Optimal Spatial Design of Capacity and Quantity of Rainwater Harvesting Systems for Urban Flood Mitigation

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1 Wate 2015, 7, ; doi: /w Aticle OPEN ACCESS wate ISSN Optimal Spatial Design of Capacity and Quantity of Rainwate Havesting Systems fo Uban Flood Mitigation Chien-Lin Huang 1, Nien-Sheng Hsu 1, *, Chih-Chiang Wei 2 and Wei-Jiun Luo 1 1 Depatment of Civil Engineeing, National Taiwan Univesity, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan; s: d @ntu.edu.tw (C.-L.H.); madmichae@hotmail.com (W.-J.L.) 2 Depatment of Maine Envionmental Infomatics, National Taiwan Ocean Univesity, No. 2, Beining Road, Jhongjheng Distict, Keelung City 20224, Taiwan; d @ntu.edu.tw * Autho to whom coespondence should be addessed; nsshue@ntu.edu.tw; Tel.: ; Fax: Academic Edito: Atau Rahman Received: 8 July 2015 / Accepted: 15 Septembe 2015 / Published: 23 Septembe 2015 Abstact: This study adopts ainwate havesting systems (RWHS) into a stomwate unoff management model (SWMM) fo the spatial design of capacities and quantities of ain bael fo uban flood mitigation. A simulation-optimization model is poposed fo effectively identifying the optimal design. Fist of all, we paticulaly classified the chaacteistic zonal subegions fo spatial design by using fuzzy C-means clusteing with the investigated data of uban oof, land use and dainage system. In the simulation method, a seies of egula spatial aangements specification ae designed by using statistical quatiles analysis fo ooftop aea and ainfall fequency analysis; accodingly, the coesponding educed flooding cicumstances can be simulated by SWMM. Moeove, the most effective solution fo the simulation method is identified fom the calculated net benefit, which is equivalent to the subtaction of the facility cost fom the deceased inundation loss. It seves as the initially identified solution fo the optimization model. In the optimization method, backpopagation neual netwok (BPNN) ae fist applied fo developing a wate level simulation model of uban dainage systems to substitute fo SWMM to confom to newly consideed intedisciplinay multi-objective optimization model, and a tabu seach-based algoithm is used with the embedded BPNN-based SWMM to optimize the planning solution. The developed method is applied to the Zhong-He Distict, Taiwan. Results demonstate that the application of tabu seach and the BPNN-based simulation model into

2 Wate 2015, the optimization model can effectively, accuately and fast seach optimal design consideing economic net benefit. Futhemoe, the optimized spatial ain bael design could educe 72% of inundation losses accoding to the simulated flood events. Keywods: ainwate havesting system; stomwate unoff management model; backpopagation neual netwok; tabu seach; spatial design of capacity and quantity; optimization; uban flood mitigation 1. Intoduction In ecent yeas, on account of global climate change and the inceasing occuence of exteme hydological events, coupled with the fact that Taiwan is densely populated and ovedeveloped in catchment aeas, the amount of flooding caused by heavy ain often exceeds the scale of the oiginally designed standad. Additionally, the dainage system in Taiwan is insufficient, which causes the wate level to ise extemely quickly duing typhoons and heavy ainfall. The pumping station of the uban dainage system cannot handle such lage amount of flood in ecent yeas, this leads to flooding and the subsequent loss of life and popety. In esponse to this challenging situation, new modes, measues and solutions should be developed to achieve the goal and evaluate the feasibility fo flood mitigation. Low-impact development (LID) povides techniques fo innovative uban envionmental planning, management, and envionmental potection. The fequently used techniques include ain baels, geen oofs, pemeable paving, oadside ecological spaces, ainwate havesting systems (RWHS), and othes. The LID facilities have elatively lowe costs in educing peak and total unoff compaed to taditional flood contol measues fo building undegound pipeline culvets. Moeove, LID facilities can povide additional benefits, such as wate consevation, uban beautification, and impovement of the ecological envionment. Among these facilities, RWHS can be implemented on in-place wate havesting, which diffes fom the taditional dainage concept of the end-tace centalization pocess. RWHS ae containes that collect oof unoff duing stom events and can eithe elease o e-use the ainwate duing dy peiods. RWHS collect unoff fom ooftops and convey it to a cisten tank. Futhemoe, RWHS ae easy to obtain, cause less pollution and costs at a lowe isk, and involve no wate ight disputes. In shot, these systems can seve as flood detention means and altenative wate souces that ae wothy of boad use. Pevious studies egading RWHS can be divided into two categoies. The fist one is the capacity design of RWHS unde the consideation of domestic wate supply those pimaily employ a simulation method fo planning. The elated studies ae descibed as follows: Liaw and Tsai (2004) [1] developed a simulation model including poduction to estimate the most cost effective combination of the oof aea and the stoage capacity that best supplies a specific volume of wate. Liaw and Chiang (2014) [2] developed a egional-level and dimensionless analysis fo designing a domestic RWHS. Moeove, egading design using economic and dimensionless analysis-based optimization appoach, Chiu et al. (2009) [3] optimized the most cost-effective ainwate tank volumes fo diffeent dwelling types using maginal analysis. Campisano and Modica (2012) [4] developed a dimensionless methodology fo the optimal design of domestic RWHS. Fom these studies, we can find out that

3 Wate 2015, pevious studies have scacely designed the capacity of RWHS consideing flood eduction benefits using an intedisciplinay integated systematic analysis appoach. In addition, the capacity design of RWHS is pimaily limited to small communities and lacks full consideation of all metopolitan catchment with vaiations in spatial capacity and quantity design of RWHS. The second categoy egading RWHS is simulation and evaluation of the effectiveness and eliability of domestic RWHS with a vaiety of pattens on the wate supply objects. The eseach subjects include: (1) evaluating the potential fo potable wate savings by using ainwate in esidential sectos [5,6]; (2) estimating nonpotable household potential, sustainability and pefomance of stoage type of RWHS [7 9] and investigating the potential benefits fom shaing RWHS with neaby neighbos with a stoage-eliability-yield analysis (Seo et al., 2015 [10]) using ainfall data; and (3) establishing the pobabilistic elationships between stoage capacities and deficit ates of RWHS [11] and that of between the efficiency of ual domestic ainwate management and tank size, tank opeation and maintenance, espectively [12]. Howeve, these studies seldom conside the suface and sewe physical flowing phenomenon afte ainwate patially intecepted by RWHS and patially flowing to gound and uban dainage system. To addess these poblems, thee ae numeous studies evaluating and assessing the pefomance and eliability of RWHS using numeical o hydological model. The elated studies ae, fo example, Jones and Hunt (2010) [13] evaluated the pefomance of RWHS by a monitoing study with a compute model (Rainwate Haveste 3.0), Basinge et al. (2010) [14] assessed the eliability of RWHS using a novel model based on a nonpaametic ainfall geneation pocedue utilizing a bootstapped Makov chain, and Palla et al. (2011) [15] poposed nondimensional paametes with a suitable behavioal model accoding to a daily mass balance equation to investigate optimum pefomance of RWHS. Howeve, these studies almost only estimated the efficiency of RWHS fo nonpotable household wate saving that did not assess the feasibility fo flood mitigation. In addition, the pefomance of RWHS fo stomwate etention has been studied, such as [16 18]. Howeve, these studies seldom simulated, evaluated and account fo the inundated loss of each actual flood event in tems of the space design pattens of RWHS. The pupose of this study is to develop a set of novel simulation-optimization models to identify the most effective spatial design fo a quantity and capacity aangement of RWHS in uban dainage aeas consideing fast and effective optimization of flooding loss eduction and facility cost minimization. The effective chaacteistic zonal subegions fo spatial design ae paticulaly classified by using fuzzy C-means (FCM) clusteing with the investigated data of uban oof, land use and ainfall chaacteistic among dainage aea, and a seies of epesentative egula spatial aangements specification ae designed by using statistical quatiles analysis fo ooftop aea and ainfall fequency analysis. A backpopagation neual netwok-based [19,20] wate level simulation model is embedded in the optimization model, and used to substitute fo the hydologic/hydaulic-based stom wate management model [21,22] to confom to newly consideed intedisciplinay multiobjective optimization model, and combine it with tabu seach (Glove, 1986; Glove and Laguna, 1997 [23,24]) to achieve the optimization pocess.

4 Wate 2015, Development of Methodology 2.1. Pocedues The methodology of this study is divided into two pats: a simulation method and a hybid simulation-optimization method. Infomation obtained fom the simulation method is enteed into the optimization model to poduce the optimal solution. The flowchat of the methodology can be shown in Figue 1, and the steps ae descibed as follows. Figue 1. Flowchat of the methodology. Step 1-1: Investigate the data of uban oof, land use and dainage system. Then design the egula spatial quantity and capacity aangement of diffeent types of RWHS in SWMM by using statistical quatiles analysis fo ooftop aea and ainfall fequency analysis, and classify zonal subegions fo design of RWHS by using FCM cluste algoithm. Step 1-2: Input the actual stom events to the constucted SWMM model to simulate the flooding and wate level of the contol points fo diffeent spatial RWHS designs and ain types.

5 Wate 2015, Step 1-3: Convet the flooding amount into inundation loss and subtact the equipment cost to simulate the net benefit with vaious types of designs, and then obtain the best RWHS design of simulation method. Step 2-1: Devise a suitable solution obtained fom the simulation method as initial seaching solution of the optimization method. Establish a wate level simulation model fo the uban dainage system that can substitute fo U.S. EPA SWMM using time sequence data obtained fom the simulation method with the BPNN. Then, the BPNN-based wate level simulation model is embed into the defined optimization model which is composed of an objective function and constaints. Step 2-2: Employ a tabu seach algoithm to obtain the optimal solution of the optimization method, and then obtain the excellent spatial design of RWHS consideing the uban flood eduction benefits Development of Simulation Model fo Spatial Aangement of Quantity and Capacity This study outlines vaious specifications fo the ain bael spatial distibution and quantity design appoach and applies SWMM to simulate the bust pipes and flooding situation fo each case in numeous ainstom events. The egula spatial quantity and capacity aangement of diffeent types of RWHS ae designed by using statistical quatiles analysis fo ooftop aea and ainfall fequency analysis, and the zonal subegions fo design of RWHS ae classified by using FCM cluste algoithm. Moeove, it estimates the economic net benefit. The design pattens fo vaious cases involve (1) ain baels distibuted thoughout the entie egion; (2) concentation on the downsteam of the flooding egion; and (3) concentation on the upsteam of the flooding egion. The detailed developed methodology is descibed in the following Classified Methodology of Zonal Subegions fo Design of Rainwate Havesting System In an uban dainage aea, the spatial distibution of building ooftop aea and teain is highly divegent and complex. The available ooftop mateial fo installing RWHS is the suface which diectly eceives the ainfall and povides wate to the system. It can be a paved aea like a teace o coutyad of a building, o an unpaved aea like a lawn o open gound. A oof made of einfoced cement concete (RCC), galvanized ion o cougated sheets can also be used fo wate havesting. Besides, the efficiencies of actual wate stoage in an identical ainfall cluste can appoximately eflect a specific ange with fewe vaiations because of the similaity of ainfall intensity and duation [25], so the aveage pecipitation is also devised as designed basis. In ode to educe unnecessay seaching solution space and be convenient fo effective uban planning, this study applies FCM cluste algoithm to classify the study aea to chaacteistic zonal subegions. The building egion with simila geophysical chaacteistic of ooftop aea, teain height and ainfall will be clusteed into same subegions. The FCM algoithm [26] is one of the most widely used fuzzy clusteing algoithms. The FCM algoithm attempts to patition a finite collection of n elements X = { x1, x2,..., xn} ( x i is set as a vecto of ooftop aea, teain height and aveage pecipitation in this study) into a collection of fuzzy clustes with espect to some given citeion. Given a finite set of data, the algoithm etuns a list of c cluste centes C = { c1, c2,..., cc} and a patition weighting matix W = wij [0,1], i = 1,2,..., n, j = 1,2,..., c, whee each element w i, j tells the degee to which element x i belongs to cluste objective function ( J ) which is expessed as follows: c j. The FCM aims to minimize an

6 Wate 2015, whee patition weighting matix ( following Equations: n c m 2 ij xi cj 1 (1) i= 1 j= 1 Min J = w m R m w ij ) and cluste centes ( c j ) can be calculated using the w ij = x 1 c c i j k = 1 xi ck 2 m 1 (2) c j = n i= 1 n i= 1 w m ij w x m ij i 0 w 1 c j= 1 w ij ij = 1 (3) Design Methodology of Capacity and Quantity of Regula Rainwate Havesting Systems In an uban dainage aea, the design pinciple of RWHS fo flood mitigation is to stoe stom ainwate as much as possible to maximize economic uban flood eduction benefits while the designed specification must be subject to the limitation of available building ooftop aea. The designed paametes fo RWHS include capacity (volume) and quantity (aanged density). This study invents an appoach to geneate a seies of epesentative egula spatial capacity and quantity aangements of RWHS. The volume of ain bael ( S ) is specialized as available design aea ( A l ) multiplying to ainfall intensity of taget desied stoed pecipitation of the specific etun peiods ( P RP T ) (Equation (4)), in ode to mitigate the heavy ains induced flood. The vaiable P RP T can be evaluated by ainfall fequency analysis using the pobability distibution of nomal, log nomal, exteme-value type I, Peason type III o log-peason type III (adopted by this study; Lee and Ho, 2008 [27]). In addition, the aanged density is set as how many aeas aange one ain bael in SWMM. Hence, it is a key facto to detemine the epesentational aanged aea which can be subject to the lowest and highest limitation in pactical uban buildings. This study applies statistical quatiles analysis with investigated spatial ooftop aea to detemine the epesentational aanged aea (Equation (5)). S [1,2,..., ] = RP l L Al PT T [1,2,..., D] min min med q% q% Al = [ Mina ( ), WAa ( ), WAa ( ), Mina ( ), WAa ( )] (5) min med q% whee a, a, and a ae minimum, medium and q pecentage of quatiles ooftop aea on subegion, espectively; and WA means weighted aveage. (4)

7 Wate 2015, Assessment Index of Designed Goodness This study identifies the annual net benefit afte establishing the RWHS as an indicato to evaluate the flooding eduction effect of diffeent design appoaches. The annual net benefit is the aveage annual flooding loss eduction minus the annual cost. This eduction is deived fom the flooding loss without employing the RWHS design appoach minus the flooding loss with employing it. The annual cost is the aveage annual setup cost of the RWHS Computation of Inundation Loss In pactice, the flooding loss is diectly popotional to inundated depth which is diectly popotional to total volume of bust pipes. SWMM can calculate the bust pipe amount (i.e., volume) in the manhole at each point in time though the simulation. Moeove, the spatial-tempoal flooding scope and depth can also be calculated by the tempoal-spatial bust pipe volume with the volume-depth-width elationship in the inundation egion. The calculation of flooding loss can be divided into esidential and commecial disticts. Accodingly, we can calculate the flooding loss using the chaacteistic cuve equation constucted by investigated data that the evaluated facto is total volume of bust pipes (use 2 tem polynomial function as example): non RWHS total-non total-rwhs total-non total-rwhs 2 [ Lp, Lp ] = b0 + b1[ Fp, Fp ] + b2[ Fp, Fp ] (6) T T total-non total-rwhs non RWHS [ Fp, Fp ] = Fp ( t), Fp ( t) t= 1 t= 1 total-non whee F p and no RWHS design and with RWHS design, espectively; and F non () t and (7) total-rwhs F p is the total volume of bust pipes in the flooded aeas at contol point p with p F prwhs () t is the volume of bust pipes at moment t and contol point p with no RWHS design and with RWHS design, espectively Intoduction of SWMM The United States Envionmental Potection Agency (US EPA) SWMM model is a dynamic ainfall unoff simulation model used fo single-event to long-tem (continuous) simulation of the suface/subsuface hydology quantity and quality fom pimaily uban/sububan aeas [21,22]. The hydology component of SWMM opeates on a collection of subcatchment aeas with and without depession stoage to pedict unoff fom pecipitation, evapoation and infiltation losses fom each of the subcatchment. In addition, the LID aeas on the subcatchment can be modeled to educe the impevious and pevious unoff. SWMM tacks the flow ate, flow depth, and wate quality in each pipe and channel duing a simulation peiod composed of multiple fixed o vaiable time steps. In the simulations, the unoff component of SWMM (RUNOFF) opeates on a collection of subcatchment aeas that eceive pecipitation and geneate unoff. The outing potion of SWMM tanspots this unoff though a system of pipes, channels, stoage/teatment devices, pumps, and egulatos.

8 Wate 2015, Model Paametes and Routing The adopted model paametes fo simulation in subcatchments ae suface oughness, depession stoage, slope, flow path length; fo Infiltation, is Hoton-based max/min ates and decay constant; and fo Conduits, is Manning s oughness. A study aea can be divided into any numbe of individual subcatchments, each of which dains to a single point. The subcatchment width paamete is nomally estimated by fist estimating a epesentative length of oveland flow, then dividing the subcatchment aea by this length. Ideally this should be the length of sheet flow (<100 m), which is typically significantly slowe than channelized flow. The outing options of SWMM include steady flow outing, kinematic wave outing and dynamic wave outing. Dynamic wave outing solves the complete one-dimensional Saint-Venant flow equations and theefoe poduces the most theoetically accuate esults. These equations consist of the continuity and momentum equations fo conduits and a volume continuity equation at nodes. With this fom of outing it is possible to epesent pessuized flow when a closed conduit becomes full, such that flows can exceed the full nomal flow value. The excess flow is eithe lost fom the system o can pond atop the node and e-ente the dainage system. Dynamic wave outing can account fo channel stoage, backwate, entance/exit losses, flow evesal, and pessuized flow, because it couples togethe the solution fo both wate levels at nodes and flow in conduits. Due to the capability and demand of this study, dynamic wave outing is applied fo outing The Rainwate Havesting Function within Low-impact Development Components The LID function is integated within the subcatchment component of SWMM and allows futhe efinement of the oveflows, infiltation flow and evapoation in ain bael, swales, pemeable paving, geen oof, ain gaden, bioetention and infiltation tench. LID takes many foms but can geneally be thought of as an effot to minimize o pevent concentated flows of stom wate leaving a site [28]. The RWHS is one of the LID techniques in SWMM, and the RWHS is assumed to consist of a given numbe of fixed-sized cistens pe 1000 ft 2 (o 90 m 2 ) of ooftop aea captued Development of Optimization Model In the developed optimization model of this study fo the optimal spatial aangement and capacity design of RWHS, the objective function is devised as the optimized annual net benefit. The constaints include the uppe and lowe limits of the ain bael capacity and quantity, estimate equation of the ain bael annual cost, equation conveting the bust pipe volume into flooding loss, and BPNN dainage system simulation equation, among othes. This study geneates data fom the fully constucted SWMM combined with the simulation method. Futhemoe, we utilize the BPNN model to substitute fo US EPA SWMM to confom to newly consideed intedisciplinay multi-objective optimization model and embed it into the optimization model. The pupose is to quickly and effectively poduce optimal solutions with no limit of multi-embedded intedisciplinay simulation model. The fomulaic desciptions of the optimization model ae descibed below.

9 Wate 2015, Objective Function The objective function of RWHS optimization model is annual net benefit that is equal to the flooding loss deduction minus the facility cost of RWHS. The geate the value, the bette it is; nevetheless, because the objective function aims to obtain the minimum value, we use the objective function to maximize the annual net benefit and obtain the minimum negative net benefit: P R non Min Z = Lp Lp N S R Tc S N p= 1 = 1 RWHS (, ) [1,2,..., ] ( ) (8) whee T c is the cost of the RWHS, N is the numbe of ain baels in subegion, L non epesents the flooding loss with no ain baels established, and Lp is the flooding loss at contol point p. In addition, S denotes the capacity of the ain bael in subegion, R is the quantity of the total subegion, and P epesents the quantity at the flooding contol point, wheein decision-making vaiables ae the quantity of ain baels in each N and S Constaints (1) Quantity Constaints of Rain Baels To ensue that the quantity of ain baels does not exceed the possible maximum quantity of each design subcatchment in each household that the quantity aangement must meanwhile be subject to physical constaints, it is necessay to define the uppe and lowe limits of the quantity of ain baels. The constaints can be expessed as: max 0 N N (9) whee max N is the maximum quantity of ain baels in subegion. (2) Capacity Constaints of Rain Baels To ensue that the capacity of ain baels aligns with the physical size limitations without exceeding the uppe and lowe limits of the ain bael design, we set the constaints as: max 0 S S (10) max whee S epesents the maximum capacity of ain baels in subegion that can be estimated by investigated available ooftop design aea multiplying to ainfall intensity of taget desied stoed pecipitation of the set maximum possible etun peiods (Section 2.2.2). (3) Annual cost function of ainwate havesting systems In this study, the RWHS cost calculation employs the cost equation poposed by Liaw and Tsai (2004) [1], which was obtained though maket eseach and analysis. This annual cost equation can be descibed as: 2 Tc( Ca, A) = a+ bca + ca (11)

10 Wate 2015, whee Tc( Ca, A ) is the cost of RWHS, and function of the capacity C a (m 3 ) and the oof aea A (m 2 ). (4) Equation fo Tansfeing Flooding to Inundation Loss In this study, flooding loss is conveted fom the total volume of bust pipes with a elationship chaacteistic cuve equation (Equations (6) and (7)). (5) Routing Equation of Dainage System The wate level calculation of the dainage system uses BPNN to constuct an altenative simulation model. The outing equation at each contol point can be descibed as: i ( j ) H p() t = f net () t (12) whee H p () t is the wate level of the dainage system at contol point p at time t; and f is the activation i function. The accumulated weight value of the n 1-th laye output value net () t is calculated by: whee In addition, net t w y t b i n n 1 n j () = ij i () j i n w ij epesents the connection weights of the n-th laye j-th neuon and n 1-th laye i-th neuon. n b j denotes the bias weights of the n-th laye j-th neuon. n yi j 1 () t (13) is the input vaiable of the model, which includes the pecipitation, wate level, and capacity and quantity of ain baels in each subegion Solution of Optimization Model We employ tabu seach to select the optimal solution fo the spatial aangement and capacity design of RWHS unde consideation of the benefits of uban flood eduction. Tabu seach is widely applied to management and planning issues; it can efficiently identify nonlinea o optimal solutions. Futhemoe, it can be easily combined with the optimization model, and it quickly and automatically selects the best solution fo the decision-making vaiables. Besides, the decision vaiables of this study include zonal capacity and quantity of RWHS, and the quantity must be a natual numbe. A most impotant advantage of tabu seach is that the seaching moving distance can be set as intege, so this study selects tabu seach as an optimization algoithm. (1) Tabu Seach Poposed by Glove (1986) [23] and Glove and Laguna (1997) [24], tabu seach guides the seach diection and egion using diffeent types of memoy. Duing the seach, a seach diection o egion can be favoed o pohibited accoding to the memoy and ules. Additionally, the seach can exit a local optimum egion and avoid epeated seaches though the definition of a tabu list, which includes the type and length of the seach vaiables and associated objective function values. In each iteation, it only seaches to find the best candidate solution. Hence, this seach mechanism can significantly impove the seach efficiency and accuacy and obtain the best global solution.

11 Wate 2015, (2) Optimizing the Spatial Design of Quantity and Capacity by Tabu Seach We use tabu seach to select the optimal ain bael spatial aangement and capacity design in each flood event; its flowchat is shown in Figue 2. The selection method sets the decision-making vaiables in the optimization model i.e., the quantity and capacity of the ain baels in each egion as the tabu seach solution. The steps ae descibed below. Figue 2. Flowchat of optimizing the spatial design of capacity and quantity of ainwate havesting systems using tabu seach Step 1: Set the initial seaching solution of tabu seach (the best solution in the simulation method), input the altenative BPNN model, and calculate the objective function value of the optimization model; i.e., the annual net benefit of the design patten. Step 2: Calculate the objective function value of the neighboing solution and choose the best neighboing solution. Step 3: Check if the best neighboing solution is in the tabu list. If a best solution has aleady been seached, select the second best neighboing solution; if a best solution has not yet been seached, move the seach location fom the pesent solution to the best neighbo solution. Afte moving, update the tabu list.

12 Wate 2015, Step 4: To ecod the optimal solutions identified thus fa, apply the elite stategy to compae the best seaching solution in this iteation with the optimal solution pio to the seach. Step 5: Afte the seach pinciples stop woking, the optimal spatial aangement and capacity design appoach fo ain baels can be obtained fo the whole event Development of BPNN-Based SWMM Model Stuctue of BPNN-based SWMM This study develops a novel altenative BPNN-based simulation model to substitute fo US EPA SWMM and embed it into the optimization model fo the fast, accuate and automated optimizing pocess. Any newly consideed intedisciplinay multi-objective optimization model, embedded simulation model and optimizing algoithm can be involved and integated. Chang et al. (2010) [29] developed a two-stage pocedue undelying the clusteing-based hybid inundation model, which is composed of linea egession models and ANNs (atificial neual netwoks) to build a 1-h-ahead egional flood inundation foecasting model. Howeve, egading to the study of modeling long lead-time continuous unsteady inundation level of an uban dainage system using ANNs still have not been eseached. The inputs of BPNN-based altenative model include the bounday condition, initial condition and simulated taget that must be enteed in SWMM (e.g., pecipitation, the LID design appoach and wate level of dainage system). Because the aim of this study is to detemine flooding loss, the flooding and wate pipe level ae included in the input item. In addition, to obtain the best design appoach fo ain bael spatial aangement and capacity, we include the quantity and capacity of the ain baels in the input item and set the wate level/flooding at t + 1 moment as the output item. Besides, the success of BPNN-based simulation appoach is mostly dependent on constuction data (including taining and validation pat), which means data should be epesentative well enough in ode to constuct the input-output elation. In ode to achieve this goal, this study develops a etieving method of epesentative constuction data using statistical quatiles analysis fo ooftop aea and ainfall fequency analysis (Section 2.2.2). The BPNN-based dainage system wate level simulation model is constucted in thee pats: a single-moment taining, single-moment validation, and complete-event simulation and veification. The single-moment simulation taining and veification is pimaily the calculation mechanism of the SWMM steady simulation. The complete-event simulation and veification adds the single-moment calculation units and povides feasibility veification fo the unsteady simulation. In the complete-event simulation, we equie a bounday condition at the stat time (t0), the meteoological-hydological condition, and the spatial design patten of the RWHS. We ente the tained BPNN single-moment calculation units and then obtain the simulation value at t + 1 fom the output item. Accodingly, the cycle of continuous iteative calculations is epeated until the end of the moments, when the complete-event flooding and wate levels of the dainage system can be simulated. The BPNN was developed by Rosenblatt (1958) [19] and Rumelhat and McClelland (1986) [20]. Constucted by the multilaye pecepton, it belongs to a multilaye feedfowad netwok and handles the nonlinea elationship between the input and output by a supevisual leaning appoach. The commonly used BPNN is a thee-tie stuctue neual netwok, which includes an input laye, a

13 Wate 2015, hidden laye, and an output laye. The input value of the neuons connected by associated weights between diffeent layes in the netwok is diectly tansfeed into the hidden laye. Then, afte the weighted accumulation ( f ), we obtain an output value and pass it onto the output laye following the n same ule. The output value ( y j ) of numbe j of the n-th laye is the convesion function value of the n 1 laye neuon output value, which is shown as follows: n n y j = f ( net j ) (14) The weight-accumulated value of the output value of the n 1 laye n net j is shown as follows: net w y b (15) n n n 1 n j = ji i j i In this study, the hidden laye adopts the tan-sigmoid (Equation (16)) as the tansfe function, while the output laye is linea. BPNN utilizes the gadient steepest descent method to calculate and adjust the netwok weight and bias values. This is accomplished to minimize the eo of the output value and actual taget value fo obtaining a calculation mode of pecise leaning. y e = e net j j e net j net net + e j j (16) Altenative Applicability Assessing Index of BPNN-based SWMM To assess if the developed BPNN-based SWMM is capable to be the altenative model of opeating inteface-esticted SWMM, this study adopts the mean absolute eo (MAE) and coefficient of coelation (CC) as altenative applicability index, which ae descibed below. (1) MAE MAE n BPNN SWMM Ysim () t Ytaget () t i= 1 (17) = BPNN SWMM whee Ysim () t is the simulation value of BPNN-based SWMM at time t, Ytaget () t is the taget value to substitute US EPA SWMM, and n is the numbe of data. A smalle MAE indicates that the altenative applicability of the BPNN-based SWMM is bette than the othe BPNN-based models. n (2) CC CC = BPNN BPNN ( sim ) SWMM ( Ysim () t ) ( Ytaget () t ) n Y () t Y () t Y () t Y () t BPNN SWMM BPNN SWMM sim taget sim taget SWMM ( taget ) Y () t 2 Y () t n n (18) A lage CC indicates that the vaiation tend between the simulation value of BPNN-based SWMM and US EPA SWMM is close that epesents the developed BPNN-based SWMM is moe suitable to be the altenative model of US EPA SWMM than the othe BPNN-based models.

14 Wate 2015, Application 3.1. Study Aea The Zhong-He Distict is an aea of km 2 located in the southwest cone of the Taipei Basin. Its southen end has a high altitude and gadually lowes nothwad. In some aeas, the Zhong-He Distict has exteme slope changes, which can lead to floods because of the locations of these changes at the intesections of mountainous teain and the gound. Othe aeas ae also vulneable to flooding on account of thei moe gentle teains o insufficient dainage capacities. Examples include the aea nea Jyu-Guang Road and Min-Siang Steet, shown in Figue 3a; contol point 1 (CP1), Guo-Guang Steet; contol point 2 (CP2), Min-Siang Steet; and contol point 3 (CP3), Jyu-Guang Road. These latte thee locations ae low lying such that the teain height diagam can be shown in Figue 3b. It is, theefoe, elatively difficult fo the wate to dain fom these aeas, causing flooding and life and popety loss fom ainstoms. Thus, these locations ae set as contol points fo the flood damage assessment. Figue 3. Study aea: (a) spatial distibution of dainage system, zonal subegions fo design of ainwate havesting system using the fuzzy C-means cluste algoithm and the low-lying contol points; (b) teain height above sea level.

15 Wate 2015, Analyzed Results of the Simulation Model fo Spatial Design of Quantity and Capacity Classified Results of Zonal Subegions fo Design of RWHS This study applies FCM cluste algoithm with pactical investigated ooftop aea data to classify the study aea to chaacteistic zonal subegions. In ode to choose a most economic mode of zonal subegions, this study pecedes sensitivity analysis to diffeent numbe of clustes fo the distance of cental locations. The distance of each two cental locations fo clusteing cental numbe 3 anges fom 547 m 2 to 722 m 2 ; distance fo clusteing numbe 4, anges fom 547 m 2 to 1075 m 2 ; distance fo clusteing numbe 5, anges fom 391 m 2 to 1117 m 2 ; and distance fo clusteing numbe 6, anges fom 375 m 2 to 1134 m 2. The aveage distance between each combination of two cental locations fo clusteing numbe 3 to 6 ae 656 m 2, 714 m 2, 673 m 2 and 685 m 2, espectively. Hence, clusteing numbe 4 can cove wide designed aea than the othe clusteing numbes with most efficient zonal mode. Afte setting the clusteing cente numbe as 4 and calculating using FCM cluste algoithm, the catchment ange of zonal subegions (Figue 3a). The fou cente coodinates (TM2 X, TM2 Y) ae Region 1 (296565, ), Region 2 (297360, ), Region 3 (296860, ) and Region 4 (297247, ), espectively. The numbe of available building oof fo aanging ain bael of Region 1 is 440 which is mostly composed of schools and esidences; numbe of available oof of Region 2 is 385, composed of paks and commecial buildings; numbe of Region 3 is 943, composed of community high buildings and housing; and numbe of Region 4 is 728, composed of industial buildings and esidences Spatial Designed Results of Specific Repesentative Regula RWHS (1) Capacity and Quantity The designed paametes fo RWHS include capacity (volume) and quantity (aanged density: how many aeas ( A l ) aange one ain bael). This study designs epesentative egula specification of RWHS by using statistical quatiles analysis (to estimate epesentative A l ) and ainfall fequency analysis (to estimate epesentative P RP T ). The statistical quatiles analysis esults of available ooftop min aea of each subegion on Zhong-He dainage aea is shown in Figue 4. This study adopts Min( a ), WA a, min ( ) WA a and 25% ( ) WA a among fou subegions ( = 1 4) that the values ae 55.0 m 2 (A1), med ( ) 82.4 m 2 (A2), m 2 (A3) and m 2 (A4), espectively, to ensue all designs of volume and aanged density can actually be applied to the building of Zhong-He dainage aea. The adopted etun peiod (T) of P RP T ae 2, 5, 25, 50 and 100 yeas, and the designed ainfall duation is 6 hous. Finally, the designed egula volume of ain bael ae RP A P, RP A P, RP A P, RP A P, RP A P and 4 100yea 1 2yea 2 5yea 2 50yea 3 50yea 4 25yea RP A P that the values ae 3.03 m 3 (S1), 6.14 m 3 (S2), 9.12 m 3 (S3), m 3 (S4), m 3 (S5) and m 3 (S6), espectively, to ensue that the designed volume can handle all kinds magnitude of stom ainwate of etun peiods.

16 Wate 2015, Figue 4. Boxplot of available ooftop aea of each subegion in the study aea. (2) Spatial Aangement of Designed Cases Thee wee 284 sub-catchments in the study aea. Aeas with ain baels included business, mixed esidential, industial, office, and school disticts. We conducted designs of the space, density, and capacity to set the locations of the ain baels. Accoding to the spatial design style, we established fou types of aangements (Cases 1 4) fo the simulation method. The ain baels of Case 1 wee aanged at whole sub-catchments; those fo Case 2 wee set mainly at inundated sub-catchments; those fo Case 3 wee aanged at easily inundated sub-catchments but without oute space; and those fo Case 4 wee set upsteam fom the inundated sub-catchments. Figue 5 shows the uban dainage system setup fo the thee Zhong-He Distict cases. Figue 5. Spatial aangement of egula design of ainwate havesting systems.

17 Wate 2015, In tems of the setup of the ain bael quantity, we employed density to establish it in SWMM. To compae its flood detention effects, we set the density as: (1) one fo evey 55.0 m 2 unde the ain bael pe household (Case X-1); one fo evey 82.4 m 2 (Case X-2); one fo evey m 2 (Case X-3); and one fo evey m 2 (Case X-4). The ain bael quantity of each case with each spatial aangement is shown in Table 1. In the capacity design, we divided the capacity of ain baels into 3.03 m 3 (Case X-Y-1), 6.14 m 3 (Case X-Y-2), 9.12 m 3 (Case X-Y-3), m 3 (Case X-Y-4), m 3 (Case X-Y-5), and m 3 (Case X-Y-6) to compae the simulated effect of flood detention. Table 1. Quantity (numbe) of ain bael of each designed egula case. Case No. Case X-1 Case X-2 Case X-3 Case X-4 Case X Case Case Case Calibation and Validation of US EPA SWMM The distibution of sewe system constuction and flood contol point ae shown in Figue 3a. Because the New Taipei sewe wate level and flow monitoing system had not yet been built, the model calibation and validation could only be executed within the ange of flooding depth. We theefoe employed the flooding aeas, wate logging time, eceding time, and flooding depth fom 12 August 2009 Rainstom Suvey Data fo the model calibation. In addition, we used the 16 June 2012 Rainstom Event fo the model validation to examine its feasibility. The simulated output of SWMM was the volume of bust pipes (flooding) and wate level; theefoe, the flooding had to be conveted into flooding depth fo compaison. The actual ecods of the calibated event s thee contol points and SWMM simulation esult both showed flooding; howeve, the validated event s actual ecod and SWMM simulation esult showed that only CP3 had flooding, wheeas no flooding was found at the othe contol points. We checked the simulated calculation esults of the calibation and validation event. The simulated depths of each flooding contol point wee all located within the actual flooding ecod ange (Figues 6 and 7). It was theefoe confimed that the model paametes wee well calibated and complete. The values of calibated paametes ae shown in Table 2. Figue 6. Cont.

18 Wate 2015, Figue 6. Calibation esults of stomwate unoff management model (SWMM). Figue 7. Validation esults of SWMM (Jyu-Guang Road). Table 2. Values of the calibated paametes in SWMM. Title Suface Roughness Hoton-Based Max/Min Infiltation Manning s Roughness Coefficient Rates/Decay Constant Coefficient fo Conduits Region ~ ~4.6 (mm/h)/0.9~1.6 (mm/h)/1.8~2 (1/h) 0.013~0.016 Region ~ ~5.8 (mm/h)/1.1~1.9 (mm/h)/1.6~1.9 (1/h) 0.015~0.017 Region ~ ~3.5 (mm/h)/0.5~0.9 (mm/h)/2~2.2 (1/h) 0.011~0.015 Region ~ ~3.9 (mm/h)/0.7~1.2 (mm/h)/1.9~2 (1/h) 0.012~0.014

19 Wate 2015, Simulated Analytical Results of the Designed Spatial Aanged Regula Cases fo RWHS (1) Rainstom Events Employed fo Simulation-Optimization As the foundation fo selecting the optimal spatial design of RWHS, we gatheed data fom fou ainstom events that occued fom 2009 to 2012 in the Zhong-He Distict which the epesentative etun peiod of total pecipitation ae 50, 100, 125 and 75 yea, espectively (Table 3). The duation of heavy stom ains wee about 6 hous which all caused lage amount of inundation loss. Table 3. Adopted pecipitation hyetogaph of ainstom events fo simulation-optimization (mm). Time Seies Numbe (HOUR) Repesentative Retun Date Peiod of Total Pecipitation 1 July yea 12 August yea 21 June yea 12 August yea (2) Results and Discussion We enteed the spatial design appoach of all cases into SWMM to simulate and calculate the aveage annual net benefit of setting the RWHS in the ainstom events within the study yeas. We then compaed the esult to a scenaio without RWHS. The cuve equations of inundation loss of CP1 CP3 ae expessed in Equations (19) (21), espectively, and the annual cost function of RWHS is expessed total in Equation (22). The unit of L CP1, L CP2, L CP3 and T C is US dollas, and the unit of F CP1, F is m 3. The unit inundation loss of CP2 is obviously lage than the othe two contol points. total CP3 ( CP ) F and total 2 LCP1= F R = (19) 2 ( ) ( ) L = 8.89 F F R = (20) total total 4 2 CP2 CP2 CP2 ( ) CP L = F R = (21) 5 total 2 CP1 1 total CP2 2 TC = Ca A (22) The esults of Case 1 can be egaded as the most significant flood eduction effect fo the RWHS. Howeve, because the cost of RWHS was vey lage, all net benefits esulted in a negative value. The design appoach fo the lagest net benefit in the Cases 2, 3 and 4 consideed individually ae Cases 2-1, 3-1, and 4-1, espectively, and the compaison vaying along with volumes is shown in Figue 8. The simulation analysis esults demonstate: (1) The function of flooding damage and eseving the facilities cost fo each spatial layout appeaed as convex and concave cuves, theeby changing with the capacity of the ain baels. We subtacted the convex cuve fom the concave cuve to obtain the best solution with the lagest net benefit; (2) The best solution was when the RWHS wee set upsteam of the flooding aea, which was Case 4-1; the capacity of the ain bael was 12 m 3, and the net

20 Wate 2015, benefit fo each yea was US dollas; (3) In each case, the ain bael s best capacity was between 12 and 15 m 3 ; geate benefits wee poduced when the ain bael was set in the easily flooded aea. Figue 8. Compaative diagam of annual net benefit of each egulaly designed case Constuction Results of BPNN-based SWMM Thee wee 12 input items of BPNN-based SWMM, which included: catchment pecipitation, CP1 CP3 full pipe pecentage of wate flow, the quantity of Regions 1 4 ain baels, and the capacity of Regions 1 4 ain baels. The taining and validating esults ae descibed as follows: Taining and Validating Results of Single-moment Simulation We used the 2:1 pinciple to divide the ainfall-unoff data of the uban dainage system geneated in each event using the simulation methods into two pats taining and validation. When classifying, we stove to dispese them in cases with diffeent designs. The quantity of all events was 288; i.e., 3 (spatial aangement quantity) 4 (ain bael intensity quantity) 4 (stom event quantity) 6 (ain bael capacity). Thee wee 198 taining events and 90 validation events. Because the time inteval fo the data of each event was 1 min, the sum of taining data was 44,442 and the sum of the validation data was 20,070. Afte seveal epeated tests of neuons in the hidden laye, we compaed the appaisal indicatos and detemined that thee wee seven final hidden laye neuons. The simulated esults of taining and validation fo full pipe pecentage of wate flow ae shown in Figues 9 and 10, espectively. The MAE of CP1 CP3 in a single-moment level full-pipe simulation among validation events was 0.010%, 0.014% and 0.032%, espectively. The CC value was 0.990, 0.995, and 0.983, espectively. The esults showed that the single-moment eo of the full pipe pecentage was small and demonstated an accuate simulation tend. Theefoe, the taining and validation esults of the single-moment simulation wee good and could be continued in the entie-event simulation. Howeve, the MAE of CP1 CP3 in a single-moment volume bust-pipes simulation among validation events was cms, cms, and cms, espectively. The CC value was 0.947, 0.783, and 0.916, espectively. The esults indicated that BPNN-based SWMM demonstated bette pefomance fo wate level simulation. Nevetheless, it was moe difficult to be accuate in tems of the volume of bust pipes.

21 Wate 2015, Figue 9. Taining esults of single-moment full pipe pecentage simulation of wate flow: (a) at CP1; (b) at CP2; and (c) at CP3.

22 Wate 2015, Figue 10. Validation esults of single-moment full pipe pecentage simulation of wate flow: (a) at CP1; (b) at CP2; and (c) at CP3.

23 Wate 2015, Sensitivity Analysis Result To undestand the pefomance of the poposed BPNN-based wate flow simulation model, this study deeply pefomed sensitivity analysis and the esults ae shown in Table 4. Results show that the output (full pipe pecentage at time t + 1) sensitivity of CP3, CP2 and CP1 with egad to input: pecipitation at time t (change in 0.2 mm/min) is 3.46%, 5.15% and 5.26%, espectively. Accoding to histoical expeimental ecods, assuming about 67% of flood can be emoved by fee flow outlet and pumping facilities, the dainage system can suffe about 12.1 mm/h of heavy ains with no flooding that coincide with the ainfall design standad of 5-yea etun peiod (12.4 mm/h), so it epesents the model pefomance and capability fo the input of pecipitation is available. Futhemoe, the output sensitivity of CP1 CP3 with egad to input: full pipe pecentage at t (change in 1%/min) is within the ange fom 0.51% to 1.12%. The change in the downsteam wate flow of CP1 is moe sensitive to the othe contol points that coincide with the hydaulic theoy, so the developed model is scientific enough to model wate flow phenomenon. Besides, the output sensitivity of CP1 CP3 with egad to input: aanged quantity (change in 100 numbes) is within the ange fom 1.81% to 6.75%, and the output sensitivity of CP1 CP3 with egad to input: aanged capacity (change in 3 m 3 ) is within the ange fom 0.44% to 2.15%. The change in upsteam quantity and capacity of RWHS (Regions 3 and 4) make moe sensitivity to the othe low-lying subegions (Regions 1 and 2) that coincide with the analytical esults of simulation method (Section 3.2.4), so the developed model is available fo the embedded optimizing pocess. Table 4. Sensitivity analysis of the backpopagation neual netwok (BPNN)-based wate flow simulation model. Input Aveage Vaiance of Output (Full Pipe Pecentage) of CP3 at t + 1 of CP2 at t + 1 of CP1 at t + 1 Pecipitation at time t (change in 0.2 mm/min) 3.46% 5.15% 5.26% Full pipe pecentage of CP3 at t (change in 1%/min) 1.12% 0.51% 0.72% Full pipe pecentage of CP2 at t (change in 1%/min) 0.59% 1.00% 0.53% Full pipe pecentage of CP1 at t (change in 1%/min) 0.96% 0.98% 1.00% Aanged quantity of Region 1 (change in 100 numbe) 3.22% 2.68% 2.74% Aanged quantity of Region 2 (change in 100 numbe) 2.38% 3.54% 1.81% Aanged quantity of Region 3 (change in 100 numbe) 2.40% 5.02% 3.42% Aanged quantity of Region 4 (change in 100 numbe) 4.40% 3.30% 6.75% Aanged capacity of Region 1 (change in 3 m 3 ) 1.43% 1.19% 0.88% Aanged capacity of Region 2 (change in 3 m 3 ) 0.49% 0.86% 0.44% Aanged capacity of Region 3 (change in 3 m 3 ) 1.43% 2.15% 1.75% Aanged capacity of Region 4 (change in 3 m 3 ) 1.16% 1.29% 1.62% Validation Results of the Entie-event Iteative Simulation The validation esults of the entie-event iteative continuous simulation of the developed BPNN-based model ae shown in Table 5. The MAE of the wate level simulation was quite small (less than 15% fo all cases), and the MAE fo CP1 CP3 was 0.065%, 0.07%, and 0.106%, espectively. Moeove, all CC values eached 0.96; the CC values fo CP1 CP3 wee 0.968, 0.970, and 0.963, espectively. These esults indicate that the BPNN-based SWMM developed by ou eseach can

24 Wate 2015, accuately and quickly simulate the wate level change of ainstom events. Theefoe, its altenative model can be eliable embedded in the optimization model to quickly and automatically povide an optimal design appoach while the window-based man-made opeating inteface of hydaulic model cannot be linked with optimization model and algoithm. Figue 11 depicts the validation esult of Case duing the 12 August 2012 Rainstom Event, which epesents the fouth spatial distibution, the thid ain bael aangement intensity (one fo evey 150 m 2 ), and the second design capacity (6 m 3 ). Table 5. Unsteady continuous simulated esults fo validation of BPNN-based SWMM. Unsteady Simulated Guo-Guang Steet (CP1) Min-Xiang Steet (CP2) Ju-Guang Road (CP3) Events MAE (%) CC MAE (%) CC MAE (%) CC Designed Case on 1 July Designed Case on 1 July Designed Case on 12 August Designed Case on 12 August Designed Case on 21 June Designed Case on 21 June Designed Case on 12 August Designed Case on 12 August Designed Case on 12 August Aveage Figue 11. Cont.

25 Wate 2015, Figue 11. Unsteady continuous simulated esults of Case 4 duing the 12 August 2012 Flood Event using BPNN-based SWMM Optimization Results In this applied case, the tabu list can be shown as [ Z, N1, N2, N3, N4, S1, S2, S3, S 4]. Moeove, the tabu list length was set to 300, and the seaching iteative numbe was 1,000. In the seaching solution, the moving distance of S and N was 1 and 10, espectively. The initial solution was the best design appoach of the simulation method of Case (one ain bael fo evey 50 m 2 ; capacity of 12 m 3 ). Afte optimizing by tabu seach, the optimal seaching esults ae shown in Figue 12, and compaison on full pipe pecentage of wate flow and flooding volume between optimal ain bael design, best design of simulation method and oiginal no design of the thee contol points is shown in Figue 13. Results show that because of aangement of ain baels, the optimized design and best design of simulation method can eliminate total flood in the dainage system as much as possible compaing to oiginal cicumstances of no ain bael. Howeve, because the best design of simulation method mostly aange ain baels on the upsteam of the study aea, the initial stoed effect fo flood mitigation is obvious. Howeve, afte the ain baels ae full, the oveflow fom upsteam would impact the low-lying stoed wate shaply with lage amount of momentum because of highly hydaulic gadient. These cicumstances cause the low-lying contol points would instead undetake flooding tansitoily. Moeove, the optimized design can eliminate the peak flow as much as possible and adapt the flow velocity as less as possible to minimize the flooding at the contol points, because of moe elastic spatial aangement consideing the distibution of dainage system and teain. In the optimal spatial design appoach fo ain baels, spatial quantity was mainly located upsteam, and ain baels with geate volume in easily flooded aeas had a bette flood eduction effect. The BPNN-based SWMM developed by ou institute may have some eos in the calculation esults; theefoe, ou institute etuned the optimal solution to the US EPA SWMM to simulate the wate level and volume of the bust pipes, and to calculate the actual flooding loss. Results indicate that the evaluated eo of inundation loss by using BPNN-based SWMM compaing to US EPA SWMM is about 7.99%; and egading the evaluated eo of net benefit, is about 4.15%; that is within acceptable

26 Wate 2015, ange. The stepwise calculated esults fo net benefit ae shown in Table 6. The aveage inundated loss while no installing ain baels was US dollas; and of optimized design, was US dollas. The optimized spatial design of RWHS could educe 72% of inundation losses accoding to the fou simulated flood events. Besides, the annual net benefit of the best solution in the simulation method was US dollas (Figue 13), and the annual net benefit of hybid simulation-optimization method was US dollas (12.75% bette than using the single simulation method), which is quite good. It indicates that the optimization model developed by ou institute can seach fo the optimal solutions fo spatial quantity and capacity aangement of RWHS with consideation of flood etention benefits. Figue 12. Optimized design esults of capacity and quantity of ainwate havesting systems fo Zhong-He dainage system. Figue 13. Cont.

27 Wate 2015, Figue 13. Compaison on full pipe pecentage of wate flow and flooding volume between optimal ainwate havesting systems (RWHS) design, best design of simulation method and oiginal no design: (a) CP1; (b) CP2; and (c) CP3. Table 6. Net benefit of optimized design of ainwate havesting systems. Flood Event 1 July August June August 2012 Aveage Inundated loss while no installing ain baels (US dollas) Inundated loss of optimized design (US dollas) Deceased inundated loss (US dollas) Benefit pecentage of flood mitigation (%) 76.2% 79.8% 62.1% 70.0% 72.0% Cost (US dollas) Annual net benefit (US dollas)