lable at ScienceDirect

Journal of Environmental Management 137 (2014) 146e156

Contents lists avai

Journal of Environmental Management

journal homepage: www.elsevier .com/locate/ jenvman

Improving risk estimates of runoff producing areas: Formulatingvariable source areas as a bivariate process

Xiaoya Cheng a, Stephen B. Shaw b, Rebecca D. Marjerison a, Christopher D. Yearick c,Stephen D. DeGloria d, M. Todd Walter a,*aDepartment of Biological and Environmental Engineering, Cornell University, Ithaca, NY 14853-5701, USAbDepartment of Environmental Resources Engineering, State University of New York College of Environmental Science and Forestry, Syracuse, NY 13210, USAcUpper Susquehanna Coalition, 4729 State Route 414, Burdett, NY 14818, USAdDepartment of Crop and Soil Sciences, Cornell University, Ithaca, NY 14853, USA

a r t i c l e i n f o

Article history:Received 12 September 2013Received in revised form20 January 2014Accepted 2 February 2014Available online

Keywords:Storm runoffBivariateVariable source area (VSA)Curve number (CN)Soil topographic indexNonpoint source (NPS) pollutionWater quality

* Corresponding author. Tel.: þ1 607 255 2488; faxE-mail address: mtw5@cornell.edu (M.T. Walter).

http://dx.doi.org/10.1016/j.jenvman.2014.02.0060301-4797/� 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Predicting runoff producing areas and their corresponding risks of generating storm runoff is importantfor developing watershed management strategies to mitigate non-point source pollution. However, fewmethods for making these predictions have been proposed, especially operational approaches that wouldbe useful in areas where variable source area (VSA) hydrology dominates storm runoff. The objective ofthis study is to develop a simple approach to estimate spatially-distributed risks of runoff production. Byconsidering the development of overland flow as a bivariate process, we incorporated both rainfall andantecedent soil moisture conditions into a method for predicting VSAs based on the Natural ResourceConservation Service-Curve Number equation. We used base-flow immediately preceding storm eventsas an index of antecedent soil wetness status. Using nine sub-basins of the Upper Susquehanna RiverBasin, we demonstrated that our estimated runoff volumes and extent of VSAs agreed with observations.We further demonstrated a method for mapping these areas in a Geographic Information System using aSoil Topographic Index. The proposed methodology provides a new tool for watershed planners forquantifying runoff risks across watersheds, which can be used to target water quality protectionstrategies.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Contamination of freshwater is a chronic problem world-widethat has serious, well-documented ecosystem and human healthconsequences. Nonpoint source (NPS) pollution from agriculture “isthe leading source of water quality impacts on surveyed rivers andlakes, the second largest source of impairments to wetlands, and amajor contributor to contamination of surveyed estuaries andground water” (US EPA, 2005). More recently urban NPS pollutionhas also been noted as a major contributor to some water bodies.Specific pollutants noted in the National Water Quality Inventoryreports to congress over the past two decades have includedpathogens, nutrients, and sediments, all common in agriculturalstorm runoff, as well as metal which are common in urban runoff(US EPA, 2009). The fact that the water quality impacts of NPSpollution, especially from agriculture, have persisted for over half of

: þ1 607 255 4080.

a century suggests that we need more effective, possibly targetedstrategies for mitigating this problem.

One for approach for controlling non-point source (NPS) pollu-tion that has been suggested is to restrict or avoid polluting activ-ities in areas where there is a high risk of generating storm flow(e.g., Walter et al., 2000, 2001; Gburek et al., 2002; Agnew et al.,2006; Walter et al., 2007); the term hydrologically sensitive area(HSA) is sometimes used to refer to areas with high risk of gener-ating storm runoff. One challenge to adopting this strategy is easilyand accurately predicting and mapping storm runoff risks over awatershed. This is difficult in regions like the northeastern U.S.because most storm runoff in the region is generated from rela-tively small but dynamic portions of the landscape, i.e., so-calledvariable [runoff] source areas (VSA) (e.g., Dunne and Black, 1970;Frankenberger et al., 1999; Fiorentino and Iacobellis, 2001). TheseVSAs are areas in a watershed susceptible to accumulating morewater than the soil pore space can accommodate and, once the soilwater holding capacity is exceeded, additional rain or snow meltbecomes “saturation excess” storm runoff (Ward, 1984). Strictly

X. Cheng et al. / Journal of Environmental Management 137 (2014) 146e156 147

speaking, soils do not always have to be saturated to the soil surfaceto generate storm runoff. Lyon et al. (2006), Lyon and Lembo (2006)and Dahlke et al. (2012a,b) observed rapid storm runoff in head-water watersheds in upstate, NY when the shallow water table waswithin 10 cm of the soil surface.

While practical engineering methods for predicting runoff vol-umes and rates and their associated risks have been developed andare widely accepted (McCuen, 2002; Michele and Salvadori, 2002;Mishra and Singh, 2006), there has been less attention paid todeveloping similar methods for predicting risks associated withspecific locations where runoff is generated, such as VSAs. Typicallyengineers are interested in designing infrastructure that willwithstand very large runoff volumes and rates. These types ofevents are associated with very intense rainfall that exceeds theinfiltration capacity of the soil across most of the landscape(a runoff process attributed to Horton, 1933, 1940). Under thesecircumstances, it is common to assume runoff volume is related tosimple metrics of land use and soil type, and the runoff rate de-pends on metrics related to watershed size and slope (e.g., USDA-NRCS, 1986). It is also common to assume that the storm runofffrequency, or return period, is equal to the frequency of the asso-ciated rainfall event. The most common approaches for estimatingstorm runoff volumes and rates, which incorporates these as-sumptions, use the Soil Conservation Service (SCS, currently theNatural Resources Conservation Service e NRCS) Curve Number(CN) method (e.g., USDA-SCS, 1972; USDA-NRCS, 1986).

When considering NPS pollution, engineers and managers areoften interested in runoff events large enough to happen severaltimes a year, not the events that only happen once a decade ormorethat are most often considered when designing stormwater infra-structure. In the northeastern USA, where this research is focused,Hortonian runoff is relatively uncommon (Walter et al., 2003) andmethods are needed to predict the location and frequency of themore common VSAs. Indeed, there have been very few methodsproposed to predict VSAs for water quality protection. The methodsthat have been proposed either require complicated, continuouswatershed modelling (e.g., Agnew et al., 2006) or are overlysimplistic, assuming that VSAs can be approximated with streambuffers and that the frequency of runoff generation is equal to therainfall frequency (e.g., Gburek et al., 2002). The objective of thisproject was to develop a simple approach to estimate the fraction ofrunoff generating areas and the corresponding probability. Weexplore potential watershed characteristics that might be used toquantify VSAs in unguaged watersheds and we also propose amethod for mapping the predicted runoff producing areas, i.e.,VSAs based on the topographic wetness index concept (e.g., Bevenand Kirkby, 1979; Walter et al., 2002).

2. Materials and methods

2.1. Quantifying VSA risk estimates

Over the past decade a few researchers have suggested that theSCS-CN method could be used to predict areas generating stormrunoff for watershed planners and land managers (e.g., Gbureket al., 2002; Walter et al., 2009). The SCS-CN method was origi-nally developed to predict storm runoff (USDA-SCS, 1972):

Q ¼ P2ePe þ S

(1)

where Q is the runoff volume over the watershed (mm), S is themaximum available soil storage (mm), and Pe is the effective pre-cipitation (mm); Pe ¼ total precipitation (P) minus initial abstrac-tion (Ia); Ia is the minimum amount of rainfall that is necessary to

initiate runoff. Although Ia¼ 0.2S is a traditional assumption, recentresearch shows Ia varies for different study areas or events (Jiang,2001; Shaw and Walter, 2009; Dahlke et al., 2012a). In our study,we set Ia ¼ aS, in which a is constant for each basin and can becalibrated so that the least-squares differences between observedand predicted runoff is minimized. We chose this rainfall-runoffequation in part because of its persistent popularity largely attrib-uted to its simplicity and reliance on readily available data (Ponceand Hawkins, 1996; Garen and Moore, 2005).

Although it is typical to determine S using tables that implicitlyassume the runoff mechanism is Hortonian flow (Walter and Shaw,2005), Steenhuis et al. (1995) showed that the SCS-CN equation canbe interpreted as predicting saturation excess runoff from VSAs.Gburek et al. (2002) introduced a simple approach to estimatingthe amount of area producing runoff (Ap) based on the followingequality:

QðAwsÞ ¼ Pe�Ap

�(2)

where Aws is the total watershed area. The VSA-fraction of awatershed that is generating runoff (Af ¼ Ap/Aws), i.e., “saturated”areas, can be calculated as (Gburek et al., 2002; Walter et al., 2009):

Af ¼ QPe

(3)

Q/Pe is also referred to as the runoff coefficient (Merz andBlöschl, 2009). Substituting Eq. (1) into Eq. (3) gives:

Af ¼ PePe þ S

(4)

One implicit problem in the way the SCS-CN method is used isthat the runoff exceedence probability or return period is assumedto be the same as that of causative storm events. This is generallynot the case (Shaw and Riha, 2011) and almost definitely not truefor areaswhere the process of runoff production is governed by VSAhydrology (Walter et al., 2009). Besides precipitation, antecedentsoil moisture conditions also influence runoff generation, often incomplex ways (Macrae et al., 2010; Merz and Blöschl, 2009).Because it is derived from the traditional SCS-CN method, Eq. (4)faces the same challenge, i.e., the risk that a given fraction of awatershed will generate runoff needs to be linked to both theprecipitation amount and antecedent wetness conditions.

Shaw and Walter (2009) addressed this issue with respect torunoff risk by using a bivariate approach to the SCS-CNmethod (Eq.(1)). Based on work by Troch et al. (1993), they accounted forantecedent wetness conditions by linking antecedent soil storagevolume, which influences S in Eq. (1), to base-flow (Qbase) imme-diately preceding the storm event. The same approach can beapplied to estimate risks associated with the fraction of a water-shed generating runoff (Af):

Pr�Af ¼ Afi

�¼

XMðAfiÞ

PrðPe ¼ PeiÞ � PrðS ¼ SiÞ (5)

where M(Afi) ∊ {(Pei,Si)jh(Pei,Si) ¼ Afi}, h is determined from Eq. (4),and Pr(S¼ Si) is a function of Pr(Qbase¼Qbase,i); note, we assume theoccurrence of Pe and S are independent over short time spans.Descriptively, this function calculates the probability of a given Af

by summing the joint probabilities of all pairs of Pe and S that resultin the Af value of interest.

Researchers have yet to link identifiablewatershed characteristicsto S in the context of VSA hydrology; recall, in the context of Hor-tonian storm runoff engineers typically assume S is related to landuse and soil type. So, following Shaw and Walter (2009), antecedent

X. Cheng et al. / Journal of Environmental Management 137 (2014) 146e156148

conditions were incorporated into the proposed methodology byfirst back-calculating S from observed pairs of Q and Pe for stormsthat occur following a representative range of base-flows (Qbase), bysubstituting Pe with aS and rearranging Eq. (1) into Eq. (6):

S ¼�ðaQ � Q � 2aPÞ �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðaQ � Q � 2aPÞ2 � 4a2

�P2 � PQ

�q2a2

(6)

A power function is fit to the SeQbase relationship for a water-shed allowing the estimation of S from Qbase (Shaw and Walter,2009) The probability distribution of S is based on the probabilitydistribution of corresponding Qbase, which was developed based onthe temporal histogram or “fraction of time” of Qbase. An example ofthis is shown in our methods for clarification. Note, as describedhere, the method is limited to gauged watersheds.

2.2. Mapping the predicted runoff producing areas

In order to use Af risks to develop strategies to protect waterquality, it is important to map these risks across a watershed. Lyonet al. (2004) proposed using topographic wetness indices to mapSCS-CN estimates of Af, and this concept has been adopted intoseveral watershed models (e.g., Schneiderman et al., 2007; Eastonet al., 2008; Walter et al., 2009; Buchanan et al., 2012) andrecently successfully correlated against soil moisture measure-ments (Buchanan et al., 2013). These studies generally used aversion of the soil topographic index (STI) proposed for watershedsdominated by shallow restrictive layers, such as those with a fra-gipan or with shallow depth to bedrock (Walter et al., 2002)

STI ¼ ln�

a

DKsat tan b

�(7)

Fig. 1. Nine studied sub-basins (lighter areas) and related US Geological Survey stream gaunumbers for a-n are: 30770502, 30608502, 30719502, 30867002, 30511302, 30175202, 3026respectively. (Map created by Xiaoya Cheng).

where a is the upslope contributing area per unit contour length(m), D is the soil depth above the impervious layer (m), Ksat is theaverage soil permeability (a.k.a. saturated hydraulic conductivity)(m d�1), and tanb is the local topographic slope (e). High STI-valuesindicate areas that have a high propensity of being wet with drierareas having low values of STI. One likely problem with Eq. (7) isthat it may not correctly capture the distribution of VSAs in largebasins that have large valley bottoms with deep alluvium. In thesecases it may be advisable to remove the DKsat term from Eq. (7),which reduces the STI to the simple topographic index (TI) intro-duced by Beven and Kirkby (1979). Regardless of the STI/TI used,VSAs correspond to the fraction of thewatershedwhere the highestSTI or TI is equal to Af (Lyon et al., 2004).

2.3. Example application

We applied the proposed bivariate method for estimating VSAstorm runoff risk to nine sub-watersheds in the Upper Susque-hanna River Basin (USRB); note, the USRB coalition was interestedin our analysis for developing new NPS pollution strategies, so wefocused on this basin.

2.3.1. Description of Upper Susquehanna site and datasetsThe USRB is located in the southern tier of New York State and

extends slightly into Pennsylvania (Fig. 1). This basin encompassesthe headwaters of the Chesapeake Bay estuary, a large and diverseecosystem in the USA. The USRB is 19,430 km2 (7500 mi2) with20,920 km (13,000 miles) of roads and 27,360 km (17,000 miles) ofstreams. It is covered by 59% forest, 28% agricultural land, 5% urban/suburban land, 4% openwater/wetlands, and 4% other types of land(Fry, 2011). The station numbers of the National Weather Service(NWS) rain gauges and the US Geological Survey (USGS) streamgauges that we used in this study are listed in Fig. 1 and Table 1,respectively.

ges (triangles) and National Weather Service rain gauges (circles). NWS rain gauge ID1001, 36183806, 30477201, 30002301, 30008501, 30398301, 30862702, and 30551202,

Table 1Characteristics of nine studied sub-basins and the entire basin.

Sub-basin A B C D E F G H J

USGS gauge no., 15- 02500 00500 00000 30500 25981 21500 23500 09000 10000Areaa (km2) 1350 2540 270 200 260 80 150 760 380Average slopeb (�) 6.5 7.6 8.1 6.5 7.3 6.9 8.1 7.2 7.4Average elevationb (m) 453 503 541 398 509 548 562 464 484Average soil depthc (cm) 104 99 75 97 74 / / / 80Average annual rainfalld (mm) 1073 1079 1099 946 874 943 952 1069 1077Average temperatured (�C) 0e15Land usee (%) Forest 48 59 61 54 51 74 70 52 62

Agriculture 35 27 30 22 41 20 20 31 24Developed 3 5 4 16 4 1 5 5 3Open water/Wetlands 8 7 3 3 0 1 1 7 6

Number of events used to establish S-Qbase 19 16 16 36 18 16 11 18 16CN for traditional SCS-CN method 71 72 70 75 72 71 71 74 73

a The Upper Susquehanna Coalition (no date).b Gesch (2007) and Gesch et al. (2002).c USDA NRCS SSURGO.d The PRISM Climate Group at Oregon State University (2006).e Fry (2011).

X. Cheng et al. / Journal of Environmental Management 137 (2014) 146e156 149

We used three criteria in choosing the sub-basins: 1) Size:Considering the representativeness of the observed data fromstream gauges and rain gauges, we mainly chose basins of rela-tively small size, less than 700 km2 (300 mi2); to investigate theeffect of basin size on runoff generation, we included two largerbasins (A and B, Fig. 1) e note, the SCS-CN method is inappropriatefor very large basins like the entire USRB; 2) Data Availability: We

Fig. 2. S vs. Qbase for nine studied sub-basins of the Upper Susquehanna River Basin. The lettvalues from observed PeQ data and base-flow immediately preceding the rain event, Qbase; lgraph.

selected the sub-basins with most available data; 3) Location: Wechose the sub-basins distributed across the USRB e by choosingbasins with at least 10 years of flow data and 40 years of rainfalldata we were able to identify nine basins with a reasonably gooddistribution across the USRB (Fig. 1); requiring larger datasetsresulted in fewer basins and considering basins with fewer dataresulted in less statistical confidence. General watershed

ers correspond to the sub-basins in Table 3. Circles represent pairs of back-calculated S-ines are best-fit power-functions; power functions and associated R2 are shown in each

Table 2Root mean square errors (mm) between calculated and observed storm runoff (datashown in Fig. 3).

Sub-basin A B C D E F G H J

Bivariate 2.8 2.5 3.2 3.0 3.3 3.7 1.8 1.7 2.9Traditional SCS-CN 10.1 16.8 9.3 7.2 7.9 5.0 12.1 9.5 10.4

X. Cheng et al. / Journal of Environmental Management 137 (2014) 146e156150

characteristics and land use types of each sub-basin are summa-rized in Table 3.

Weather data and rainfall frequencies were taken from theNational Oceanic and Atmospheric Administration (NOAA) weatherstations (circles in Fig. 1), which are available from the US NationalClimate Data Center. We also used daily stream-flow data from theUS Geological Survey (USGS) gauges located at the outlet of eachbasin (triangles in Fig. 2) to determine storm runoff and Qbase-values for each watershed. Hydrograph separation was done usingthe local minimum method, which is automated in the web-basedhydrograph analysis tool (WHAT) (Lim et al., 2005).

2.3.2. Specific bivariate procedureWe used the following steps develop risk estimates for Af.

i) We developed rainfall frequency-of-occurrence histogramsfor each watershed based on the most recent 40-years ofdata. We segregated daily rainfall amounts (including dayswhen rainfall was zero) into 9 bins. We found nine bins waslarge enough to represent the frequency of different sized

Fig. 3. Comparison of risks associated with storm runoff volumes among bivariate SCS-CN (speriods are based on maximum exceedence series (1998e2008) using the Weibull formula

events, but small enough so as to allow joint probabilitycalculations to be carried out in a spreadsheet.

ii) We developed frequency-of-occurrence histograms (1998e2008) for Qbase for each watershed by segregating Qbase-values into 28 bins. As with precipitation, we found 28 binswas a reasonable balance between representing variations infrequency and minimizing the number of computations.

iii) We back calculated S from PeQ pairs for several well definedstorm hydrographs for each watershed (1998e2008).Because the SCS-CN method does not work well for verysmall rainfall-runoff events (Shaw and Walter, 2009;Buchanan et al., 2012), we only used events associated withdaily rainfall higher than 5 mm (0.2 inch). We used inversedistance weighted (IDW) interpolation of gauges within andsurrounding the basin to estimate precipitation values foreach sub-basin. We used power-law functions to relate S toQbase for each watershed. The number of PeQ pairs used toestablish the relationship between S and Qbase for the ninesub-basins ranges from 11 (basin G) to 36 (basin D) (Table 1).

iv) To create frequency histograms of S for each basinwe use theS(Qbase) power-law functions (step (iii) to translate the 28Qbase-values in our base-flow histograms (step ii) to a cor-responding S-values. The frequency-of-occurrence value foreach of the 28 Qbase-values was assigned to the corre-sponding S-value to develop an S frequency histogram.

v) We calculated Af for each PeS pairing from the histogramsdeveloped in (ii) and (iv). The probability of occurrence foreach Af was determined from Eq. (5), i.e., the product of

olid line), traditional SCS-CN (dashed line), and observations (circles) e observed return.

X. Cheng et al. / Journal of Environmental Management 137 (2014) 146e156 151

the frequencies-of-occurrence associated with the P- andS-values used to calculate Af.

Vi) The probability of non-exceedence is calculated by rankingAf-values from lowest to highest and cumulatively summingthe probabilities of occurrence. The probability of exceed-ence, of course, is one minus the probability of non-exceedence and the return period is the inverse of theprobability of exceedence.

2.3.3. Comparing bivariate VSA-risks to VSA-risk based ontraditional tabulated approach

For the nine subbasins, we applied the bivariate method forestimating Af associated with VSA risks and compared the resultswith VSA risks of producing storm runoff predicted by simpler,traditionally-based SCS-CN method, as proposed by Gburek et al.(2002). To compare our bivariate approach to estimate Af to thatproposed by Gburek et al. (2002) we had to determine CN using thetraditional, tabulated method. To do this, land use data were ob-tained from the NLCD (NLCD, 2006, zone 63, USGS). Hydrologic soilgroupwas set as C sincemore than 85% areas of the study site are inC group. Hydrologic conditionwas assumed to be good. The averageCN for each basin is listed in Table 1.

There are no long-term direct measurements of variable sourceareas, i.e., directly measured areas of stormwater generation likethose made by Dunne and Black (1970) or Dahlke et al. (2012a,b).Therefore, we are unable to make a direct comparison between ourrisk estimates of Af and direct observations. However, we do apply

Fig. 4. Comparison of risks associated with runoff producing areas (Af) between bivariate SCSthe mapping example.

two indirect comparisons that can provide some indication as tothe reasonability of our estimates. First we compared return pe-riods of measured storm runoff from the nine sub-basins in theUSRB (Fig. 1) against estimates made using the Shaw and Walter(2009) method and estimates made using the traditional SCS-CNmethod. We assumed that if the bivariate method could notreasonably estimate observed runoff quantities, it would not belikely to estimate Af. We compared our calculated Af to an“observed” Af (i.e., the runoff ratio) determined using Eq. (3). This“observed” Af was computed using five large storm runoff eventswith return periods between 1 and 5 years from basins B, D, and E.As shown in Fig. 4, the Af is relatively constant above a return periodof 1 year thus we were not concerned with matching events of theexact same return period. Basins D and E were chosen because theyare of similar size and represent the watersheds with the largestfractions of developed and agricultural land, respectively, i.e., landuses associated with NPS pollution. Basin B was chosen because itwas the largest and represented an intermediate distribution ofland uses relative to the other eight. We assumed the runoff returnperiod would correspond roughly to the return period for Af, andcalculated an “observed” Af using Eq. 3.

3. Results

3.1. Comparison between bivariate and traditional approaches

The relationships between S and Qbase for each sub-basin fittedby power functions (Fig. 2) were varied. Basins H and J had the

-CN (solid line) and traditional SCS-CN (dashed line). Af ¼ 32% for sub-basin J is used in

Table 3Comparison of bivariate and traditional SCS-CN methods for a 2-year return period.As shown, for the bivariate method, the 2-year Af return period is based on differentcombinations of Pe and S values than the 2-year return period Q.

Sub-basin Method Pe (mm) S (mm) Q (mm) Pe (mm) S (mm) Af

A Bivariate 50 215 9.4 18 68 20%Bivariate 65 388 9.4 30 120 20%Bivariate 72 480 9.4 62 248 20%Traditional 62 104 22.9 62 104 37%

F Bivariate 54 275 9.0 36 42 45%Bivariate 71 490 9.0 72 88 45%Bivariate 90 805 9.0 98 120 45%Traditional 58 104 20.5 58 104 36%

X. Cheng et al. / Journal of Environmental Management 137 (2014) 146e156152

highest correlations (R2 ¼ 0.79 and 0.80, respectively), while basinsC and G had the lowest correlations (R2 ¼ 0.48 and 0.42, respec-tively). It is not obvious what made the differences, although both Cand G are small and steep, such that daily flow may not accuratelycharacterize their storm responses. Also, G had the fewest SeQbasedata (Table 1).

Runoff depth, Q, and the associated return periods determinedusing the bivariate method matched the observed Q-return periodsbetter than those predicted by traditional SCS-CN method (Fig. 3,Table 2). This corroborates the findings of Shaw and Walter (2009).Interestingly, the strength of the S-Qbase relationship does not seemto have an obvious impact on the strength of the Q-return periodestimates; although basin C is not well predicted for small returnperiods. Here, the traditional SCS-CN method systematically over-predicts Q. According to the bivariate method, risks associatedwith storm runoff volumes vary from basin to basin, while thetraditional SCS-CN method predicts similar Q-return period

Fig. 5. Soil topographic index map (a) and map of “saturated” runoff generating areas

relationships for all the sub-basins (Fig. 3). For a 5 year returnperiod, basin D has the highest runoff volume which is around27 mm, while basin G has the lowest value of 13 mm. These runoffresults were generated as a reference to the earlier work and as anindirect test of whether our estimations of Af are likely to be reli-able. The good match with the observed runoff risks lends supportto the idea of applying the bivariate method to predict Af risks.

As with Q, the proposed bivariate risks associated with Af werenotably different than those estimated with the more traditionalSCS-CN-based method proposed by Gburek et al. (2002) (Fig. 4).Similar to our findings with respect to Q (Fig. 3), the proposedbivariate method of estimating Af risks results in more variabilityamong sub-basins than does the traditional SCS-CN-basedapproach (Fig. 4). For instance, sub-basin D has substantiallyhigher Af compared to all other basins. The 2 year Af was approxi-mately 60% for sub-basin D compared to 17% for sub-basin B.Interestingly, unlike the Q comparisons (Fig. 3), in which thetraditionally-based SCS-CN method resulted in systematicallyhigher predictions of Q than the bivariate approach, there was nosimilar systematic difference for Af (Fig. 4). This can be explained bythe differences in calculating the corresponding return period be-tween the two methods. Take sub-basins A and F as examples(Table 3). The traditional SCS-CN approach assumes that theprobability distribution of Q and Af are equal to the probabilitydistribution of rainfall events and S is constant. Therefore, for agiven return period, the Pe for estimating Q and Af is the same(Table 3). However, for bivariate SCS-CN approach, risks of Q and Af

are determined by both the probability distribution of rainfallevents and antecedent soil moisture status, so Q and Af of the samereturn period can be caused by different pairs of Pe and S (Table 3).Therefore, though for both basins, Q estimates by bivariate

associated with a saturation frequency of once every two years (b) for sub-basin J.

X. Cheng et al. / Journal of Environmental Management 137 (2014) 146e156 153

approach are lower than the more tradition SCS-CN based Q esti-mate, Af can exhibit different trends between the two approaches.

Since, as mentioned in the methods, there are no long-term,direct, field measurements of Af available, we were not able tovalidate the bivariate method directly. But, using five moderatelylarge storm events in each of the sub-basins B, D, and E for whichrunoff (Q), and presumably Af, are around 1e5 years return period,the mean Af were 23%, 58%, and 49% for basin B, D, and E, respec-tively. For our proposed bivariate method, the estimated average Af

associated with return period between 1 and 5 years are 17%, 62%,and 47% for basin B, D, and E, respectively (Fig. 4). Using the moretraditional SCS-CN method (Gburek et al., 2002), the average Af ofreturn period between 1 and 5 years are 38%, 40%, and 36%,respectively. Although this test is somewhat cursory, it is clear thatAf-values drawn from observed events are much closer to thebivariate method’s estimate than the more traditionally-based SCS-CN approach, providing a reasonable validation of the ability of thebivariate method to predict a physically accurate Af.

Fig. 6. Soil topographic index map (a) and topographic index map

The main difference between the bivariate approach and thetraditional SCS-CN method is that the bivariate method accountsfor both rainfall and antecedent soil moisture conditions, while thetraditional method only considers rainfall. The disagreement of thetwo methods re-emphasizes that the risk associated with Q or Af

does not depend solely on the probability or return period of thecausative storm event, but is also influenced by the antecedent soilwetness conditions. Merz and Blöschl (2009) also found a lowcorrelation between the traditional SCS-CN method and runoffcoefficients (Af in this paper) based on measured Q and P.

3.2. Mapping VSAs

As a mapping example, we used the 1-year Af for basin J, whichconstitutes 32% of the basin’s area (Fig. 4J). This corresponds to anSTI of 7.3 (Fig. 5a), i.e., 32% of basin has an STI greater than 7.3(Fig. 5b). While this STI-mapping approach appears to workreasonably well for small to moderate sized watersheds, we

(b) for the Upper Susquehanna River Basin. TI ¼ ln (a/tanb).

Fig. 7. Comparisons among sub-basins C, D, and G of risks associated with runoffvolumes (a) and risks associated with runoff producing areas (b).

X. Cheng et al. / Journal of Environmental Management 137 (2014) 146e156154

experienced two potential problems at the scale of the UpperSusquehanna Basin: 1) the soil survey data describing soil proper-ties sometimes abruptly changes at county boundaries resulting inun-likely discontinuities in STI (The primary cause of these dis-continuities is that the soil depth value for the same map unit issubstantially different in adjacent counties) and 2) valley bottomsgenerally have very low STI (indicating relatively dry soil condi-tions) because the accumulated alluvium has a relatively largedepth (D in Eq. (7)) (Fig. 6a). In reality, the effective depth in thevalley bottoms should be the water table depth, but this is a dy-namic characteristic that is not easily incorporated into a topo-graphic index. Using a TI (i.e., omit the soil properties from Eq. (7))instead of and STI results in higher runoff risks in the valley bot-toms (Fig. 6b). The TI is predicated on the assumption that gravi-tational redistribution of soil water and groundwater is moreimportant to defining soil wetness patterns than basing thesepatterns on soil properties. This is probably most valid if there islittle variability in soil depth or the soil is very deep throughout thebasin.

4. Discussion

The ultimate goal of this project is to improve our ability to mapstorm runoff risks so that high-risk runoff generating areas, a.k.a.,hydrologically sensitive areas or HSAs (Walter et al., 2000; Agnewet al., 2006; Qiu et al., 2007), can be protected from potentiallypolluting activities. Unlike previously proposed methods for iden-tifying these sensitive areas, this method combines realistic pat-terns of runoff generation (e.g., in contrast to Gburek et al., 2002)and considers both the frequency of rainfall and antecedent con-ditions (e.g., in contrast to Walter et al., 2009). The method isrelatively simple compared to previously proposed approaches thatrequire decades of simulation modelling (e.g., Walter et al., 2000,2001; Agnew et al., 2006). These earlier approaches typicallyused a distributed hydrological model (Frankenberger et al., 1999)to simulate w30-years of distributed soil moisture and runoffgeneration to estimate the probability of runoff-risk or frequency ofsoil saturation for each point (raster) in the watershed. While thebivariate approach proposed here appears to show promise, thereare some obvious challenges in generalizing the method beyondthe watersheds used in this study.

One challenge is determining the SeQbase relationship, orsomething analogous, for ungauged basins. Note, it is this rela-tionship that controls the basin-to-basin differences in risk esti-mates of Q and Af predicted by the bivariate method. None of thepotentially controlling landscape factors in Table 1 seemed to haveobvious correlations with the constants in the SeQbase relationships(Fig. 2), suggesting that the watershed-specific drivers are likelycomplicated and interact, i.e., there is not an obvious, dominantfactor. Attempts by other researchers, most notably Roland andStuckey (2008), to create statistical models relating discharge toland use characteristics in this region similarly found few explan-atory variables of variance. Notably, once watershed area wasaccounted for, Roland and Stuckey found that wetland storageexplained a small component of variability among basins, but thatmost variability remained unexplained.

As the one exception, we did notice that the most urbanizedsub-basin, D (Table 1), had the highest Q and Af values and thesmallest (most negative) exponent in the SeQbase relationship(Fig. 2). We compared Q risks and Af risks for basin D to basins C andG, which had much smaller proportions of developed but weresimilar with respect to the other characteristics; C is slightly largerthan D, and G is slightly smaller than D (Table 1). The more ur-banized basin D has a notably higher Q and Af than sub-basins C andG (Fig. 7), which corroborates the typical expectation that

watersheds with more impervious surfaces will probably generatemore storm runoff. Note also, that while storm runoff fromimpervious areas is typically described as Hortonian flow, and wehave couched Af in the context of saturation excess flow associatedwith VSAs, one could conceptualize impervious areas as portions ofthe landscape with very little soil water deficit, similar to an areawith nearly saturated soils. Regardless, from a water qualityperspective, the impervious areas can be important sources of NPSpollution and deserve targeted management to mitigate this.

So while the generalization of the approach proposed here forquantifying storm runoff risks across a watershed remains an openarea of investigation there are some approaches that are promising.Archibald et al. (2013) have developed a regionalized function thatrelates S to antecedent wetness conditions in rural, agriculturalwatersheds, i.e., where NPS pollution is especially problematic.Combining this with Fennessey and Vogel’s (1990) approach forregionalizing flow duration curves for ungauged basins is a logicalnext-step. In the interim, the Af-return period relationships devel-oped here could be used to identify HSAs for targeted land man-agement by selecting the relationship from the study watershedthat is most similar to one of interest.

The second major challenge is determining how to map theHSAs at different scales and for different parts of the landscape,especially uplands vs. valley bottoms (Fig. 6). Buchanan et al. (2013)show that the STI and TI can capture relative soil moisture

X. Cheng et al. / Journal of Environmental Management 137 (2014) 146e156 155

differences well in upland areas with the STI working best withhigh-resolution (e.g., 3 m) LiDAR data and the TI working best withmore standard USGS DEMs (e.g., 10 m resolution). At large-scales,that will include deep-soil valley bottoms, the TI probably betterrepresents spring conditions, when the water table is near thesurface in the valley bottoms and the STImay be more indicative ofconditions during the summer and early fall.

5. Summary and conclusion

We proposed and demonstrated a bivariate approach that ac-counts for both rainfall and antecedent soil moisture status within awatershed to make risk estimates of runoff generating VSAs. Theobjective of such an approach is to identify the highest risk areas,HSAs, so they can be targeted for management to reduce NPSpollution. Compared to traditional SCS-CN method, our proposedmethod generates more accurate estimates of storm runoff volumeand presumably more accurate estimates of runoff generatingareas. The topographic index concept can be used to map therelative runoff risks. Our approach effectively combines and ex-tends the previous re-interpretations of the SCS-CN rainfall-runoffmodel by Gburek et al. (2002), Lyon et al. (2004), and Shaw andWalter (2009). Some unresolved issues that need more attentioninclude: 1) developing ways to extend risk predictions to un-gauged watersheds, 2) resolving problems with generating topo-graphic indices associated with discontinuities in soil properties atcounty boundaries and with valley bottoms where the water tableeffectively limits the soil depth.

Acknowledgements

This project was funded in part by a grant from the National FishandWildlife Foundation’s Chesapeake Bay Stewardship Fund and incooperation with the Upper Susquehanna Coalition. We would liketo thank the Cornell Soil and Water Lab for their support andassistance in this work. We also appreciate the constructive sug-gestions by two anonymous reviewers and the associate editor,which have improved this manuscript substantially.

References

Agnew, L.J., Lyon, S., Gérard-Marchant, P., Collins, V.B., Lembo, A.J., Steenhuis, T.S.,Walter, M.T., 2006. Identifying hydrologically sensitive areas: bridging the gapbetween science and application. J. Environ. Manag. 78, 63e76.

Archibald, J.A., Mullen, M., Berry, C., Stedman, R., Walter, M.T., 2013. Online hy-drologic tool to minimize phosphorus loading from agriculture (H23A-1230).In: 2013 Fall Meeting, AGU, San Francisco, Calif., 9e13 Dec.

Beven, K.J., Kirkby, M.J., 1979. A physically based, variable contributing area modelof basin hydrology. Hydrol. Sci. Bull. 24, 43e69.

Buchanan, B.P., Easton, Z.M., Schneider, R.L., Walter, M.T., 2012. Incorporating var-iable source area hydrology into a spatially distributed storm runoff model.J. Am. Water Resour. Assoc. 48 (1), 43e60.

Buchanan, B.P., Fleming, M.L., Richards, B.K., Qiu, Z., Schneider, R.L., Walter, M.T.,2013. Evaluating topographic wetness indices across Central New York agri-cultural landscapes. Hydrol. Earth Syst. Sci. (HESS) Discuss. 10, 14041e14093.

Dahlke, H.E., Easton, Z.M., Lyon, S.W., Walter, M.T., Destouni, G., Steenhuis, T.S.,2012a. Dissecting the variable source area conceptesubsurface flow pathwaysand water mixing processes in a hillslope. J. Hydrol. 420, 125e141.

Dahlke, H.E., Easton, Z.M., Walter, M.T., Steenhuis, T.S., 2012b. A field test of thevariable source area interpretation of the curve number rainfall-runoff equa-tion. ASCE J. Irrig. Drain. 37 (3), 235e244.

Dunne, T., Black, R.D., 1970. Partial area contributions to storm runoff in a small NewEngland watershed. Water Resour. Res. 6, 1296e1311.

Easton, Z.M., Fuka, D.R., Walter, M.T., Cowan, D.M., Schneiderman, E.M.,Steenhuis, T.S., 2008. Re-conceptualizing the soil and water assessment tool(SWAT) model to predict saturation excess runoff from variable source areas.J. Hydrol. 348 (3e4), 279e291.

Fennessey, N., Vogel, R.M., 1990. Regional flow-duration curves for ungauged sitesin Massachusetts. ASCE J. Water Resour. Plan. Manag. 116 (4), 530e549.

Fiorentino, M., Iacobellis, V., 2001. New insights about the climatic and geologiccontrol on the probability distribution of floods. Water Resour. Res. 37, 721e730.

Frankenberger, J.R., Brooks, E.S., Walter, M.T., Walter, M.F., Steenhuis, T.S., 1999. A GIS-based variable source area hydrology model. Hydrol. Process. 13, 805e822.

Fry, J.A., 2011. Completion of the 2006 national land cover database for theconterminous United States. Photogramm. Eng. Remote Sens. 77, 858.

Garen, D.C., Moore, D.S., 2005. Curve number hydrology in water quality modeling:uses, abuses, and future directions. J. Am. Water Resour. Assoc. (JAWRA) 41,377e388.

Gburek, W., Drungil, C., Srinivasan, M., Needelman, B., Woodward, D., 2002. Vari-able-source-area controls on phosphorus transport: bridging the gap betweenresearch and design. J. Soil. Water Conserv. 57, 534.

Gesch, D.B., 2007. The national elevation dataset. In: Maune, D. (Ed.), DigitalElevation Model Technologies and Applications: the DEM Users Manual, seconded. American Society for Photogrammetry and Remote Sensing, Bethesda,Maryland, pp. 99e118.

Gesch, D., Oimoen, M., Greenlee, S., Nelson, C., Steuck, M., Tyler, D., 2002. The Na-tional Elevation Dataset: Photogrammetric Engineering and Remote Sensing,vol. 68 (1), pp. 5e11.

Horton, R.E., 1933. The role of infiltration in the hydrologic cycle. Trans. Am. Geo-phys. Union 14, 446e460.

Horton, R.E., 1940. An Approach toward a Physical Interpretation of InfiltrationCapacity, vol. 5, p. 24.

Jiang, R., 2001. Investigation of Runoff Curve Number Initial Abstraction Ratio. M.S.thesis. Univ. of Ariz., Tucson.

Lim, K.J., Engel, B.A., Tang, Z., Choi, J., Kim, K.S., Muthukrishnan, S., Tripathy, D.,2005. Automated web Gis based hydrograph analysis tool, What1. JAWRA J. Am.Water Resour. Assoc. 41, 1407e1416.

Lyon, S.W., Lembo, A.J., 2006. Defining probability of saturation with indicatorkriging on hard and soft data. Adv. Water Resour. 29, 181e193.

Lyon, S.W., Walter, M.T., Gérard-Marchant, P., Steenhuis, T.S., 2004. Using a topo-graphic index to distribute variable source area runoff predicted with the SCScurve-number equation. Hydrol. Process. 18, 2757e2771.

Lyon, S., Seibert, J., Lembo, A., Walter, M., Steenhuis, T., 2006. Geostatistical inves-tigation into the temporal evolution of spatial structure in a shallow watertable. Hydrol. Earth Syst. Sci. 10, 113e125.

Macrae, M., English, M., Schiff, S., Stone, M., 2010. Influence of antecedent hydro-logic conditions on patterns of hydrochemical export from a first-order agri-cultural watershed in Southern Ontario, Canada. J. Hydrol. 389, 101e110.

McCuen, R.H., 2002. Approach to confidence interval estimation for curve numbers.J. Hydrol. Eng. 7, 43.

Merz, R., Blöschl, G., 2009. A regional analysis of event runoff coefficients withrespect to climate and catchment characteristics in Austria. Water Resour. Res.45, W01405.

Michele, C.D., Salvadori, G., 2002. On the derived flood frequency distribution:analytical formulation and the influence of antecedent soil moisture condition.J. Hydrol. 262, 245e258.

Mishra, S.K., Singh, V.P., 2006. A relook at NEH-4 curve number data and antecedentmoisture condition criteria. Hydrol. Process. 20, 2755e2768.

Ponce, V.M., Hawkins, R.H., 1996. Runoff curve number: has it reached maturity?J. Hydrol. Eng. 1, 11e19.

Qiu, Z., Walter, M.T., Hall, C., 2007. Managing variable source pollution in agricul-tural watersheds. J. Soil. Water Conserv. 63 (3), 115e122.

Roland, M.A., Stuckey, M.H., 2008. Regression Equations for Estimating Flood Flowsat Selected Recurrence Intervals for Ungaged Streams in Pennsylvania. ScientificInvestigations Report 2008-5102. USGS.

Schneiderman, E.M., Steenhuis, T.S., Thongs, D.J., Easton, Z.M., Zion, M.S., Neal, A.L.,Mendoza, G.F., Walter, M.T., 2007. Incorporating variable source area hydrologyinto curve number based watershed loading functions. Hydrol. Process. 21 (25),3420e3430.

Shaw, S.B., Riha, S.J., 2011. Assessing possible changes in flood frequency due toclimate change in mid-sized watersheds in New York State, USA. Hydrol. Pro-cess. 25 (16), 2542e2550.

Shaw, S.B., Walter, M.T., 2009. Improving runoff risk estimates: formulating runoffas a bivariate process using the SCS curve number method. Water Resour. Res.45, W03404.

Steenhuis, T.S., Winchell, M., Rossing, J., Zollweg, J.A., Walter, M.F., 1995. SCSrunoff equation revisited for variable-source runoff areas. J. Irrig. Drain. Eng.121, 234e238.

The PRISM Climate Group, 2006. United States Average Monthly or Annual Pre-cipitation, 1971e2000. The PRISM Climate Group at Oregon State University.URL: http://www.prism.oregonstate.edu/products/ (accessed 09.01.10.).

Troch, P.A., Detroch, F.P., Brutsaert, W., 1993. Effective water-table depth to describeinitial conditions prior to storm rainfall in humid regions. Water Resour. Res. 29(2), 427e434.

U.S. Environmental Protection Agency (EPA), March 2005. Agricultural NonpointSource Fact Sheet. EPA 841-F-05-001 URL: http://water.epa.gov/polwaste/nps/agriculture_facts.cfm, (accessed 12.12.13.).

U.S. Environmental Protection Agency (EPA), 2009. National Water Quality In-ventory Report to Congress. URL: http://www.epa.gov/ow/305b/, (accessed12.12.13.).

U.S. Department of Agriculture (USDA) Natural Resources Conservation Service(NRCS) e Soil Survey Staff e Soil Survey Geographic (SSURGO) Database for NYand PA. URL: http://soildatamart.nrcs.usda.gov, (accessed 01.11.10.).

U.S. Department of Agriculture (USDA), Natural Resources Conservation Service(NRCS), 1986. Urban Hydrology for Small Watersheds. TR-55. http://www.cpesc.org/reference/tr55.pdf (accessed 31.12.13.).

X. Cheng et al. / Journal of Environmental Management 137 (2014) 146e156156

U.S. Department of Agriculture (USDA) Soil Conservation Service (SCS), 1972.Hydrology. In: National Engineering Handbook. U.S. Gov. Print. Off, Washington,D.C.

Walter, M.T., Shaw, S.B., 2005. Discussion1. JAWRA J. Am. Water Resour. Assoc. 41,1491e1492.

Walter, M.T., Walter, M.F., Brooks, E.S., Steenhuis, T.S., Boll, J., Weiler, K., 2000. Hy-drologically sensitive areas: variable source area hydrology implications forwater quality risk assessment. J. Soil. Water Conserv. 55, 277.

Walter, M.T., Brooks, E., Walter, M.F., Steenhuis, T.S., Scott, C., Boll, J., 2001. Evalua-tion of soluble phosphorus loading from manure-applied fields under variousspreading strategies. J. Soil. Water Conserv. 56, 329e335.

Walter, M.T., Steenhuis, T.S., Mehta, V.K., Thongs, D., Zion, M., Schneiderman, E.,2002. Refined conceptualization of TOPMODEL for shallow subsurface flows.Hydrol. Process. 16, 2041e2046.

Walter, M.T., Mehta, V.K., Marrone, A.M., Boll, J., Gérard-Marchant, P., Steenhuis, T.S.,2003. Simple estimation of prevalence of Hortonian flow in New York Citywatersheds. J. Hydrol. Eng. 8, 214.

Walter, T., Dosskey, M., Khanna, M., Miller, J., Tomer, M., Wiens, J., 2007. The scienceof targeting within landscapes and watersheds to improve conservation effec-tiveness. Soil Water, 63e89.

Walter, M.T., Archibald, J.A., Buchanan, B., Dahlke, H., Easton, Z.M., Marjerison, R.D.,Sharma, A.N., Shaw, S.B., 2009. New paradigm for sizing riparian buffersto reduce risks of polluted storm water: practical synthesis. J. Irrig. Drain. Eng.135, 200.

Ward, R.C., 1984. On the response to precipitation of headwater streams in humidareas. J. Hydrol. 74, 171e189.