Impact of Forecasted Land Use Change on DesignPeak Discharge at Watershed and Catchment Scales:

Simple Equation to Predict ChangesDaniel Habete, P.E., M.ASCE1; and Celso M. Ferreira, Ph.D., A.M.ASCE2

Abstract: Common engineering methods for the computation of peak discharge are generally based on the assumption of a stationarywatershed. This assumption can potentially lead to inaccurate estimates of peak discharge when considering the lifetime of engineeringstructures. Future land use change is one of the possible causes of non-stationarity in watershed runoff. This study focuses on a methodto integrate the readily available integrated climate and land use scenarios (ICLUS) data sets from the environmental protection agency (EPA),with geographic information system (GIS) and hydrologic modeling. This framework is applied to evaluate the impact of the forecasted landuse change on the design peak discharge in the rapidly urbanizing region in Northern Virginia (US) at the watershed (Anderson formula) andcatchment [calibrated storm water management model (SWMM)] scales. The results show that the impervious area in the rapidly urbanizingDifficult Run watershed is expected to increase by 99.1% (2070) from the year 2010. This increase could cause the peak discharges toincrease by 107.9% (SWMM) and 22.1% (Anderson formula) for the 2-year storm event. Simple and easy-to-use regression equationis presented to estimate the changes in design peak discharges based on drainage area and the change in percent of impervious area forthe return periods of 2, 10, 25, 50, and 100 years. The results of this study, in addition to supporting local planning and managing of landdevelopment activities, also demonstrate a viable alternative to incorporate the impacts of future land use change on design peak discharge.DOI: 10.1061/(ASCE)HE.1943-5584.0001384. © 2016 American Society of Civil Engineers.

Introduction

Watersheds are nonstationary systems which are in a continuousstate of change due to human or natural causes (McCuen 2012).Future land use change is one of the possible causes of runoffnon-stationarity, transforming the watershed into a dynamic sys-tem. Urbanization is the primary cause of land use change dueto developments such as houses, roads, parking lots, etc. and isa result of increases in population, economy and transportation(Han et al. 2009). According to McCuen (2005), land use changecan be considered one of the main causes of many hydrologic de-sign problems. Designing hydrologic and hydraulic structures suchas, reservoirs, culverts, and bridges requires accurate estimates ofthe design peak discharge for a given return period. This is impor-tant for the structures to perform their intended purpose safely.Most methods for the computation of the design peak discharge,such as frequency analysis and regression equations, generallyassume that the watershed is a stationary system. Hydrologic analy-sis performed under the assumption of a stationary watershed maylead to underestimating the design peak discharge (Moglen 2003).This assumption could lead to under sizing hydrologic and hy-draulic structures, which can lead to increased drainage problems(Moglen 2003).

Nevertheless, hydrologists have paid considerable attention tothe effect of urbanization for years (Chow et al. 1988). Percentof imperviousness is commonly used as an index to representthe level of urbanization (McCuen 2005). Several researchers havebeen using imperviousness as an index to evaluate the impact ofurbanization on stormwater systems (e.g., Lee and Heaney 2003),rainfall-runoff relationship and other hydrologic processes (Li et al.2013; Beightey and Moglen 2002; DeFries and Eshleman 2004;Wang et al. 2007; Chen et al. 2009), flow volume (e.g., Kim et al.2002), streamflow (Johnson et al. 2015; Gyawali et al. 2015; Zhenget al. 2013), biological habitat (Estes et al. 2015), future availabilityof water resources (Mateus et al. 2015), agricultural watershed(Potter 1991), and general urban environmental quality (Arnoldand Gibbons 1996).

The impacts of impervious area changes in hydrological proc-esses are well documented. The increase of impervious areas alsogenerates increases in peak discharge, total water volume, but itreduces the time of concentration, groundwater recharge, and baseflow (Leopold 1968; Dunne and Leopold 1978). Also, Salas andObeyseker (2014) reported that urbanization decreases the returnperiod and increases the risk of structure failure. McCuen (2005)described flood frequency analysis (FFA) as one of the most com-monly used statistical methods to estimate design peak dischargefor a given return period; however, FFA assumes annual peak flooddata are homogenous, which usually leads to inaccurate estimatesof peak discharge. Accordingly, McCuen (2005) developed a peakadjustment factor plot as a function of exceedance probability andthe percent of impervious area to adjust observed peak dischargeimpacted by urbanization. Also, Salas (1993) performed a statisti-cal analysis to remove the effect of urbanization from the mean andstandard deviation of a discharge record. These methods did notreflect watershed hydrologic processes nor did they incorporatethe spatial and temporal distribution of a land use change (Beighleyand Moglen 2003). Hence, Beighley and Moglen (2003) proposed

1Graduate Student, Dept. of Civil, Environmental and Infrastructure En-gineering, George Mason Univ., Fairfax, VA 22030 (corresponding author).E-mail: dhabete@gmu.edu

2Assistant Professor, Dept. of Civil, Environmental and InfrastructureEngineering, George Mason Univ., Fairfax, VA 22030. E-mail: mferrei3@gmu.edu

Note. This manuscript was submitted on July 2, 2015; approved onJanuary 11, 2016; published online on March 21, 2016. Discussion per-iod open until August 21, 2016; separate discussions must be submittedfor individual papers. This paper is part of the Journal of HydrologicEngineering, © ASCE, ISSN 1084-0699.

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a method to adjust the observed annual peak discharge for a givenurbanized watershed to represent a fixed land use condition byincorporating the effect of spatial and temporal distribution andthe watershed hydrologic process. However, the majority of previousstudies were focused on the impact of historical land use changeon a hydrologic response of a watershed (Yan and Edwards 2013).

The impacts of land use changes on watersheds have been wide-spread across the United States (U.S.) (Butcher et al. 2010).Although predicting land cover change has always been a chal-lenge, in recent years the U.S. Geologic Survey (USGS) (USGS2013) and the U.S. environmental protection agency (EPA) haveforecasted land use changes. The EPA has generated the integratedclimate and land use scenarios (ICLUS) data sets for the entire U.S.at a 1 square kilometer resolution in a raster format and available bydecade to 2100. The ICLUS data sets are readily available for use inthe entire U.S. (U.S. EPA 2014). This data has already been used toexplore the sensitivity of stream flow and water quality to climateand land use change (e.g., Johnson et al. 2012). Johnson et al.(2012) used the ICLUS data to evaluate the impact of the forecastedclimate and land use change (year 2050) on stream flow at thewatershed scale and their result indicated that stream flow was lesssensitive to land use change than climate change; however, theypointed out that land use changes at a smaller scale could havea larger impact on streamflow. In this study, we demonstrate amethod to incorporate land cover changes in design peak dis-charges by utilizing the readily available land cover forecasts inthe US. Therefore, the two main objectives of this study are:1. Evaluate the impact of the forecasted land use change on the

design peak discharge at the watershed and catchment scalesin the rapidly urbanizing Difficult Run watershed; and

2. Develop regression equation to predict the change in designpeak discharge as a function of drainage area and the changein percent of impervious area at the catchment scale as a viablealternative to incorporate the impact of future land use changeon the design peak discharge.

Methodology

The overall framework of this study is summarized in Fig. 1.The authors have selected the rapidly urbanizing Difficult Run

watershed in Northern Virginia (U.S.) as the study area (Fig. 2).The ICLUS data sets were obtained from the U.S. EPA website(U.S. EPA 2014) and used to represent the land use changes. ArcGISwas used to extract the percent of impervious area from the selectedICLUS data sets at the watershed and catchment scales. The FairfaxCounty Public Facility Manual Anderson Formula, referred to here-after as the Anderson formula (Anderson 1970; Fairfax County2013c), was used to simulate design peak discharge at the watershedscale. The calibrated storm water management model (SWMM) wasused to compute design peak discharge at catchment scale. Sensitiv-ity analyses were performed to evaluate the sensitivity of design peakdischarge to the percent of impervious area at the watershed andcatchment scales. Finally, simple and easy-to-use regression equa-tion was developed to predict the change in design peak dischargeas a function of drainage area and the change in percent of imper-vious area. The details of each section are discussed below.

Study Area

To explore the impact of increasing urbanization on design peakdischarge, the authors selected the rapidly developing suburbanDifficult Run watershed, located in the north central portion ofFairfax County, Virginia (Fig. 2). It has a drainage area of approx-imately 149 km2 at the outlet were the USGS gage station 01646000is located (USGS 2014b). The entire Difficult Run watershed iswithin the Piedmont physiographic region. The hydrologic soilgroups of the watershed are mainly B, C, and D. More detailedinformation about the characteristics of the Difficult Run watershedcan be found at the Fairfax County website (Fairfax County 2013b).For the purpose of this study, a watershed is defined as an area ofa land that allows water to flow to the outlet during a storm event.A catchment is a smaller part of a watershed that has homogenouscharacteristics such as land use/land cover, soil type, slope, and in-filtration characteristics, and a subwatershed is a group of two ormore catchments. Therefore, a catchment is a subset of subwatershedand a subwatershed is a subset of watershed.

Forecasted Impervious Area

For this study, the forecasted land use changes from the ICLUS datasets were used to represent the percent of impervious areas into the

Fig. 1. Overall framework of the study

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future. The ICLUS data sets (A1, A2, B1, B2, and BC) are readilyavailable in a raster format by decade from 2010 to 2100. Thesedata sets are generated based on four factors: economic, environ-mental, global, and regional developments (U.S. EPA 2009).The selected ICLUS data sets are based on the same assumptionsthat population growth and migration that emphasize the intergov-ernmental panel on climate change (IPCC) A2 greenhouse gasemissions storylines (U.S. EPA 2009). ArcGIS was used to extractthe percent of impervious areas of the Difficult Run watershed andits 490 catchments for every decade between and including 2010–2070. The average percent of impervious areas at the watershed andcatchment scales were computed using the zonal statistics as tabletool, within the spatial analyst toolbox of ArcGIS. Zonal statisticsas table tool summarizes the mean value of the percent of imper-vious area within the watershed and catchments.

Fairfax County Public Facility Manual AndersonFormula

The Anderson formula is a regional regression equation developedfor use in Northern Virginia and Southern Maryland for a drainagearea greater than 0.81 km2 (200 acres) (Anderson 1970; FairfaxCounty 2013c). Eq. (1) (Anderson formula) was used to evaluatedesign peak discharges based on the percent of impervious areas atthe watershed scale for the return periods of 2, 10, 25, 50, and100 years

Q ¼ 230 × K × R × A0.82 × T−0.48 ð1Þ

where Q = peak runoff rate (cfs); A = drainage area (sq. miles); andK = coefficient of imperviousness and can be found using Eq. (2),where I is percent of impervious area (Anderson 1970; FairfaxCounty 2013c)

K ¼ 1.0þ 0.015 × I ð2Þ

where T = lag time in hours and computed using Eq. (3), assumingthat the watershed tributaries are a sewer network, and the mainchannels are in natural conditions (Anderson 1970; Fairfax County2013c)

T ¼ 0.9 ×

�LffiffiffiS

p�

0.5ð3Þ

where L = longest stream distance in miles; S = average slope(ft=mi:) between points located 10 and 85% of the L measured up-stream from the point of interest. The flood frequency ratio (R) is afunction of storm recurrence interval in year and percent of imper-vious area. To compute the R value Eq. (4) was used (Anderson1970)

Ri ¼Rn þ 0.1 × I × ð2.5 × R100 − RnÞ

1þ 0.015 × Ið4Þ

where Ri = flood frequency ratio for a given percent of imperviousarea, R100 = flood ratio for 100-percent-impervious basin, and Rn =flood ratio for a natural drainage basin. The values of Rn are 0.9,2.2, 3.3, 4.4, and 5.5, for return periods 2-year, 10-year, 25-year,50-year, and 100-year, respectively. Similarly, the values of R100

are 0.9, 1.45, 1.8, 2.0, and 2.2, for return periods 2-year, 10-year,25-year, 50-year, and 100-year, respectively (Anderson 1970).

Storm Water Management Model (SWMM)

The SWMM was developed by U.S. EPA and is a dynamic sim-ulation model that can be used for single or continuous simulation(Rossman 2004) and has been used widely for water quality andquantity analyses in urban watersheds (e.g., Yan and Edwards2013). For this study, the SWMM developed for the DifficultRun watershed was obtained from Fairfax County. The SWMMwas calibrated by adjusting the parameters until the computed peakdischarge matches the annual maximum instantaneous peak dis-charge data at the USGS gage (station # 01646000) from 1935to 2006. The purposes of this model are to evaluate the impactsof future developments and to assess the effect of the existingand proposed low impact development (LID) and best managementpractices (BMPs) on water quality and quantity in the Difficult Runwatershed (Fairfax Country 2013b). In this model, the DifficultRun watershed was subdivided into 490 homogenous catchments.The Horton infiltration method was used for the losses computa-tion, and the kinematic wave method was used for flow routing. InSWMM, infiltration is computed only for the pervious area of thecatchment. For this study, the infiltration coefficients necessary for

Fig. 2. Location of the study area

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the Horton method such as the decay constant, drying time, maxi-mum and minimum infiltration rates are kept constant; since eachpervious fraction of the catchment is homogenous with similar in-filtration characteristics for future scenarios as well. More detailedinformation about the Difficult Run watershed modeling procedurecan be found at the Fairfax County website (Fairfax County2013b). The authors used the SWMM to evaluate the sensitivityof the design peak discharge due to the percent of impervious areafor the return periods of 2, 10, 25, 50, and 100 years.

Design Storm

Design storm was one of the input variables used in the SWMM tosimulate design peak discharge. The Natural Resources Conserva-tion Service (NRCS) Type II temporal distribution for precipita-tions over a period of 24-h and uniform in space was used in theSWMM. The design storm depths for 24-h duration are 8.1 cm(2-year), 12.4 cm (10-year), 15.5 cm (25-year), 18.2 cm (50-year),and 21.4 cm (100-year), which were obtained from the NationalOceanic and Atmospheric Administration (NOAA) Atlas 14(NOAA 2014).

Sensitivity Analyses

The Anderson formula and the SWMMwere used to predict designpeak discharges under changing impervious area for the storm re-turn periods of 2-year, 10-year, 25-year, 50-year, and 100-year. Foreach return period, the relative change of design peak discharge wascalculated using Eq. (5a). In all scenarios, the predicted designpeak discharges computed in the year 2020, 2030, 2040, 2050,2060, and 2070 were compared with the design peak dischargecomputed in the year 2010

rΔQ ¼ ΔQQn;2010

× 100 ð5aÞ

ΔQ ¼ Qn;t −Qn;2010 ð5bÞwhere ΔQ = change of design peak discharge (cms), rΔQ =relative change of design peak discharge in percentage, Qn;t =design peak discharge for storm return period n in year t, andQn;2010 = design peak discharge for storm return period n in theyear 2010. For this study, peak discharge rate comes from Ander-son formula and the SWMM.

Similarly, the relative change of forecasted impervious areaswas computed by Eq. (6a)

rΔI ¼ ΔII2010

× 100 ð6aÞ

ΔI ¼ It − I2010 ð6bÞwhere ΔI = change of forecasted impervious area in percentage,rΔI = relative change of the impervious area in percentage, It =forecasted impervious area in year t, and I2010 = impervious area inthe year 2010. Finally, sensitivity of rΔQ to rΔI was evaluated atthe watershed scale (Anderson formula) and catchment scale(SWMM) and then the results of the two models were comparedand contrasted.

Regression Analysis

Regression analysis is a statistical tool that can be used toinvestigate the relationship between dependent variables and

independent variables and has been commonly used for hydrologicanalyses. For example, the USGS has developed regional regres-sion equations for Virginia to estimate a design peak discharge asa function of one independent variable (i.e., drainage area) (USGS2014a). For this study, the following steps were followed to developregression equation to predict change in design peak discharges as afunction of change in impervious area and drainage area:1. Obtain independent variables.

a. The areas (A) for each of the 490 catchments werecomputed;

b. Using the extracted percent of impervious areas of each of the490 catchments for every decade between and including2010–2070, the ΔI were computed by Eq. (6b); and

c. The values computed in step a (A) and step b (ΔI) were usedas predictor variables.

2. Obtain dependent variable.a. The SWMMwas used to compute the design peak discharges

for each of the 490 catchments by varying the percent of im-pervious area for the return periods of 2, 10, 25, 50, and100 years;

b. Using the design peak discharges computed in step 2 (a), theΔQ were computed by Eq. (5b); and

c. The ΔQ computed in step 2 (b) was used as dependentvariable.

3. Regression Analysesa. The regression equation was developed by the ΔQ (depen-

dent variable) regressed on the ΔI and A (independentvariables).

The coefficient of determination (R2) and the Root MeanSquared Error (RMSE) were used as indicators for the accuracyof the developed regression equation.

Results and Discussion

Forecasted Impervious Area

The authors extracted the percent of impervious areas for each ofthe five available ICLUS data sets A1 (23.3%), A2 (19.2%), B1(23.1%), B2 (20.2%), and BC (20.9%) for the year 2010. Thenfor the year 2010, historical data such as residential and commercialbuildings, minor roadways, parking, and driveways were used tocompute the percent of impervious area. The comparisons of theresults of the analyses indicated that the ICLUS A2 data sets valueis very close to the value of the historical 2010 impervious area(19.5%). Therefore, the A2 data sets were selected to representthe land use change into the future for this study.

The forecasted spatial and temporal distributions of the imper-vious area in the Difficult Run watershed are shown in Fig. 3. Theresults of the analyses indicated that the impervious areas for theyears 2010, 2020, 2030, 2040, 2050, 2060, and 2070 were 19.2%,24.3%, 28.8%, 31.4%, 34.1%, 36.4%, and 38.2% respectively atthe watershed scale. This rate of increase is proportional to the ex-pected population growth rate (Fairfax County 2013a). Individualcatchment analysis, summarized in Table 1, indicates that imper-vious area will likely increase in all catchments. The largest in-crease in impervious area will likely be seen in the Glade (TG)subwatershed with 92.5 and 174.8% increase over the 2010 levelsfrom 2020 to 2070. The smallest changes will likely be seen in theOld Courthouse Spring Branch (OCSB) subwatershed with only51.5% increase (2070) over the 2010 baseline level.

It is important to note that the uncertainty of the selectedICLUS data sets was not examined in this study, although themodel and the input data used to develop the ICLUS data sets

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may introduce additional uncertainty in the predicted imperviousareas. Also, no BMPs on the newly added impervious area are as-sumed. Nevertheless, the results of this study suggested that thepercent of impervious areas in the Difficult Run watershed willvery likely increase in the future, demonstrating that communitiesshould incorporate increases of impervious areas on its hydrologicand hydraulic design planning.

Evaluating the Impact of Forecasted Land Use Changeon Design Peak Discharge Using the AndersonFormula at the Watershed Scale

The lag time was calculated using Eq. (3) and assumed to be con-stant for all simulations. In the Anderson formula method thereare only three different formulas available for computing lag time:

Fig. 3. Spatial-temporal distributions of the predicted percent of impervious areas in the Difficult Run subwatersheds, for the year: (a) 2010; (b) 2020;(c) 2030; (d) 2040; (e) 2050; (f) 2060; (g) 2070

Table 1. Forecasted Percent of Impervious Areas for the 18 Difficult Run Subwatersheds

SubwatershedSubwatershedarea (km2) I (%) 2010 I (%) 2020 I (%) 2030 I (%) 2040 I (%) 2050 I (%) 2060 I (%) 2070

The glade (TG) 3.1 15.9 30.6 37.1 39.6 40.8 41.9 43.7Lower difficult run (LDFR) 10.2 9.5 13.4 15.7 19.6 21.6 26.5 28.2Middle difficult run (MDR) 6.9 11.8 15.1 19.3 23.0 26.4 30.5 31.8Sharpers run (SR) 1.7 13.0 13.8 20.8 23.6 26.8 31.2 40.1Little difficult run (LDR) 10.3 13.5 17.8 23.1 26.9 30.3 33.4 34.3Captain hickory run (CHR) 6.2 12.4 16.4 21.1 22.7 27.4 29.5 30.1Dog run (DC) 1.9 16.5 25.1 27.0 29.8 33.2 35.1 36.1Upper difficult run (UDR) 22.7 16.7 22.5 27.4 30.8 34.1 36.3 37.5Angelico branch (AB) 2.0 16.8 20.8 26.5 31.1 33.0 34.1 36.8Piney run (PR) 8.3 16.8 20.2 24.9 27.2 31.7 34.5 38.1South fork run (SFR) 6.8 18.5 24.8 29.8 32.8 34.8 35.1 40.3Rocky branch (RB) 8.9 18.8 24.1 30.7 31.9 34.9 35.8 37.5Wolftrap creek (WC) 14.4 21.3 27.3 32.2 34.6 35.1 39.0 39.6Rocky run (RR) 7.3 24.4 28.2 32.1 34.3 37.1 38.8 40.2Snakeden branch (SB) 9.0 28.6 36.2 38.5 41.0 42.2 44.2 46.5Colvin run (CR) 15.1 26.4 30.9 35.7 37.4 40.1 41.0 43.1Piney branch (PB) 10.1 25.3 29.2 33.1 35.4 38.4 38.5 41.5Old courthouse spring branch (OCSB) 4.1 30.7 32.4 35.3 37.7 40.9 43.4 46.5

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formula for natural watershed, formula for developed watershed,and formula for completely sewered and developed watershed(Fairfax County 2013c). This is one of the limitations of using thisformula because these methods may not reflect the different level ofdevelopments in a subwatershed and may lead to a generalized es-timation of lag time. The Anderson formula was used to examinethe impacts of the forecasted impervious area on design peak dis-charge at the watershed scale. The results of the computed 2-year,10-year, 25-year, 50-year, and 100-year design peak discharges areshown in Fig. 4(a) (Top), which show that design peak dischargescould increase in the future in the Difficult Run watershed. For eachreturn period, the relative changes of design peak discharge forevery decade between and including 2020–2070 from the year2010 were computed using Eq. (5a) and the results are summarizedin Fig. 4(a) (Bottom). The results revealed that a return period isinversely proportional to a percent of relative change of design peakdischarge. This means, as the return period increased, the changeof design peak discharge decreased. For example, the imperviousarea was changed by 99.1% from the year 2010 to the year 2070.This change caused the design peak discharge to increase by22.1% (2-year), 11.0% (10-year), 6.5% (25-year), 2.5% (50-year),and 0.0% (100-year). The increases in the design peak dischargeare due to the increases of the forecasted impervious area.

Interestingly, the slope of the graph for the 100-year returnperiod in Fig. 4(a) (Bottom) is zero, which means the peak dis-charge calculated using Anderson formula did not change as theimpervious area changed. This could be explained as follows:the peak runoff rate was computed using Eq. (1). The area is con-stant and the lag time was assumed to be constant for all scenarios,so Eq. (1) can be summarized as Eq. (7)

Q ¼ ðconstantÞ × K × R ð7Þ

The only variables in Eq. (7) are K and R. Replacing K withEq. (2) and R with Eq. (4) resulted in Eq. (8)

Q ¼ ðconstantÞ × ð1þ 0.015 × IÞ

×

�Rn þ 0.1 × I × ð2.5 × R100 − RnÞ

1þ 0.015 × I

�ð8Þ

For each return period, the values of Rn and R100 are listed underthe Methodology section of this paper. Substituting the values of Rnand R100 in Eq. (8) and simplifying it resulted Eq. (9)

Fig. 4. (a) Top: predicted design peak discharges, bottom: relative change in peak discharge (rΔQ), 2020–2070; (b) top: predicted design peakdischarges, bottom: relative change in peak discharges (rΔQ), 2020–2070

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Q ¼

8>>>>>>>>>><>>>>>>>>>>:

ðconstantÞ × ð0.96þ 0.144 × IÞ for T ¼ 2-year

ðconstantÞ × ð2.20þ 1.430 × IÞ for T ¼ 10-year

ðconstantÞ × ð3.30þ 0.120 × IÞ for T ¼ 25-year

ðconstantÞ × ð4.40þ 0.060 × IÞ for T ¼ 50-year

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

ðconstantÞ × ð5.5Þ for T ¼ 100-year

ð9Þ

Eq. (9) indicated that for only the 100-year return period, therate of runoff computed using the Anderson formula was not im-pacted by the change in percent of impervious area. This impliesthat the Anderson formula is not capable of showing the impact ofthe impervious area changes on the design peak discharge for largestorm events such as a 100-year storm. Therefore, it is important toaccount for the Anderson formula limitations when it is used toevaluate the impact of land use change on design peak dischargefor large storm events.

Evaluating the Impact of Future Land Use Change onDesign Peak Discharge Using the SWMM at theCatchment Scale

In contrast to the Anderson formula, this analysis subdivided theDifficult Run watershed into 490 homogenous catchments andevaluated the impact of the forecasted impervious area on designpeak discharge. The results of the simulation are summarized inFig. 4(b) (Top). The graphs of Fig. 4(b) (Top) show that the designpeak discharge continues to increase every year in the Difficult Runwatershed for each return period. In addition, the results of the per-cent of relative change of the design peak discharge to the changeof percent of impervious areas are shown in Fig. 4(b) (Bottom).Similar to the Anderson formula, the results of the SWMM showedthat the relative change of the design peak discharge is inverselyproportional to a return period. For instance, when the imperviousarea changed by 99.1%, the design peak discharge increased by107.9% (2-year storm), 51.0% (10-year storm), 38.3% (25-yearstorm), 29.7% (50-year storm), and by 26.9% (100-year storm).These results resemble a report stated that the effect of imperviousarea on peak discharges is generally much greater for smaller stormevents (e.g., 2-year) than for higher storm events (e.g., 100-year)(Robinson et al. 1998). As the storm becomes heavier, the soilbecomes more saturated and the storage of the soil pores is lessavailable to absorb additional rainfall. Under this condition, even-tually the watershed act like an impervious surface. Therefore, indesigning engineering structures it is important to account for theexpected change of the design peak discharge due to the forecastedland use change. This is important for structures to perform theirintended purpose safely.

Comparison of Models Results

For all return periods, the SWMM yielded higher relative change ofdesign peak discharge compared to the Anderson formula (Fig. 5),though there is a strong positive correlation between the model re-sults. For example, the change of the impervious area from the year2010 to 2070 is expected to increase by 99.1%; this could cause thedesign peak discharge to increase by 107.9% (SWMM) and 22.1%(Anderson formula) for the 2-year storm event. The SWMM incor-porated the spatial and temporal distribution of land use effect at490 catchment levels. On the other hand, the Anderson formulaconsidered land use at a watershed level. This result resembles aprevious study that showed subdivision generally causes the peakdischarge to increase (Casey et al. 2015). Moreover, the physical

representation of the Difficult Run watershed and the model formu-lations in the SWMM are different from the Anderson formula.These could be some of the factors that lead the SWMM to producea higher relative change of design peak discharges compared to theAnderson formula results.

It is clear that Anderson formula is not capable of showing theimpact of future land use changes on design peak discharge espe-cially for larger storms (e.g., 100-year). In addition, more sophis-ticated models, such as SWMM, require more input data and timeto set up the simulation. Therefore, simple and easy-to-use regres-sion equation is a viable alternative to incorporate the impact offuture land use changes on design peak discharges.

Developed Regression Equation

Quantifying the change of design peak discharge due to the changeof the forecasted percent of impervious area for a given watershedis important to adjust engineering design to the lifetime of a struc-ture. Regression analysis was performed to develop simple andeasy-to-use regression equation to predict the change in designpeak discharges as a function of the change in percent of imper-vious area and drainage area. The general model for the developedregression equation is shown in Eq. (10). The coefficients with 95%confidence bounds for the general model that correspond to thereturn periods of 2, 10, 25, 50, and 100 years are summarized inTable 2

ΔQðA;ΔIÞ ¼ C1 × ðAC2Þ × ðΔIC3Þ ð10Þwhere ΔQ = change of design peak discharge (cms); ΔI = changeof forecasted impervious area in percentage; A = drainage area(km2); and C1, C2, and C3 = coefficients of regression equationshown in Table 2.

The developed Eq. (10) yielded R-square values greater than0.88 and small RMSE (cms) for each return period, which indicatethat the equation has acceptable accuracy for prediction of changein design peak discharges. The Eq. (10) is intended to provide

Fig. 5. Comparison of percent of relative change in peak discharge(rΔQ) compute by the SWMM and Anderson formula for the year2020, 2030, 2040, 2050, 2060, and 2070 from the year 2010

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estimates of change in design peak discharges that are easier tocompute than using sophisticated hydrologic model like SWMM.In order to clearly show the relationship betweenΔQ andΔI whendrainage area is constant, the authors selected one of the largestcatchments in the Difficult Run watershed and plotted the valuesofΔQ andΔI. The result of the analysis, shown in Fig. 6, indicatesthat ΔQ is directly proportional to ΔI for each return period.

Application

An example application of the developed Eq. (10) is presented inthis section. The example tests how accurate Eq. (10) is outside ofthe Difficult Run watershed. The catchment area within the JohnnyMoore Creek (JMC) watershed (Fig. 2) was selected for the test.The contributing drainage area of the selected catchment at its out-let is approximately 0.7 km2. In the year 2010, the impervious areaof the selected catchment was 9.5%. Based on the U.S. EPA ICLUSforecasted land use data, the percent of impervious area of the se-lected catchment are expected to be 12.2% (2020), 13.2% (2030),17.7% (2040), 20.6% (2050), 23.4% (2060), and 26.7% (2070).Design peak discharges were computed using Eq. (10) and the

JMC watershed SWMM (JMC SWMM) by changing the computedimpervious area. The results of the computations are shown in Fig. 7for the return periods of 2, 10, 25, 50, and 100 years. Comparisonsof the results shown in Fig. 7 indicate that the developed regressionequation predict very well outside of the Difficult Run watershed.The relative errors between the JMC SWMM and regressionequation are between 0.2–7.7% (2 year), 0.1–8.4% (10-year),0.1–4.5% (25-year), 0.5–1.9% (50-year), and 0.1–1.4% (100-year).Therefore, Eq. (10) can be used in an area that has similar character-istics as the Difficult Run watershed.

Conclusions

The rapidly urbanizing Difficult Run watershed was selected to in-vestigate the impact of forecasted land use change on the designpeak discharge at the watershed and catchment scales. The authorsused ArcGIS to extract the percent of impervious areas of theDifficult Run watershed from the readily available EPA’s ICLUSdata sets for each decade between and including 2010–2070, underthe assumption of the IPCC A2 greenhouse gas emission storyline.

The future land use data under A2 scenario were selected for thisstudy based on a comparison with 2010 historical data. Although,the data related to the other scenarios (A1, B1, B2, and BC) werenot checked in this study, but a higher land use change is normallyexpected under the highest level of CO2 concentration in A2 sce-nario. Also, the selection of another data sets may lead to differentresults. The sensitivity of design peak discharge to the extractedland use change was evaluated by simulating the hydrologic re-sponse of the Difficult Run watershed over the forecasted landuse change using the SWMM and Anderson formula for 2-,10-, 25-, 50-, and 100-year storm return periods. Also, simple andeasy-to-use regression equation was developed to estimate thechange in design peak discharge due to the change in imperviousarea for a given drainage area. Therefore, it is vital to accountfor the impact of the forecasted land use changes on design peakdischarges.

The results of the analyses of the selected ICLUS data sets in-dicated that the impervious area within the Difficult Run watershedcould change significantly. At the watershed scale the change of theimpervious areas from the year 2010 to the years 2020, 2030, 2040,2050, 2060, and 2070 could increase by 26.5%, 50.1%, 63.4%,77.9%, 89.7%, and 99.1%, respectively. Moreover, the results ofthis study indicated that the impervious area is not expected tochange uniformly across the watershed. The impervious area ofthe TG watershed could change by 174.8% (2070) while the OCSBsubwatershed could change by 51.5% (2070) from the year 2010.The increases of the forecasted impervious areas in the DifficultRun watershed make the watershed a non-stationary system.

Simulation of the hydrologic responses of the rapidly urbanizedDifficult Run watershed over the forecasted percent of imperviousareas indicated that design peak discharges are expected to increase

Table 2. Coefficients with the 95% Confidence Bounds for the Developed General Model for Each Return Period and Its Regression Statistics

Returnperiod

Coefficients Regression statistics

C195% confidence

bounds C295% confidence

bounds C395% confidence

bounds R-squared RMSE

2-year 0.13 (0.12, 0.15) 0.81 (0.79,0.82) 1.03 (1.00, 1.06) 0.89 0.2610-year 0.21 (0.19, 0.23) 0.83 (0.82, 0.84) 1.04 (1.01, 1.07) 0.90 0.4125-year 0.25 (0.23, 0.27) 0.86 (0.84, 0.87) 1.04 (1.01, 1.07) 0.89 0.5250-year 0.29 (0.27, 0.32) 0.85 (0.84, 0.87) 1.01 (0.99, 1.05) 0.88 0.59100-year 0.36 (0.33, 0.39) 0.86 (0.85, 0.88) 1.01 (0.99, 1.05) 0.88 0.70

Fig. 6. Result of the SWMM simulation for the largest catchment in theDifficult Run watershed for the return periods of 2, 10, 25, 50, and100 years

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significantly. For instance, from the year 2010–2070, the imper-vious area is expected to increase by 99.1%. This change couldcause design peak discharge to change by 107.9% (SWMM) and22.1% (Anderson formula) for the 2-year storm event in the Diffi-cult Run watershed. In addition, results demonstrated that sensitiv-ity of design peak discharges to the forecasted land use changedecreases as the storm event increases. For example, when theimpervious area increased by 99.1%, the design peak dischargecomputed by the SWMM were increased by 107.9% (2-year),51.0% (10-year), 38.3% (25-year), 29.7% (50-year), and 26.9%(100-year). The results revealed that there is a risk for design peakdischarges to increase over time and therefore has important effectsin designing hydrologic or hydraulic structures. Increases of water-shed peak discharge are significant for main-stream/regional typestructures like culverts and bridges as opposed to stormwater man-agement ponds. Thus, planning for the change in design peak dis-charges due to future land use change could help to reduce the riskof under-sizing and premature failure of the designing structures.

The authors have developed simple regression equation to esti-mate the change in design peak discharges for the return periods of2, 10, 25, 50, and 100 years. This equation is intended to provide aquick and easy alternative to compute the change in design peakdischarge due to the change in impervious area for a given water-shed. The equation was tested outside of the Difficult Run water-shed and produced an acceptable accuracy. The developed equationis a viable alternative to incorporate the impact of future land usechanges on design peak discharges since the Anderson formula isnot capable of showing the impact of forecasted land use change ondesign peak discharge for larger storms. Also, other sophisticatedmodels such as SWMM require more input data and more time toset up the simulation run.

Since the ICLUS data sets are readily available for the entireU.S., design engineers can use the method presented in this paperto understand how future land use change might impact the designpeak discharge within a desired region in the U.S. While the ICLUSdata sets are available for the U.S. that might not be the case anywere around the globe. However, if land cover predictions are avail-able this methodology can easily be applied anywhere around the

globe. Hence, engineers can make appropriate adjustments to thecomputed design peak discharge under the assumption of a staticwatershed. In addition county officials, such as those in FairfaxCounty, may use the results of this study for evaluating, planningand managing land development activities that require estimates ofpeak discharge.

It is also important to note that land disturbing activities that canpotentially change the runoff volume of an area are required by lawin the Commonwealth of Virginia to implement stormwater controlmeasures to mitigate the impact of the development on stormwaterrunoff. However, the analyses performed in this study do notconsider these requirements. For this study, the authors assumedthat all future increases in impervious areas will have similarcharacteristics to the impervious area when Anderson formulawas developed, which may not consider stormwater control mea-sure. In addition, the BMPs associated with the SWMM used forthe analysis were added into pre-existing developed land as op-posed to BMPs as part of the required mitigation associated withthe land disturbing activity.

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