The StormWISE Model: Prortzng Subwatersheds and Land-Uses for Stormwater BMP Implementaton. Arthur E. McGarty 1 1 Department of Engneerng, Swarthmore College, Hcks Hall, 500 College Avenue, Swarthmore, PA 19081; PH (610) 328-8077; emal: amcgarty@swarthmore.edu Abstract StormWISE (Storm Water Investment Strategy Evaluator) s a new model for prortzng stormwater BMP mplementaton projects on the bass of ther costs and pollutant load reducton benefts. It s the result of more than a decade of water qualty montorng and computer-based modelng at Swarthmore College on nonpont polluton from stormwater runoff n urban watersheds. StormWISE s desgned for modelng at a hgh level of aggregaton, and, as a result, the data nput requrements can be kept farly reasonable. Pollutant load estmates, aggregated by subwatershed, are obtaned from a loadng model such as AVGWLF or SWMM, or, f avalable, from montorng data. Ste specfc BMP cost data are used to calbrate watershed-level costperformance functons by equatng margnal costs at multple ponts on the BMP mplementaton saturaton curve for each landuse category. An entre watershed s modeled, and the output dsplays those subwatersheds and landuse categores where the greatest effort should be appled to locate specfc stes for BMP mplementaton projects that wll obtan, at mnmum cost, the requred pollutant reductons. StormWISE s free and open source, and t ncludes, bult n, the free MapWndow GIS dsplay nterface. StormWISE can be downloaded from http://watershed.swarthmore.edu. Acknowledgements Development of the StormWISE model was supported by the Unted States Envronmental Protecton Agency Cooperatve Agreement Project: AW-83238401-0, 11/30/2006. Programmers: Mcajah Z. McGarty and Scott Fortmann-Roe. Introducton Ths paper provdes gudance on the applcaton of the StormWISE model for the beneft of potental users. StormWISE s desgned to assst watershed managers n ther search for BMP mplementaton stes. The model apples optmzaton methods from the felds of Management Scence and Operatons Research to develop mathematcal models and computer software tools for prortzng projects that mplement best management practces for storm water runoff. The model, named StormWISE, for Storm Water Investment Strategy Evaluator, s desgned to generate optmal strateges for targetng dranage areas and land use categores for nonpont polluton reducton projects. In the model, data on BMP cost and pollutant removal effcences are combned wth data on nonpont pollutant loads, by subwatershed, to produce outputs that help users dentfy projects that can maxmze the effectveness of avalable funds. StormWISE s categorzed as a screenng model because t s desgned for use at a hgh level, typcally n the early stages of a watershed management plannng process. It does not select specfc stes for projects drectly, but ts output can substantally narrow the range of varaton wth respect to project stes and BMP technologes. The model also provdes an objectve way to choose among competng proposals for fundng of BMP mplementaton projects that s based on sound scentfc and economc modelng methodologes. 1
Background StormWISE was developed as part of a research program conducted at Swarthmore College over the past ten years, ncludng a Secton 319 watershed assessment (McGarty, 2001), three mplementaton projects funded by Pennsylvana s Growng Greener program (McGarty, 2004), two research projects funded by the federal Coastal Zone Nonpont Polluton program (McGarty and Horna, 2005a, 2005b and 2005c), and a cooperatve agreement wth the U.S. Envronmental Protecton Agency (McGarty, 2006a). These reports are avalable for download from http://watershed.swarthmore.edu. The theory underlyng the model s descrbed n the Coastal Zone and EPA reports, and n recent conference proceedngs (McGarty, 2006b and 2006c). StormWISE was orgnally developed and calbrated for the specfc set of crcumstances (geographc, hydrologc, land use, etc.) exstng n an ntensvely developed muncpalty n the Phladelpha suburbs (Sprngfeld Townshp) that s experencng urban nonpont polluton problems. Presently, we are buldng upon experence ganed from applyng StormWISE n suburban Phladelpha by extendng the model for use by urban watershed managers n other areas of the country. Recent development actvtes on StormWISE have addressed the followng goals: (1) evaluatng the potental for use of the model wth dfferent nonpont loadng models, (2) selecton of an approprate Geographc Informaton System (GIS) nterface for communcatng results to decson makers, (3) development of a method for adaptng the model s BMP cost functons to nclude multple local cost factors, (4) examnaton of optons for the optmzaton solver software that s used to generate optmal solutons, and (5) ntegraton of the model components nto software that can be dstrbuted to potental users of the StormWISE. Sgnfcant progress has been made n each of these areas durng the prevous two years. Verson 1.0 of the software s now avalable for free download, wth source code. Also, the model s GIS capabltes are actvated usng the royaltyfree MapWndow system developed at the Unversty of Idaho. BMP Cost Model Theory Optmzaton technques have been appled n the feld of Water Resources snce the 1960 s (ReVelle, et al., 1967), but only recently to management of nonpont pollutants n stormwater runoff. The key theoretcal component of the StormWISE screenng model s the BMP performance-cost trade off functon, whch plots the amount of pollutant loadng reducton acheved n a subwatershed-szed dranage area versus the level of resources devoted to mplementaton of management practces, expressed n unts of thousands of dollars. The mathematcal form of the functon s that of a surface saturaton phenomena n physcal systems n whch a lmted number of surface stes are avalable, and the effectveness of the drvng forces that populate the stes dmnshes as the fracton of stes already populated ncreases towards 100%. One example s the Langmur adsorpton equaton (Langmur, 1918) that s wdely used to model equlbrum adsorpton of gas or lqud molecules on surfaces n response to ncreasng partal pressure or concentraton. When the equaton s appled to the problem of populatng potental stes for BMP projects, the drvng force s the level of economc resources devoted to a dranage area and the response s the fracton of land area (and the assocated stormwater runoff) that can be treated. Other research on optmal placement of BMP s for watershed-based stormwater management has demonstrated the same behavor as that modeled by the Langmur equaton (see, for example, Yu, et al., 2002 and La, et al., 2005 and 2006). These studes show that ste-specfc 2
models that generate optmal placement strateges for BMP s have solutons characterzed by rapd ncreases n pollutant loadng reducton n response to ntal expendtures, as the least expensve projects at readly avalable stes and havng economes of scale (the low hangng frut ) are mplemented followed by dmnshng cost effectveness as the more expensve projects are taken on at the more problematc stes. Ths functon s also used n technology assessment studes, such as a recently completed market penetraton study for new energy effcency technologes [Moore, et al. 2005]. 350 300 Sedment Removed (ton) 250 200 150 100 50 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Captal Cost ($1000) Vrgna DOT study (Yu, 2002) Nonlnear Model Curve Ft Fgure 1. Langmur surface saturaton equaton ft to data from results of an optmal BMP placement model developed by Yu, Zhen, and Zha (2002) n a watershed-based study of BMP placement for mnmzaton of cost. (Fgure taken from McGarty and Horna, 2005, wth permsson) The Langmur surface saturaton equaton appled to BMP performance and cost over a subwatershed-scale dranage area takes the form shown n Equaton (1), below: f X = (1) ( H + X ) where: f = fracton of land area treated by BMPs X = resources devoted to BMPs ($1000) H = half-cost the resources requred to treat one-half of the land area ($1000) 3
Equaton (1) s used to calculate reductons n annual nonpont polluton by multplyng f by the annual pollutant loadng and by factors that nfluence the pollutant removal effcency, as shown n Equatons (2) and (3), below. max R = f R (2) where: R = annual reducton n pollutant loadng (tons sedment, or pounds nutrents) = annual reducton n pollutant loadng f 100% of land area s treated max R R max = f Tη BMP L (3) where: f = fracton of total annual runoff that s treatable (eg. 90% for 1-nch T desgn storm precptaton) = estmated annual pollutant removal effcency for treatable runoff BMP L = annual pollutant loadng for each land use (tons sedment, or pounds nutrents) η The use of equatons (1) (3) to model optmal mplementaton of BMP s on the watershed scale was frst proposed by McGarty and Horna (2005). Fgure 1, above, taken from that study, shows how well these equatons ft data from the ste specfc BMP placement optmzaton model developed by Yu, et al. (2002) for the Vrgna Department of Transportaton. We see that a smple set of analytcal functons havng two parameters, H and R max, can be used to represent the results of many thousand complex calculatons nvolvng detaled smulaton models drven by an optmzaton engne (scatter search, n ths case). Calbraton of Watershed BMP Cost Functons In prevous applcatons of the screenng model, a sngle-pont calbraton was used to obtan estmates of the parameter H. Ste specfc costs were used assocated wth the BMP technology that, accordng to judgment of watershed managers, would most lkely be requred at the pont where runoff from one-half of the dranage area s beng treated. The margnal cost of that technology was computed from publshed cost curves that account for economes of scale (see, for example Schuler, 1987). The methodology for constructng watershed-based cost functons has been extended to enable multple BMP technologes to be used for calbratng the performance-cost equaton. If we let A represent the land area treated by BMP s wthn a dranage area A d, then f n equaton (1) s the rato of these two areas. Substtutng ths rato for f n equaton (1), solvng for X, and dfferentatng wth respect to A gves the result below: 4
dx da ( H / Ad ) ( 1 f ) 2 h = = 2 ( 1 f ) (4) where: h = half cost per unt dranage area ($/acre) dx = margnal BMP cost, obtaned from ste specfc data ($/acre) da We can solve equaton (4) for h to obtan: dx da h = ( 1 f ) 2 (5) Equaton (5) shows that the half cost can be calbrated for any pont on the pollutant removal versus cost curve. Our prevous studes fxed f at 50% for ths calbraton, but we see that any value of f could be used. A further extenson of the methodology s to enable multple values of f to be used smultaneously n a multpont calbraton. Consder m dfferent BMP technologes, each havng dx dfferent margnal costs. Let y = for = 1,2, K, m represent the margnal costs for each da BMP technology, obtaned from ste specfc data based on realstc experence wth BMP mplementaton projects. Arrange the m dfferent BMP technologes so that y 1 has smallest cost, y 2 s second smallest, etc. and y m s the most expensve. Then, based on consderatons of how applcable each BMP technology s n the geographc regon where the model s appled and on the varous land use categores where t can be appled, estmate the range of applcaton for each BMP technology n terms of f. For example, one result of applyng ths method to a specfc dranage area s that for commercal land uses, the least expensve BMP havng margnal cost y1 can be appled to only 15% of the acreage, the second least expensve BMP havng margnal cost y 2 can be appled to the next 20%, and the thrd least expensve BMP havng margnal cost y 3 can be appled to the next 25%, where y 1 < y 2 < y 3. A lnear optmzaton model has been formulated to fnd the value of h whch yelds the best ft of a saturaton functon of the form of equaton (1) to the data. Ths model s shown below: m Mnmze e + + e = 1 Subject to: ' h y = = 1,2, K, m ( 1 f ) 2 ' + e y y e = 1,2, K, m 5
0 f f 1 u = 1,2, K, m + e, e, f 0 = 1,2, Km where u s the upper lmt for the range of BMP (0.15, 0.20, and 0.25 n the example ' above), y s the margnal cost of BMP estmated from the curve, y ' y s the devaton of the actual margnal cost for BMP I from ts estmated value. Ths formulaton mnmzes the sum of the absolute devatons of the data from the curve. Ths curve fttng technque s recognzed n the feld of Robust Statstcs to be superor to the more commonly used least-squares technque when the data are lkely to contan outlers. BMP cost data typcally vary over wde ranges, so ths technque was chosen for the BMPFIT component of the StormWISE system. An example of the applcaton of BMPFIT to commercal and resdental land uses s shown n Fgure 2. Fgure 2. Margnal costs ($/acre) from several dfferent BMP technologes are used to determne the best ft values for the half-cost h for both commercal and resdental land-use categores (upper plots) and these half-costs are used to generate saturaton curves that demonstrate how StormWISE models BMP costs. 6
StormWISE Model Example and Screenshots Sample applcatons of StormWISE are provded wth the download package. Excerpts from the Tacony example are shown here. Runoff and nonpont pollutant loadngs from Tacony Creek n Northeast Phladelpha were modeled usng the AVGWLF model (Evans, et al., 2004), whch s a GIS-based mplementaton of the GWLF model (Hath, 1987). Only three subwatersheds were delneated for ths example to keep the level of detal manageable for a tutoral. However, applcatons of StormWISE wll typcally nvolve many more subwatersheds. The only lmtaton on the number of dranage areas that can be modeled s the capablty of the optmzaton solver that s used. StormWISE s dstrbuted wth the free verson of the AMPL optmzer (Fourer, et al., 2003) whch can handle up to 300 varables and constrants. Users have the opton to purchase the commercal verson of AMPL whch can handle a vrtually unlmted number of varables. The number of varables requred depends on the number of pollutants, land-uses, and subwatersheds. For example, wth the free verson of AMPL, wth three pollutants and fve land-uses, a total of 15 subwatersheds can be handled. Decreasng the number of pollutants ncreases the potental numbers of land-use categores and subwatersheds. Data Input and Edtng. A utlty program called GWLF_postprocessor, dstrbuted wth StormWISE, s used to automatcally generate the StormWISE nput fle. The screenshot n Fgure 3 shows one layer of a three-dmensonal table used to dsplay and edt pollutant loadngs for each land-use category n each of the three numbered subwatersheds that were delneated for ths example. The loadngs, n Tons, for Sedment n the Tacony example are shown. Note that when a partcular land use does not exst n a subwatershed dranage area, a * character ndcates that the loadng value s not possble. The user can manually edt these and all other nput data to the model usng such tables. Fgure 3. StormWISE Pollutant Load Data Input and Edtng Screen 7
Dsplay of Model Output Wth or Wthout GIS. Fgure 4 shows the output screen when the user requests a reducton of 5 tons annually of sedment over the entre study area (.e. from all three dranage areas). After enterng a value of 5 n the Desred Reducton column, the user selects the menu opton Analyze/Run or smply clcks the Run tool. The table now shows how much sedment reducton to pursue by nstallng BMP s n each of the three dranage areas. The optmal nvestment levels (n $1000 unts) to drect towards each dranage area are shown as well as the amounts of pollutant removal acheved by that nvestment. Note that although the user made no request regardng the amount of TOT_N and TOT_P to reduce, some reductons n these pollutants are acheved anyway because BMP s that remove sedment also typcally remove nutrents. Also, note that the total cost of achevng these pollutant reductons s estmated to be $50,000 and that most of t should be drected towards projects n dranage area 9664 and no projects should be pursued n dranage area 9654, f overall cost mnmzaton s the only objectve nfluencng the decson. In realty, the decsons regardng where to place BMP s depend on mult-objectve consderatons such as flood control, and other practcal consderatons. Thus, model results can not be nterpreted strctly. On the other hand, these results can help watershed managers approach the very dffcult problem of prortzng projects n a way that acheves the greatest pollutant reducton for a certan level of nvestment. Another way of statng ths result s that the model predcts that any alternatve BMP nvestment strategy n ths subwatershed would result n ether a cost hgher than $50,000 to acheve the same 5 tons annually of sedment removal, or sedment removal of less than 5 tons for the same nvestment of $50,000. The dsplay can be modfed to show results for each specfc land-use category and for any combnaton of land-uses. Also, f GIS shapefles are not avalable for the study area, StormWISE wll dsplay the results as a smple pe dagram. Summary and Conclusons The StormWISE model, whch has been under development for the past four years, s now avalable as n a software package for the Wndows operatng system whch can be downloaded for free. It s dstrbuted under the Mozlla Publc Software agreement, whch allows royalty-free use of the software, as well as access to the source code. The software provdes a graphcal user nterface and ncludes GIS dsplay of model output. StormWISE s useful to watershed managers who want to approach BMP ste selecton problems strategcally from a watershed perspectve. It provdes gudance on whch dranage areas (subwatersheds) and land-use categores should be gven prorty for locatng BMP mplementaton projects that control stormwater quantty and qualty based on desred watershed-wde sedment and nutrent loadng reductons and mnmzaton of BMP costs. A communty of StormWISE users s begnnng to emerge n the feld of watershed management. Ths paper provdes gudance to potental users who want to understand more about how the model works and about the range of problems to whch t can be appled. 8
Fgure 4. StormWISE Prortzaton Output Screen wth GIS dsplay References Evans, B.M., S.A. Sheeder, K.J. Corradn, and W.S. Brown, 2004. AVGWLF Verson 5.0 Users Gude, Envronmental Resources Research Insttute, The Pennsylvana State Unversty, Unversty Park, PA. Fourer, Robert, Davd M. Gay, and Bran W. Kernghan, AMPL: A Modelng Language for Mathematcal Programmng, Second Edton, Thompson Brooks/Cole Publshers. Hath, D.A. and L.L. Shoemaker, 1987. Generalzed Watershed Loadng Functons for Stream Flow Nutrents, Water Resources Bulletn, 23 (3), pp. 471-478. La, F., L. Shoemaker, and J. Rverson, 2005. Framework Desgn for BMP Placement n Urban Watersheds, ASCE Conference Proceedngs Paper, Proceedngs of the 2005 World Water and Envronmental Resources Congress, ed. by Raymond Walton. La, F., J. Zhen, J. Rverson, and L. Shoemaker, 2006. SUSTAIN An Evaluaton and Cost- Optmzaton Tool for Placement of BMPs, ASCE Conference Proceedngs Paper, Proceedngs of the 2006 World Envronmental and Water Resources Congress, ed. by Randall Graham. 9
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