Incorporating Variable Source Area Hydrology into a Curve Number Based Watershed Model

1 Incorporating Variable Source Area Hydrology into a Curve Number Based Watershed Model Elliot M Schneiderman1; Tammo S Steenhuis2; Dominique J Thongs1; Zachary M Easton2; Mark S Zion1; Andrew L Neal2; Guillermo F Mendoza1; M Todd Walter2 10 11 121New York City Department of Environmental Protection, 71 Smith Avenue, Kingston, NY 12401, 13USA 14 152Department of Biological and Environmental Engineering, Cornell University, Ithaca, NY 1614853, USA 17 18 19 20 21Correspondence to: Elliot M Schneiderman, New York City Department of Environmental 22Protection, 71 Smith Avenue, Kingston, NY 12401, USA E-mail: eschneiderman@dep.nyc.gov 23(ph 845 340 7571 fax 845 340 7575) 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 1 1Abstract: 2Many water quality models use some form of the SCS-curve number (CN) equation to predict 3storm runoff from watersheds based on an infiltration-excess response to rainfall However, in 4humid, well-vegetated areas with shallow soils, such as in the northeastern US, the predominant 5runoff generating mechanism is saturation-excess on variable source areas (VSAs) We re6conceptualized the SCS-CN equation for VSAs, and incorporated it into the General Watershed 7Loading Function (GWLF) model The new version of GWLF, named the Variable Source 8Loading Function (VSLF) model, simulates the watershed runoff response to rainfall using the 9standard SCS-CN equation, but spatially-distributes the runoff response according to a soil 10wetness index We spatially validated VSLF runoff predictions and compared VSLF to GWLF 11for a sub-watershed of the New York City Water Supply System The spatial distribution of 12runoff from VSLF is more physically realistic than the estimates from GWLF This has important 13consequences for water quality modeling, and for the use of models to evaluate and guide 14watershed management, because correctly predicting the coincidence of runoff generation and 15pollutant sources is critical to simulating non-point source (NPS) pollution transported by runoff 16 17 18Key Words: curve number; variable source area hydrology; runoff; watershed modeling; GWLF; 19non-point source pollution 1Introduction: 2Watershed models that simulate streamflow and pollutant loads are important tools for managing 3water resources These models typically simulate streamflow components, baseflow and storm 4runoff, from different land areas and then associate pollutant concentrations with the flow 5components to derive pollutant loads to streams Storm runoff is the primary transport 6mechanism for many pollutants that accumulate on or near the land surface Accurate simulation 7of pollutant loads from different land areas therefore depends as much on realistic predictions of 8runoff source area locations as on accurate predictions of storm runoff volumes from the source 9areas 10 11The locations of runoff production in a watershed depend on the mechanism by which runoff is 12generated Infiltration-excess runoff, also called Hortonian flow (e.g., Horton 1933, 1940), occurs 13when rainfall intensity exceeds the rate at which water can infiltrate the soil Soil infiltration rates 14are controlled by soil characteristics, vegetation, and land use practices that affect the infiltration 15characteristics of the soil surface In contrast, saturation-excess runoff occurs when rain (or 16snowmelt) encounters soils that are nearly or fully saturated due to a perched water table that 17forms when the infiltration front reaches a zone of low transmission (USDA-SCS, 1972) The 18locations of areas generating saturation-excess runoff, typically called variable source areas 19(VSAs), depend on topographic position in the landscape and soil transmissivity VSAs expand 20and contract in size as water tables rise and fall, respectively Since the factors that control soil 21infiltration rates differ from the factors that control VSAs, models that assume infiltration-excess 22as the primary runoff-producing mechanism will depict the locations of runoff source areas 23differently than models that assume saturation-excess 2In humid, well-vegetated areas with shallow soils, such as the northeastern United States, 3infiltration-excess does not always explain observed storm runoff patterns For shallow soils 4characterized by highly permeable topsoil underlain by a dense subsoil or shallow water table, 5infiltration capacities are generally higher than rainfall intensity, and storm runoff is usually 6generated by saturation-excess on VSAs (Dunne and Leopold 1978, Beven 2001, Srinivasan et 7al., 2002, Needleman et al., 2004) Walter et al (2003) found that rainfall intensities in the 8Catskill Mountains, NY rarely exceeded infiltration rates, concluding that infiltration-excess is 9not a dominant runoff generating mechanism in these watersheds 10 11The Generalized Watershed Loading Function (GWLF) model (Haith and Shoemaker 1987, 12Schneiderman et al., 2002) uses the US Department of Agriculture (USDA) Soil Conservation 13Service (SCS, now NRCS) runoff curve number (CN) method (USDA-SCS 1972) to estimate 14storm runoff for different land uses or hydrologic response units (HRUs) GWLF, like many 15current water quality models, uses the SCS-CN runoff equation in a way that implicitly assumes 16that infiltration-excess is the runoff mechanism In short, each HRU in a watershed is defined by 17land use and a hydrologic soil group classification via a “CN value” that determines runoff 18response CN values for different land use / hydrologic soil group combinations are provided in 19tables compiled by USDA (e.g., USDS-SCS 1972, 1986) The hydrologic soil groups used to 20classify HRUs are based on infiltration characteristics of soils (e.g., USDA-NRCS 2003) and thus 21clearly assume infiltration-excess as the primary runoff producing mechanism (e.g Walter and 22Shaw, 2005) 23 1Here, we describe a new version of GWLF termed the Variable Source Loading Function (VSLF) 2model that simulates the aerial distribution of saturation-excess runoff within the watershed The 3VSLF model simulates runoff volumes for the entire watershed using the standard SCS-CN 4method (as does GWLF), but spatially distributes the runoff response according to a soil wetness 5index as opposed to land use/hydrologic soil group as with GWLF We review the SCS-CN 6method and the theory behind the application of the SCS-CN equation to VSAs, validate the 7spatial predictions made by VSLF, and compare model results between GWLF and VSLF for a 8watershed in the Catskill Mountains of New York State to demonstrate differences between the 9two approaches 10 11Review of SCS-CN Method: 12The SCS-CN method estimates total watershed runoff depth Q (mm) for a storm by the SCS 13runoff equation (USDA-SCS 1972): 14 Q 15  Pe   Pe  S e  (1) 16 17where Pe (mm) is the depth of effective rainfall after runoff begins and Se (mm) is the depth of 18effective available storage (mm), i.e., the spatially-averaged available volume of retention in the 19watershed when runoff begins We use the term effective and the subscript “e” to identify 20parameter values that refer to the period after runoff starts Although Se in Eq is typically 21written simply as S, this term is clearly defined for when runoff begins as opposed to when 22rainfall begins (USDA-SCS 1972); thus we refer to it as Se 23 1At the beginning of a storm event, an initial abstraction, Ia (mm), of rainfall is retained by the 2watershed prior to the beginning of runoff generation Effective rainfall, Pe, and storage, Se, are 3thus (USDA-SCS 1972): P e = P – Ia (2a) Se = S – Ia (2b) 8where P (mm) is the total rainfall for the storm event and S (mm) is the available storage at the 9onset of rainfall In the traditional SCS-CN method, Ia is estimated as an empirically-derived 10fraction of available storage: 11 12 Ia = 0.2 Se (3) 13 14Effective available storage, Se, depends on the moisture status of the watershed and can vary 15between some maximum Se,max (mm) when the watershed is dry, eg during the summer, and a 16minimum Se,min (mm) when the watershed is wet, usually during the early spring The Se,max and 17Se,min limits have been estimated to vary around an average watershed moisture condition with 18corresponding Se,avg (mm) based on empirical analysis of rainfall-runoff data for experimental 19watersheds (USDA-SCS 1972, Chow et al., 1988): 20 21 Se,max = 2.381 Se,avg (4) 22 Se,min = 0.4348 Se,avg (5) 23 1Se,avg is determined via table-derived CN values for average watershed moisture conditions (CNII) 2and a standard relationship between Se and CNII  100  S e,avg 254  1  CN II  (6) 6However, for most water quality models, Se,avg (mm) is ultimately a calibration parameter that is 7only loosely constrained by the USDA-CN tables CNII and Se,avg can be derived directly from 8baseflow-separated streamflow data when such data are available (USDA-NRCS 1997, NYC 9DEP 2006) 10 11In the original SCS-CN method, Se varies depending on antecedent moisture or precipitation 12conditions of the watershed (USDA-SCS 1972) For VSA watersheds, a preferred method varies 13Se directly with soil moisture content We use a parsimonious method adapted from the USDA 14SPAW model (Saxton, 2002) The value of Se is set to Se,min when unsaturated zone soil water is 15at or exceeds field capacity, and is set to Se,max when soil water is less than or equal to a fixed 16fraction of field capacity (a parameter termed spaw cn coeff in VSLF) which is set to 0.6 in the 17SPAW model but can be calibrated in VSLF Se is derived by linear interpolation when soil water 18is between Se,min and Se,max thresholds 19 20SCS-CN Equation Applied to VSA Theory: 21The SCS-CN equation, Eq 1, constitutes an empirical runoff/rainfall relationship It is therefore 22independent of the underlying runoff generation mechanism, i.e., infiltration-excess or saturation23excess In fact, the originator of Eq 1, Victor Mockus (Rallison 1980), specifically noted that Se 1is either “controlled by the rate of infiltration at the soil surface or by the rate of transmission in 2the soil profile or by the water-storage capacity of the profile, whichever is the limiting factor” 3(USDA-SCS 1972) Interestingly, in later years he reportedly said “saturation overland flow was 4the most likely runoff mechanism to be simulated by the method…” (Ponce 1996) 6Steenhuis et al (1995) showed that Eq could be interpreted in terms of a saturation-excess 7process Assuming that all rain falling on unsaturated soil infiltrates and that all rain falling on 8areas that are fully or partly saturated, , becomes runoff, then the rate of runoff generation will be 9proportional to the fraction of the watershed that is effectively saturated, Af, which can then be 10written as: 11 12 Af  Q Pe (7) 13 14where ΔQ is incremental saturation-excess runoff or, more precisely, the equivalent depth of 15excess rainfall generated during a time period over the whole watershed area, and ΔPe is the 16incremental depth of precipitation during the same time period Eq precisely defines Af when 17Q is defined as saturation-excess runoff If Q includes runoff generated by other 18mechanisms, including infiltration excess runoff or upslope subsurface flow, then Af may be 19overestimated Since the soil upslope is unsaturated (with a low hydraulic conductivity) we 20expect the flow from upslope to be small In the remaining Q is exclusively saturation21excess runoff 22 1By writing the SCS Runoff Equation (1) in differential form and differentiating with respect to 2Pe, the fractional contributing area for a storm can be written as: Af = Se  Pe + S e 2 (8) 6According to (8) runoff only occurs on areas which have a local effective available storage e 7(mm) less than Pe Therefore by substituting e for Pe in eq we have a relationship for the 8percent of the watershed area, As, which has a local effective soil water storage less than or equal 9to e for a given overall watershed storage of Se: As = 10 Se  e + S e 2 (9) 11 12Solving for e gives the maximum effective (local) soil moisture storage within any particular 13fraction As of the overall watershed area for a given overall watershed storage of Se: 14 15 16    e  S e   1  (1  As )  (10) 17 18or, expressed in terms of local storage,  (mm), when rainfall begins (as opposed to when runoff 19begins): 20     S e   1  I a  (1  As )  (11) 3Equation 11 is illustrated conceptually in Fig For a given storm event with precipitation P, the 4location of the watershed that saturates first (As = 0) has local storage  equal to the initial 5abstraction Ia, and runoff from this location will be P – Ia Successively drier locations retain 6more precipitation and produce less runoff according to the moisture – area relationship of eq 11 7The driest location that saturates defines the runoff contributing area (Af) for a particular storm of 8precipitation P The reader is reminded that both Se and Ia are watershed-scale properties that are 9spatially invariant 10 11As average effective soil moisture (Se) changes through the year, the moisture-area relationship 12will shift accordingly as per Eq 10 However, once runoff begins for any given storm, the 13effective local moisture storage, e, divided by the effective average moisture storage, Se, 14assumes a characteristic moisture-area relationship according to Eq 10 that is invariant from 15storm to storm (Fig 2) 16 17Runoff q (mm) at a point location in the watershed can now also be expressed for the saturated 18area simply as: 19 20 q = Pe –e for Pe >e, 21 22and for the unsaturated portion of the watershed: 10 (12) 1watershed wetness, which is a conceptual improvement over the constant S approach used by 2Steenhuis et al (1995) and Lyon et al (2004) In addition, the method presented here predicts 3spatially variable runoff depths within a saturated area, whereas the Lyon et al (2004) approach 4assigns a single runoff depth to the entire saturated area Since this is an average depth, the Lyon 5et al (2004) approach will under predict the amount of runoff generated near streams, which may 6be a critical area of non-point contaminant loading in many watersheds Some other minor 7differences between the Lyon et al (2004) approach and the new version are that the initial 8abstraction used here is a constant fraction of the average storage while Lyon et al (2004) used a 9water budget approach In both cases Ia changes with watershed wetness so it is not obvious that 10one approach is more realistic than the other 11 12Accurate prediction of the spatial distribution of runoff production has important consequences 13for simulation of pollutants that are typically transported by runoff Many water quality 14protection concepts have been developed based on results from models like GWLF, which link 15runoff and pollutant concentrations to land use As a result, we have sometimes focused too much 16attention on specific land uses and largely ignored the interaction between land management and 17landscape position; indeed, Garen and Moore (2005) have explicitly noted this problem for all 18models that use the SCS-CN method in similar ways For example, our GWLF simulations 19suggest that nutrient management should be focused entirely on cornfields (Fig 9c, e) However, 20VSLF, which better represents the spatial hydrological patterns, indicates that control of nutrients 21from areas near streams might be more logical locations to focus water quality protection efforts 22In this case grasslands located in high runoff producing areas constitute a potentially important 23land use to manage (Fig 9d, f) More importantly, VSLF provides a more complete picture of 20 1intra-watershed processes and facilitates a broader range of potentially important NPS pollution 2processes It should probably be noted that the original GWLF (Haith and Shoemaker, 1987) was 3not designed to give this level of spatially explicit detail, and VSLF represents the way that 4models may get diverted over time from their original scope of purpose (e.g., Garen and Moore, 52005; Walter and Shaw, 2005) 7Conclusions: 8The SCS-CN method for estimating runoff is used in many current nonpoint source pollution 9models to simulate infiltration-excess runoff These models assume that runoff generation and 10pollutant loading are tightly linked to land use, and other factors that directly impact soil 11infiltration capacity For humid, well-vegetated watersheds, however, saturation-excess on VSAs 12is the predominant runoff mechanism, and runoff generation is more indicative of landscape 13position than land use We describe an alternative SCS-CN-based approach to predicting runoff 14that is applicable to VSA watersheds and should be relatively easy to implement in existing 15models We spatially validated the predictions made by the model and, as a demonstration, 16showed that in watersheds where saturation-excess is the dominant runoff process the new VSLF 17model provides a much more valid spatial distribution of runoff generation than current SCS-CN 18based water quality models 19 20Acknowledgments: 21We would like to acknowledge our reviewers, one of which pointed out that that variable source 22areas not have to be saturated to the surface to produce runoff This is correct and has led us to 23redefine the definition of storm runoff and variable source areas Other reviewers also made very 21 1helpful comments and due to their efforts the manuscript has improved greatly The USDA2CSREES, USDA-NRI, and NSF-REU programs partially funded the involvement of the Soil and 3Water Lab from Cornell’s Biological and Environmental Engineering Department 22 1References: 2Agnew, L.J., S Lyon, P Gérard-Marchant, V.B Collins, A.J Lembo, T.S Steenhuis, M.T Walter 32006 Identifying hydrologically sensitive areas: Bridging science and application J Envir Mgt 478: 64-76 6Arnold, J.G., R Srinivasan, R.S Muttiah, J.R Williams 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in water quality 31modeling: Uses, abuses, and future directions” by Garen and Moore J Am Water Resour Assoc 3241(6): 1491-1492 33 34Western, A.W., R.B Grayson, G Bloschl, G.R Willgoose, T.A McMahon 1999 Observed 35spatial organization of soil moisture and its relation to terrain indices Water Resources Research 3635(3): 797-810 37 38Western, A.W., S.L Zhou, R.B Grayson, T.A McMahon, G Bloschl, D.J Wilson., 2004 Spatial 39correlation of soil moisture in small catchments and its relationship to dominant spatial 40hydrological processes Journal of Hydrology 286(1-4): 113-134 41 42 43 44 45 25 1Figure Captions: 3Figure Relationship of available local moisture storage,  , to the fraction of watershed area 4contributing runoff (As) 6Figure Relationship of effective local moisture storage, e , normalized to effective average 7moisture storage Se, to the fraction of watershed area contributing runoff (As) 9Figure Location Map of the Cannonsville watershed 10 11Figure A) Observed and VSLF simulated event runoff (mm) from the Cannonsville watershed, 12and B) scatterplot of observed vs predicted event runoff for 1992-1999 Observed event runoff 13estimated by baseflow separation of daily streamflow hydrograph Nash-Sutcliffe efficiency was 140.86 15 16Figure Probability of saturation for runoff-event predictions for a Cannonsville sub-watershed 17using VSLF model and the Soil Moisture Distribution and Routing (SMDR) model Soil moisture 18sampling transects used in Fig are shown on the VSLF map 19 20Figure Observed and simulated soil moisture levels at the initiation of rainfall (long dashed 21line) and runoff (solid line) from three transects in the watershed Grey area represents observed 22sampling error Short vertical dashed line represents a transition between wetness index classes 23based on the topographic index 24 25Figure Scatter plot of observed and the Variable Source Loading Function (VSLF) model 26simulated soil moisture levels from five dates and three transects in both the growing and 27dormant seasons in the R-Farm sub watershed Since numerous observed values fall with in the 28same index class along the transect, the mean observed value was regressed against each 29individual index class Horizontal bars represent the standard error of the observed saturation 30degree for each index class 31 32Figure Scatter plot of the Generalized Watershed Loading Function (GWLF) model versus the 33Variable Source Loading Function (VSLF) model simulated event runoff for the Cannonsville 34watershed 35 36Figure Maps, for an example sub-area of Cannonsville watershed, of (a) Land use; (b) wetness 37index; (c) mean July runoff predicted by GWLF; (d) mean July runoff predicted by VSLF; (e) 38mean April runoff predicted by GWLF; (f) mean April runoff predicted by VSLF Corn fields are 39outlined in heavy black lines 40 26 250 200 150  100 P 50 Ia Q Retained 0 0.2 0.4 0.6 As Af 0.8 1 2Figure Relationship of available local moisture storage,  , to the fraction of watershed area 3contributing runoff (As)  e /Se As 9Figure Relationship of effective local moisture storage, e, normalized to effective average 10moisture storage Se, to the fraction of watershed area contributing runoff (As) 27 3Figure Location map of the Cannonsville watershed 28 (A) Runoff (mm) 120 Measured Predicted 60 1992 1993 1994 1995 1996 Year Runoff (mm) 120 Measured Predicted 60 1996 1997 1998 Year 1999 2000 (B) Predicted (mm) 120 90 60 30 0 30 60 90 Measured (mm) 120 8Figure A) Observed and VSLF simulated event runoff (mm) from the Cannonsville watershed, 9and B) scatterplot of observed vs predicted event runoff for 1992-1999 Observed event runoff 10estimated by baseflow separation of daily streamflow hydrograph Nash-Sutcliffe efficiency was 110.86 29 4Figure Probability of saturation for runoff-event predictions for a Cannonsville sub-watershed 5using VSLF model and the Soil Moisture Distribution and Routing (SMDR) model Soil moisture 6sampling transects used in Fig are show on the VSLF map 30 2Figure Observed and simulated soil moisture levels at the initiation of rainfall (long dashed 3line) and runoff (solid line) from three transects in the watershed Grey area represents observed 4sampling error Short vertical dashed line represents a transition between wetness index classes 5based on the topographic index 31 3Figure Scatter plot of observed and the Variable Source Loading Function (VSLF) model 4simulated soil moisture levels at runoff from five dates and three transects in both the growing 5and dormant seasons in the R-Farm sub watershed Since numerous observed values fall with in 6the same index class along the transects the mean observed value was regressed against each 7individual index class Horizontal bars represent the standard error of the observed saturation 8degree for each index class 32 GWLF Runoff (cm) r2=0.99 0 VSLF Runoff (cm) 3Figure Scatter plot of the Generalized Watershed Loading Function (GWLF) model vs the 4Variable Source Loading Function (VSLF) model simulated event runoff for the Cannonsville 5watershed 33 a) Land Use b) Wetness Index stream corn forest-deciduous water road-rural alfalfa grass forest-coniferous grass-shrub Dry Wet 10 Wetness Index Class c) GWLF: July Runoff d) VSLF: July Runoff e) GWLF: April Runoff f) VSLF: April Runoff Dry 0.0 Wet 10.7 Runoff Depth (cm) 0.5 km 3Figure Maps, for an example sub-area of Cannonsville watershed, of (a) Land use; (b) Wetness 4index; (c) Mean July runoff predicted by GWLF; (d) Mean July runoff predicted by VSLF; (e) 5Mean April runoff predicted by GWLF; (f) Mean April runoff predicted by VSLF Corn fields are 6hatch marked and outlined in heavy black lines 34 ... 18locations of areas generating saturation-excess runoff, typically called variable source areas 19(VSAs), depend on topographic position in the landscape and soil transmissivity VSAs expand 20and... contributing area (Af) for a particular storm of 8precipitation P The reader is reminded that both Se and Ia are watershed- scale properties that are 9spatially invariant 10 11As average effective... predicts 3spatially variable runoff depths within a saturated area, whereas the Lyon et al (2004) approach 4assigns a single runoff depth to the entire saturated area Since this is an average depth,