October 2011TERRA Watershed Model OverviewHydrologic, Sediment Transport, andChemical Transport Model FormulationsMark Velleux, Paul Paquin,Aaron Redman, and Robert Santore2Tool for Antimicrobial AssessmentszScreening process for agricultural pesticides iswell-established, but not for antimicrobialszAntimicrobials differ from agricultural pesticides“[D]etermining human and ecological risks fromexposure to antimicrobial pesticides requires differenttypes of measurements and models than thoseneeded for pesticides largely applied to crops andother plants.” (http://www.epa.gov/oppad001/)zTERRA is a tool that can address the spatiallydistributed nature of antimicrobial copper usesBasis for TERRA DevelopmentzSurface water is often derived from watershed sourceszMany water-borne chemical have their source far from theirpoint of impact:upland source, downstream impactzDegree of Interaction between land and receiving waters iscontrolled by the surface component of the hydrologic cyclezNeed to understandlink between rainfall, runoff, soil erosionand chemical delivery to receiving waterszExample: Total Maximum Daily Load (TMDL) assessments,pesticide exposure concentrations, etc.zIt all starts with rainfall and the hydrologic cycle...3InfiltrationThe Hydrologic CycleInfiltrationOur focus is rainfall-runoff and itsinfluence on chemical exposures4Spatial and Temporal Scales of InterestzDifferent processes predominateat different space and time scaleszOur focus: watershed scale...zLand surface and stream channelszSpace scale: ~1 to ~10,000 km2zTime scale: storm events, annual+zGrid scale vs. model performancezLumped Parameter: entire watershed(Blue Line)zSemi-Distributed: sub-watershedwithin watershed(Orange Lines)zDistributed: many cells withinwatershed(Purple Boxes)zGrid scale: < 1,000 m,often 30-90 m5Conditions for each compartmentare represented as an average ofeverything in that compartment...Grid Size Alters Computed Sediment Delivery30-m90-m150-m210-m330-m270-m300-m110101010110 10 1010Drainage areaA(mi )

S DRt2-1-2-2-1 2 34SDR= 0.31A(Ain mi )tt2-0.3SDR= 0.41A(Ain km )tt2-0.3Drainage areaA(km )t210110 10 10 10-1234(after Boyce, 1975)6TERRA Watershed Model OriginszTERRA: Two-dimensional Exposure Rainfall-Runoff AnalysiszPublication and peer-review history under the name TREX:Two-dimensional Runoff Erosion and ExportzDerived from the CASC2D family of watershed modelsdeveloped at Colorado State University (USEPA sponsored)zChemical transport capability derived from USEPA WASPfamily of exposure models: IPX (EPA/600/R-01/074)zFully distributed (grid-based), physically-based processeszUses GIS to pre/post-process model inputs and outputszEvent hydrology, sediment transport, chemical transport7Erosion of UplandSources...Why Was TERRA Developed?zNeeded a tool to link upland sources todownstream effects at the watershed scaleDownstreamImpacts...8TERRA Watershed model: Two-DimensionalExposure Rainfall-Runoff Analysishttp://www.engr.colostate.edu/%7Epierre/ce_old/Projects/TREX%20Web%20Pages/TREX-Home.html9Model ImplementationzHydrology:zRainfall (Uniform, Distributed, more options in future)zInfiltration and Transmission Loss (Green and Ampt)zOverland (2-D) and Channel (1-D) Flow (Diffusive Wave)zSediment Transport:zAdvection (and Dispersion)zErosion and DepositionzChemical Transport:zPhase Distribution (Equilibrium Partitioning)zTransport by Phase: Dissolved, Bound, ParticulatezInfiltration of Dissolved and Bound (Mobile) Phase10Some TERRA-Related Model Uses (Part 1)11SiteArea (km2)Study PurposeReferenceMacks Creek, ID32hydrologyJulien and Saghafian(1991)Taylor Arroyo, CO120effects of military maneuversDoe et al. (1996)Hickahala/Senatobia, MS560hydrology, grid scaleMolnar and Julien (2000)Belize River, Belize1,493hydrology, extreme floodsWagenseil (1999)Hassayampa Creek, AZ1,111flashflood forecastingJorgeson (1999)Cave Creek, AZ349flash flood forecastingJorgeson (1999)Spring Creek, CO25flash flood modelingOgden et al. (2000)Little Washita, OK536initial soil moisture,infiltrationSpah (2000)Some TERRA-Related Model Uses (Part 2)12SiteArea (km2)Study PurposeReferenceQuebrada Estero, CostaRica2.5hydrology, flooding,urbanizationMarsik and Waylen (2006)Goodwin Creek, MS20.7hydrology, sediment, gridscale effectsJohnson et al. (2000)Julien and Rojas (2002)Rojas et al. (2008)Arkansas River, CO12,000hydrology, extreme floodsEngland et al. (2007)California Gulch, CO30.6hydrology, sediments,metals (Cd, Cu, Zn)Velleux et al. (2006)Black Earth Creek, WI0.08hydrology, floodingBoyington (2010)Naesung Stream, Korea1,825hydrology, sedimentsVelleux et al. (2011)Experimental Test Plotsbench-scalechemicals (RDX, TNT)Johnson et al. (2011)13Hydrologic Model FormulationTERRA Watershed Model:Hydrology Model Formulationhttp://www.engr.colostate.edu/%7Epierre/ce_old/Projects/TREX%20Web%20Pages/TREX-Home.html14Surface Hydrology Processes in TERRAzHortonian (precipitation excess) Runoff (events)zRainfall: gages (points) or radar (area)zInterception, Surface Depression StoragezGreen and Ampt Infiltration/Transmission Lossz2-D Diffusive Wave Overland Flow Routingz1-D Diffusive Wave Channel Routing15Land Surface and Stream ChannelszTwo separate domains (and state variables):zOverland PlanezChannel Network (nested in overland plane)zOverland and channel areas interact via floodplainzChannel Geometry: general trapezoid...Trapezoidal (B > 0, Z > 0)Rectangular (B > 0, Z = 0)Triangular (B = 0, Z > 0)zChannel top width (T)≤80% of grid cell width (W)hbankTB1ZW16Gross RainfallzTwo Options: (1) point values, (2) gridded valueszPoint values (gage data):zSpatial interpolation by Inverse Distance Weighting (IDW)with user-defined exponent and radius of influencezGages linearly interpolated in time before spatial IDWzGridded values (radar data):zPre-processed to match model grid scalezValues constant over time interval between updates()()∑∑=nPnnPnngrossyxddii1,17Interception and Net RainfallzInterception is the retention of gross rainfall byvegetated (and constructed) surfaces before therainfall reaches the groundzPhysically, controlled by surface tension and gravityzTypically amounts to ~ 1-2 mm (more or less) of rainfallzRepresented as rainfall depth retained per unit timezNet rainfall is gross rainfall minus interception0oninterceptifor0oninterceptiforonintercepti,yx,,,=>−=grossyxgrossyxnetyxiii18Infiltration and Transmission LosszGreen and Ampt (1-D, vertical):zSingle eventszNo soil moisture redistribution (limited to events!)zFor infiltration: neglectHw()( )reeecwhFSHHKf 

# θφθ θ−=⎥⎦⎤⎢⎣⎡−++=1119Hydrology: Overland Flow (2-D)zContinuity and Momentum, Diffusive Wave:zFlow depth must exceed depression storage depthyhSSxhSSnShqfiyqxqthoyfoxfyxfyxyxyxyx∂∂−=∂∂−====−=∂∂+∂∂+∂∂355.0,,,, 

# β

αα

β20Hydrology: Channel Flow (1-D)zContinuity and Momentum, Diffusive Wave:zFlow depth must exceed dead storage depth of channelxhSSSRnAQvqtAxQoxfxfhxL∂∂−====∂∂+∂∂5.0667.0121Floodplain CouplingzControls: water surface elevation and bank heightTo ChannelTo Overland Plane22Data Needed To Run The Hydrology ModelzDigital elevation model (DEM) data: S0zSoil and Sediment characteristics:KH,Hc,φ,θrzLand use characteristics: interception, ManningnzPrecipitation data (time series):igrosszChannel characteristics: topology,B,Z,hbankzInitial conditions: water depths overland (hov), inchannel (hch), and depth of wetting front (Fov,Fch)23Main Hydrology Model ParameterszInfiltration:zsaturated (effective) hydraulic conductivity,KhzOverland and Channel FlowzManningnzHowever, these constants are not really constant!zSoil characteristics vary with depth and a subsurfacelayer may control hydraulic conductivity and infiltrationzManningnvaries with flow depth, submergence, etc...24This is why calibration is beneficial25Sediment Transport Model FormulationOverland Erosion and Deposition...Hillslope Erosion...26Valley Deposition...TERRA Watershed Model:Sediment Transport Model Formulationhttp://www.engr.colostate.edu/%7Epierre/ce_old/Projects/TREX%20Web%20Pages/TREX-Home.htmlSurface ElevationChange Over Timetz∂∂Soil &Sediment27Surface Sediment Transport ProcesseszOverland: Sheet and rill soil erosionzChannels: bed erosion (degradation/aggradation)zAdvection: total load (transport capacity)zDeposition: gravity sedimentation modified byprobability of depositionzSurface elevation change over time (dynamic bed)zLots of (not fully tested) for cohesive and noncohesive transport...28Point of Departure: Soil Erosion and USLEzUniversal Soil Loss Equation: USLE→MUSLE→RUSLE...zImplied incipient motion threshold is zero...zBest Use: Long-term annual average erosionPCKSLRJErosion*****=DEMHydraulics (i.e. flow)?Climate (Rainfall)Land UseSoilsEmpirical,no physics!29Overland Erosion (Applied in 2-D)zModified Kilinc-Richardson equation for sheet and rillerosion (total load→bed load):PCKhvWQSsmtonsqcft15.025500)//(035.266.1⎟⎠⎞⎜⎝⎛−=SoilsDEM (and Hydraulics)Added Incipient Motion ThresholdLand UseHydraulics30Generalized Overland Transport CapacityzErosion is a function of overland flow and slope etc.:zkis a function of soil type and erodibility, cohesion, particlesize, etc.zParameters:β= 1.4 (1.0 – 1.8),λ= 1.4 (0.9 – 1.8)zCan express incipient motion threshold as:q’= (q–qc)[] 

# λβSqkTLMqt=//31zModified Engelund and Hansen equation:( )[ ]( )5.05.011105.0⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛−−⎟⎠⎞⎜⎝⎛−=sfhsfcfwdGSRgdGSVVSGGCChannel Erosion (1-D)HydraulicsParticle CharacteristicsAdded Incipient Motion Threshold32Data Needed To Run The Sediment ModelzEverything for the hydrologic model plus...zParticle types:ds,ws, optional:τcd,vc...zSoil and Sediment characteristics:K, grain size...zLand use characteristics:C,PzSoil and Sediment stacks: areal and verticaldistribution of soil and sediment characteristicszInitial conditions: concentrations in surface water33Main Calibration ParameterszErosion:zSoil erodibility (K), erosion threshold as critical velocity(vc) or shear stress for erosion (τce)zDeposition:zParticle fall velocity (ws), shear stress for deposition (τcd)zOther parameters (but usually less variable):zLand cover and management practice factors (C,P)zEffective diameter of fine, cohesive soil/sediment (ds)34Grid Scale Matters for Erosion!zGoodwin Creek, MS Case Study: Rojas et al. 2008zModel grid, soils, and land use resampled to fiveupscaled resolutions: 90, 150, 210, 270 and 330-m.zCell aggregation alters land surface (slope) andchannel network (drainage density).zThis affects surface hydrology and soil erosioncalculations: infiltration, flow volume, peak flow,time to peak, gross erosion, deposition, etc...zScale effects for other model parameters?35Effect of Grid Size on SlopeNearly complete loss of resolution as grid size increases...Grid Scale Maximum and Average SlopeDecrease While Minimum Slope IncreasesMean SlopeDecrease: 3%→1%Maximum SlopeDecrease: 13.5%→2%Minimum SlopeMinor Increase: 0.25%•Flow and sediment transport depend on slope...37Erosion and Deposition Over Time**Net difference between erosion and deposition.38Alteration of Sediment Transport Patterns30 m(0.22 acres)90 m(2 acres)150 m(5.5 acres)210 m(11 acres)270 m(18 acres)330 m(27 acres)From whichlocations dosoils reallyerode?What if there aresorbed chemicalson soils?Even if eroded soilmass is correct, iscorrect chemicalmass eroded?39As Grid Size Increases SDR Is Unrealistic30-m90-m150-m210-m330-m270-m300-m110101010110 10 1010Drainage areaA(mi )

S DRt2-1-2-2-1 2 34SDR= 0.31A(Ain mi )tt2-0.3SDR= 0.41A(Ain km )tt2-0.3Drainage areaA(km )t210110 10 10 10-1234(after Boyce, 1975)4041Chemical Transport Model FormulationTERRA Watershed Model:Chemical Transport Model Formulationhttp://www.engr.colostate.edu/%7Epierre/ce_old/Projects/TREX%20Web%20Pages/TREX-Home.htmlSurface Elevation Change Over Timetz∂∂Soil &Sediment,tc∂∂zc∂∂42Model ImplementationzHydrology:zRainfall (Uniform, Distributed, more options in future)zInfiltration and Transmission Loss (Green and Ampt)zOverland (2-D) and Channel (1-D) Flow (Diffusive Wave)zSediment Transport:zAdvection (and Dispersion)zErosion and DepositionzChemical Transport:zPhase Distribution (Equilibrium Partitioning)zTransport by Phase: Dissolved, Bound, ParticulatezInfiltration of Dissolved and Bound (Mobile) PhasePlus: Non-equilibrium,reactive particle phase43Chemical Transport ProcesseszEquilibrium partitioning and phase distributionzNon-equilibrium reactive particle phase:zA particle state variable that reacts with the end product of reactionbeing a chemical state variablezUseful for simulating granular “pure phase” chemicals such as slagweathering, metals release from granules, DU release from rods...zDeposition: gravity sedimentation with option to modify byprobability of deposition (Gessler, Krone, Parthenaides)zSoil and sediment chemical concentration change over timezChemical reactions, products and pathways:zChemical state variables and react and interconvertzCan be used to simulate non-equilibrium partitioning44zChemicals can start transport in one phase and may bedelivered downstream in a different phase...zPhase distribution controlled by partition coefficient (¶pn),solids concentration (m), DOC binding coefficient (¶DOC),and DOC concentration (CDOC):Cd= freely dissolved chemical concentration (pore volume basis),rn= chemical concentration sorbed to particle “n”, Cb= boundchemical concentration (on a pore volume basis)Chemical Partitioning and BindingdnnpCr=¶∑=+=Nnxnpnnpnpxm1¶1¶¶ 

# ν45zThe mass fraction of chemical associated with dissolved(fd), bound (fb), and particulate phase (for “n” phases) (fpn):Multi-Phase Chemical Distribution∑=++=NnnpxnbDOCdmCf1¶¶11∑=++=NnnpxnbDOCbDOCbmCCf1¶¶1¶∑=++=NnnpxnbDOCnpxnnpmCmf1¶¶1¶11=++∑=NnnpbdfffThe total chemical is the sum of all phases46Aspects of ImplementationzUser-defined number of chemical types (unlimited)zTwo separate domains (and state variable sets):zOverland Plane and soil stackzChannel Network and sediment stackzOverland and channel areas interact via floodplainzSoil and sediment stacks allow 3-D representationof chemical distributionszGranular non-equilibrium phase not included inreported chemical concentration (post-process!)47Data Needed To Run The Chemical ModelzEverything for the hydrologic model plus...zEverything for the sediment model plus...zChemical characteristics:KPOC, KDOC, reactionrates, yields, products, and pathways...zInitial chemical concentrations in surface water(overland and channels), soils, and sedimentszEnvironmental characteristics:CDOC,foc(for eachparticle type), temperature,pH, wind speed...48Chemical Transport ParameterszPartitioning and Binding:zKp(KPOC), Kb(KDOC)zProcess Rates and Mass Transfer Coefficients...zParameters depend on processes simulatedzEnvironmental parameters and constants:zPOC, DOC, pH, temperature lapse rate, wind speedzDepend on processes simulated...4950TERRA SummarySummaryzTERRA:zGrid-based, fully-distributed, physically-basedwatershed modelzThree Components:zHydrology (rainfall, surface runoff, and infiltration)zSediment Transport (any number of solids types)zChemical Transport and Fate (any number of chemicals)zGIS-based model set-up using GIS software (ArcGIS):zinput pre-processing (delineate watershed, channels, soil, etc.)zoutput post-processing (animate model results, map algebra, etc.)51What TERRA Can SimulatezSingle Rainfall Events and Pseudo-Continuous RainfallzOverland and Channel Flow:zBi-directional floodplain water (sediment and chemical) transferszSediment Transport:zAny number of grain sizes (particle types)zErosion and deposition overland and in channel networkzChemical Transport and Fate:zAny number of chemicalszEquilibrium partitioning (other reactions...)52ÅIncludes impervious areas!More Features Can Be Added As NeededzSome things TERRA doesn’t simulate right now:zEvapotranspiration, lateral groundwater flowzGully erosion, channel initiationzBank erosion/accretion, meandering, bar formationzStorm sewers (closed conduits)zHowever, TERRA is modular in design so featurescan be added as needed over timezFor example, features were added to the model toallow simulation of distributed point sources forantimicrobial copper simulations...53Accounting for Sub-Grid Scale FeatureszLandscape features can occur at spatial scales that aresmaller than the model grid scalezExamples include buildings, sidewalks, roads (imperviouscover), individual lawns, etc.zSpatial averages are used to account for sub-grid scalefeatures within each cell (e.g.Kh, Manningn, USLEK):54()imperviousnaturalhurbanhfKK−=1,,()()...11+−+−=imperviousimperviouslawnlawnurbanfnfnnLooking Beyond Model FormulationzModel formulation means:zProcesses represented in TERRA computer codezTo use TERRA as an evaluation tool, conditions formodel application are defined based on:zChemical useszPhysical setting corresponding to useszLandscape specific to setting and useszThese three factors (uses, setting, and landscape)define thescenariofor exposure assessment...55October 2011Any Questions?