1-a model to couple overland flow and infiltration into macroporous vadose zone

A model to couple overland flow and infiltration into macroporousvadose zone

H. Ruana, T.H. Illangasekareb*aUSDA-ARS-NPA, Great Plains System Research Unit, P.O. Box E, 301 S. Howes Street, Fort Collins, CO 80522, USA

bDivision of Environmental Science and Engineering, Colorado School of Mines, Golden, CO 80401-1887, USA

Received 17 March 1997; received in revised form 9 June 1998; accepted 9 June 1998

Abstract

Most vegetated land surfaces contain macropores that may have a significant effect on the rate of infiltration of water underponded conditions on the ground surface. Owing to the small-scale variations of the land topography (microtopography), onlyportions of the land area may get ponded during the process of overland flow. As the macropores transmit water at muchhigher rates than the primary soil matrix, higher macropore activation in ponded areas produces larger effective infiltrationrates into the soil. Therefore, overland flow and infiltration into the macroporous vadose zone are interrelated. Representingthe microtopographic variation of the land surface by a simple sine wave function, a method was developed to relate theponding area to the average ponding depth which was determined by overland flow. A numerical model coupling overlandflow and infiltration into the macroporous vadose zone was developed. Overland flow was simulated using the St. Venantequations with the inertia terms neglected. A single macropore model was used to simulate the infiltration into the macro-porous vadose zone. The interaction between overland flow and the infiltration into the macroporous vadose zone wasanalyzed for a hypothetical watershed. The sensitivity analysis revealed that the interaction of macropore flow and overlandflow is significant. For the conditions tested, the macropore flow and the overland flow were found to be more sensitive to themacroporosity and less sensitive to the microtopographic surface variation.q 1998 Elsevier Science B.V. All rights reserved.

Keywords:Macropore flow; Overland flow; Infiltration; Vadose zone; Simulation and interaction

1. Introduction

Field soils in vegetated areas are often macropor-ous. Earth worm holes and decayed root channels arecommon in field soils. Flow in macroporous soilsexhibits considerably non-uniform velocities. Suchphenomena are referred to as preferential flow(Beven, 1991). Flow in soils with rectangular orcylindrical macropores (cracks, decayed root chan-nels, and earth worm holes) is often described by

the geometry-based approach (Edwards et al., 1979;Beven and Clarke, 1986).

The total infiltration rate into macroporous soils isdetermined by both infiltration into the soil matrix andflow into the macropores. Macropore flow is initiatedwhen there is surface ponding. Small depressions areponded first owing to the microtopography of the soilsurface. Only the macropores in ponded areas areactivated when water enters the macropores open atthe ground surface, and the ponded areas change withoverland flow. Therefore, macropore flow can beaffected by overland flow.

Although macropore flow and overland flow are

Journal of Hydrology 210 (1998) 116–127

0022-1694/98/$ - see front matterq 1998 Elsevier Science B.V. All rights reserved.PII S0022-1694(98)00179-6

* Corresponding author. Fax: +1 303 273 3413; e-mail: [email protected]

interrelated, overland flow has not been considered asa possible controlling factor in macropore flow. Theprimary purpose of this research is to understand andmodel the combined and interrelated flow system,including macropore flow, soil matrix flow, and over-land flow. As a comprehensive data set for validationwas not available, this model is presented as a theo-retical model that will help in providing insights to thecoupled processes of overland flow and macroporeflow. Such a model can be used in the design of futurefield experiments.

2. Flow in macropores and soil matrix

The geometry-based approach describes flow inmacropores (macropore flow), flow in the soil matrix(matrix flow), and the interactions between the twoflows based on the geometry of the macropores.This approach was developed basically for flow insoils with cylindrical macropores, of which the geom-etry is relatively simple.

The macropore-geometry model developed byEdwards et al. (1979) uses simplified macroporeflow conditions. Edwards et al. (1979) suggest atwo-dimensional model of flow through a verticalcylindrical macropore in the center of the soil cylin-der. They used Richards’ equation for the flow in thesoil matrix and a mass balance for the flow in themacropore.

In undisturbed field soils the majority of macro-pores formed by earthworm holes and decayed rootchannels are cylindrically shaped (Beven and Germann,1982). In this research, only cylindrical macroporesare considered and the geometry-based approach forflow modeling is used. Macropore flow in the vadosezone is initiated only during intensive rainfall or irri-gation events and, therefore, occurs only in a shortperiod of time. Within such a short period of timeduring a storm event, evapotranspiration is negligible.Because most macropores are vertically oriented, theyare assumed to be vertical in most model formulations(Beven and Germann, 1982) including the one pre-sented in this paper.

Richards’ equation is generally accepted as beingadequate to describe flow in the soil matrix in amacroporous system. Because flow in the vicinity ofa single macropore is almost axisymmetrical, it is

convenient to use cylindrical coordinates. Usingthree-dimensional cylindrical coordinates, Richards’equation can be written as (Edwards et al., 1979)

dv

dh]h]t

=]

]zK

](h−z)]z

� �+

1r

]

]rrK

]h]r

� �+

1r2

]

]JK

]h]J

� ��1�

whereh is the pressure head of soil water,v is thewater content (which is a function ofh), K is theunsaturated hydraulic conductivity (which is a func-tion h or v), z is the vertical coordinate (downward aspositive),r is the radius coordinate, andJ is the anglecoordinate. Assuming that the pressure head is sym-metrical in J coordinate (radially axisymmetric),Eq. (1) becomes the two-dimensional Richards’equation in cylindrical coordinates (Bruggeman andMostaghimi, 1991)

dv

dh]h]t

=]

]zK

](h−z)]z

� �+

1r

]

]rrK

]h]r

� �(2)

The Galerkin finite element method is chosen to solveEq. (2) to obtain the water pressure headh and, sub-sequently, the water content distribution within thesoil matrix. Matrix flow is two-dimensional in axis-symmetrical coordinates and has four differentboundaries (see Fig. 1).

The soil’s macroporosity is used to determine thecolumn radius. Macroporosity is defined as the totalcross-sectional areas of macropores in a unit surfacearea. Macroporosity equals cross-sectional area of amacroporea times the number of macropores per unitsurface areab. The surface area of the columnAs isthen equal to 1/b (see Fig. 1). The number of macro-pores per unit surface area is not always an integer.

The flow in macropores is simplified. It is assumedthat macropores in ponding areas are fully filled withwater. Also, the volume of water in macropores isnegligible compared with the rainfall. The macro-pores in non-ponding areas are empty.

To solve Eq. (2), the relationships between watercontentv and pressure headh and between unsatu-rated hydraulic conductivityK and pressure headhor water contentv are required. In this model, thereare four options to input the first relationship (theretention curve), namely (1) Brooks and Corey’smodel (Corey, 1994), (2) van Genuchten’s model

117H. Ruan, T.H. Illangasekare/Journal of Hydrology 210 (1998) 116–127

(van Genuchten, 1980), (3) the exponential model(Russo et al., 1991), and (4) linear interpolationfrom a data set which is measured from a retentioncurve.

There are also four options for the second relation-ship K,h or K,v. The first three options are estab-lished using the first three models of the retentioncurve combined with Mualem’s model (Mualem,1976). The fourth option ofK,h or K,v is linearinterpolation using measured data from long columnor other methods (Green et al., 1986).

3. Overland flow

Overland flow is a term used to describe two-dimensional flow over an inclined land surface. Inmost situations of overland flow the frictional forceis dominant since the water depth is shallow. Underthis condition, the kinematic wave equation isaccepted to be adequate to describe overland flow

(Abbott et al., 1986). In kinematic wave formulationsthe two-dimensional components of the velocity vec-tor are given by

u=kxI1=2x h2=3

p (3)

v=kyI1=2y h2=3

p (4)

The continuity equation is given by

]hp

]t=

](uhp)]x

+](vhp)

]y+R− I (5)

whereu and v are the flow velocities in thex and ydirections respectively,hp is the ponding depth whichwill be formulated for the undulating surfaces,kx andky are the Strickler roughness coefficients for thexandy directions,I x and I y are the water surface gra-dients in thex andy directions,R is the rain intensity,and I is the infiltration rate which includes the infil-tration into both the soil matrix and macropores. Theboundary conditions depend on inflow and outflowconditions at a particular site. A certain minimum

Fig. 1. Schematic of a single-macropore flow model.

118 H. Ruan, T.H. Illangasekare/Journal of Hydrology 210 (1998) 116–127

ponding depth is necessary to initiate overland flow(Luce and Cundy, 1992).

The water surface gradientsI x and I y are given by

Ix =](zs +hp)

]x(6)

Iy =](zs +hp)

]y(7)

wherezs is the elevation of the land surface. Substi-tuting Eqs. (3) and (4) into the continuity equation inEq. (5) yields

]hp

]t=

]

]x(kxI

1=2x h5=3

p ) +]

]y(kyI

1=2y h5=3

p ) +R− I (8)

Eq. (8) is a non-linear partial differential equation. Asimulation domain of overland flow is shown in Fig. 2.

4. Interaction between macropore and overlandflow

The slope of the land surface elevation can bedivided into two components. The first component isthe regional slope variation which is represented bythe constant slope (]zs/]x, ]zs/]y) within each finitegrid. The second component is random slope varia-tion, which occurs at a much smaller scale (Fig. 3). Inthe classical formulation of overland flow usingEq. (8), this random variation of soil surface elevation(microtopography) is not considered. However, theserandom variations play an important role in the initia-tion of macropore flow.

The relationship between the macropore fractionthat is activated and the average ponding depth iscomplex. In this formulation, the following

Fig. 2. A hypothetical watershed.


assumptions are made in order to examine the primaryinteraction between overland flow and macroporeflow and to avoid the complicated description of therandom variation of ground elevation as defined bythe microtopography. First, only the mean values ofthe random variation are considered. The variation is

assumed as a sine wave with a constant amplitude(Fig. 3(a))

hs =A sin(qxs) cos(qys) (9)

wherehs is the soil surface height from the averagesoil surface elevationzs, A is the amplitude of the

Fig. 3. Variation of land surface within an area of less than 1 m2 and macropore flow activation (cm).


microtopographic variation,ys is a coordinateaxis parallel to the flow direction,xs is the axisperpendicular to the flow direction, andq is the fre-quency of the variation along thexs andys directions.Fig. 3(a) shows the microtopographic variation basedon Eq. (9). The flow direction changes at differentlocations. It should be noted thatxs and ys are notfixed axes, as they vary with the flow direction whichchanges at different locations.

Water ponded on the soil surface described byEq. (9) cannot flow before the depressions are filled.In this initial development, we further assumed thatthe microtopographic surface varies only in thexs

direction (perpendicular to the flow direction) sothat all ponded water can flow as overland flow. Inthis case, the microtopographic variation of the soilsurface (Fig. 3(b)) is written as

hs =A sin(qxs) (10)

The relation between ponding depth and ponding areacan be obtained using a control area which is definedas a unit length in theys direction by a length of 2p/qin thexs direction (Fig. 3(b)). The ponding area (frompoint a to point b of Fig. 3(c)) within the control areaequals the length from point a to point b times theunit length in theys direction (Fig. 3(c)). The lengthfrom point a to point b equalsxs0 − (−xs0 − p/q)which is 2xs0 + p/q. Because the control area repre-sents the whole soil surface, the relative ponding areaof the control area equals the relative ponding area forthe whole soil surface. The relative ponding areaAp

is defined as the ponding area per unit soil surfacearea (i.e. total ponding area divided by the total soilsurface area).Ap is written as

Ap =2xs0+ (p=q)

2p=q(11)

where xs0 is the xs value at the right-side pondingboundary (point b) (Fig. 3(c)).

The ponding depth changes withxs. The average

ponding depthhav is used to represent the pondingdepth and is defined as the ponding water volumedivided by the ponding area. The control area isused again to derive the average ponding depth. Theponding area in the control area is 2xs0 + p/q. Theponding water volume in the control area is computedin two parts. The first part is the volume from point ato point b and between thexs axis and the soil surface.The second part is the volume from point a to point band between thexs axis and the water surface. Theponding water volume is the first part minus the sec-ond part. This first part volumev1 can be obtainedusing integration

v1=�xs0

−xs0 − (p=q)[ − A sin(qxs)] dxs (12)

The second part volumev2 is simply

v2= −A sin(qxs0)[2xs0+ (p=q)] (13)

Therefore, the average ponding depth is

The average ponding depth over the ponding areahav

is considered to be the ponding depthhp in Eq. (8).Combining Eqs. (11) and (14),xs0 can be eliminatedand an expression for average ponding depth can bederived as

hav =A

pAp[cos(pAp +p)pAp −sin(pAp +p)] (15)

Using Eq. (15), the average ponding depth can beobtained if the relative ponded area is known. If theaverage ponding depth is known, the relative pondedarea is difficult to get from Eq. (15). A trial and errormethod or interpolation from anhav − Ap table needsto be used to obtain the ponding area from the aver-age ponding depth.

When hav $ A, all the macropores are activated.Also, macropores are assumed to be evenly distribu-ted over the land surface. It is reasonable to assumethat macropores in the ponding area are fully acti-vated, i.e. fully filled with water. The total flowwithin each grid is obtained by summing the flow in

hav =

�xs0

−xs0− (p=q)[ − A sin(qxs)] dxs − [ − A sin(qxs0)][2xs0+ (p=q)]

2xs0+ (p=q)(14)


all activated macropores within the grid influencezone.

As flow can occur only in the area where there isponding, overland flow can only be computed whenthe ponding area is known. Initial conditions are set forconditions of no overland flow and hence zero pondingarea. During simulations, when overland flow firstoccurs, the ponding area is computed by setting theexcess water (excess rain water after infiltration) equalto the volume of ponded water (mass balance). Theponded water in terms of depth over the whole areaequals the average ponding depthhav times the relativeponding areaAp. Therefore, the excess rain water overinfiltration hex when starting to pond is

hex =havAp =Ap

[cos(pAp +p)pAp −sin(pAp +p)]

(16)

As the ponding area (Ap2p/q) at the current time stepis not known, the ponding area at the previous timestep is used to approximateAp in Eq. (16). Before theactivation of any macropores, the infiltration at thefirst time step is only due to matrix infiltration. Atsubsequent time steps the macropore flow is com-puted and is included as a sink term in the massbalance analysis to compute the average pondingdepth. For each time step, iterations of the com-putations are incorporated to keep a proper massbalance.

In the formulation of the continuity equation inEq. (8), it is assumed that overland flow occurs onall the land surface. Hence, to incorporate the factthat overland flow occurs only in the ponded area,Eq. (8) needs to be modified. The excess water,which is the difference between rainfall and infiltra-tion (R − I) over all the land surface, is accumulatedonly in the ponded areaAp. Therefore, the modifiedgoverning equation for overland flow with macroporeactivation is

Ap]hp

]t=Ap

]

]x(kxI

1=2x h5=3

p ) +Ap]

]y(kyI

1=2y h5=3

p )

+ (R− I ) �17�or

]hp

]t=

]

]x(kxI

1=2x h5=3

p ) +]

]y(kyI

1=2y h5=3

p ) + (R− I )=Ap

(18)

Although the channel flow due to the microtopogra-phy is different from the overland flow, we stillassume that within each channel the flow is similarto the overland flow. The termI in Eq. (18) includesthe infiltration directly into the land surfaceI i andmacropore flowI m

I = I i + Im (19)

The macropore flowI m is computed using a singlemacropore flow model. Macropores which are acti-vated at different times can have different flow ratesat a given time. Two factors affect rate of flowthrough macropores. The first is the water contentnear the macropore when the macropore is activated.As the water content in the vicinity of a macropore isdefined by the time-dependent water content in thesoil matrix, the initial water contents at macroporeactivation will change with time due to the precedingvertical infiltration. The later the macropore is acti-vated during a storm or flood event, the deeper thewetting front, and the higher the initial water content.The high initial water content around macropores candecrease the macropore flow rate by decreasing thelateral infiltration from macropores into the soilmatrix. Fig. 4(a) demonstrates the macropore flowrate of two macropores that are activated at differenttimes. Macropore 2 has a lower flow rate when acti-vated compared with macropore 1.

The second factor that affects macropore flow rateis the time intervalDt between the specified time (thecurrent time step of the numerical simulation) and themacropore activation time (the time when the soilsurface near the macropore is ponded). The longerthe time interval, the smaller the macropore flowrate due to the downward migration of the wettingfront. In other words, macropore flow of a singlemacropore decreases with time (Fig. 4(a)).

In the present formulation a uniform and high rain-fall intensity is assumed, so that once a ponding area isformed it does not become unponded during the simu-lation. When ponding area increases the macroporesin the newly ponded area become activated. At eachtime step after starting of ponding new macropores getactivated. In implementing the model algorithm to acomputer code, it is too complex to simulate all themacropores that have different activation times andinitial water contents because of the large simulationeffort needed for a single macropore. Macropores that


Fig. 4. (a) A sketch of macropore flow that changes with time and its activation time. (b) Simulated flow rate of macropores which areactivated in 15 specified times.


are activated within a time period are assumed to havethe same macropore flow rate. In Fig. 4(a), macropore2 represents all macropores (a group) that are acti-vated between (t1 + t2)/2 and (t2 + t3)/2. Therefore,only a limited number of macropores are simulatedand used for the sink termI m in the overland flowcomputation. The macropore flowI m is the summationof time-varying flow of different groups of macro-pores that are activated at different times

Im = ∑j =k

j =1[Qmj(tk − tj)Apj ]=As (20)

where tk is the current time,t j is the time at thebeginning of thejth time interval, Qmj(Dt) is themacropore flow rate at timeDt = tk − t j after activa-tion for macropores that are activated within thejthtime interval, andApj is the area fraction that isponded within thejth time interval

Ap(tk) = ∑j =k

j =1Apj (21)

In the classical formulation of infiltration from landsurfaces, the total infiltrationI i includes the infiltra-tion through the ponding areaI i1 and the non-pondingareaI i2. The surface infiltration into the ponding areaI i1 is computed using the single macropore flowmodel in a similar way toI m

I i1 = ∑j =k

j =1[Qimj(tk − tj)Apj ]=As (22)

whereQimj(Dt) is the classical ponded infiltration rateinto the ponded soil surface computed using thesingle macropore flow model in a similar way toQmj(Dt).

The infiltration into the non-ponding areaI i2 iscomputed using a one-dimensional vertical infiltrationflow model

I i2 = I io(1−Ap) (23)

where I io is the infiltration computed using a one-dimensional flow model. The special case of themacropore flow model without a macropore is usedas the one-dimensional flow model in this study.

5. Simulation of a hypothetical watershed andsensitivity analysis

As no comprehensive experimental or field data setwas available for model testing, a hypotheticalwatershed was used to examine the interactionbetween macropore flow and overland flow based onthe governing equations developed in the previoussections. The watershed is a rectangle (100× 50 m2)and varies in its elevation (Fig. 2). The surface eleva-tion was designed so that there is no water flowthrough boundaries except the downstream boundary(see the dashed line in Fig. 2). Water was dischargedfrom the watershed into a river (the dashed line). Thefollowing function has the four boundary conditionsof the required watershed

z=Z 1+sin py

2y0

� �+cos p

xx0

� �� (24)

wherez is the surface elevation,Z is one-third of themaximum elevation difference and is used to changethe land slope,x andy are the coordinates, andx0 andy0 are the lengths in thex and y directionsrespectively.

The Strickler roughness coefficient is selectedbetween 1 and 10 (Bathurst, 1986). The soil propertiesare assumed to be homogeneous horizontally andlayered in the vertical direction. Brooks and Corey’smodel (Corey, 1994) was used for the retention andhydraulic conductivity functions. The values ofBrooks and Corey’s parameters are listed in Table 1.Rainfall intensity was 3.6 cm h−1.

Table 1

Soil properties (Brooks and Corey model)

Saturated hydraulicconductivity (cm h−1)

Displacementhead (cm)

Pore distributionindex

Water content (v/v) Depth (cm)

Residual Saturated Initial

Layer 1 1.0 − 35 0.36 0.1 0.46 0.2 6.5Layer 2 0.5 − 35 0.36 0.1 0.40 0.25 73.5


As stated in Section 4, macropore flow wascomputed for macropores which are activated at 15times, namely at 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,25, 27, 29 min. Each one of them represents a timeinterval of 2 min. (0–2, 2–4, and so on). Macroporesize was assumed to be 4 mm and macropore lengthwas 40 cm. The results of the 15 macropore flows are

plotted in Fig. 4(b). These results were used tocalculate the total macropore flow in a unit landarea using Eq. (20).

Different values of the Strickler roughnesscoefficient, the slope parameterZ, the microtopo-graphic variationA, and macroporosity were used toexamine the sensitivity of the overland flow (and thus

Fig. 5. Break up of rainfall for eight different scenarios at different times.


the total infiltration) to these parameters. For the refer-ence scenario (number 4), the Strickler roughnesscoefficient was 10,Z = 1.0 m, microtopographic var-iation amplitudeA = 1.0 cm, and macroporosity was0.00035. The frequencyq is assumed to be one overone unit of length, althoughq is eliminated in thecomputation.

To evaluate overland flow, the total discharge intothe river (cumulative discharge volume per unit landarea) is plotted versus time. Also, the cumulativeponding water (volume per unit land area) is plottedversus time for mass balance purposes. The cumula-tive ponding water is that part of the total watervolume that belongs to neither macropore flow noroverland flow.

For comparison, three simple scenarios of overlandflow were first simulated without macropore flow. Thefirst scenario was simply a smooth watershed withoutany infiltration. There was no microtopographic var-iation of the land surface. The second scenario is thesame as the first scenario except with microto-pographic variations perpendicular to the flow direc-tion (A = 1.0 cm). The results are plotted in Fig. 5(a)for scenario 1 and Fig. 5(b) for scenario 2. The smoothsurface retained more water than the rough surfacescenario. It should be pointed out that dead ponding(where water is retained and cannot flow) was notconsidered. It was assumed that all ponding watercan flow as overland flow and that the flow directionis not affected by the microtopographic variation. Thereason for the discrepancy between scenario 1 andscenario 2 is that the averaged water depth of thegeometrically rough surface (Eq. (14)) is larger thanthat of the geometrically smooth surface whenA ismuch larger than the water depth. The third scenariowas the same as the second scenario except for addingthe infiltration into the soil surface (without consider-ing macropore flow). The results are plotted inFig. 5(c). Much less water was discharged into theriver and was retained on the land compared withthe first two scenarios. The reason is obvious, sincesome water infiltrated the soil. The fourth scenariowas modified from the third scenario by addingmacropore flow with macroporosity equal to 0.00035.

The fourth scenario was also the reference scenariofor the following four scenarios (the fifth to eighthscenarios). The results are shown in Fig. 5(d). Theamount of discharge into the river and the ponding

water was decreased further due to more waterflowing into the soil.

To examine the sensitivity of the macropore flowand overland flow to four land characteristics, fourmore scenarios were designed based on the fourthscenario (the reference scenario). The fifth scenariowas designed to examine the flow sensitivity to theStrickler roughness coefficient by decreasing it from10 to 5 (the actual roughness is increased). Macroporeflow increased by 0.05 cm (10%) compared withthe reference scenario at 30 min (always comparedwith the reference and at 30 min for all the lastfour scenarios). Ponding depth increased by 50%and the discharge decreased 30% (Fig. 5(e)). Ahigher roughness (or lower Strickler roughnesscoefficient) decreased the overland flow, increasedthe ponding depth and, therefore, increased themacropore flow.

The sixth scenario was designed to examine thesensitivity to the microtopographic variation ampli-tude A by decreasing it from 1.0 cm to 0.5 cm. Thetotal macropore flow increased 30%. The pondingwater remained the same and the discharge decreased(Fig. 5(f)). With a smaller microtopographic variationthe ponding area is larger with the same pondingdepth and, therefore, macropore flow increases.

The seventh scenario was designed to examine thesensitivity to the change of the land surface slope bydecreasingZ from 1.0 m to 0.5 m. The maximum sur-face elevation difference (3Z) was decreased from 3 mto 1.5 m. Macropore flow increased 7%. The pondingwater increased 15%. The discharge decreased 18%(Fig. 5(g)). A watershed with a smaller slope has lessoverland flow and thus more macropore flow.

The last scenario was designed to examine the sen-sitivity to the macroporosity by doubling the macro-porosity from 0.00035 to 0.0007. The macropore flowwas also doubled (100%). Both ponding and dis-charge water volumes were significantly decreased(Fig. 5(h)).

The results of the last five scenarios showed that themacroporosity was, relatively speaking, the most sen-sitive characteristic. The land slope was the least sen-sitive characteristic. Although the macropore flow andthe overland flow may not change linearly with thesefour characteristics, the results obtained here showqualitative sensitivities to the characteristics in theranges of the values examined.


6. Conclusions

Many researchers have studied macropore flow inmacroporous soils. In their analyses the macroporeactivation was simplified. It was assumed that macro-pores are activated uniformly in the field and that allexcess rain water flows into macropores uniformly.However, land surface may not necessarily be flat orsmooth. Macropores are activated non-uniformly,depending on the microtopography of the land sur-face. Some macropores may not be activated at all,whereas others are activated as soon as excess water isgenerated. Macropores may be activated only in theponding area. The ponding area is decreased by over-land flow. Therefore, macropore activation andmacropore flow can be affected by overland flowand vice versa.

A numerical model coupling overland flow andinfiltration into the layered macroporous vadosezone was developed. Overland flow was simulatedusing the St. Venant equations with the inertia termsneglected. A single macropore model was used tosimulate the infiltration into the macroporous vadosezone. Assuming the microtopographic variation of theland surface is a sine wave perpendicular to the flowdirection, an equation was established to relate theponding area to the average ponding depth. The sen-sitivity analysis of the interaction for a hypotheticalwatershed revealed that macropore flow and overlandflow can affect each other significantly. The macro-pore flow and the overland flow were more sensitiveto the macroporosity and less sensitive to the micro-topographic variation.

Acknowledgements

This research was supported partially by a grantfrom the US Department of Energy, and a grantfrom the US Environmental Protection Agencythrough Great Plain–Rocky Mountain HazardousSubstance Research Center at Kansas State Univer-sity. We thank Iggy Litaor for his contributions todiscussions of some of the ideas used in this research,

Laj Ahuja for his suggestions on the manuscript of thispaper, and the reviewers, Han Stricker and JoelGoldenfum, for their valuable comments.

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