Modeling hydrology and sediment transport in vegetative …...Modeling hydrology and sediment transport in vegetative filter stripsq Rafael Mun˜oz-Carpenaa, John E. Parsonsb,*, J.

Modeling hydrology and sediment transport in vegetative filterstripsq

Rafael Muñoz-Carpenaa, John E. Parsonsb,* , J. Wendell Gilliamc

aInstituto Canario de Investigaciones Agrarias, Apdo 60 La Laguna, 38200Tenerife, SpainbDepartment of Biological and Agricultural Engineering, North Carolina State University, Raleigh, NC 27695-7625, USA

cSoil Science, North Carolina State University, Raleigh, NC 27695-7625, USA

Received 23 June 1998; accepted 19 October 1998

Abstract

The performance of vegetative filter strips is governed by complex mechanisms. Models can help simulate the field condi-tions and predict the buffer effectiveness. A single event model for simulating the hydrology and sediment filtration in bufferstrips is developed and field tested. Input parameters, sensitivity analysis, calibration and field testing of the model arepresented. The model was developed by linking three submodels to describe the principal mechanisms found in natural buffers:a Petrov–Galerkin finite element kinematic wave overland flow submodel, a modified Green–Ampt infiltration submodel andthe University of Kentucky sediment filtration model for grass areas. The new formulation effectively handles complex sets ofinputs similar to those found in natural events. Major outputs of the model are water outflow and sediment trapping on the strip.The strength of the model is a good description of the hydrology within the filter area, which is essential for achieving goodsediment outflow predictions or trapping efficiency. The sensitivity analysis indicates that the most sensitive parameters for thehydrology component are initial soil water content and vertical saturated hydraulic conductivity, and sediment characteristics(particle size, fall velocity and sediment density) and grass spacing for the sediment component. A set of 27 natural runoffevents (rainfall amounts from 0.003 to 0.03 m) from a North Carolina Piedmont site was used to test the hydrology component,and a subset of nine events for the sediment component. Good predictions are obtained with the model if shallow uniform sheetflow (no channelization) occurs within the filter.q 1999 Elsevier Science B.V. All rights reserved.

Keywords:Surface runoff; Erosion modeling; Sediment; Vegetative filter strips

1. Introduction

Runoff carrying sediment from nonpoint sources

has long been recognized as a major pollutant ofsurface water. Sediment-bound pollutants, such asphosphorous and some pesticides are also a majorpollution concern. Several management practiceshave been suggested to control runoff quantity andquality from disturbed areas. One such managementpractice is vegetative filter strips (VFS), which can bedefined as (Dillaha et al., 1989) areas of vegetationdesigned to remove sediment and other pollutantsfrom surface water runoff by filtration, deposition,infiltration, adsorption, absorption, decomposition,

Journal of Hydrology 214 (1999) 111–129

0022-1694/99/$ - see front matterq 1999 Elsevier Science B.V. All rights reserved.PII: S0022-1694(98)00272-8

q Paper No. BAE 98-08 of the Journal Series of the Departmentof Biological and Agricultural Engineering, NC State University,Raleigh, NC 27695-7625 (USA). The use of trade names in thispublication does not imply endorsement by the North CarolinaAgricultural Research Service of the products named or criticismof similar ones not mentioned

* Corresponding author. Tel.: 919 515 6750; Fax: 919 515 7760;e-mail: [email protected]

and volatilization. These bands of planted or indigen-ous vegetation separate a water body from a land areathat could act as a nonpoint pollution source. Vegeta-tion at the downstream edge of disturbed areas mayeffectively reduce runoff volume and peak velocityprimarily because of the filter’s hydraulic roughness,and subsequent augmentation of infiltration. Decreas-ing flow volume and velocity translates into sedimentdeposition in the filter as a result of a decrease intransport capacity (Wilson, 1967). Barfield et al.(1979) and Dillaha et al., (1986) reported that grassfilter strips have high sediment trapping efficiencies aslong as the flow is shallow and uniform and the filter isnot submerged.

As sediment is deposited from runoff in these vege-tated zones, sediment-bound nutrients are alsoremoved (Bolton et al., 1991; Flanagan et al., 1989).For nutrients attached to sediment (i.e. organic phos-phorous, ammonium and organic N) the depositionprocess largely controls the effectiveness of the filterarea, whereas infiltration is the controlling factor forsoluble nutrients (such as nitrates and inorganic ortho-phosphates).

Several short-term studies have concentrated onevaluating the effectiveness of grass filter strips intrapping sediment and nutrients (Young et al.,1980; Daniels and Gilliam, 1989; Dillaha et al.,1989; Magette et al., 1989). They reported trappingefficiencies exceeding 50% for sediment and nutrientsadsorbed to sediment, while dissolved nutrient trap-ping was not as efficient and sometimes an increase innutrient losses has been reported (Dillaha et al., 1989;Magette et al., 1989).

Other areas that may be effective in improving offsite surface water quality are riparian areas. They aredefined (Lowrance et al., 1986; Mitsch and Goselink,1986) as vegetated ecosystems along a water bodythrough which energy, materials, and water pass.These areas encompass uplands, wetlands and combi-nations of both land forms. Cooper et al. (1987) esti-mated that as much as 90% of the sediment wasdeposited in the riparian area for a North Carolinawatershed. Lowrance et al. (1986) concluded thatriparian areas in Georgia were effective sinks for sedi-ment.

Researchers (Dillaha et al., 1989; Parsons et al.,1991) have found that the filter length (Lt) controlssediment trapping up to an effective maximum length

value, thereafter, additional length does not improvefilter performance. This maximum effective lengthdepends on the source area, topography, and thehydraulic characteristics of the strip.

Several modeling efforts have been undertaken tosimulate VFS efficiency in removing pollutants fromsurface waters. Researchers at the University ofKentucky (Barfield et al., 1978, 1979; Hayes, 1979;Hayes et al., 1982, 1984; Tollner et al., 1976, 1977)developed and tested a model (GRASSF) for filtrationof suspended solids by artificial grass media. Themodel is based on the hydraulics of flow, and transportand deposition profiles of sediment in laboratoryconditions. This physically based model takes intoaccount a number of important field parameters thataffect sediment transport and deposition through thefilter (sediment type and concentration, vegetationtype, slope and length of the filter). Flow is describedby the continuity equation and steady state infiltration,i.e. flow decreases linearly from upstream to down-stream in the filter.

Wilson et al., (1981) modified and incorporatedGRASSF into SEDIMOT II, a hydrology and sedi-mentology watershed model. A simple algorithm tocalculate the outflow hydrograph was incorporatedinto the model and up to three different slope changesthroughout the filter could be considered. The modeldoes not handle time dependent infiltration, an accu-rate description of flow through the filter, and changesin flow derived from sediment deposition during thestorm event.

Several authors (Flanagan et al., 1989; Williamsand Nicks, 1988; Nicks et al., 1991) have used theCREAMS model (Knisel, 1980) to evaluate theperformance of VFS. However, as pointed out byDillaha and Hayes (1991), CREAMS does not simu-late the principal physical processes affecting trans-port in VFS and its applicability is questionable. TheCREAMS simulations modify the erosion parametersof the downslope area to reflect increased roughnessin the filter. However, the hydrology component doesnot take into account the changes in runoff volume orpeak rates from the site caused by the filter.

The purpose of this work is to present and evaluateusing experimental field data, a model (VFSMOD) tostudy hydrology and sediment transport through VFS.The model combines the strength of: a) a numericalsubmodel to describe overland flow and infiltration, b)

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the University of Kentucky’s algorithm developedspecifically for the filtration of suspended solids bygrass. This model formulation effectively handlescomplex sets of inputs similar to those found innatural events. The improvements of this combinedmodel over the GRASSF or SEDIMOT II modelsare the inclusion of: (a) state of the art descriptionof flow through the filter; (b) changes in flow derivedfrom sediment deposition; (c) physically based timedependent soil water infiltration; (d) handling ofcomplex storm pattern and intensity; and (e) varyingsurface conditions (slope and vegetation) along thefilter.

2. Model development

Several processes must be described to simulatehydrology and sediment transport in filter strips. Theproblem can be divided into two major mechanisms:hydrology, and sediment transport and deposition.Hydrology in this context involves overland flow rout-ing and soil water infiltration. Overland flow routingdescribes the water movement over the land surfaceby calculating flow rates at positions along the hillslope (Woolhiser, 1975). Sediment transport depictsthe distribution of sediment concentrations along thehill slope at different time steps. These two mechan-isms must be modeled concurrently as the solution tothe sediment transport relies on flow values at differ-ent times and locations given by the hydrology part ofthe problem.

Two main submodels, one for each of the mechan-isms, are linked together to produce a field-scalesingle storm model. The model routes the incominghydrograph and sedimentograph from an adjacentfield through a VFS and calculates the outflow, infil-tration and sediment trapping efficiency for that event.

2.1. Hydrology submodel: overland flow and soilinfiltration

The hydrology submodel presented by Mun˜oz-Carpena (1993) and Mun˜oz-Carpena et al.,(1993a,b) consists of a Petrov–Galerkin quadraticfinite element (FE) overland flow submodel basedon the kinematic wave approximation (Lighthill andWhitham, 1955):

2h2t

12q2x iet rt2 f t; 1

q ahm Sp

0

nh5=3; 2

wherex is flow direction axis (m),t is time scale (s),h(x,t) is vertical flow depth (m),q(x,t) is discharge perunit width (m2/s), ie(t) is rainfall excess (m/s),r(t) israinfall intensity (m/s),f(t) is infiltration rate (m/s),S0is bed slope (m/m) at each node of the system,a andm are the coefficients for coupling uniform flow Eq.(2) (Manning’s),n is Manning’s roughness coefficientdependent on soil surface condition and vegetativecover at each node of the system. The initial andboundary conditions are:

h 0; 0 # x # L; t 0;h h0; x 0; t . 0;

3

where h0 can be 0, a constant or a time dependentfunction, such as the incoming hydrograph from theadjacent field.

The overland flow model was coupled, for eachtime step, with an infiltration submodel based on amodification of the Green–Ampt equation forunsteady rainfall (Chu, 1978; Mein and Larson,1971, 1973; Skaggs and Khaheel, 1982; Mun˜oz-Carpena et al., 1993b):

fp Ks 1 KsMSavFp ; 4

Kst 2 tp 1 t0 F 2 M Sav ln 1 1 FM Sav� �

;

5wherefp is the instantaneous infiltration rate, or infil-tration capacity, for ponded conditions (m/s),Ks is thesaturated vertical hydraulic conductivity (m/s),M u s 2 u i is the initial soil-water deficit (m

3/m3), Sav isthe average suction across the wetting front (m),Fp isthe cumulative infiltration after ponding (m),F is thecumulative infiltration for the event (m),t is the actualtime (s),tp the time to ponding, andt0 is the shift of thetime scale to correct for not having ponded conditionsat the start of the event.

Rainfall excess,ie in Eq. (1), is calculated for agiven rainfall distribution for each node and time

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step by the infiltration model. The hydrograph repre-senting runoff from the adjacent field is input as a timedependent boundary condition at the first node of theFE grid. The program allows for spatial variation ofthe parametersn andS0 over the nodes of the system(Fig. 1). This feature of the program ensures a goodrepresentation of the field conditions for differentrainfall events. The model can be operated to provideinformation on the effect of soil type (infiltration),slope, surface roughness, filter length, storm patternand field inflow on VFS performance (i.e. reduction of

the runoff peak, volume and velocity) (Mun˜oz-Carpena et al., 1993b). It also describes the flow rate(q), velocity (V), and depth (h) components through-out the filter for each time step.

The numerical solution is subject to kinematicshocks, or oscillations in the solution that developwhen a sudden change in conditions (slope, roughnessor inflow) occurs. When linking the kinematic waveand the sediment transport models, the soil surfaceconditions are also changed for each time step, furtherincreasing the potential for the kinematic shock

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Fig. 1. Domain discretization for the FE overland flow submodel.

Fig. 2. Filter description for the sediment transport algorithm.

problem. VFSMOD implements a Petrov–Galerkinformulation (non-standard) FE to solve Eqs. (1) and(2). This solution procedure reduces the amplitudeand frequency of oscillations with respect to the stan-dard Bubnov–Galerkin method (Mun˜oz-Carpena etal., 1993a), thus improving the model stability andthe sediment transport predictions which depend onoverland flow values.

2.2. Sediment transport submodel

The University of Kentucky algorithm considersthat during a rainfall/runoff event, field runoff reachesthe upstream edge of the filter with time dependentflow rateqin (cm

2/s), and sediment loadgsi (g/cm/s).The vegetation produces a sudden increase in hydrau-lic resistance that slows the flow, lowers its transportcapacitygsd (g/cm-s), and produces deposition of thecoarse material (particle diameter dp. 0.0037 cm)carried mostly as bed load transport. The sedimenttrapped in this first part of the filter forms a geome-trical shape that varies depending on the thickness ofthe deposited sediment layer at the entry of the filter,Y(t) (m), and the effective top of vegetation,H (cm). Atriangular shape at the adjacent field area and thebeginning of the filter is formed whenY(t) , H.After Y(t) H, a trapezoidal wedge is formed (Fig.2) with three well defined zones: the upslope face ofthe wedge (with zero slope),O(t) (cm); the upper faceof the wedge (parallel to the soil surface),A(t); and thedownslope face,B(t), with an equilibrium depositionslope Se for each time step (Fig. 2). Together thesefirst filter zones are termed ‘‘wedge zone’’, and itslength changes with time as sediment is deposited.

Zone O(t), external to the filter, is important inexplaining field observations where a portion of thesediment is deposited in the field area adjacent to thefilter. After the wedge has formed, no sediment isdeposited in zoneA(t) and the initial load,gsi,moves through to the next zone,B(t). In this zone,deposition occurs uniformly with distance to thedeposition edge, with transport mostly as bed load.The model assumes that the sediment inflow load,gsi, is greater than the downstream sediment transportcapacitygsd at point 2 (Fig. 2). The algorithm calcu-lates thegsd value for each time step and compares itwith the sediment inflow load. Ifgsd. gsi, all sedimentis transported through the first part of the filter

(wedge),gs2 gsd, and the sediment is filtered at thesuspended sediment zone (lower part of the filter). Ifgsd , gsi deposition at the wedge occurs and the frac-tion not deposited is filtered at the lower part of thefilter, gs2 gin 2 gsd. The calculation procedureutilizes a modified Manning’s open channel flowequation, equation of continuity and Einstein’s totaltransport function. Flow values at the filter entry andpoints 1 and 2 in Fig. 2 (qin, q1, q2 respectively) areneeded for these calculations.

After the downside of the wedge, two zonesC(t)andD(t) form the ‘‘suspended load zone’’ or ‘‘effec-tive filter length’’, L(t) (Fig. 2). On zoneC(t), sedi-ment has covered the indentations of the surface sothat bed load transport and deposition occurs but thesoil slope,Sc, is not significantly changed. All bedload transported sediment is captured before reachingzoneD(t), so only suspended sediment is transportedand deposited in this zone until the flow reaches theend of the filter with sediment loadgso. The sedimenttrapping algorithm for the suspended load zonefollows Tollner et al., (1976) equation based on aprobabilistic approach to turbulent diffusion for non-submerged flow. Flow values at point three and filterexit, q3 andqout respectively (Fig. 2), are needed forthese calculations. Details of the implementation ofthe submodel are given in Mun˜oz-Carpena (1993).

Mixed particle distribution is not included in themodel formulation. The sediment filtration algorithmcoded is that of the original work from Barfield et al.,(1978, 1979) and Tollner et al., (1976, 1977). Toaccount for real mixed particle sediment, a moresimplified approach is taken similar to that used inthe USDA-ARS KINEROS model (Woolhiser,1990). In this model the median sediment particlediameter (d50), read from the sediment particle distri-bution graph, represents an effective mean value forthe plot and is used in the sediment filtration algorithmto predict sediment deposition. Ranges for sedimentparticle diameters for various soil textures can be esti-mated from work presented by Woolhiser et al.,(1990).

2.3. Linkage between submodels

Flow conditions at the entry, exit and three innerpoints (1, 2, and 3) of the filter are needed for thesediment transport calculations (qin, q1, q2, q3 and

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qout in Fig. 2). The GRASSF and SEDIMOT II modelsuse a simple approach to calculating those values anddo not consider the complex effects of rainfall, infil-tration, and flow delay caused by the filter. A moreaccurate description of the flow conditions is obtainedfrom the hydrology submodel presented before. Inturn, the sediment transport model supplies informa-tion on changes in surface conditions (topography,roughness) due to sediment deposition during theevent that affect overland flow.

During the simulation, feedback between thehydrology and sediment models is produced. The

hydrology model supplies the flow conditions at thefive locations (entry, 1, 2, 3, and exit) set in the lasttime step (Fig. 2). The other parameters that interactthrough the linkage are the length, slope, and rough-ness in each of the sections (entry, 1, 2, 3, and exit).

After solving the sediment transport problem for atime step, new values of roughness and/or slope areselected as nodal values for the FE grid in zonesA(t)and B(t), whereasC(t) and D(t) remain unchanged(Fig. 2). Changes in surface saturated hydraulicconductivity values (Ks) are considered negligible.The new surface parameters are fed back into the

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Fig. 3. Field layout and instrumentation at the experimental site.

hydrology model for the next time step. Surfacechanges are accounted for in this way.

The time step for the simulation is selected bythe kinematic wave model to satisfy convergenceand computational criteria of the FE methodbased on model inputs (Mun˜oz-Carpena et al.,1993a,b).

The incoming sedimentograph,gsi (g/s) duringthe simulation is obtained by multiplying the aver-age sediment concentration for the event,Ci (g/cm3) by the inflow rate,qin (m

3/s), The implicitassumption is that water inflow is the major factorcontrolling the dynamic sediment inflow, more sothat the varying sediment concentration throughoutthe storm. This assumption was tested by compar-ing curve shapes and mass of the incoming fieldsedimentographs with the reconstructed sedimento-graphs (Ci * qin) for the simulated events and foundto be acceptable. The proposed method improvesthe usability of the model as theCi can be calcu-lated from composite samples for the storm whichare simpler to obtain from existing erosion plotexperiments.

At the end of the simulation, the model outputsinclude: information on the water balance (volumeof rainfall, field inflow, filter outflow and infiltra-tion), hydrograph, sediment balance (field inflow,filter outflow and deposition), sedimentograph, filtertrapping efficiency, and sediment deposition patternwithin the filter (Muñoz-Carpena and Parsons,1997).

3. Model testing

A field experimental site was set up for the purposeof calibrating and testing the model. Model inputswere measured or estimated from filter conditionsand rainfall/runoff data collected for two years. Onesubset of the recorded events was used for calibratingthe model and another for testing.

3.1. Experimental field setup

A field site in the North Carolina Piedmont regionwas selected to monitor the performance of VFS andriparian areas (Parsons et al., 1991). The soil at the siteis a Cecil clayey, kaolinite, thermic, Typic Hapludultwith a silty-loam surficial horizon (Parsons et al.,

1994). Six runoff plots with 4 m wide by 37 m longcropland source areas were constructed at the field.The slopes on the plots varied from 5% to 7%. Fieldrows were parallel to the slope to maximize runoff anderosion and enable testing of the filters under theworst conditions.

Surface runoff was collected at the field edge fortwo of the runoff plots (Fig. 3). Runoff from thesecontrol plots (no filter) was assumed to equal that ofthe adjacent field plots with filters. Two other plotshad grass filter strips 4.3 m long and the remainingtwo had 8.5 m long strips. For these buffers, the ratioof the area of the field to the filter was 9 : 1 and 4.5 : 1,respectively. The grass stand was a mixture of fescue,bluegrass and bermuda grass. Two riparian filter plotswere located further down slope. These areas weresteep (18%–20% slope) with a vegetation mixtureof trees and bushes. The surface runoff from the twonon-filter plots was distributed at the upper edge of thetwo riparian plots. The riparian plots were 1.3 m widewith lengths of 4.3 and 8.5 m (area ratios of 27 : 1 and13.5 : 1).

The quantity of runoff from each of the eightsampling points was measured with HS type flumes(0.15 m depth) (Brakensiek et al., 1979). The runofffrom each plot was collected by a rain gutter andthen piped to the flumes (Fig. 3). Water levels inthe HS flumes were monitored with a potentiometer– float assembly. A half bridge with a 2 V excita-tion was used with the potentiometers providingvoltage levels to measure water elevations in theflumes.

A portable datalogger (Campbell Scientific-CR10)was used at the site to monitor rainfall and surfacerunoff, and activate the water quality samplers. Atipping bucket rain gauge measures rainfall intensitiesand volumes at 5 min intervals (Fig. 3). The datalog-ger monitors and records the flume water levels duringstorm events every 30 s. Discrete automatic waterquality samplers were installed on each of the eightplots. The samplers contain 24 one-liter bottles. Thewater quality sampler took a sample whenever theflume water level increased or decreased by 5 mmor more. The inlets for the samplers were located ina plywood trough downstream of the flume. Collectedsamples were analyzed for sediment concentrationsand particle size distributions (Gee and Bauder,1986).

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3.2. Input parameters for the model

3.2.1. Model inputs for the hydrology submodelThe input parameters for the hydrology part of the

model (overland flow1 infiltration) are summarizedin Table 1. More details on the selection of theseparameters can be found in Mun˜oz-Carpena (1993)and Muñoz-Carpena and Parsons, (1997). Differentprocedures were used to identify these parametersfor field testing the model.

The filter length and width were measured directlyin the field. Nodal slopes were determined by a topo-graphical field survey. A dense grid was laid down onthe areas (a total of 191 points: 24 points in each of theshort strips, 45 in each long strip). The transversalvalues of slope (to the direction of flow) were aver-aged to obtain a width-averaged set of slopes for eachstrip. These values were used for simulation purposes.A 1-D grid of 50 nodes was selected for each stripwith 7–14 segments of equal slope. The range ofslopes can be found in Table 1.

Manning’s roughness coefficients were estimatedfrom the literature values to match field conditions(Woolhiser, 1975; Engman, 1986; Woolhiser et al.,1990; Arcement and Schneider, 1989). These valueschange seasonally as a function of the vegetativeconditions of the cover (higher values in summer,lower values in winter). Based on the references,the range considered in the field testing was 0.10–0.60 for grass buffers and 0.10–0.45 for riparianvegetation.

The saturated water content (u s) was measured inthe laboratory from undisturbed soil cores, andsuction at the soil wetting front (Sav) was determinedfrom soil suction curves obtained from the soil coresfrom each filter area (Klute, 1986). Saturated verticalhydraulic conductivity values at the surface,Ks, werealso measured from soil cores in the laboratory (Kluteand Dirksen, 1986). Infiltrometer tests wereconducted in the field (Bower, 1986). These valueswere highly variable ranging from 2.78× 1027 to1.33× 1025 m/s.

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Table 1Field parameters governing the model

Symbol Description Values Units

General N Number of modes 27–50 –CR Courant’s number 0.8 –TTIME Total simulation time 1800–3900 s

Hydrology component L Filter length 4.25–8.50 mW Filter width 1.27–3.87 mSok Slope at each node (k 1,N) 0.02–0.20 –nk Manning’s n (k 1, N) 0.10–0.45 s/m1/3Ks Saturated hydraulic conductivity 2.5× 1026–3.5× 1025 m/su s Saturated water content grass filters: 0.311

riparian filters: 0.306m3/m3

u i Initial water content 0.100–0.310 m3/m3

Sav Sunction at the wetting front grass filters: 0.379riparian filters: 0.088

m

Sediment Component nm Modified grass Manning’s n 0.012 s/cm1/3

nb Manning’s n for bare soil 0.04 s/m1/3

dp Median particle size, d50, ofincoming sediment

0.0003–0.0029 cm

g s Sediment weight density 2.60–2.65 g/cm3

Vf Fall velocity of sediment 0.0004–0.0760 cm/sSs Media spacing grass filters: 2.2

riparian filters: 10.0cm

H Media height 15 cmP Porosity of deposited sediment 0.434 –CI Inflow concentration 0.00075–0.03402 g/cm

3

COARSE proportion of fine sediment 100 %

3.2.2. Model inputs for the sediment submodelThe field parameters that describe the sediment

filtration process in this model are summarized inTable 1. The modifiednm and grass spacing,Ss, valueswere selected from the type of vegetation in the grassfilters (Hayes et al., 1982). For a fescue/bluegrass/

bermuda grass mixture found at the experimentalsite, a value ofn 0.012 s/cm1/3 andSs 2.2 cm isrecommended. The spacing value matches vegetationcounts measured at the experimental site (Mun˜oz-Carpena, 1993). For the riparian area,Ss 10.0 cmwas selected by field inspection.

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Fig. 4. (a-b) Sensitivity of model hydrological outputs to saturated hydraulic conductivity (a) and soil initial moisture content (b) values.

The parameterH was selected as 15 cm for ourfield situation, where the grass was maintainederect at least at that height. The porosity of thedeposited sediment,P, was selected as 0.434(Hayes, 1979).

Ranges for sediment particle size (d50), fall velocityand density were chosen from soil texture based ontabulated data (Woolhiser et al., 1990). Soil texture ofthe surficial soil horizon was measured from a total of15 samples taken at different surface points in theagricultural field source area (upper, medium andlower sections), and the filter areas. For the surficialsilty-loam at the experimental site, a range of medianparticle sizes (d50) from 0.0003 to 0.005 cm, wasselected. The actual value for each event dependsnot only on soil texture but also on flow conditions(energy of the overland flow). As fall velocity isrelated to particle size, the termparticle classwillbe used to denote these two characteristics plus sedi-ment density.

The average sediment inflow concentration for themodel, Ci (g/cm

3), was obtained from field data foreach event by dividing the total sediment, comingfrom the agricultural source area into the filters, bythe total volume of water inflow giving a range from0.00075 to 0.03402 g/cm3 (Table 1).

3.3. Analysis of sensitivity of the model to the inputparameters

A sensitivity analysis was performed to gain someinsight in the dependence of model outputs on certainmodel parameters and to assist in the model calibra-tion. Some initial testing showed that the main para-meters controlling the hydrology outputs wereKs andu i whereas the model was fairly insensitive to changesin u s and Sav values. Previous research (Mun˜oz-Carpena et al., 1993a) showed that Manning’sncontrols mainly the time to peak of the outgoinghydrograph.

A detailed sensitivity analysis was conducted forthe parametersKs, u i and Manning’sn. Starting withmeasured values (Ksl 1.33 × 1025 m/s, u s 0.311 cm3/cm3), three sets of 115 simulations eachwere carried out for a range of (0.05Ksl , Ks ,4 Ksl) (23 steps), and (0.5u s , u i , u s) (5 steps).For each set, a differentn was selected (n 0.1–0.5). In these simulations, field measured values foru s and Sav were used (Table 1) and the additionalinputs (filter characteristics, rainfall distribution andfield inflow) were taken from an event recorded at theexperimental site on 06/30/91 for a grass strip 4.3 mlong.

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Fig. 5. Sensitivity of model sediment outputs to media spacing and sediment class

Several quantities for the output hydrographs wereobtained and compared for each simulation: delaytime (td), time to peak (tp), peak flow rate (Qp), andtotal runoff volume (Vol). The results of the sensitiv-ity analysis show that the output values Vol,td, andQpare sensitive to the parametersKs and u i. Fig. 4(a)shows how a 100% increase inKs translates into a100% decrease in Vol andQp, and a 100% increasein td. Fig. 4(b) shows how a 60% increase inu i led to a20% and 40% increase in Vol andQp, respectively,and a 50% decrease intd. The tp was not significantlyaffected by the changes inKs or u i (not shown). Aninteraction betweenKs and u i was observed for lowvalues ofKs. This is explained by the fact that forlower values ofKs the delay time is controlled bythe soil moisture deficit (higher deficit, greaterdelay), but for higherKs values, infiltration is suffi-cient to absorb the instantaneous rainfall intensity andthe field inflow, regardless of the initial moisture defi-cit.

Initial testing on the sediment component of themodel showed that the main parameters controllingsediment outflow are media spacing,Ss, and particleclass. Variations in the modified Manning’snm hadrelatively little effect on the output and the mediaheight,H, was only visible for large events after the

trapezoidal wedge was formed at the filter. A detailedanalysis was performed by varying grass spacing(0.05 , Ss , 10 cm) and particle classes (clay, silt,sand, small aggregates and large aggregates) (USDASoil Survey Staff, 1975; Mun˜oz-Carpena, 1993). Theremaining model inputs were obtained from the samefield event as described before, and settingKs Ksl,u I 0.20,nm 0.012 cm/s1/3, andH 15 cm.

Fig. 5 shows the sediment outflow to be sensitive toparticle class and grass spacing. Increases in totalsediment outflow predictions of 100%–120% tookplace for each of the USDA Soil Survey Staff(1975) particle classes whenSs was increased 500%.For finer sediment classes most of the reduction tookplace in the lower range of the grass spacing values(0.05, Ss , 10 cm) and the outflow became insensi-tive to further increases inSs, whereas for the coarsersediment (sand) the increase was uniform. The expla-nation lies in the fact that for finer sediment the filtra-tion process is performed mostly from suspendedsediment in the suspended load zone of the filter(L(t) in Fig. 2), whereSs is the governing parameter,whereas for sand most of the filtration takes place asdeposition in the sediment wedge which depends onbed load transport relations and not onSs.

An additional batch of simulations was conducted

R. Muñoz-Carpena et al. / Journal of Hydrology 214 (1999) 111–129 121

Fig. 6. Interaction between sensitive hydrological parameters and sediment outflow for some sediment classes.

to test the interaction between hydrology sensitiveinputs and sediment outputs. Initial values of saturatedhydraulic conductivity and initial soil moisturecontent were chosen (Ks Ksl, u i u io 0.218),then varied (0.95Ksl # Ks # 2Ksl; 0.70u io # u i #1.3u io u s), and sediment output recorded for eachsimulation. This procedure was repeated for each ofthe five particle classes mentioned earlier. Fig. 6depicts the results for two of the sediment classes(clay and large aggregates). The analysis yielded simi-lar results for four sediment classes (clay, silt, small,aggregates and sand) wherea ^ 100% change in theKs value results in an averagê 25% change insediment outflow, with some variation around thataverage (̂ 20%–38%) introduced by theu i value.The remaining particle class (large aggregates)showed to be less sensitive to changes in hydrologyparameters, with only a 3.5% variation in sedimentoutflow obtained in the procedure (Fig. 6). This isbecause of the fact that large aggregates are quicklyretained at the entrance of the filter and infiltrationdoes not play a significant role in the trapping process.

3.4. Model testing procedure

The procedure was divided into two steps: an initialcalibration using a subset of field data for each eventand subsequent field testing using the remaining datafor the event. The calibration and testing of the

hydrology component was done first as the sedimentcomponent builds on these results. The parametersoptimized in the calibration process were those forwhich the model was found to be most sensitive (Ks,u i, and d50).

Two data subsets were prepared for each eventwhere runoff data was collected from the two filterlengths, one subset for each filter length (4.25 and8.5 m). Calibration of the hydrology component wasperformed by adjusting Ks andu i to match observedoutflow data (Vol, td, tp, Qp) on one of the filterlengths. Testing was carried out for that event byrunning the model for the other filter length with theparameters from the calibration run (modifying onlythe length and slope on the filter) and comparing theresults with the observed data for that filter.

After calibration of the hydrology submodel, thesediment submodel was calibrated following thesame approach by adjusting sediment class (d50)within the suggested range (0.0003–0.005 cm) tomatch total sediment outflow and minimize errorbetween predicted and observed pollutographs. Nohydrology inputs were modified during this process.There was insufficient field data to perform a completefield testing of the sediment component in the mannerdescribed earlier, though the response obtained duringthe calibration using parameter ranges consistent withphysical characteristics at the site show the ability ofthe model to describe the field process.

R. Muñoz-Carpena et al. / Journal of Hydrology 214 (1999) 111–129122

Table 2Statistics used to assess quality of the model results

Description Symbol Equation Auxiliary Equations Best Fit

Pearson square moment PSM nP

YoiYpi 2 P

YoiP

YpinP

Y2oi 2 P

Yoi2q

nP

Y2pi 2 P

Ypi2q 2 1.0

Weighted Pearsonmoment

PWMAB

nP

YoiYpi 2 P

YoiP

YpinP

Y2oi 2 P

Yoi2q

nP

Y2pi 2 P

Ypi2q A 1

2

PY2oi 1PY2piPYoi

B 12

PY2oi 1PY2piPYpi

^ 1.0

Sample correlationcoefficient for the 1:1 line

R21 : 1 1 21=n 2 2PYoi 2 Ypi21=n 2 1PYoi 2 �Yoi2 1.0

Root mean square error RMSE

1nPRes2i 2 1n PResi 2

rRe si (Yoi 2 Ypi) 0.0

Means square error MSE1

n 2 1PRes2i 2 1n PResI 2 Re si (Yoi 2 Ypi) 0.0

R. Muñoz-Carpena et al. / Journal of Hydrology 214 (1999) 111–129 123T

able

3F

ield

calib

ratio

nan

dte

stin

gof

the

hydr

olog

yco

mpo

nent

No.

Eve

ntV

Rai

nn

Ks

uI

Vol

t dt p

Qp

FP

red.

Obs

.E

rror

Pre

d.O

bs.

Err

orP

red.

Obs

.E

rror

Pre

d.O

bs.

Err

orSa

(mm

)(m

/s)

(m3 )

(%)

(s)

(%)

(s)

(%)

(m3 /

S)

(%)

Fie

ldC

alib

ratio

n1

183

291

g425

.20.

101.

33×

102

50.

200

1.08

801.

1210

22.

9%11

8681

246

.1%

1653

1622

1.9%

2.06×

102

31.

89×

102

39.

0%2

112

292

g411

.90.

401.

33×

102

50.

310

0.16

740.

1873

210

.6%

619

695

211

.0%

1122

1295

213

.4%

3.88

×10

24

3.46

×10

24

12.1

%3

112

292

r111

.90.

452.

10×

102

50.

200

0.13

940.

1129

23.5

%89

381

59.

5%10

7113

55221

.0%

2.99

×10

24

2.62

×10

24

14.1

%4

151

292

g43.

00.

405.

00×

102

60.

308

0.18

740.

1905

21.

6%80

354

547

.4%

1610

1865

213

.7%

1.62

×10

24

1.25

×10

24

30.4

%5

168

292

g44.

60.

405.

00×

102

60.

275

0.10

690.

1184

9.7%

417

455

8.4%

909

1025

11.3

%2.

04×

102

41.

66×

102

42

23.1

%6

178

292

g433

.00.

401.

33×

102

50.

100

1.65

201.

6120

22.

5%64

669

47.

0%91

593

52.

2%3.

15×10

23

2.50

×10

23

225

.7%

717

82

92r1

33.0

0.30

1.71

×10

25

0.10

01.

9990

2.29

8013

.0%

455

455

0.1%

863

935

7.7%

3.26

×10

23

3.70

×10

23

11.9

%8

309

292

g86.

90.

401.

00×

102

50.

311

0.29

380.

2896

21.

5%31

124

52

27.2

%74

766

52

12.4

%1.

05×

102

35.

06×

102

42

107.

8%9

309

292

r16.

90.

303.

50×

102

50.

100

0.11

040.

1120

1.4%

541

575

5.9%

603

635

5.0%

1.53

×10

23

1.54

×10

24

289

.3%

1030

92

92r2

6.9

0.30

1.00

×10

25

0.30

60.

5514

0.62

4611

.7%

309

335

7.6%

619

1265

51.1

%1.

86×

102

36.

47×

102

42

188.

1%11

331a

292

g413

.00.

401.

33×

102

50.

305

0.64

820.

6411

21.

1%31

739

519

.8%

598

545

29.

7%2.

28×

102

32.

46×

102

37%

1233

1a2

92r2

13.0

0.30

1.71

×10

25

0.30

50.

6687

0.71

186.

1%30

339

523

.2%

589

665

11.5

%1.

80×

102

31.

83×

102

32%

1333

1c2

92g8

9.4

0.40

2.50

×10

26

0.31

11.

0860

1.03

502

4.9%

306

365

16.1

%12

4511

152

11.7

%1.

30×

102

31.

06×

102

32

22%

1433

1c2

92r2

9.4

0.30

3.00

×10

25

0.20

00.

5606

0.50

692

10.6

%78

836

52

116.

0%11

6210

552

10.1

%8.

87×

102

45.

67×

102

42

56%

1524

293

g47.

10.

401.

33×

102

50.

305

0.32

400.

3687

12.1

%30

939

521

.7%

619

1175

47.3

%5.

72×

102

45.

68×

102

42

1%16

242

93r1

7.1

0.30

3.50

×10

25

0.20

00.

2803

0.27

17-3

.2%

519

605

14.2

%11

9214

7519

.2%

4.48

×10

24

3.95

×10

234

-13%

Fie

ldT

estin

g17

183

291

g825

.20.

10b1.

33×

102

50.

200

0.42

100.

4429

24.

9%16

8616

223.

9%17

9318

022

0.5%

1.34

×10

23

9.68

×10

24

38.5

%18

112

292

g811

.90.

401.

33×

102

50.

308

0.05

240.

0550

24.

7%62

375

52

17.5

%14

8016

252

8.9%

1.14

×10

23

8.55

×10

25

33.8

%19

112

292

r211

.90.

452.

10×

102

50.

200

0.00

000.

0000

0.0%

00

0.0%

00

0.0%

0.00×10

0.00

×10

0.0%

2015

12

92g8

3.0

0.40

5.00

×10

26

0.30

80.

0000

0.00

000.

0%0

00.

0%0

00.

0%0.

00×10

0.00

×10

0.0%

2116

82

92G

84.

60.

405.

00×

102

60.

300

0.04

030.

0469

1421%

790

1055

25.1

%11

2810

852

4.0%

1.30

×10

24

7.92

×10

25

264

.1%

2217

82

92g8

33.0

0.40

1.33×

102

50.

100

1.36

301.

4710

7.3%

648

425

252

.6%

1027

965

26.

4%3.

24×

102

32.

52×

102

32

28.5

%23

178

292

r233

.00.

301.

71×

102

50.

100

1.84

301.

7900

23.

0%45

942

52

8.1%

891

905

1.5%

3.33×

102

32.

52×

102

32

0.6%

2433

1a2

92g8

13.0

0.40

1.33×

102

50.

305

0.49

640.

5240

5.3%

316

395

20.0

%72

072

50.

8%1.

63×

102

31.

44×

102

32

13%

2533

1c2

92g4

9.4

0.40

1.33

×10

25

0.30

50.

7706

0.73

962

4.2%

777

515

250

.9%

1166

1115

24.

6%1.

09×

102

39.

01×

102

32

21%

2624

293

g87.

10.

401.

33×

102

50.

305

0.13

180.

1608

18.0

%30

439

523

.1%

1261

1475

14.5

%3.

77×

102

42.

82×

102

42

34%

2724

293

r27.

10.

303.

50×

102

50.

200

0.00

000.

0000

0.0%

00

0.0%

00

0.0%

0.00×10

0.00

×10

20.

0%

aF

ilter

sas

defin

edin

Fig

.4

bF

ilter

sbe

fore

gras

sde

velo

pmen

tat

the

begi

nnin

gof

the

expe

rimen

talp

erio

d

3.4.1. Statistical parameters used in the model testingprocess

Several types of statistics provide measures of thegoodness of fit between simulated and observedvalues (James and Burgues, 1982; McCuen andSnyder, 1975). Table 2 summarizes five statisticsthat were used during model testing. A pairedt-test

was also conducted to test if there was a significantdifference in the means of predicted versus observedvalues (Ostle and Malone, 1988). The assumptions forthe pairedt-test were that both the simulated andobserved data were from a normally distributed popu-lation and the null hypothesis was that the means fromthe two populations were equal.

3.4.2. Field calibration and testing of the hydrologycomponent

A set of 27 events from the experimental site(1991–1993) was chosen to compare the predictionsof the model with field values. Table 3 summarizesthese results.

In the field calibration process initial values ofKsKsl, nk 0.30 andu i 0.875u s (Ksl andu s are themeasured values as described in Table 1) were chosen

R. Muñoz-Carpena et al. / Journal of Hydrology 214 (1999) 111–129124

Fig. 7. (a–d) Comparison of observed versus predicted values for the hydrology component.

Table 4Measures of goodness of fit of the hydrology component

R21 : 1 PSMa PWMa MSEa RMSEa

Vol 0.99 0.92 0.92 4.55× 1023 6.62× 1022Td 0.76 0.75 0.79 25108 155.5tp 0.82 0.80 0.83 35357 184.5Qp 0.82 0.81 0.88 1.55× 1027 3.86× 1024

a As defined in Table 2

and then varied within the range of̂ 80% to fit theobserved data (cases 1–16 in Table 3). The optimalvalues found in each case were used in the validationof hydrographs from other strips within the same date-event (cases 17–27 in Table 3). This approachassumes thatKs and nb vary within the strips owing

to season and deposition of sediment from previousevents.

The predicted set of results presented in Table 3was compared with the observed values for theoutputs: Vol, td, tp, Qp. These values are plottedagainst a 1 : 1 line (line of perfect agreement) in

R. Muñoz-Carpena et al. / Journal of Hydrology 214 (1999) 111–129 125

Fig. 8. (a–b) Example of results obtained during the field calibration (a, case #6 in Table 3) and testing (b, case #22 in Table 3) of the hydrologycomponent.

Fig. 7(a–d). Good predictions were obtained ingeneral though some outliers were found in thetpandQp sets. Statistics obtained for all these quantitiesare summarized in Table 4. The best model predic-tions were obtained for the total outflow volume, Vol,and the worst for delay time,td. For each of the para-meters, a pairedt-test was done. Similar to the otherstatistics, the t-test results indicated that predictions ofVol and td were good while the means for predictions

of tp and Qp were statistically different from theobserved means, probabilities greater than 0.95.

Fig. 8 shows the results for a calibration run on agrass filter of 4.25 m followed by the testing run onthe grass filter of 8.50 m for the same event. Thesimulated hydrograph for the calibration run fit theobserved values. The testing run on the 8.5 m grassfilter underpredicted the peak although the shape wasin good agreement with the observed hydrograph.

R. Muñoz-Carpena et al. / Journal of Hydrology 214 (1999) 111–129126

Table 5Field calibration of the sediment component

No. Event VFSa Ss(cm) Sediment Inflow Sediment Outflow (g) Error (%) PWMR21 : 1d50 (cm)

b CI (g/cm3)c Total sediment (g) Predicted Observed

1 1122 92 g4 2.2 0.0003 0.00108 287.0 30.5 30.9 1.3 0.92 0.872 1122 92 r1 10.0 0.0006 0.00075 188.9 17.9 16.3 9.2 0.71 0.643 151b2 92 g4 2.2 0.0003 0.00244 968.3 20.1 20.0 0.72 0.71 0.644 178a2 92 g4 2.2 0.0029 0.03402 64759.5 2229.0 1738.3 2 28.2 0.91 0.845 178a2 92 g8 2.2 0.0029 0.03402 54884.2 4340.4 3989.2 2 8.8 0.75 0.556 178a2 92 r2 10.0 0.0029 0.03402 54884.2 12475.5 12862.1 3.0 0.78 0.737 331a2 92 g4 2.2 0.0008 0.00793 5788.0 2488.0 2497.1 0.4 0.74 0.668 331a2 92 g8 2.2 0.0004 0.00793 5788.0 345.0 429.2 19.5 0.73 0.519 0242 93 g4 2.2 0.0003 0.01147 6187.8 639.0 662.5 2 3.5 0.78 0.62

a Filters as defined in Figure 4.b Expected range for silty-loam soil surface; silt; 0.0003 < d50 < 0.005 cm (Woolhiser et al., 1991).c Measured for each storm.

Fig. 9. Example of results obtained during the field calibration of the sediment component (case No.4 in Table 5).

Although the quality of the predictions was gener-ally good, calibration or testing of the model wasdifficult in some cases especially where the calibrationwas poor (case 8, PWM 0.47,R21 : 1 0.27). Non-laminar flow as a result of channelization of the flowduring the season and other experimental artifactsmay account for these results.

3.4.3. Field calibration of the sediment componentA subset of nine cases from the experimental site

were chosen to compare sediment outflow predictionswith field data (cases 2–4, 6–7, 11, 15 and 24 in Table3). The input parameters used as a first approximationwere those measured or derived from field conditions.The only adjustment needed in two of the nine caseswas adjusting the d50 value within literature values forthis kind of soil (Woolhiser et al., 1990). Thisconfirms the idea that a correct handling of the filterhydrology, as the one provided in this study, is essen-tial to obtain acceptable sediment outflow predictionswhen simulating natural (dynamic) events.

All predicted sediment graphs were compared withthe observed data and thePWM and R21 : 1 statisticscalculated. Table 5 summarizes these results. Goodpredictions are obtained with the model in all buttwo cases. Comparisons of the average predicted sedi-ment loss with the observed sediment loss with thepairedt-test indicated that the means were statisticallyequal for probabilities of 0.66 or greater.

Fig. 9 shows an example from an event where thewater runoff and sediment load from the field area wasrouted through a grass filter ofL 4.3 m (Case 4 inTable 5). The other parameters not included in Table 5and used in all the simulations are as discussed in themodel inputs section: modified Manning’snm 0.012 s/cm1/3; media height,H 15 cm; and porosityof deposited sediment,p 0.434. The statistics calcu-lated for this case wereR21 : 1 0.85 and PWM 0.91.

4. Conclusions

A single event, one-dimensional model, was devel-oped and field tested. Field testing included selectionand analysis of inputs, a sensitivity analysis ofselected variables, and calibration and comparisonof model results with field data.

The strength of this model compared with previous

efforts lies in the better representation of field hydrol-ogy that leads to better sediment outflow predictions.The model applies a fundamental approach to thehydrology process by solving the physical equations(FE solution to the kinematic wave equation andGreen–Ampt Infiltration approximation). This solu-tion is linked (in time and space) with the Universityof Kentucky VFS model for sediment filtrationthrough VFS.

The sensitivity analysis indicated that the mostsensitive parameters were soil initial water contentand vertical saturated hydraulic conductivity for thehydrology component of the model and particle class(particle size, fall velocity and sediment density), andgrass spacing for the sediment component. Criticalattention should be given in the selection of theseparameters when running this model.

The model was tested for a North Carolina Pied-mont experimental site. In general, good agreementwas obtained between observed and predicted values.Some sources of variability were discussed. One suchsource was the complexity of the ‘‘natural’’ events.The handling of overland flow as sheet flow couldpose problems when a filter is not properly maintainedas suggested by some authors (Dillaha et al., 1986).

Field variability is an inherent source of error in anymodel validation, thus parameters to describe hydrol-ogy and sediment transport in VFS areas are highlyvariable. A range of variation in the saturated hydrau-lic conductivity parameters was needed to fit themodel to observed data. This variation is explainedby changes in surface conditions caused by seasonaland biological factors.

The nature of the mathematical formulation of theoverland flow model and its numerical solution is alsoconsidered. Eulerian methods (FEs, finite differences)suffer from numerical oscillations when suddenchanges in field conditions occur (kinematic shocks).The problem is minimized in this model formulationby the use of an improved numerical method (Petrov–Galerkin) (Muñoz-Carpena et al., 1993b).

Acknowledgements

This study is supported in part by USDA-SCS, US-EPA, NC-WRRI and Southern Region Project S249.The first author wishes to express appreciation for the

R. Muñoz-Carpena et al. / Journal of Hydrology 214 (1999) 111–129 127

economic support he received as a 1990–1993Doctoral Fellow of the Instituto Nacional deInvestigaciones Agrarias y Alimentarias of Spain(INIA-Ministry of Agriculture) and as a 1997 Fellowof the Study Leave for Researchers Program of INIAin cooperation with USDA-OICD and the NorthCarolina State University. The authors warmlythank Mr. Charles A. Williams, Dr. Ray B. Daniels,Mr. Bill Thompson and Ms. Bertha Crabtree fortheir assistance in the experimental aspects of thisproject.

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