implementation of LID controls. LID implementation allows for optimization in the selection, placement, and sizing of many LID controls

throughout a site or watershed. Multi-objective optimization provides the ability for one to develop multiple trade-off solutions (an example of this being a cost-benefit curve) prior to making preference decisions. This allows stormwater professionals to present the stakeholders with a range of potential solutions and include their preferences into the design process. It can also be utilized when conducting higher level planning exercises, such as a drainage master plan, in order to evaluate the potential benefits of LID implementation on a sewershed scale without spending significant effort in the design. Optimizing LIDs for cost allows one to compare the costs of many potential LID solutions to other stormwater structures and devices. For this research a simulation-optimization model was developed to generate costbenefit information for the selection of LID controls. This study uses SWMM, Borg MOEA, and cost functions in order to examine the potential of LID controls to reduce total runoff over the study area and stormsewer peak flows at various cost levels. The optimization-simulation model developed is able to conduct multiobjective optimization so that cost-benefit curves can be easily generated. The model allows users to analyze the significance of various design parameters for LID controls.

2 Site Description A sewershed in Windsor, Ontario, Canada was used as a study area to develop and test the optimization-simulation model. The sewershed in question is a 77 ha, residentially zoned, suburban sewershed. Excluding undeveloped areas, the study area is 49.5% covered by impervious surfaces with slopes generally less than 1%. The distance from the location of the flow monitor in the sewershed to the nearest rain gauge is about 1.2 km. The sewershed possesses characteristics which could make it poorly suited to

LID implementation including primarily hydrological group D soils (clay and clay loam) with only a small portion underlain by type C sand. The seasonally high water table is estimated to rise to a depth of about 1 m. The sewershed primarily utilizes curb and channel drainage and is served by a stormsewer system which congregates at the flow monitor depicted in Figure 2 before flowing into a trunk sewer.

Figure 1 Land-use map of study area, a 77 ha sewershed in Windsor, Ontario, Canada.

3 Methodology An optimization-simulation method was developed for the purpose of finding optimal strategies for the deployment of LID stormwater controls. This type of model can provide stormwater practitioners with clearer design choices without having to make preference decisions a priori (Deb 2001). Figure 2 depicts the layout of the system that was constructed as well as the data requirements. In this optimization-simulation

methodology the simulation model SWMM is used as a fitness function for the Borg MOEA (the optimization algorithm) with the other fitness function being the cost functions that were developed for this study. The components depicted in Figure 2 are explained in greater detail in the following sections.

Borg MOEA problem setup Site Characteristics

Construct SWMM model

Observed climate and flow data

Calibrate and validate SWMM model

No

Model performance is acceptable?

Borg MOEA generates new solution

Base SWMM input file

Site characteristics

Select and design LID controls

LID design guidelines

Decision variables are plugged into cost functions

SWMM is executed and total runoff and target maximum peak flow are extracted

Objective values attached to solution

Yes Climate data

Cost information

SWMM input file is updated with Borg MOEA decision variables

Borg MOEA tests the fitness of the solution

No

Number of functional evaluations reached? Yes Output elite archive of optimal solutions

Figure 2 Description of the components, processes, and data requirements for the optimization-simulation model.

3.1 Hydrological Modelling 3.1.1

Model Setup

This study employs SWMM (version 5.1) to simulate urban hydrological processes with the study area and the effects of adding LID controls. SWMM has been an effective tool for modeling urban drainage networks and the recent versions include an LID toolbox for the simulation of a number of LID controls. SWMM has previously been used to study low impact development, including those studies previously mentioned (Damodaram and Zechman 2013; Karamouz and Nazif 2013; Oraei Zare et al. 2012; Zhang 2009) as well as some others (Bosley 2008; Damodaram et al. 2010; Elliott and

Trowsdale 2007; Maharjan et al. 2009; McGarity 2010; Palanisamy and Chui 2015; Palla and Gnecco 2015; Qin et al. 2013; Rosa et al. 2015; Zahmatkesh et al. 2015). The study area was divided into 292 non-uniform subcatchments. The subcatchment properties were determined through GIS data, satellite imagery, and site inspection. The network of links and nodes was created based on sewer maps obtained from the City of Windsor. SWMM allows the option of choosing either Green-Ampt method, Horton’s method or the SCS curve number (CN) method for determining infiltration. The CN method was developed to calculate the runoff and eventually infiltration volumes in small urban watersheds which is the focus of this study. This method was selected to compute infiltration losses because it has been previously used in studies focused on the optimization of an urban stormwater system (Maharjan et al. 2009) and optimizationsimulation of LID controls using SWMM (Zhang 2009). The CN method was used because of its basis on a single parameter and responsiveness to the runoff producing characteristics of urban watersheds. Both of these were listed as strengths of the method by Ponce and Hawkins (1996). The dynamic wave method was selected as the routing method because of its ability to account for channel storage, backwater effects, entrance/exit losses, flow reversal, and pressurized flow (Rossman 2010). The main parameters for subcatchments are area, percent impervious area, width, slope, infiltration parameters, Manning’s roughness coefficients for overland flow for pervious and impervious surfaces, depression storage depth for pervious and impervious surfaces, percent zero, and internal routing parameters. The percent impervious area and slope were determined using Google Earth. The width was set as the distance from the

back of the subcatchment to the street, as suggested in Gironás et al. (2009) and then altered during the calibration process. The function of the width is essentially to determine the overland flow distance which runoff must travel before becoming channelized. The infiltration parameters, mainly the curve number, Manning’s roughness coefficients and storage depths were determined based on the sewershed characteristics mentioned in section 2 and the tables in the appendices of the SWMM manual (Rossman, 2010). These values were later calibrated. The internal routing parameters describe if runoff from impervious areas is routed to pervious areas before the subcatchment outlet and if so what percentage of the runoff from impervious area is. These were set largely based on inspection of the sewershed, primarily to where downspouts were routing roof water. The percent zero is the percent of the impervious area on which there is no surface storage (primarily roofs). This value was calibrated to 30% which lies in the typical range reported in Zhang (2009). There are a few additional input parameters. The evaporation was set to only occur during dry periods and was based on the monthly pan evaporation. Because these evaporation rates were used and snowmelt is not considered, there is no need for a climate file with temperatures. The equation selected for force main was the DarcyWeisbach equation. The start and end times were selected to include the entire precipitation events and some time before and after where there is no precipitation. As for the time controls, the reporting interval was set to 5 minutes, the wet calculation time step was set to 20 seconds while the dry step was set to 40 seconds. The routing time step was set to 3 seconds because a very short time step is required for dynamic wave routing. With these parameters, the calculation error was consistently very low.

3.1.2

Calibration and Validation

Flow data collected from a flow monitor (position displayed in Figure 1) and precipitation time series were used to calibrate the SWMM model. The precipitation time series used was the mean reading of the three rain gauges that surround the study area. Previous studies have used Manning's roughness coefficient, depression storage depth, infiltration parameters (e.g. curve number), subcatchment width, subcatchments percent imperviousness, subcatchment slope, percentage of impervious surfaces with no depression storage, and channel roughness values as calibration parameters (Bosley 2008; Liong et al. 1991; Warwick and Tadepalli 1991; Zhang 2009). To calibrate the model, adjustments were made to the subcatchments' imperviousness, widths, curve numbers, and the percentage of the impervious surfaces with no depression storage. In order to represent the hydrological processes in a realistic manner, the model was simulated on a continuous time scale. However we do not know the initial soil moisture conditions in the sewershed. Therefore, starting the simulation somewhat earlier than the period over which calibration is performed, we will be able to overcome any potential uncertainties in the initial conditions. Some of the hydrological simulation models refer this to warmup period which helps in establishing the starting conditions better. Two series of continuous simulations, each containing multiple precipitation events, were used for calibration and validation. Rainfall and flow monitoring data were provided by the City of Windsor. Though precipitation data were available from October 10th, 2012 to January 15th, 2014, the selection of events was limited by the time period in which the flow monitor data was available. Reliable flow monitor data were only available from July 11th, 2013 to midNovember of the same year. From this dataset, two subsets of events one each for calibration and validation, needed to be chosen. While the flow data from any time

interval could have been used, the data collected between July 15 and July 24, 2013 was arbitrarily chosen for calibration and the flow data collected between August 26 and August 31, 2013 were used for validation. A subset of events refer to the events that occurred in close proximity to each other and were simulated as one continuous simulation so that the model could be tested against consecutive series of events where initial saturation conditions would be changing. The ability of the model to reproduce the observed results was numerically evaluated by calculating the Nash-Sutcliffe efficiency (NSE) for each series of events. The NSE values for calibration and validation were 0.79 and 0.93, respectively. The results, in terms of time series of flows, are displayed in Figures 3 and 4.

3

0

Flow Rate (CMS)

20 2 1.5 1

rain

30

Model

40

Observed

50 60

0.5

70

0

15 Minute Rain Intensity (mm/h)

10

2.5

80

7-15-13 2:37

7-16-13 2:37

7-17-13 2:37

7-18-13 2:37

7-19-13 2:37

7-20-13 2:37

7-21-13 2:37

7-22-13 2:37

7-23-13 2:37

7-24-13 2:37

Figure 3 Calibration of the SWMM model for the events from July 15 th to 24th, 2013

3

0

Flow Rate (CMS)

20 2

30

Rain 1.5 1

Model

40

Observed

50 60

0.5

70

0 8-26-13 19:52

80 8-27-13 19:52

8-28-13 19:52

8-29-13 19:52

8-30-13 19:52

Figure 4 Validation of the SWMM model for the events from August 26th to 31st, 2013

8-31-13 19:52

15 Minute Rain Intensity (mm/h)

10

2.5

3.1.3

LID Controls

SWMM 5 includes an LID toolbox which allows LID measures to be implemented in the model making the evaluation of these controls much easier. The LID toolbox includes the ability to define rain gardens, bioretention cells, infiltration trenches, green roofs, permeable pavements, rain barrels and vegetative swales. The LIDs are represented in the SWMM model through the parameterization of several layers, though not all LIDs have all the layers. The creation of treatment trains can be done by creating subcatchments simply for a single LID controls and then route these subcatchments to each other. Five LID controls were deemed appropriate for use in the study area or a similar residential neighbourhood were selected for this study. They include rain barrels, porous pavement, bioretention (both engineered bioretention and simple rain gardens) and infiltration trenches. Depending on the LID control, selected parameters of the design were optimized, within reasonable ranges, while the other required SWMM parameters were set based on LID design standards and study area characteristics, such as land-use, available area, soil infiltration characteristics, slopes, and depth to the water table. The design guidelines and parameters for the LID controls were obtained from Center for Watershed Protection (2010), CVC (2010), Ontario MOE (2003), Rossman (2010), Woods-Ballard et al. (2007). The sources and unit costs used to calculate the capital costs of LID implementation were obtained through vendors, The City of Windsor, and developers. The subcatchment routing to LIDs was determined based on which LIDs were present in a given subcatchment. The routing schemes can be seen in Table 1. LID properties were optimized as decision variables, the details of which are discussed in 3.2.3.

Table 1 Routing schemes for runoff from impervious surfaces to LID controls

Combination RB PP

Maximum % Impervious Area Treated RB PP BR IT Sum

Notes

47

0

0

0

47

Rain barrels capturing entire roof

0

15

0

0

15

Permeable driveway capturing 1/4 of roof (less other imp. Area because of PP) + a little (e.g. walkway around the door)

0

BR IT RB + PP

0

28.3

0

28.3

Captures 1/4 of driveway + 1/2 of roof

0

0

0

34.3

34.3

Calculated using functions provided in Google Earth

58

2

0

0

60

RB + BR

35.25

0

16.51

0

51.76

Bioretention takes 1/4 of roof runoff and 1/4 of driveway runoff. Rain barrels routed to pervious to simulate routing to rain garden.

RB + IT IT + BR

23.5

0

0

25

48.5

Infiltration trench captures back roofs and a little more.

0

0

28.3

34.3

62.56

Infiltration trench captures back half of roof plus a little more; bioretention captures up to 1/2 roof plus 1/4 driveway

IT + PP

0

15

0

34.3

49.3

Solutions do not interfere with each other. Roof proportion increases because of the driveways being replaced with PP.

PP + BR

0

2

29

0

31

RB + PP + BR RB + PP + IT RB + BR + IT

43.5

2

14.5

0

60.5

29

2

0

31

62

11.75

0

20

26

57.75

Rain barrel and bioretention only get 1/4 of roof while infiltration trench gets 1/2 and a little more (e.g. back porch). Bioretention can take some additional runoff.

IT + BR + PP

0

2

29

34.3

65.3

Infiltration trench and bioretention each can receive up to half of the roof runoff, infiltration trench can receive a little more.

RB + PP + BR + IT

29

2

18

22

71

Roof runoff split between rain barrels, bioretention and infiltration trench. Bioretention and infiltration trench receive a little extra runoff from other surfaces.

Roof represents higher % of total with PP. Also, PP captures very little outside its own surface with the roof accounted for.

Bioretention takes 1/2 of roof runoff since permeable pavement is not designed to take much flow from other areas and doesn't off infiltration in this case. Bioretention takes a little more than 1/4 of the roof. Rear portion of the roof directed to the infiltration trench.

*BR = Bioretention (the same values apply for rain gardens); IT = Infiltration trench; PP = Permeable pavement; RB = Rain barrel

3.2 Optimization Multi objective optimization refers to the maximizing, or more often, the minimizing of multiple objectives F(x) = [f1(x), f2(x),..., fn(x)] where x = x1, x2,...,xn represent the decision variables. The decision variables define the decision space where the feasible region is the set of solutions in the space which satisfy any constraints placed on the decision variables (Deb 2001). A single solution is a set of n values corresponding to a feasible value for each decision variable. For example, for the design and placement of rain barrels the decision variables might be the number of rain barrels per house constrained between 0 and 4, and the size of the rain barrels constrained to one of the commonly available sizes on the market. The optimization goal for this study was to find the pareto-optimal front for the objectives of minimizing peak flow in the stormsewers, total stormwater runoff, and cost. Such a procedure may be represented as the development of cost-benefit curves. The decision variables are various LID design parameters related to their definition in the SWMM input file. The fitness functions which evaluate the solutions (taking the decision variables and returning objective values) are the SWMM model itself as well as cost functions. This whole system is created by linking the SWMM model to the Borg MOEA so that there can be a feedback process where Borg alters some SWMM input parameters and receives outputs from the SWMM model. Borg MOEA is an advanced genetic algorithm (GA). One unique benefit of GAs is their ability to find multiple optimal solutions in a single run (Deb 2001). Furthermore, GAs allow for a more evenly distributed pareto-optimal set than what we may get by

running several runs of a single optimization problem and altering the weights a-priori (Deb 2001). GAs are very adaptable and can be applied to a wide variety of problem types and scales (Sivanandam 2007). The fitness functions used are also very adaptable. For example, a fitness function might be a simple mathematical formula which uses the decision variable values to produce objective function values, or it could be a hydrological model which uses the decision variables as some of its input parameters and produces outputs which are used as objective values. One thing that can make it easier to use a GA is that they require no prior knowledge of the objective space (Sivanandam 2007). One final benefit of GAs relevant to this study is that they are specifically designed to discover pareto-optimal fronts (Sivanandam 2007). 3.2.1

Borg MOEA

There are several genetic algorithms available to be used in multiobjective optimization and several improvements have been made over time. For this study the genetic algorithm of choice is the Borg Multi-Objective Evolutionary Algorithm (MOEA) (Hadka and Reed 2013). Borg MOEA combines and enhances several processes used successfully in previous GAs. It has been used for water resource problems, for example d’Ervau (2013), however it has not yet been widely used as it is still new. Tested against six state-of-the-art MOEAs on several test problems, Borg met or exceeded the performance of the other MOEAs on most of the tests (Hadka and Reed 2012). A complete description of the Borg MOEA and important components can be found in Hadka and Reed (2013). Borg is freely available for research purposes from borgmoea.org. Borg MOEA is an elitist genetic algorithm, meaning that in addition to the population, Borg also stores an elite archive of solutions. The elite archive has more

stringent dominance criteria than the population. It is maintained throughout a run of Borg and output product and the conclusion of the run. A new solution is added to the population if it dominates at least one member of the population. The dominated member of the population is replaced and if more than one member of the population is dominated by the new solution then one of the dominated solutions is removed at random (Hadka and Reed 2013). 3.2.2

Objectives

There are many possible combinations of low impact development controls which might be implemented in an urban or sub-urban area. But, the primary objective of the optimization process is to find combinations of LIDs that will optimally reduce sewershed-wide runoff and peak flow in the stormsewers while reducing the cost. When implementing stormwater controls it is ideal to get the maximum performance (reduction) at the lowest cost. Equations 1, 2, and 3 represent the three objectives for optimization by the Borg algorithm. It should be noted that Borg minimizes all objectives. Objective 1: (1)

where

denotes the cost of LID type j in subcatchment i, the cost being a function of

the LID type j, the size S, and the number of units of that LID in a given subcatchment. The cost of each LID type is based on cost functions aggregated into groups. Objective 2: (2)

Objective 3: (3)

where

is the maximum flow rate through the point of interest in the stormsewer (most

downstream point modelled and location of flow monitor used for calibration) during the duration of the simulation.

denotes the runoff from subcatchment i at time t (where k

is simply the end point of the simulation). Overall, the objective of the optimization process is to find the most effective combinations of LID controls at various cost levels. In other words, the primary goal of the optimization process is to generate cost-benefit curves. 3.2.3

Decision Variables

For this study 24 decision variables were selected. The decision variables selected focus on the types of LIDs selected and also, but to a lesser extent, the sizing and location of the LIDs. The LIDs are interdependent in that whichever combinations of LIDs are present in a given subcatchment influences the percent of the impervious area in each subcatchment that routes runoff to each LID. The decision variables are listed in Table 2. Note that the first decision variable is numbered "0" for consistency with the C programming used where the first member of an array is called with a 0. The placement of LIDs was optimized by dividing LIDs into groups based on runoff zones and soil types. Runoff zones are three groupings that were created based on the runoff coefficient of each subcatchment where LIDs might be placed. Note that this is related to the implementation of decision variables, and not a division between scenarios. This was done based on the results of a test run of the hydrological model without any LID controls. Runoff group 1 consists of all the subcatchments with runoff coefficients of

at least one standard deviation below the mean value, group 2 was all the subcatchments within 1 standard deviation from the mean, and group 3 subcatchments are at least one standard deviation above the mean. Runoff group 1 contains 30 subcatchments with a total of 133 houses, group 2 contains 172 subcatchments with a total of 624 houses, and runoff group 3 contains 40 subcatchments with a total of 99 houses. The total number of subcatchments listed is fewer than the total in the model because the subcatchments are not uniform and not all contained suitable locations for the LID controls being considered. Although there are far more subcatchments and houses in group 2 the number in the other groups should be sufficient to determine if there is, for example, a cost efficiency benefit to investing in high runoff areas. Gaining this information is the purpose of dividing the subcatchments into different groups which can be individually optimized. The LIDs were not optimized by individual subcatchments because of the high number of subcatchments included in the model. Increasing the number of groupings would be one way to increase the focus on the placement of LIDs. The decision variables related to the LID size were constrained within reasonable parameters for the space available and type of LID control. Table 2 Decision variables

Decision Variable 0, 1, 2 3, 4, 5 6, 7, 8 9, 10, 11

12, 13, 14

Explanation

Range

Number of rain barrels per house for subcatchments in runoff zones 1, 2, and 3.

0 to 4

Change by 1

The placement of an infiltration trench in runoff groups 1, 2, and 3, all soil types included. The placement of permeable pavement driveways in runoff groups 1, 2, and 3. The placement of rain gardens (or bioretention units for the new development scenarios) in runoff zones 1, 2, and 3, all soil types included. Surface area (m2) of infiltration trenches in zones 1, 2, and 3 with underlying sand or clay.

0 or 1

1

0 or 1

1

0 or 1

1

20 to 300

10

15, 16, 17 18, 19, 20

21, 22, 23

Surface area (m2) of infiltration trenches in zones 1, 2, and 3 with underlying clay loam. Surface area (m2) of rain gardens in zones 1, 2, and 3 with underlying sand or (for the new development scenarios) the area of bioretention units in zones 1, 2, and 3 with underlying clay loam. Surface area (m2) of rain gardens in zones 1, 2, and 3 with underlying clay or clay loam or (for the new development scenarios) the area of bioretention units in zones 1, 2, and 3 with underlying clay or sand.

20 to 300 4 to 28

10

4 to 28

4

4

3.3 Connecting the Models The goal of the optimization is to find the pareto-optimal front for the objectives of reducing stormsewer peak flow and total runoff in the study area while also minimizing the cost. Such a procedure may be represented as the development of costbenefit curves. The decision variables are various LID design parameters related to their definition in the SWMM input file. The fitness functions, which evaluate the solutions (taking the decision variables and returning objective values) are the model itself as well as cost functions. This whole system is created by linking the SWMM model to the Borg algorithm so that there can be a feedback process where Borg alters some SWMM input parameters and receives outputs from the SWMM model. SWMM essentially serves as a fitness function for the Borg algorithm. Figure 5 demonstrates the essential data flow between SWMM and Borg.

Borg generates new solution

SWMM input file is updated with Borg decision variables

Decision variables are plugged into cost functions

SWMM is executed and total runoff and target maximum peak flow are extracted

Objective values attached to solution

Add solution to population or archive?

Figure 5 Coupled optimization-simulation model framework

3.4 Optimization Simulation Tests For this study there are a total of 15 different scenarios for which the optimization-simulation model was run. These scenarios are composed of five different LID implementation scenarios; each being tested for three different design storms. The three design storms are 5 year, 25 year, and 100 year return period storms. SCS Type 2 24-hour storms were used. The total rainfall volumes for each event were obtained from Environment Canada's intensity duration frequency (IDF) curves for the Windsor Airport weather station. These divisions allow for observations on the usefulness and costeffectiveness of LID stormwater controls at various LID adoption levels as well as

observations on how the performance of LID solutions, of varying adoption rates, perform during storms of various intensities. For each scenario, 12500 functional evaluations were completed. There are five different LID adoption scenarios. They include retrofit low and high LID adoption, and new development low, high and unrestricted adoption. The retrofit scenarios represent the addition of LID stormwater controls to the sewershed as it currently exists. The new development scenarios consider the implementation of LID controls in the development of the sewershed. The new development scenarios do not represent comprehensive LID designs as they still only supplement the existing style of development. A true comprehensive approach to low impact development would include concerns regarding water and ecology throughout the planning process. In addition to the LIDs included in the new development scenarios in this study, a more comprehensive approach to LID might also implement shared green spaces which can also assist in stormwater control, cluster development to leave more space untouched, and take advantage of natural waterways and flow paths. The new development scenarios in this study do have the advantage of some reduced construction costs where construction is more efficient, as well as increased adoption rates. Increased adoption rates are possible because a new development can be built to include permeable pavement or infiltration trenches. A developer could choose to implement LID strategies or the LID strategies could be mandated for new development (e.g. Toronto's green roof policy). People are also more likely to use a rain barrel or rain garden if it can come installed in their home and they do not have to expend any effort to implement them.

Table 3 lists the maximum LID adoption percentages used for the five LID implementation scenarios. The adoption rates are selected in order to be close to what might be achieved in reality while also being able to study the benefit of LIDs at various adoption rates. Adoption rates as low as 1% were not used because this would mean that changes to decision variables would result in very minute feedback from the simulation model. The unrestricted scenario was included in order to study the maximum benefit LIDs could achieve. Table 3 Maximum adoption rates of each LID control by percent of houses or subcatchments

(%) LID Control Rain barrel Rain garden/ bioretention Permeable pavement Infiltration trench

Retrofit

New Development High Unrestricted 25 100 25 100

Low 5 5

High 10 10

Low 10 10

2

5

10

100

100

5

25

25

100

100

4 Results and Discussion The optimization-simulation model was able to produce cost-benefit curves for the implementation of LIDs in the study area as well as generate useful information on optimizing LID design in low infiltration areas. The performance of LIDs was evaluated for all three design storms for each of the five LID implementation scenarios. The graphs shown in Figures 6 through 9 were created to only show the non-dominated solutions in each of the two reduction objectives and cost (i.e., the results were filtered rather than displaying the entire pareto-optimal front in three dimensions). Note that the cost values presented are the estimates for the capital costs associated with the construction of the LID stormwater controls. Design, engineering, maintenance, and land acquisition costs are not considered.

Table 4 provides a summary of the maximum reductions of peak flow and total runoff possible in each scenario. Note that the maximum peak flow reduction and maximum runoff reduction are not always achieved in the same solution/LID configuration. Tables 5 and 6 show some of the most cost effective solutions from each scenario and Tables 8 and 9 show the decision variables (number and sizes of LIDs) corresponding to those solutions. Low impact development is not commonly designed for extreme precipitation events; however, the results demonstrate that LID controls can still offer significant reductions to both peak flow and total runoff. Even so, the LIDs performed poorly on a cost-benefit basis. The retrofit and new-development low LID adoption scenarios were not able to achieve large reductions and the larger reductions seen in the new-development high LID adoption and the unrestricted scenarios came at significant cost. One common thread across all LID adoption scenarios is that the reduction percentages decreased during the 100-year return period event. The following sections present the results of each scenario in greater depth. Table 4 Summary of maximum reduction for peak flow and total runoff in each scenario

Peak Flow Reduction (m3/s)

Retro-Low - 5 year Retro-Low - 25 year Retro-Low - 100 year Retro-High - 5 year Retro-High -25 year Retro-High - 100 year New-Low - 5 year New-Low - 25 year New-Low -100 year

0.04 0.06 0.08 0.17 0.26 0.32 0.19 0.27 0.32

Peak Flow Reduction (%)

1.17% 1.27% 1.23% 4.65% 5.14% 4.64% 5.20% 5.47% 4.64%

Total Runoff Reduction (ha.m)

0.02 0.03 0.03 0.06 0.09 0.10 0.06 0.09 0.08

Total Runoff Reduction (%)

0.67% 0.63% 0.53% 1.75% 1.79% 1.49% 1.77% 1.81% 1.19%

Cost (mean of best runoff solution and best peak flow solution if different) $153,000 $214,000 $263,000 $509,000 $1,004,000 $872,000 $882,000 $1,364,000 $577,000

New-High - 5 year New-High - 25 year New High - 100 year Unrestricted - 5 year Unrestricted - 25 year Unrestricted - 100 year

0.80 0.88 1.28 1.02 1.32 2.02

21.30% 17.57% 18.61% 27.31% 26.43% 29.33%

0.45 0.45 0.49 0.45 0.50 0.58

12.83% 9.32% 7.59% 12.84% 10.53% 9.10%

$12,163,000 $9,942,000 $9,552,000 $7,834,000 $8,752,000 $8,947,000

4.1 Cost Benefit Curves 4.1.1

Retrofit Solutions

In the low adoption scenario the overall reduction capacity is very low for both peak flow reduction and total runoff reduction. As is the case for every scenario, the percentage by which the peak flow can be reduced by LID controls is less than the percentage by which the runoff can be reduced. The runoff reductions are severely limited by the poor hydraulic conditions of the soils whereas the storage provided by the LIDs is still able to alter the flow timings and reduce peak flows. The retrofit scenarios feature both low costs and low reductions to both peak flow and total runoff. The cost-effectiveness (reduction per money spent) is similar to the other scenarios. Even with similar cost-effectiveness to the other scenarios, these results cast doubt on to whether this level of LID retrofitting would be useful for limiting peak flow or runoff for the large precipitation events studied. Between the low and high retrofit scenarios there is an increase in the costeffectiveness of the peak flow reduction that could be attributed to loosening restrictions on infiltration trenches. The number of subcatchments that an infiltration trench may be installed is increased from 5% of feasible subcatchments in the retrofit, low adoption scenario to 25% in the retrofit, high adoption scenario. This increase is greater than the increase for other LID types. Infiltration trenches are the dominant LID type expressed in

the pareto-optimal solutions, especially for peak flow reduction. They achieve this by providing relatively inexpensive storage. Rain gardens were more effective for runoff reduction because their design included amended soil with a slightly improved infiltration rate. Figure 6 shows the solutions for each of the design storms filtered such that only the solutions which are non-dominated in the objectives of peak flow reduction and cost minimization are included.

0.35

Peak Flow Reduction (cms)

0.30

0.25

0.20

Low 100 Year

0.15

Low 25 Year 0.10

Low 5 Year High 100 Year

0.05

High 25 Year High 5 Year

0.00 $0

$2,00,000

$4,00,000

$6,00,000

$8,00,000

$10,00,000

$12,00,000

Total LID Cost Figure 6 Solutions non-dominated in peak flow reduction and cost for the retrofit scenarios

The slope of the series in the graph is not uniform because the jumps in peak flow reduction differ depending on whether the changes are due to changes in the sizing of rain gardens and/or infiltration trenches, changes in the numbers of a given LID, or changes in the combinations of LIDs present in any solution. The diminishing returns in investment occur once the adoption of a better performing LID has been completed and

further increases in peak flow reduction can only be achieved by investing in less efficient LIDs. Therefore, the amount of peak flow reduction that can be achieved, before a significant point of diminishing returns is reached, depends on the constraints on the adoption of the most efficient LID types in each scenario. These insights also serve as examples of the types of the information that can be extracted from the results of a multiobjective optimization. 0.12

Total Runoff Reduction (ha.m)

0.10

0.08

0.06 Low 5 Year Low 25 Year

0.04

Low 100 Year High 5 Year

0.02

High 25 Year High 100 Year 0.00 $0

$2,00,000

$4,00,000

$6,00,000

$8,00,000

$10,00,000

Total LID Cost Figure 7 Solutions non-dominated in total runoff reduction or cost for the retrofit scenarios

4.1.2

New Development Scenarios

The cost-benefit curves for the new development are similar to the retrofit scenario in that the reduction percentage for peak flow is significantly better than the reduction percentage for total runoff. The maximum percent reduction in peak flow for each storm event also comes at a much lower cost than the maximum runoff percent reduction in total runoff for the same events. An important difference from the retrofit

$12,00,000

scenarios to the new development scenario is a change from simple rain gardens to more complex bioretention units. The bioretention units are better for peak flow reduction because they offer more storage space where water can be detained; however, they perform worse for runoff reduction as they infiltrate less water. Another change is there is an increase in the maximum possible adoption level for permeable pavement; however, this is not a significant factor as permeable pavement does not prove to be a costeffective solution. In the new development, high LID adoption scenario, the maximum adoption of some of the LIDs significantly increases. For this scenario, permeable pavement driveways can now be placed at all the houses in the sewershed, and infiltration trenches can be placed in any subcatchment eligible for LIDs. The result is a large spike in the reduction percentages for both peak flow reduction (reduction exceeding 21% is possible) and total runoff reduction (reduction exceeding 12% is possible). This reduction does come at a higher cost but the cost-effectiveness is no less than for previously discussed scenarios. A relationship between the reduction percentages achieved by the LID controls and the intensity of the design storms persists across each scenario. That is, as the intensity of the storms increases, the reduction percentages decrease. This is the case for both peak flow reduction and total runoff reduction, although the drop-off is greater for peak flow. The cost-benefit curves in Figure 8 shows the peak flow reduction for the 5 year storm for each of the three new development scenarios. For peak flow reduction the most efficient solutions are once again dominated by infiltration trenches and the reduction

efficiency starts to drop-off once other LID types have to be relied upon for additional improvement. Some of the high performing solutions also include bioretention units. For the unrestricted LID adoption scenario, a higher peak flow reduction is achieved without a significant reduction in cost-effectiveness. Figure 9 compares the runoff reduction for each of the new development scenarios under the 5 year storm event. The design flexibility possible in the unrestricted scenario produces a significant increase in costeffectiveness.

Peak Flow Reduction (cms)

1.2

1

0.8

0.6

0.4 Low Adoption 0.2

High Adoption Unrestricted

0 $0

$5,00,000

$10,00,000

$15,00,000

$20,00,000

Total LID Cost Figure 8 Solutions non-dominated in peak flow reduction or cost for the new development scenarios

$25,00,000

0.5

Total Runoff Reduction (ha.m)

0.45 0.4 0.35 0.3 0.25 0.2 0.15 Low Adoption

0.1

High Adoption

0.05

Unrestricted 0 $0

$10,00,000$20,00,000$30,00,000$40,00,000$50,00,000$60,00,000$70,00,000$80,00,000$90,00,000 $1,00,00,000

Total LID Cost Figure 9 Solutions non-dominated in total runoff reduction or cost for the new development scenario

The cost effectiveness achieved in all the scenarios is quite similar for most of the low-cost solutions; however, the amount of reduction (both of peak flow and total runoff) that can be achieved in the new development, high LID adoption and new development, unrestricted LID adoption scenarios is much greater. Infiltration trenches and bioretention units provide most of that reduction for peak flow, and also contribute significantly to runoff reduction. When planning a new development both of these LID practices could possibly be incorporated into shared spaces such that they did not require each member of the community to individually adopt them. To further demonstrate the results provided by the model and to help understand the design capabilities the peak flow reduction data series for the 5 and 100 year storms are further analyzed, with labels applied in Figure 10. Figure 10 includes solutions which are dominated in the objectives of peak flow reduction and cost minimization so that

observations can be made about what causes drop-offs in peak flow reduction. Some of the poor performing solutions in the low cost section of the figure are those that include bioretention units with very small areas. Bioretention units, with small surface areas, and which are receiving a large portion of the runoff from impervious surfaces may be overloaded leading to higher flow rates through the underdrains. Other drops are attributable to when the number or area of infiltration trenches, and to a lesser extent bioretention units, are reduced while permeable pavement is added. These changes might result in an increase in runoff because permeable pavement can be effective at reducing runoff; however, the changes also lessen peak flow reduction.

2.5

PP added, IT & BR reduced and then restored

Increasing IT & BR

2

Peak Flow Reduction (cms)

- IT Area BR included Some RB

1.5

IT, BR, PP

Low area BR included

1

0.5

All LIDs

+ PP - IT & BR Area

Drops caused by adding PP, removing IT & BR. Then IT & BR is restored

- IT Area + Small BR

0

5 Year Storm 100 Year Storm

-0.5

$0

$20,00,000

$40,00,000

$60,00,000

$80,00,000

$1,00,00,000

$1,20,00,000

Total LID Cost Figure 10 Explanation of raw results for peak flow reduction in the new development-unrestricted scenario

$1,40,00,000

4.2 Secondary Data It is apparent that the multiobjective optimization component of the optimizationsimulation model generates significantly more information than what would be obtained by simply searching for the maximum achievable reductions under constraints or testing specific solutions. The production of the cost benefit curves provides insight into LID combinations that can provide relatively high levels of performance for relatively lower cost (before higher levels of diminishing returns are observed). These more cost-effective solutions are presented in Tables 5 and 6. Patterns in the decision variables, some of which have already been discussed, can provide insights into effective LID design in the study area. The decision variables corresponding to the cost effective solutions are presented in Tables 8 and 9. Table 7 provides acronyms to help with understanding Tables 8 and 9. 4.2.1

Cost Effective Solutions

The solutions presented in Tables 5 and 6 represent a selection of solutions that offer relatively high performance before reaching a point of diminishing returns. The solutions presented here are able to achieve a high percentage of the maximum reductions shown in Table 4 at a fraction of the cost. Being able to identify where investment in LIDs will begin to offer diminishing returns is valuable information to any large scale LID implementation plan. Table 5 Summary of most cost-effective solutions for peak flow reduction

Peak Flow Reduction (m3/s) Retro-Low - 5 year Retro-Low - 25 year

0.03 0.05

Peak Flow Reduction (%) 0.90% 1.05%

Total Runoff Reduction (ha.m) 0.01 0.01

Total Runoff Reduction (%)

Cost (mean of best runoff solution and best peak flow solution if different) 0.23% $ 77,000 0.24% $108,000

Retro-Low - 100 year Retro-High - 5 year Retro-High -25 year Retro-High - 100 year New-Low - 5 year New-Low - 25 year New-Low -100 year New-High - 5 year New-High - 25 year New High - 100 year Unrestricted - 5 year Unrestricted - 25 year Unrestricted - 100 year

0.07 0.16 0.21 0.26 0.17 0.19 0.30 0.66 0.72 1.21 0.81 0.99 1.24

1.00% 4.17% 4.24% 3.75% 4.68% 3.87% 4.34% 17.63% 14.51% 17.57% 21.74% 19.81% 18.07%

0.01 0.03 0.05 0.06 0.04 0.04 0.07 0.14 0.17 0.25 0.18 0.23 0.31

0.23% 0.98% 1.08% 0.92% 1.13% 0.93% 1.09% 4.01% 3.55% 3.93% 5.08% 4.83% 4.84%

$144,000 $375,000 $506,000 $582,000 $309,000 $289,000 $468,000 $1,790,000 $1,768,000 $3,577,000 $2,003,000 $2,405,000 $2,658,000

Table 6 Summary of most cost-effective solutions for total runoff reduction

Peak Flow Reduction (m3/s) Retro-Low - 5 year Retro-Low - 25 year Retro-Low - 100 year Retro-High - 5 year Retro-High -25 year Retro-High - 100 year New-Low - 5 year New-Low - 25 year New-Low -100 year New-High - 5 year New-High - 25 year New High - 100 year Unrestricted - 5 year Unrestricted - 25 year Unrestricted - 100 year 4.2.2

0.03 0.06 0.08 0.04 0.11 0.07 0.08 0.19 0.30 0.62 0.52 0.88 0.55 1.07 1.03

Peak Flow Reduction (%)

Total Runoff Reduction (ha.m)

0.93% 1.19% 1.23% 1.02% 2.20% 0.95% 2.17% 3.76% 4.34% 16.56% 10.45% 12.78% 14.82% 21.35% 14.96%

0.02 0.03 0.03 0.03 0.06 0.08 0.03 0.06 0.07 0.18 0.20 0.22 0.22 0.30 0.34

Total Runoff Reduction (%) 0.67% 0.63% 0.53% 0.95% 1.26% 1.18% 0.96% 1.29% 1.09% 5.01% 4.24% 3.50% 6.26% 6.28% 5.23%

Cost (mean of best runoff solution and best peak flow solution if different) $168,000 $212,000 $263,000 $195,000 $438,000 $474,000 $183,000 $540,000 $468,000 $2,380,000 $2,274,000 $1,905,000 $2,888,000 $4,007,000 $2,902,000

Lower Intensity Storms and Hydrographs

The most cost effective solutions for peak flow reduction were tested on the calibration series of events. The calibration time series contains shorter return period

events than the design storms used for the optimization. On a percentage-reduction basis the LIDs performed better for the shorter return period events than for the design storms. By running specific solutions in SWMM further analysis can be conducted for those solutions. Figure 11 shows the hydrographs for cost effective solutions for each LID scenario. The overall volume of flow being conveyed by the storm sewer decreases for each event showing that the LID controls are able to infiltrate a higher proportion of runoff from smaller events. 0

3

10 2.5

20

Flow Rate (CMS)

No LID 2

Retro-Low Retro-High

1.5

30 40

New-Low New-High

1

NewUnrestricted

50 60

0.5

70 0 80 7-15-13 2:377-16-13 2:377-17-13 2:377-18-13 2:377-19-13 2:377-20-13 2:377-21-13 2:377-22-13 2:377-23-13 2:377-24-13 2:37

Figure 11 Hydrographs of typical peak flow reduction, cost-effective solutions tested during the July 15th series of events

4.2.3

Decision Variable Selection

Further detail on the LID controls selected for the most cost effective solutions is presented in this section. Closer examination of the decision variable can provide insight into LID sizing and placement. A straightforward example of a common thread between the scenarios is that the LID units are often added to the highest runoff zone (zone 3) first

15 Minute Rain Intensity (mm/h)

Rainfall

and then the middle runoff zone second. This could indicate that it is more cost-effective to invest in installing LID controls in high runoff areas. An additional unsurprisingly result is that the optimal LID area increased for higher return period events. An additional observation is that the areas for the infiltration trenches, despite their effectiveness, are generally far below their maximum allowable areas. Table 7 Acronyms used in Tables 8 and 9

Acronym RB IT RG BR PP S C L 1 2 3

Description Rain barrel Infiltration trench Rain garden Bioretention unit Permeable pavement Berrien sand Brookston clay Brookston clay loam Runoff zone 1 (low runoff coefficient) Runoff zone 2 (middle runoff coefficient) Runoff zone 3 (high runoff coefficient)

Table 8 Sizing decision Variables for cost-effective solutions from the retrofit scenarios

Scenario Retrofit low Peak Flow Retrofit high

Total Runoff

Retrofit low Retrofit high

Storm Event 5 25 100

IT SC 1 9 15 3

IT SC 2 5 7 9

IT SC 3 2 3 5

IT L 1 17 21 2

IT L 2 5 7 11

IT L 3 5 7 8

RG S 1 2 6 4

RG S 2 5 3 5

RG S 3 2 1 5

RG CL 1 2 1 7

RG CL 2 1 6 6

RG CL 3 2 1 4

5 25

15 6

5 6

4 5

2 5

5 6

4 5

1 1

4 2

1 4

3 1

3 3

2 1

100 5

9 2

8 6

7 5

4 12

8 3

6 23

1 3

6 5

1 5

1 1

1 7

1 4

25 100

9 17

7 10

2 5

20 3

6 9

5 14

6 4

5 7

3 1

1 7

7 7

5 6

5 25 100

2 6 8

3 5 4

2 3 4

3 6 3

20 2 2

2 5 5

1 1 3

5 1 7

1 1 1

3 1 3

5 5 6

2 1 3

*The values represented in the table are the decision variable values. For infiltration trenches they represent the area in m2 divided by 10 and for the rain gardens they represent the area in m2 divided by 4. **The shaded cells are those for which the LID corresponding to that area is turned on for the solution in question.

Table 9 Sizing decision variable values for the cost-effective solutions from the new development scenarios

Scenario Low

Peak Flow

High

Unrestricted

Low

Total Runoff

High

Unrestricted

Storm 5 25 100 5 25 100 5 25 100 5 25 100 5 25 100 5 25 100

IT SC 1 5 18 12 5 6 24 9 9 10 3 10 12 4 5 10 23 7 17

IT SC 2 6 6 8 8 7 9 5 7 6 3 5 8 4 4 11 3 9 7

IT SC 3 3 4 7 6 5 6 4 10 9 2 8 7 21 2 2 5 2 12

IT L 1 6 28 9 15 10 12 5 2 2 2 8 9 7 9 2 29 7 3

IT L 2 5 6 9 5 8 11 6 8 9 3 5 9 5 5 8 4 8 9

ITL 3 6 5 6 7 15 26 9 4 11 3 3 6 3 5 5 14 7 13

BR L 1 1 4 1 1 1 1 1 6 1 1 1 1 1 1 3 7 5 1

BR L 2 1 1 1 4 4 7 4 6 6 1 3 1 3 5 1 2 7 3

BR L 3 4 1 2 1 3 6 4 6 1 5 1 2 1 2 6 4 4 4

BR SC 1 1 1 5 1 3 1 3 1 3 1 1 5 4 1 1 1 1 2

BR SC 2 4 1 6 1 4 7 1 1 1 3 1 6 1 6 4 1 1 1

BR SC 3 1 3 1 1 1 4 1 1 6 1 1 1 1 5 1 1 1 2

*The values represented in the table are the decision variable values. For infiltration trenches they represent the area in m2 divided by 10 and for the rain gardens they represent the area in m2 divided by 4. **The shaded cells are those for which the LID corresponding to that area is turned on for the solution in question as for ease of viewing the decision variables related to whether or not each LID type in turned on in a given region are not shown in the table.

5 Limitations There are limitations to the simulations, which could impact the predicted performance of the LID stormwater controls. Firstly, LIDs are commonly designed to provide treatment or detention for less intense storms. Additionally, the LID designs in this study are widely generalized resulting in inefficiencies in their design. Since the subcatchment sizes and properties are not uniform, the generalization of LID designs means that a certain type of LID might be designed to be too small for some subcatchments resulting in reduced performance but also over-designed for other subcatchments resulting in increased cost. The limitations of LID routing in SWMM, which prevent routing from one LID to another, might limit the performance of the LID controls. Additionally, none of the scenarios include a full range of possible LID measures, or any combinations with any other stormwater best management practices. There are also limitations of the study which could result in an over prediction of LID performance. The flow from groundwater into the LIDs, such as could be the case if the water table were high, was not simulated. However, if high-water tables were a factor, it would be possible to add impervious liners to the LID units to preserve the peak flow reduction benefits. Finally, long term maintenance requirements and related declines in the performance of the LID controls were not included in this study.

6 Conclusions With increasing urbanization contributing to excessive stormwater runoff there is a need for new techniques, such as low impact development, to be incorporated into stormwater management systems. This study was dedicated to the development of an

optimization-simulation model which could be used to generate a wealth of information on the identification and placement of low impact development stormwater controls. This was achieved by coupling the stormwater management model (SWMM) with Borg multiobjective evolutionary algorithm (MOEA). SWMM is able to evaluate solutions passed to it by Borg and return the outputs of simulations to Borg so that Borg can determine the effectiveness of those solutions. Solutions consist of the decision variables in the optimization process which can be set to any parameter found in the SWMM input file. This study evaluated the effectiveness of low impact development measures; therefore, the decision variables were set to control the implementation of LID controls in the model. Parsing functions were developed to change all the parameters in the SWMM input file necessary to accurately reflect changes being made to LID controls. The model was tested for a sewershed, with poor infiltration characteristics, in Windsor, Ontario, Canada. The optimization-simulation model was successfully able to generate useful data on the implementation of LIDs in the sewershed. This data includes cost benefit curves, as well as insights on optimal LID combinations, sizing, and placement. This is information that stormwater professionals can use to make informed decisions regarding the planning and implementation of LIDs. For this study we were able to determine that infiltration trenches would be the most cost effective LID (of those studied), particularly for reducing peak flow. Additionally, it is the most cost effective to focus on implementing LIDs in high runoff areas first. For the sewershed in question, LIDs were able to make significant reductions in both storm sewer peak flow (up to 29%) and total runoff (up to 13%) despite the poor

infiltration characteristics of the sewershed. The reductions in peak flow were achieved by building detention storage into the catchments with LIDs. With that being said, even the more cost effective solutions may not be competitive with other stormwater best management practices or grey infrastructure for the stated objectives under the conditions modelled for the study area. However, if other benefits of LIDs such as water quality treatment were considered the benefits might outweigh the cost. Furthermore, the results show that if LIDs are implemented specifically for the purpose of water quality treatment, it is important for the designer to also consider the benefit they might add in terms of reducing peak flow or total runoff.

7 Acknowledgements The present research is funded by the Natural Sciences and Engineering Research Council (NSERC) of Canada through the Discovery grant to the senior author. The first two others were supported through OGSST scholarship and University of Windsor scholarship. We would like to thank the City of Windsor for providing the data on precipitation and stormwater flows.

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Developed simulation-optimization model to select Low Impact development controls Coupled SWMM and BorgMOEA models to optimize the LID placement in a sewershed Investigated varied levels of LID implementation and their impact on runoff reduction Determined pareto optimal solutions of LID controls to reduce peak flows and runoff volumes