carl r. ice college of engineering - modeling of overland … · 2001. 4. 2. · soil surface....

Proceedings of the 10th Annual Conference on Hazardous Waste Research 287

MODELING OF OVERLAND FLOWCONTAMINATION DUE TO HEAVY METALS

IN SHALLOW SOIL HORIZONSR.S. Govindaraju and L.E. Erickson, Departments of Civil and Chemical Engineering, Kansas

State University, Manhattan, KS 66506

ABSTRACTHeavy metals in southeast Kansas are frequently found in the shallow soil layers. Rainfallevents in this region often generate overland flows which cause the release andmigration of these chemicals into surface waters. The chemicals are then transported insurface waters to downstream locations and, as such, pose a threat to the quality of bothfields along streams and surface and ground waters. In many instances, overland flowdoes not develop immediately as a sheet over the land surface, but gradually increasesin extent in accordance with the variable source area (VSA) concept. The overland flowregions diminish once the surface water application rate ceases. This paper deals withthe modeling of surface contamination under such circumstances. Results were obtainedfor a single hypothetical plot. These simulation results indicate that source area for heavymetal removal varies in a similar manner to source area of water. Some comparisonswere made regarding the relative amounts of solute lost to overland flow and to thoseleached into the soil as a function of time. The subsurface response was found to beslower than surface response to the rainfall event.

KEY WORDSoverland flow, contamination, transport, variable source areas

INTRODUCTIONExtensive mining activities in portions ofsoutheast Kansas have resulted in signif i-cant heavy metal concentrations in soils.For example, heavy metals have beentransported, both by surface and subsu r-face waters, to the flood plains of Springriver watershed, leading to reduced plantgrowth and agricultural productivity [1-2].The magnitude and frequency of waterapplication, antecedent soil moisture cond i-tions, vegetation and soil characteristics aresome of the factors which govern what po r-tion of applied water infiltrates into the soil.Ponded conditions occur frequently , lead-ing to overland flow which provides a rapidmeans of transport for the chemicals at thesoil surface. The transport of heavy metalsmay be separated into three differentphases (i) via overland flows, which is thetopic of study in this paper, (ii) via subsu r-face flows, and (iii) via streams. This paper

presents some preliminary efforts at linkingsurface flows, subsurface flows, and a so l-ute transport component to describe solutemovement via overland flow. The solutetransport component describes the mov e-ment of a conservative tracer. A condensedversion of this paper has been tentativelyaccepted for publication in Water R e-sources Research.

There have been several modeling effortsin the past to describe chemical transportover land surfaces. Ahuja [3] states that thecommonly used models (such as ARM —Agricultural Runoff Management model [4],and CREAMS model [5]) are not satisfac-tory for predicting chemical transfer fromagricultural plots for individual rainfall-runoffevents. These models assumed that azone of effective depth of interaction existsat the soil surface, within which soil solutionconcentrations remain constant and areequal to that in the surface water [4, 6]. The

Proceedings of the 10th Annual Conference on Hazardous Waste Research288

studies of Ingram and Woolhiser [7], Ahujaand Lehman [8], and Snyder and Woolhiser[9] indicated that solute concentrations inrunoff water are usually lower than those insoil solution, thus invalidating the assum p-tion of perfect mixing between surface andsoil water. Based on experimental results[8, 10], it was concluded that the degree ofinteraction or mixing between the surfaceand soil water was not uniform and d e-creased exponentially with depth below thesoil surface. Ahuja [3] provides a review ofexperimental and mathematical modelingpractices for chemical transfer into overlandflow.

More recently, Wallach et al. [11, 12], Wal-lach and van Genuchten [13] and Wallachand Shabtai [14-16] have utilized physics-based approaches to address the problemof transfer of chemicals from land surfacesto overland flows. Wallach et al. [11] used aconvective-dispersive model for solutetransport in soil and considered rate limitedtransfer at the interface of soil surface andwater surface. They treated the runoff zoneas a well-mixed unit characterized by aresidence time. Sorption-desorption kineticswere included by Wallach and Shabtai [ 15]in their analysis. These studies have notsimulated surface water flow in a detailedmanner. Spatial variation of overland flowinitiation and development was not a d-dressed. Peyton and Sanders [17] haveemphasized the importance of mixing dueto raindrop impact action on solute traveltimes and distances in overland flows.However, their studies were restricted toimpervious surfaces.

This study focuses on solute transport inoverland flow over infiltrating surfaceswhich are neighboring streams. The pre s-ence of such streams leads to interestinghydrologic situations because regions i m-mediately bordering streams saturate ra p-idly and develop surface flow even if waterapplication rate (rainfall/irrigation) is lessthan soil hydraulic conductivity. These r e-gions of surface flow expand under pr o-

longed rainfall, as does the region overwhich the soil surface is losing chemicals tosurface flow. When rainfall/irrigation stops,these surface-contributing regions diminish.These regions, contributing to overland flow(and corresponding chemical loss), whichexpand and contract in response to waterapplication onto the soil surface and thesubsurface soil-moisture status , are calledvariable source areas (VSAs). Water tra v-els 100 to 500 times faster as overland flowthan it does as subsurface flow . In investi-gating the stream hydrograph, the r e-sponse time of any water in the system istherefore controlled by how far it has totravel to get to the stream (slope length)and the mechanics of its transfer(pathway). Methods of predicting VSA e x-pansion and shrinkage during rai n-fall/irrigation events are useful since ove r-land flow routes from the near-channelcontributing areas have practically zerotime lag (as compared to subsurface flowcontributions of water and solutes) inreaching the streams. The purpose of thispaper is to develop a preliminary physics-based model for analyzing surface flow andheavy metal transport in such situations.

The problem of mathematical modeling ofwater movement alone under VSA hydro l-ogy has received considerable attention inthe literature. Freeze [18] was the first toaddress the effect of hillslope parameterson the stream hydrograph at the outlet of ahillslope section. He found that on concaveslopes with low soil permeabilities and onmost convex slopes, the dominating contr i-bution to the stream hydrograph comesfrom overland flows on transient variablesource areas neighboring the streams.Beven [19] used a finite element model fora two-dimensional subsurface flow coupledto a one-dimensional stream flow. He dem-onstrated that the initial conditions, partic u-larly in the unsaturated zone, are of primaryimportance in determining the time andmagnitude of the hillslope hydrographpeaks. Smith and Hebbert [20] studied thesurface-subsurface flow interaction using

the kinematic wave approximation for su r-face flows in conjunction with a simplifiedbut analytical infiltration model which isapplicable to cases when rainfall exceedsinfiltration capacity of the soil. Binley [ 21,22] and others have studied the problem ofstochastic runoff generation by using aphysically based heterogeneous hillslopemodel where surface flow routing is basedon a linearized approach instead of the s o-lution of the partial differential equationsgoverning unsteady flows. Govindaraju andKavvas [23] developed a physics-basedmodel for VSA hydrology based on numer i-cal solution of overland flows, stream flowsand the subsurface saturated-unsaturatedflows with dynamic interaction at commonboundaries. Their model is used to gene r-ate the flow field in this study. Many phy s-ics-based modeling studies have emph a-sized the nonlinear nature of the rainfall-runoff relationship at small scales(agricultural plot scale). This work presentsan extension to that of Govindaraju andKavvas [23] by including a solute transportcomponent for the surface flow section.The responses of the surface and subsu r-face to flow and solute transport for an i n-dividual storm event were investigated.

MATHEMATICAL FORMULA-TION OF THE HYDROLOGIC

SYSTEMThe mathematical representation of theflow and transport processes over an agr i-cultural plot leads to a set of nonlinear pa r-tial differential equations. Analytical sol u-tions of such systems are not available ,and numerical techniques are used to solvethem. The equations used in this study fordescribing the flow processes are pr e-sented in this section. The flow equationsare presented in detail in other studies (see[23]) and are presented here for complet e-ness.

Stream flow equationsThe equations of continuity and momentumin a channel are

Q∂∂

∂∂

+ + = (1)

QVgAf = − − − −0

1∂∂

∂∂

These are the Saint-Venant equations d e-scribing the propagation of flood waves in achannel. In the above equations, x is thedistance along the horizontal direction, V isthe mean velocity of water in the channelcross-section, A is the area of flow cross-section normal to the horizontal direction, tis the time, Q is the lateral inflow enteringthe channel per unit length, S 0 is the chan-nel bed slope, y is the flow depth normal tothe flow direction, g is acceleration due togravity and S f is the friction slope or theslope of the total energy line along thechannel.

Numerical solutions to the above equationssuffer from problems of convergence andstability due to their highly nonlinear nature.Hence investigators have used simplifiedversions of these equations whenever just i-fied. Common simplification techniqueshave been discussed elsewhere [24].Gonwa and Kavvas [25] have demo n-strated that the diffusion wave approxim a-tion to the full Saint Venant equations isadequate for many cases of practical inte r-est. The diffusion wave approximation wasused in analyzing the stream flow comp o-nent in this study. Substituting the diffusionapproximation of the momentum equationinto the continuity equation (1) leads to thefollowing equation describing the floodpropagation in trapezoidal channels:

∂∂

δ α ∂∂

∂∂

Sxw+ + = −

20 (3)

For trapezoidal channels, the cross se c-tional area, A, is

A by zy= + 2 (4)

where b is the bottom width and z is theinverse of the side slope. The generalizedfriction law is represented as

V DR Syx

∂∂

where R is the hydraulic radius of the flowsection. With appropriate choice of D, mand j, the familiar Manning's law, Chezy'slaw or the Darcy-Weisbach friction relatio n-ship can be obtained from Equation 5. InEquation 3 the wave celerity C w is

( )C V mw = +1 Ω (6)

where Ω is given by the expression

( )Ω = − +1 2 1 21

in which T is the top width of the flow se c-tion. In Equation 3,

δ ∂∂

∂∂

ξ= + + −VyT

where ξ is defined as

ξ ∂∂

∂∂

zy zzx

Here P is the wetted perimeter, which fortrapezoidal sections is

( )P b y z= + +2 1 212 (10)

The diffusion coefficient α in Equation 3 isdefined as

α∂∂

T Syx0

Equations 3 to 11 constitute the nonlineardiffusion wave approximation for the d e-scription of flood propagation in trapezoidalchannels.

Overland flow equationsThe diffusion wave approximation for ove r-land flows leads to the following equation[23]

∂∂

δ α ∂∂

∂∂

xwo o oo+ + = −

0 (12)

with the generalized friction law for ove r-land flows becoming

V D h S hxo o

o= −

∂∂

where h is the depth of flow, V o is the depthaveraged overland flow velocity, S 0o

is theslope of the overland flow bed, x is the c o-ordinate along the horizontal direction and tis time. In Equation 13, Do, mo and jo areconstants. The value assigned to theseconstants depends on whether the flow islaminar or turbulent, the effect of vegetationwhich may be present, and an appropriatefriction relationship for the conditions on theplot. For overland flow applications, thedefinitions of terms appearing in Equation12 are

( )C V mowo o= +1 (14)

δ o oQ= − (15)

α ∂∂

ooV hjo

where Qo is the net lateral inflow to theoverland flow section per unit length offlow.

Saturated-unsaturated groundwater flow equations

The subsurface region is comprised ofsaturated (capillary pressure ψ > 0) andunsaturated regions (ψ < 0) which areseparated by the water table (surface atwhich ψ = 0). Some of the basic assum p-tions made in modeling subsurface flowsare: (a) only liquid flow is considered eventhough the flow may occur both in liquidand vapor form, (b) the porous medium isincompressible, and (c) Darcy's law is valid.Within these limitations, subsurface flowmay be described by a continuity equationexpressed as

[ ] ( )∂∂

ρθ ρt

div q s+ = (17)

where q is the specific discharge of water,ρ is the density of water, θ is the moisturecontent by volume of the soil, s is asource/sink term (incorporating the effectsof evapotranspiration, rain infiltration, etc.).The continuity Equation 17 is combinedwith Darcy's law which may be stated as

( )q K grad= − θ φ (18)

where K(θ) is the hydraulic conductivity ofthe soil and φ is the piezometric head whichmay be expressed as

φ ψ= + z (19)

where ψ is the capillary potential or suctionhead of the soil and z is the elevationabove some fixed datum. CombiningEquations 17, 18 and 19 leads to a singleequation for a two-dimensional slice in thevertical (x,z) plane in terms of ψ as [23]

( ) ( )

ψ ∂ψ∂

∂∂

ψ ∂ψ∂

∂∂

ψ ∂ψ∂

where C(ψ) is called as the specific mois-ture capacity of the soil medium and is e x-pressed as

( )Cdd

ψ θψ

= (21)

In Equation 20, η denotes the soil effectiveporosity and Ss is the specific storage ofthe soil defined as

( )S g C Cs w f= +ρ η (22)

where g is the acceleration due to gravity,Cw is the compressibility of water and C f isthe compressibility of the soil medium. Thesoil porosity was taken as 0.3 and thespecific storage for the soil matrix was a s-sumed to be 0.0001 m in all examples pre-sented in this paper. Thus, under isotropicconditions, only two functional relationshipsare required to solve for Equation 20: θ(ψ)and K(ψ). These functions are shown for atypical sandy soil in Figure 1. The hydraulicconductivity of the soil is usually expressedas

( ) ( ) ( )K K sat Krψ ψ= . (23)

Figure 1. Hydraulic conductivity K(ψ) and watercontent θ(ψ) versus capillary pressure ( ψ). The satu-rated soil hydraulic conductivity is 0.264 cm/min andporosity is 0.3 (adapted from [18]).

where K(sat) is the saturated hydraulicconductivity of the soil and is a constant fora given soil type and K r(ψ) is the relativehydraulic conductivity of the soil. Figure 1shows single valued relationships for thecharacteristic curves of a soil but , in gen-eral, these functions are hysteretic and ,hence, non-unique specification for K( θ)and ψ(θ) may result for a given θ depend-ing on the wetting and drying history of thesoil.

Solute transport equationsFigure 2 is a description of the flow andsurface solute transport problem. It wasassumed that the soil surface has a uniforminitial concentration of solute (Cm) to adepth ε. This region is the mixing zone.This is a different concept from effectivedepth of interaction used in previous stu d-ies. The mixing zone distributes solute tooverland flow or to subsurface flow. Thesedistribution rates are proportional to (i) infi l-tration rates, and (ii) solute concentration

gradients. A simple model was utilized atthis stage because exact relationships arenot known. A convective-dispersive tran s-port equation was used to describe themovement of a conservative solute in theoverland flow region (similar to the oneadopted by Peyton and Sanders [17])

( ) ( ) ( )∂∂

∂∂

k c Cm+ −

= − −1(24)

( ) ( ) ( )∂∂

Cm k c C k C Cm s m= − + −1 2(25)

where c(x,t) denotes the time-space d e-pendent concentration of solute in theoverland flow section, Cm(x,t) is the concen-tration in the mixing zone, C s is concentra-tion in the soil beneath the mixing zone,h(x,t) is the overland flow depth, q(x,t) d e-notes the one-dimensional flow discharge,E indicates dispersion due to raindrop i m-pact, flow and molecular diffusion, k 1 and k2

are rate constants which are proportional tor1(x,t) (the infiltration rate at the soil su r-

Figure 2. Description sketch of the agricultural plot showing the flow boundary conditions (adapted from [23, 27])and the mixing zone.

face) and r2(x,t) (the infiltration rate fromthe mixing zone into the soil below). Theabove representation treats the mixingzone as a single lumped unit in the verticaldirection.

Initial and boundary conditionsFigure 2 shows the hypothetical section oftwo similar agricultural plots separated by acentral stream. The subsurface section is30 meters long. The overland and subsu r-face flow phenomena occur on the two sideslopes and drain into the stream. Freeze[18] and Govindaraju and Kavvas [23] havediscussed the end conditions applicable tosuch sections. These are presented in Fig-ure 2. Note that the location of the point Ddetermines the extent of the ponded d o-main at any time, and the region CD is thevariable source area (Figure 2). The up-stream boundary condition for the channelwas taken as the zero inflow condition. It isusually assumed that the channel achievesuniform flow at the downstream. Thedownstream boundary condition of zero-depth-gradient was adopted for overlandflow regions. However, one could also uti l-ize a critical flow condition at the overlandflow downstream section. The upstreammoving boundary condition for overlandflow was taken as the zero depth conditionat the transient point D (see Figure 2). Thelateral inflow into the stream at any sectionis the sum of the rainfall and the contrib u-tion from the overland flow section at theoutlet point C (note that a symmetric se c-tion exists on both sides of the stream) m i-nus/plus the quantity infiltrating/exfiltratingfrom/onto the base of the stream surface.Thus the lateral inflow into the channel atany channel node is

( ) ( ) ( )Q R t Q over Qs t= + ± (26)

where R(t) is the time varying rain fallingover the width of the stream section(positive for rainfall and negative for evap o-ration), Q(over) is the overland flow contr i-bution and Qs(t) is the quantity infiltrating

into (or exfiltrating from) the soil over thewidth of the channel section.

Similarly the lateral inflow into the overlandflow nodes are determined by the algebraicsum of precipitation and infiltration into thesoil. Mathematically this is represented as

( ) ( ) ( ) ( )Q x t I x t K

= − +

ψ∂ψ

∂1 0

where I(x,t) represents the rainfall intensitycontribution to the lateral inflow and ψ(x,t)represents the capillary pressure on thesubsurface boundary nodes along CE inFigure 1. If Qo(x,t) as determined fromEquation 27 is negative, then there is nonet lateral inflow contribution to that partic u-lar overland flow node for that time instant.The situation of partially ponded areas , CD,in Figure 3 occurs when the rain intensitydoes not exceed the saturated soil hydra u-lic conductivity.

Note that Equation 27 essentially dictateswhat portion of the rainfall enters the soilthrough infiltration and what portion of therainfall contributes to overland flow. Ove r-land flows are also governed by a contin u-ity equation similar to Equation 1 as

( ) ( )∂∂

∂∂

hV Q x to o+ = , (28)

where the variables are defined as inEquation 12 except that the net lateral i n-flow to overland flow Qo(x,t) is obtainedfrom Equation 27. The second term on theright hand side of Equation 27 (call it I 2(x,t)for convenience) represents the rate ofwater infiltrating into the soil medium.Equation 27 holds even for ponded cond i-tions when the quantity of water infiltratinginto the soil depends on the rainfall, theoverland flow depth on the soil surface , andthe status of soil moisture at the surface ofthe soil. At initial times, the soil surface isdry and I2(x,t) is greater than I(x,t) and thus

Qo(x,t) is zero for this point in time andspace. As the water table rises and the in i-tial moisture deficit is satisfied, I 2(x,t)gradually becomes smaller, but there willstill be no contribution to overland flow ifthe rain intensity does not exceed the sat u-rated hydraulic conductivity of the soil. Insuch instances, overland flow will havepositive contributions when the groundwater table practically reaches the soil su r-face.

Static initial conditions were chosen for thesubsurface domain in the simulation effortsof this study. The initial condition for ove r-

land and stream flow components, dictatedby static initial conditions for the subsu r-face, is that of a dry section. The solutewas assumed to be uniformly distributed inthe mixing zone at the beginning of thesimulation. The outflow boundary conditionfor solute was chosen as one of zero grad i-ent (i.e., ∂c(L,t)/∂x = 0). At the transientpoint D on the soil surface where overlandflow begins, the concentration was chosenas c = 0 in keeping with the zero flow depthboundary condition. The initial distributionof solute in the overland flow domain and inthe subsurface region below the mixingzone was zero.

Solution methodology forconjunctive modeling

Implicit centered finite difference tec h-niques were used for solving the equationsgoverning water flow and solute transport.Details of this scheme can be obtainedelsewhere [23] and are not repeated here.Small time steps (in the order of seconds)were used in the beginning of each simul a-tion because of the highly nonlinear natureof the equations.

The equations used in the subsurface aretwo-dimensional with a one-dimensionaloverland flow description on the surface.Such a unit of overland and subsurfaceflow is called a 'slice' (see [23]). The chan-nel flow is perpendicular to the orientationof these slices (see Figure 2). The timespace varying channel flow depth serves asa boundary condition for the subsurfacenodes attached to the channel bottom(region ABC in Figure 2). To simulate thissituation, many slices are chosen along thechannel reach and each slice interacts withthe channel depending on its location alongthe channel reach. This approximates thethree-dimensional nature of flow and leadsto considerable savings in computer effort.

The problem now reduces to the simult a-neous solution of a one-dimensional streamsection and various slices. These comp o-

Figure 3. Flow discharge (3a) and solute discharge(3b) over the agricultural slope during the risingphase for several different values of elapsed timesince rainfall began. The 30 m location is adjacent tothe stream.

nents are coupled internally since solvingone component modifies the boundaryconditions or the lateral inflow/outflowconditions for the other components. Thestream depths and the overland flowdepths at each surface node and the capi l-lary potentials at each subsurface node areused as the convergence criterion quant i-ties during the iteration procedure. Conve r-gence is achieved when the maximum di f-ference for any nodal value of these quan-tities between two successive iterations isless than some preset tolerance. Eachsweep starts with the numerical solution ofthe stream flow section using the net lateralinflow from rainfall and baseflow and ove r-

land flow discharge from each slice(estimated from solution at the previoustime step). The new stream solution thusobtained prescribes a new head conditionat each slice along region ABC for the su b-surface (see Figure 2). Using this newboundary condition, obtained from the time-space varying stream depth, the subsu r-face flow components are solved for allslices. The new subsurface solutions pr e-scribe new values of net lateral inflows tooverland flows along CD or change thecapillary potentials along DE for each slice.The overland flow component is nowsolved for each slice. The new overlandflow solutions for each slice determine newboundary conditions along CDE for thesubsurface flow and provide new lateraloutflow for each slice to a particular streamlocation. This starts off a new sweep cyclewith the stream flow being solved for newlateral inflows from the subsurface and newoverland flow inputs. These cycles continueuntil all the nodes for each component inthe system converge within preset tole r-ances.

Once the flow field was obtained at eachtime step, the infiltration rates r1(x,t) andr2(x,t) were determined. Using these infi l-tration rates, the solute transport Equations24 and 25 were solved numerically.

DISCUSSION OF RESULTSThe results pertaining to surface and su b-surface flow dynamics were discussed byGovindaraju and Kavvas [23]. In this study,results from one of those simulations wasaugmented with a solute transport comp o-nent to study surface transport pheno m-ena. This paper deals with surface co n-tamination and only surface results arepresented here. Figures 3 and 4 show theresults for the slope under a rainfall eventof 0.03 cm/min intensity and a duration of1.0 hours. The soil saturated hydraulicconductivity is 0.03 cm/min in this example.

Figure 4. Flow discharge (4a) and solute discharge(4b) over the agricultural slope during the recessionphase for several different values of elapsed time.The 30 m location is adjacent to the stream.

Figure 3a shows rising profiles of overlandflow discharge over one of the side slopesand their spatial extent at different times.The distance x = 30.0 m is adjacent to thestream. A short time after rainfall com-mencement (say 4.0 mins), about 5.0 m ofthe slope immediately neighboring thestream has developed overland flow. Astime increases, the flow discharge risesand the region over which overland flowoccurs also increases. Figure 3a is a typicalresponse that is observed in hydrologicevents exhibiting VSAs. By the time therainfall stops (i.e., 1 hour), almost the whole30 m of the agricultural plot has developedoverland flow.

Figure 3b shows the corresponding solutedischarge hydrographs over the soil surfaceat various times. The solute discharge is aproduct of the flow discharge and the flowconcentration. The solute discharge overthe slope also exhibits a time-space d e-pendent variable source area along withthe flow field. The area contributing to su r-face contamination increases with time.The solute discharge hydrographs (Figure3b) do not exhibit as much curvature as theflow discharge hydrographs (in Figure 3a).

In this example rainfall stops after 1 hour.Figures 4a and 4b show the water andsolute discharge profiles respectively duringthe recession phase. Recession of flow isvery rapid, and contributions from surface

flow to the stream hydrograph diminishrapidly. The solute discharge also dimi n-ishes after rainfall stops (Figure 4b), but ata slower rate than water discharge (Figure4a). This indicates that the concentrationsin surface flow do not behave in the samemanner as the flow discharge once therainfall stops.

This conclusion is stated more explicitly inFigure 5, which shows the outflow sectionflowrates, solute discharges and conce n-trations. The flow hydrograph measures thetotal flow discharge to the stream from oneagricultural side slope as a function of time.This quantity increases until 60.0 min., atwhich time the rain stops, and then the ou t-flow hydrograph recedes rapidly. The co r-responding outflow pollutograph shows asimilar behavior. This curve represents theproduct of the flow discharge and the so l-ute concentration at the outflow sectionadjacent to the stream and determines thetime dependent pollutant load that reachesthe stream from the overland flow section.The outflow concentration is also shown inFigure 5. The concentration reaches asteady state value in about 10.0 mins andremains practically unchanged until rainstops. At this time, there is a dramatic i n-crease in concentration at the outflow se c-tion. Once the rain stops, the dilution effectof rainfall and the lateral inflow contributionto overland flow stops. Meanwhile solute isbeing transported to the outflow sectionfrom upstream flow regions, all of whichleads to a concentration build up at theoutflow section. Nevertheless, the pollut o-graph to the stream recedes after rainstops, because the recession in the flowdischarge hydrograph is faster than the i n-crease in concentration.

Figure 6 compares the relative amounts ofsolute that are washed off by overland flowand the amounts that are leached to thesubsurface below the mixing zone. Initiallythe contribution rate to subsurface flow isvery high because the infiltration rates arevery high and practically all the rainwater

Figure 5. Flow discharge (hydrograph), solute di s-charge (pollutograph) and solute concentration asfunctions of time at the outflow section of overlandflow before joining the stream.

enters the soil. As time increases, this infi l-tration rate goes down. Simultaneously,increasing portions of the surface developoverland flow, and the solute contributionrate to overland flow increases. After about35 mins, the amount of solute beingwashed off by surface flow is comparableto the amount that is being leached into thesoil. After rain ceases at 60.0 mins, theamount of solute washed off by overlandflow decreases rapidly. The subsurfacecontribution shows little change at the endof the rainfall. This indicates that the su b-surface response to change in rainfall isslower than surface flow response.

Vegetation impacts the movement of bothsurface and subsurface water. Evapotra n-spiration reduces subsurface moisture, thusincreasing infiltration capacity. The param e-ters of Equation 5 will be different if thesurface flow occurs through grasses orother plants which reduce the flow velocity.Leaves often act to reduce the velocity offalling rain drops, thus reducing erosionand sediment movement. The beneficialeffects of vegetation on water, sedimentand solute management will be consideredin future work.

SUMMARY ANDCONCLUDING REMARKS

The problem of surface contamination overheavy metal contaminated sites was a d-

dressed in this paper. Physics-based mo d-els were developed for both the flow andsurface solute transport components. N u-merical simulations over a hypothetical a g-ricultural plot adjacent to a stream wereperformed to study the behavior of solutemovement over the soil surface. The d y-namic response of variable source areasfor both water and solute movement werediscussed using the concept of movingboundaries for the overland flow domain.The upstream overland flow boundarymoves back and forth in response to infi l-tration-exfiltration processes. A physics-based distributed model was used to studythis phenomena by internally coupling thenonlinear partial differential equations forthe flow components and then augmentingthe flow model with a surface solute tran s-port model. The solute was assumed to beuniformly mixed in the subsurface in themixing zone at the beginning of simul a-tions. The purpose of the mixing zone inthis modeling effort was to distribute thesolute to overland flow above or to subsu r-face flow underneath, depending on r e-spective concentration gradients. The co n-centration in the mixing zone changes withspace (distance away from stream) andtime.

The subsurface response to rainfall interms of water and solute movement wasvery slow compared to the response ofoverland flow. Surface flow transmits waterand solute 100-500 times faster than su b-surface water. During the simulations, thesubsurface concentrations did not changeappreciably, and remained constant for allpractical purposes. The response of su r-face and subsurface components occursover different time scales and makes themodeling of such processes over long per i-ods of time difficult.

Previous studies (e.g. , [18, 26]) have de-scribed the conditions which favor the d e-velopment of variable source areas. Mode l-ing studies, which deal with prediction ofcontaminants in surface waters, need to be

Figure 6. Solute transfer rates over the whole flowsection into the subsurface region beneath the mi x-ing zone and into the overland flow region above themixing zone.

cognizant of the role of VSA hydrology. Theportion of applied chemicals that is tran s-ported by surface flow may show spatialvariation as indicated by model results. Thetiming of rainfall/irrigation after fertilizer andpesticide application on agricultural areasalso has a great influence on the fate andtransport of agrichemicals. In watershedscale studies, variable source areas needto be identified for an estimate of the fra c-tion of the area that contributes to surfacewater contamination.

Many chemicals adsorb on to the soil pa r-ticles, and are subsequently entrained intosurface flow as these particles are erodedby the moving water. This study neglectsthe transport of chemicals which arebrought into solution by this action. Thiswould require the inclusion of a surfaceerosion model coupled with solute adsor p-tion and transport model. Inclusion of thesephysical processes would result in predi c-tion of greater solute loss through overlandflow. These aspects are beyond the scopeof this study and are topics of further r e-search.

ACKNOWLEDGMENTSThis research was partially supported bythe U.S. EPA under assistance agreementR-819653 to the Great Plains-RockyMountain Hazardous Substance ResearchCenter for Regions 7 and 8. It has not beensubmitted to the EPA for peer review and ,therefore, may not necessarily reflect theviews of the agency. No official endorse-ment should be inferred. The Center forHazardous Substance Research and theEPA EPSCoR program also provided pa r-tial support.

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