Journal of Hydrology 525 (2015) 760–768

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Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol

Transport of E. coli D21g with runoff water under different solution
chemistry conditions and surface slopes
Scott A. Bradford a,⇑, Brendan Headd a, Gilboa Arye b, Jiří Šimůnek ca

US Salinity Laboratory, USDA, ARS, Riverside, CA, United States
Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Israelc
Department of Environmental Sciences, University of California, Riverside, CA, United Statesba r t i c l e

i n f oArticle history:
Received 13 August 2014
Received in revised form 20 January 2015
Accepted 20 April 2015
Available online 27 April 2015
This manuscript was handled by Laurent
Charlet, Editor-in-Chief, with the assistanceof Rizlan Bernier-Latmani, Associate Editor
Keywords:
RunoffSolution chemistry
Slope
Microorganism
Modelings u m m a r y
Tracer and indicator microbe runoff experiments were conducted to investigate the inﬂuence of solution
chemistry on the transport, retention, and release of Escherichia coli D21g. Experiments were conductedin a chamber (2.25 m long, 0.15 m wide, and 0.16 m high) packed with ultrapure quartz sand (to a depthof 0.10 m) that was placed on a metal frame at slopes of 5.6%, 8.6%, or 11.8%. Runoff studies were initiatedby adding a step pulse of salt tracer or D21g suspension at a steady ﬂow rate to the top side of the chamber and then monitoring the runoff efﬂuent concentrations. The runoff breakthrough curves (BTCs) wereasymmetric and exhibited signiﬁcant amounts of concentration tailing. The peak concentration levels
were lower and the concentration tailing was higher with increasing chamber slope because of greater
amounts of exchange with the sand and/or extents of physical nonequilibrium (e.g., water ﬂow in rills
and incomplete mixing) in the runoff layer. Lower amounts of tailing in the runoff BTC and enhanced
D21g retention in the sand occurred when the solution ionic strength (IS) was 100 mM NaCl comparedwith 1 mM NaCl, due to compression of the double layer thickness which eliminated the energy barrier
to attachment. Retained cells were slowly released to the runoff water when the IS of the runoff water
was reduced to deionized water. The amount and rate of cell release was greatest at the highest chamber
slope, which controlled the amount of exchange with the sand and/or the extent of physical nonequilibrium in the runoff layer, and the amount of retained cells. The observed runoff BTCs were well describedusing a transient storage model, but ﬁtted parameters were not always physically realistic. A model that
accounted for the full coupling between ﬂow and transport in the runoff and sand layers provided useful
information on exchange processes at the sand surface, but did not accurately describe the runoff BTCs
which were inﬂuenced by physical nonequilibrium in the runoff layer.
Published by Elsevier B.V.

1. Introduction
Microorganism contamination of surface water resources iscommon in the United States (USEPA, 1997; Abbaszadegan et al.,
2003; Borchardt et al., 2003), and has frequently been implicatedin water- and food-borne disease outbreaks (Centers for Disease
Control and Prevention, 1998; USFDA, 1998; Gerba and Smith,
2005; Pachepsky et al., 2011). High concentrations of pathogens,indicator microorganisms, and other colloids can be rapidly transported from agricultural ﬁelds, urban environments, and hillslopes
to streams or locations of surface water storage by runoff water

Abbreviations: DI, deionized; DLVO, Derjaguin–Landau–Verwey–Overbeek; IS,ionic strength.
⇑ Corresponding author. Tel.: +1 951 369 4857.
E-mail address: Scott.Bradford@ars.usda.gov (S.A. Bradford).
http://dx.doi.org/10.1016/j.jhydrol.2015.04.038
0022-1694/Published by Elsevier B.V.

(Rahe et al., 1978; Heathwaite et al., 2005; Haygarth et al., 2006).
Runoff has been reported to be the primary transport route forpathogen dissemination at the hillslope scale (Tyrrel andQuinton, 2003; Jamieson et al., 2004; Dorner et al., 2006). An
understanding of processes that inﬂuence the transport of pathogens and indicator microorganisms in runoff water is therefore
needed to assess and mitigate risks of microbial contamination of
surface water supplies to human health.
As pathogens are transported with runoff water they undergo
exchange with the soil surface. Exchange of solute and microorganisms to/from runoff water and the soil surface can be very complex,
depending on advection, dispersion, and reactions (Bradford et al.,2013). In particular, advective exchange with the soil surface (inﬁltration and exﬁltration) will depend on the surface water boundary
conditions, the surface topography, the initial soil water status,
hydraulic properties of the soil, soil structure, and subsurface

S.A. Bradford et al. / Journal of Hydrology 525 (2015) 760–768

heterogeneity. Spatial and temporal variations in these factors can
produce conditions of dynamic exchange between runoff waterand the soil surface (Wörman et al., 2007). Depression and obstruction storage of surface water will also produce relatively immobile
or stagnant zones of water connected to the mean runoff water.
Such stagnant zones include pools and eddies along runoff channels, water isolated behind rocks, gravel or vegetation, or relatively
inaccessible water due to uneven surface topography (Panday andHuyakorn, 2004). Diffusive exchange will occur between runoff
water and such stagnant zones (Wallach and van Genuchten,
1990; Govindaraju, 1996; Wallach et al., 2001). Rain drop impact
and erosion of contaminated soils and sediments are other mechanisms of pathogen exchange at the soil surface (Gao et al., 2004,
2005; Pachepsky and Shelton, 2011).
Pathogens at the soil surface may interact with soil particles
and/or vegetation and become retained, and thereby diminish theirtransport with runoff water. A multitude of physical, chemical, andbiological processes will inﬂuence the retention of microorganisms
at the soil surface. For example, microbe retention in soil and sediment is known to depend on soil properties such as surface roughness, grain size and distribution, soil structure, mineralogy, andsurface charge; properties of the water such as the water velocity,
the water saturation, and the solution pH, ionic strength (IS), andcomposition; and properties of the microorganisms such as thesize and surface charge, surface macromolecules, growth stage,
motility, and bioﬁlm (Ginn et al., 2002; Harvey and Harms, 2002;
Foppen and Schijven, 2006; Tufenkji et al., 2006; Bradford et al.,2013). Temporal changes in these same factors may produce
pathogen release. For example, a decrease in the solution IS will
result in an expansion of the double layer thickness and anincrease in the magnitude of the surface potential of the soil andmicrobe (Israelachvili, 1992; Elimelech et al., 1995) that will
reduce the depth of the secondary minimum and promote microberelease (Lenhart and Saiers, 2003; Grolimund and Borkovec, 2006;
Tosco et al., 2009; Bradford et al., 2012). Runoff water may subsequently become contaminated as a result of diffusion and exﬁltration of released pathogens.
Most microbial runoff studies to date have examined the efﬁcacy of vegetated buffer strips to remove pathogens (Atwill et al.,
2002; Tate et al., 2004; Trask et al., 2004; Kouznetsov et al.,2007; Guber et al., 2007, 2009; Guzman et al., 2010; Fox et al.,2011; Wu et al., 2011; Yu et al., 2012, 2013). Wide variations in
the removal efﬁciency of vegetative buffer strips have beenreported in the literature (Fajardo et al., 2001; Koelsch et al.,2006; Mawdsley et al., 1995; Pachepsky et al., 2006; Tate et al.,2004); e.g., ranging from almost none to complete removal. Thisvariability in performance is likely due to differences in designand operation of vegetative buffer strips, and incomplete characterization of factors inﬂuencing exchange with the soil surface.
Fox et al. (2011) reported that Escherichia coli mass reductions inrunoff water were highly correlated with the amount of water inﬁltration. However, only limited research has addressed the issue of
microbial exchange between runoff water and the soil surface.
Muirhead et al. (2006) reported that the transport behavior of aconservative tracer (bromide) and E. coli in runoff water was
almost identical. Yu et al. (2011) reported similar results for kaolinite and bromide in runoff water. However, these studies did notconsider the confounding effects of changes in solution chemistryon cell/kaolinite retention and release in the soil. Yu et al. (2013)
reported greater retention of latex microspheres to surface vegetation occurred at higher IS and for larger particles. Ferguson et al.
(2007) found that larger microorganisms (Cryptosporidium andE. coli) were more efﬁciently removed from runoff water thansmaller microbes (coliphage PRD1) in ﬁeld studies. Furthermore,
previous studies have not yet modeled the full dynamics of waterﬂow and microbial transport in runoff water and soil. Most

761

modeling studies only consider runoff and transport at the soil surface, and approximate exchange between runoff water and the soil
using simpliﬁed terms for inﬁltration and/or diffusive exchange(Guber et al., 2009; Yu et al., 2011, 2012; Wu et al., 2011; van
Genuchten et al., 2013).
The objective of this research was to study the effects of slope
and solution IS on the transport, exchange, retention, and releaseof an indicator microorganism (E. coli D21g) in runoff water. In particular, different amounts of advective exchange between the runoff water and the soil surface were achieved by varying the slope(5.6%, 8.6%, and 11.8%) of a chamber packed with ﬁne sand. The
IS of the runoff water was varied (1 and 100 mM NaCl) to obtaina wide range of cell retention and release (deionized water) conditions. Experiments were simulated using the transient storage
model and a model that describes the full coupling of ﬂow andtransport (tracer and E. coli D21g) between runoff water and thesand in the chamber.
2. Materials and methods
2.1. Electrolyte solutions and porous media
Electrolyte solutions were prepared using deionized (DI) water(pH = 5.8) to achieve 0, 1, or 100 mM NaCl solutions. Ultrapure
quartz sand (Iota Quartz, Unimin Corp. NC) was employed as a porous medium in the runoff experiments discussed below. The sandwas thoroughly rinsed with DI water to eliminate background ﬁnes
from the sand before use. The median grain size of this sand wasmeasured to be 238 lm (standard deviation of 124 lm) with alaser scattering particle size and distribution analyzer (Horiba LA
930). The saturated conductivity (Ks) of the sand in a packed column was determined to be 0.57 cm min1 using Darcy’s law andmeasurements of the hydraulic gradient during steady-state water
ﬂow. The porosity of the packed column was calculated to be 0.44
from the measured bulk density (1.49 g cm3) and an assumed
speciﬁc density of the sand (2.65 g cm3).
2.2. E. coli D21g
Experiments discussed below employed pure cultures of E. coli
D21g, which is a gram-negative, nonmotile bacterial strain that
produces minimal amounts of lipopolysaccharides and extra-cellular polymeric substances. E. coli D21g was grown 24 h before initiating experiments. A single colony of E. coli D21g was inoculated
into 1000 mL of Luria–Bertani media containing 30 lg mL1 gentamycin and incubated with shaking at 37 °C overnight. The bacterial suspension was centrifuged and rinsed three times before
diluting the concentrated suspension into the desired electrolyte
solution. Inﬂuent and efﬂuent concentrations of E. coli D21g were
determined using a spectrophotometer (Unico UV-2000, United
Products & Instruments, Dayton, NJ) at a wavelength of 600 nm
and a calibration curve. The average optical density at 600 nm forthe inﬂuent cell suspension was 0.077, which corresponds to an
input concentration (Co) of approximately 1.1 ⁄ 106 cells mL1.
2.3. Interaction energy calculations
The zeta potential of E. coli D21g and crushed ultrapure quartz
sand in the various solution chemistries was determined frommeasured electrophoretic mobilities using a ZetaPALs instrument(Brookhaven Instruments Corporation, Holtsville, NY) and the
Smoluchowski equation. The size of E. coli D21g in the various solution chemistries was measured using the laser scattering particle
size and distribution analyzer. The total interaction energy ofE. coli D21g upon approach to the quartz sand under the various

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S.A. Bradford et al. / Journal of Hydrology 525 (2015) 760–768

solution chemistries was calculated (Table 1) using Derjaguin–Landau–Verwey–Overbeek (DLVO) theory and a sphere-plateassumption (Derjaguin and Landau, 1941; Verwey and Overbeek,1948). Electrostatic double layer interactions were quantiﬁedusing the expression of Hogg et al. (1966) using zeta potentials
in place of surface potentials. The retarded London-van der
Waals attractive interaction force was determined from theexpression of Gregory (1981). The value of the Hamaker constantused in these calculations was 6.5 ⁄ 1021 J (Rijnaarts et al., 1995).
2.4. Runoff experiments
Fig. 1 presents a schematic of the setup used in the runoff studies. Experiments were conducted in a plexiglass chamber that was
2.25 m long, 0.15 m wide and 0.16 m high. Autoclaved ultrapure
quartz sand was uniformly packed into the chamber to a depthof 0.1 m. The packed chamber was placed on a metal support frame
at slopes of 5.6%, 8.6%, or 11.8%. Steady-state water ﬂow wasachieved in the chamber before initiating a transport experimentusing a peristaltic pump (Barnant Company, Barrington, Illinois)
connected to a rain simulator at the upslope portion of the chamber. The rain simulator consisted of a 13.2 cm diameter plexiglass
disc that was continuously rotated to uniformly distribute solutions from the pump on one side of the chamber to a regular network of embedded syringe tips. The solutions were pumped at aconstant water ﬂux to slowly saturate the sand in the chamber, initiate steady-state runoff conditions, and to minimize soil erosion.
The down slope portion of the chamber was equipped with a horizontal groove and ﬁtting at the soil surface to continuously collectrunoff water using a fraction collector.
Runoff experiments were conducted to determine the inﬂuenceof solution chemistry on D21g transport and removal from runoff
water. Table 2 provides a summary of the applied ﬂow rates. A step
pulse of microbial suspension was pumped into the chamber for
30 min (Phase 1). Next, eluting solution was pumped to the chamber for 90 min (Phase 2). The initial resident solution, D21g suspension, and eluting solutions had the same solution chemistryduring a given experiment. Two solution chemistries at pH = 5.8
were considered, namely: (i) 1 mM NaCl; and (ii) 100 mM NaCl.
Retention of D21g in the 1 mM NaCl was highly unfavorable (alarge energy barrier), whereas conditions were much more favorable (no energy barrier) for deposition in 100 mM NaCl (Table 1).
An additional elution with DI water for 120 min (Phase 3) occurredin some experiments to examine the potential of D21g release after
expansion of the double layer thickness and reduction of the secondary minimum. Collected efﬂuent water samples were analyzed
for D21g concentrations as described above. A mass balance in therunoff water was conducted based on information on the waterﬂow rate and D21g concentrations in the inﬂuent and runoff efﬂuent. All runoff experiments (Phases 1 and 2) were replicated andexhibited good reproducibility.
Following completion of a runoff experiment, the chamber was
lowered to a horizontal position and DI water was pumped into theTable 1
Zeta potentials and DLVO interaction energy parameters.
Ionicstrength(mM)

Sand zeta
potential(mV)

D21g zeta
potential(mV)

Energybarrier(kT)

Depth of secondary
energy minimum
(kT)

1
25
100

66.8
31.8
25.5

53.5
29.3
11.6

3270
494
NB

0.0
3.6
NA

NB – No barrier to attachment.
NA – Not applicable.
kT – normalized by the product of the Boltzmann constant and the absolutetemperature.

chamber from below through ﬁve valves located along the lengthof the chamber bottom. The chamber was then drained and theprocess was repeated at least six times. Sand samples obtained
from four different depths (from the surface to a maximum depthof 10 cm) showed no evidence of D21g growth. In addition, theoptical density readings of runoff efﬂuent prior to D21g injection
were consistently at or near zero. Taken together, these data indicated that background D21g interference was negligible using thisprocedure, and this eliminated the need to repack the large volume
of sand in the chamber each time.
Replicate salt tracer (100 mM NaCl) experiments were conducted for each chamber slope using a similar protocol as for the
D21g runoff experiments described above. In this case, the runoff
chamber was initially saturated with DI water and then sequentially eluted with 100 mM NaCl (30 min) and DI water (90 min).
Changes in the electrical conductivity (EC) of the efﬂuent runoff
samples were measured using a CS547A water conductivity probe
and a CR10X data logger (Campbell Scientiﬁc, Logan, UT).
2.5. Transient storage model
The transient storage model has commonly been employed tosimulate the transport of solutes in surface water (Thackston andSchnelle, 1970; Bencala and Walters, 1983; LeGrand-Marcq and
Laudelout, 1985; Runkel et al., 1996; Choi et al., 2000; De Smedt,
2006). The transient storage model considers advective and dispersive transport in the runoff layer, and diffusive exchange withwater in stagnant zones (e.g., the soil) using a quasi steady-state
approximation of Fick’s ﬁrst law of diffusion as:

@C m
@2Cm
@C m
¼D
 vw
 aðC m  C im Þ
@t
@x2
@x

ð1Þ

@C im
Am
¼a
ðC m  C im Þ
@t
Aim

ð2Þ

where Cm [Nc L3; Nc and L denotes the number of cells and length,
respectively] is the cell concentration in the mobile runoff water,
Cim [Nc L3] is the cell concentration in the immobile storage zone,
D [L2 T1; T denotes units of time] is the longitudinal hydrodynamic
dispersion coefﬁcient, vw [L T1] is the longitudinal runoff watervelocity, x [L] is the longitudinal coordinate, t [T] is the time, Am[L2] is the cross sectional area of the runoff water, Aim [L2] is the
cross section area of the storage zone, and a [T1] is the mass transfer coefﬁcient to/from the runoff water and storage zone. Note thatAm = whm and Aim = whim, where w [L] is the width of the runoff
chamber, hm [L] is the height of the runoff water, and him [L] is
the depth of the storage zone. The total height (hT, L) in runoff
and storage zones is hT = hm + him. The value of vw is equal to Q/
Am; where Q [L3 T1] is the runoff water ﬂux.
The transient storage model is mathematically equivalent to themobile-immobile model (van Genuchten et al., 2013), denoted
below as MIM. In this case, the MIM is derived from Eqs. (1) and(2) by replacing hm and him with the water contents in the mobile(hm) and immobile (him) regions, respectively, hT is replaced by the
total porosity (h), vw is deﬁned as the ratio of the Darcy watervelocity (qw) and hm, and a is replaced by am/hm; where am [T1]is the mass exchange coefﬁcient between mobile and immobile
regions. The Hydrus-1D software (Šimůnek et al., 2008) was used
to numerically solve Eqs. (1) and (2), and to determine model
parameters (hT, him, and a) by inverse optimization to measured
breakthrough curves (BTCs) in the runoff efﬂuent using a nonlinear
least squares routine (Marquardt, 1963).
2.6. Fully coupled model
Recent research has demonstrated that ﬂow and transport inrunoff water can be simulated using similar equations to thoseS.A. Bradford et al. / Journal of Hydrology 525 (2015) 760–768

763

Fig. 1. A schematic of the setup used in the runoff studies.

Table 2A summary of experimental conditions and transient storage model parameters.

TracerTracerTracer
D21g
D21g
D21g
D21g
D21g
D21g

IS
(mM)

Slope
(%)

Q
(mL min1)

hT
(cm)

him
(cm)

hm
(cm)

a

100
100
100
1
1
1
100
100
100

5.6
8.6
11.8
5.6
8.6
11.8
5.6
8.6
11.8

122
122
124
126
126
150
131
123
131

1.01
1.00
1.25
1.18
1.01
1.54
1.14
1.27
3.09

0.94
0.93
1.16
1.11
0.93
1.46
1.07
1.22
3.00

0.06
0.07
0.09
0.07
0.07
0.08
0.07
0.04
0.09

0.20
0.28
0.38
0.19
0.36
0.52
0.23
0.54
0.41

R2

(min1)
0.99
0.99
0.97
0.97
0.98
0.90
0.99
0.95
0.90

used in the subsurface (Richards’ and advective dispersion equations, respectively) when using appropriate functions of thehydraulic conductivity, the capacitance, and the water content at
the soil surface (Weill et al., 2009; Bittelli et al., 2010). These
hydraulic property modiﬁcations are especially simple under saturated, steady-water ﬂow conditions when a constant value ofporosity and Ks are employed in the runoff layer. This ﬁnding
implies that it may be feasible to use existing subsurface simulation routines to model fully coupled ﬂow and transport in the runoff water and the subsurface. In this work, we employ the ﬁnite
element HYDRUS (2D/3D) model (Šimůnek et al., 2011) to simulate
water ﬂow and transport in the runoff chamber.
The runoff chamber was modeled using runoff (top 2 cm) andsand (bottom 10 cm) layers parallel to the chamber slope with different soil hydraulic properties. Water ﬂow in the chamber was
simulated using the solution of Richards’ equation (Richards,
1931):



@h
@
@h
¼
K ij ðhÞ
þ K iz ðhÞ@t @xi@xj

ð3Þ

where xi (i = 1, 2) are the spatial coordinates [L], h [L3 L3] is the volumetric water content, Kij [L T1] are components of the hydraulicconductivity tensor, and h [L] is the pressure head.
Transport of a conservative tracer was simulated using an
advection–dispersion equation (ADE):



@ðhCÞ
@
@C
@q C
 i
¼
hDij
@t
@xi
@xj
@xi

ð4Þ

where C [M L3, where M denotes units of mass] is the tracer concentration in the aqueous phase, Dij [L2 T1] is the hydrodynamic
dispersion tensor, and qi [L T1] is the Darcy water velocity in thei direction.
Constant water ﬂux boundary conditions were imposed at the
upslope boundary of the runoff layer, and a seepage face was maintained at the downslope boundary of the runoff layer. No ﬂow
boundary conditions were imposed on all other exterior surfacesof the sand and runoff layers. A third-type boundary condition
was used at the inlet, and at the runoff chamber seepage face outlet.
As discussed above, the porosity of the sand in the chamber wasdetermined directly from measurements of steady-state waterﬂow in a saturated packed column. Values of Ks in the runoff layer
and the sand were estimated by inverse optimization to the runoff
BTC for the salt tracer. Other unsaturated hydraulic properties forthe sand were taken from Jacobson et al. (2009). The longitudinal
dispersivity (kL) in the sand and runoff layers was taken as 0.1 ofthe chamber length (Gelhar et al., 1985, 1992). The transverse dispersivity (kT) was taken to be 0.1 ⁄ kL in both layers.
3. Results and discussion
3.1. DLVO calculations
Table 1 presents information on the zeta potentials of D21g andquartz sand, and the DLVO energy barrier height and the depth of
the secondary minimum for D21g-quartz sand interactions underthe various solution chemistry conditions. The median size of
D21g was determined to be 1.46 lm (the standard deviation was0.57) in the various solution chemistries. The energy barrier heightdecreased and the secondary minimum increased with increasing
IS. Conditions were highly unfavorable for D21g attachment whenthe IS 6 1 mM NaCl. Conversely, retention of D21g in association
with a primary minimum is possible when the IS = 100 mM NaCl.
3.2. Runoff experiments
Fig. 2 presents BTCs for a 100 mM NaCl tracer when the runoff
chamber slope was 5.6%, 8.6%, and 11.8%. All of the BTCs exhibited

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S.A. Bradford et al. / Journal of Hydrology 525 (2015) 760–768

Fig. 2. Observed and simulated runoff breakthrough curves for a 100 mM NaCl
tracer when the runoff chamber slope was 5.6%, 8.6%, and 11.8%. The simulations
where obtained using the transient storage model (Eqs. (1) and (2)). Fitted model
parameters are given in Table 2.

an initially high pulse of tracer in the runoff efﬂuent followed byprolonged tailing at lower concentration levels. The initial pulsein the BTC reﬂects rapid transport of the tracer in the runoff water.
The height of this pulse and the tailing behavior of the BTC dependson: (i) the amount of exchange at the surface of the sand layer due
to inﬁltration, exﬁltration, and diffusion; and/or (ii) the extent ofphysical nonequilibrium transport in the runoff layer due to ﬂow
in small rivulets and incomplete mixing. Higher chamber slopes
produce lower breakthrough concentrations initially and thenhigher levels of concentration tailing. This observation indicatesthat higher slopes produced greater amounts of exchange withthe sand and/or extents of physical nonequilibrium in the runoff
layer. Each of these explanations will be discussed in detail later.
Fig. 3 presents BTCs in the runoff efﬂuent for D21g when thechamber slope was 5.6%, 8.6%, and 11.8% and the IS = 1 mM NaCl.
In this case, the peak efﬂuent concentrations and the concentration
tailing behavior for D21g were quite similar to the 100 mM NaCl
tracer results shown in Fig. 2. Similar to the tracer, the runoff
BTC height decreased and the amount of tailing increased forD21g with the chamber slope. These results indicate that minimal
amounts of D21g retention occurred in the chamber sand when thesolution IS was 1 mM NaCl, and that differences in the BTC shapewere again due to the amount of exchange and/or the extent ofphysical nonequilibrium in the runoff layer. Little D21g retention
is expected in the sand when the IS = 1 mM because of the larger
energy barrier and the minor depth of the secondary minimum(Table 1). Tracer and colloid (E. coli and kaolinite clay) transport
in runoff water have previously been reported to be nearly identical (Muirhead et al., 2006; Yu et al., 2011).
Fig. 4 presents similar information to Fig. 3, but for D21g in
100 mM NaCl. Greater amounts of D21g retention are expectedin the sand when the IS = 100 (Fig. 4) than 1 mM NaCl (Fig. 3)
because the energy barrier to attachment was eliminated(Table 1). An estimate of the amount of cell retention was obtained
from the difference in the efﬂuent mass balance for the tracer andD21g in 100 mM solution to be 0.07, 0.16, and 0.35 when thechamber slope was 5.6%, 8.6%, and 11.8%, respectively. Thisobserved increase in cell retention with chamber slope reﬂects
an increasing inﬂuence of exchange with the sand. Comparison of
Figs. 2 and 4 reveals that cell retention in the sand tended to lower
the peak height of the runoff BTC compared to the tracer, especiallyas the chamber slope increased. Interestingly, cell retention also
eliminated most of the tailing portion of the runoff BTCs thatwas observed for the tracer. Consequently, the inﬂuence ofFig. 3. Observed and simulated runoff breakthrough curves for D21g in 1 mM NaClsolution when the runoff chamber slope was 5.6%, 8.6%, and 11.8%. The simulations
where obtained using the transient storage model (Eqs. (1) and (2)). Fitted model
parameters are given in Table 2.

Fig. 4. Observed and simulated runoff breakthrough curves for D21g in 100 mM
NaCl solution when the runoff chamber slope was 5.6%, 8.6%, and 11.8%. The
simulations where obtained using the transient storage model (Eqs. (1) and (2)).
Fitted model parameters are given in Table 2.

exchange and/or physical nonequilibrium on the tailing portionof the runoff BTC was partially masked by bacteria retention in
the sand. This implies that reactive transport processes in runoff
water may potentially be misinterpreted without complimentary
information on conservative tracers.
The release and transport behavior of D21g cells were subsequently investigated during Phase 3 when the runoff solution IS
was reduced from 100 mM NaCl to DI water. This change in IS
expands the double layer thickness and can eliminate some primary minimum interactions that contribute to cell retention whenthe effects of surface roughness and Born repulsion are considered
in interaction energy calculations (Bradford and Torkzaban, 2013).
Fig. 5 presents observed release curves for D21g in the runoff efﬂuent for the various chamber slopes. Cell release and transport
occurs when the IS was reduced in the sand. Subsequently, diffusion, hydrodynamic dispersion, and exﬁltration contribute to theslow transfer of cells from the sand to runoff water. The efﬂuent
mass balance on cell release was 0.0, 0.14, and 0.24 when thechamber slope was 5.6%, 8.6%, and 11.8%, respectively. These
results demonstrate that the amount of cell release was strongly
related to the chamber slope. The chamber slope determines thequantity of exchange and/or the extent of physical nonequilibriumin the runoff layer (Fig. 2), and this subsequently impacts theS.A. Bradford et al. / Journal of Hydrology 525 (2015) 760–768

765

3.4. Fully coupled modelFig. 5. Observed release curves for D21g when the runoff chamber slope was 5.6%,
8.6%, and 11.8%. Release was initiated during Phase 3 by switching the inﬂuent
solution IS from 100 to 0 mM NaCl.

amount of retention in the sand (Fig. 4). Consequently, differencesin cell release with chamber slope mainly reﬂect the initial amountof cell retention in the sand when the IS = 100 mM NaCl solution
and the amount of exchange and/or the extent of physical nonequilibrium in the runoff layer.
3.3. Transient storage modelFigs. 2–4 also present simulated tracer and D21g BTCs in therunoff efﬂuent when the chamber slope was 5.6%, 8.6%, and11.8%. Simulations were obtained using the solution of Eqs. (1)and (2). Table 2 provides a summary of the experimental (IS, Q,
slope), ﬁtted (hT, him, and a), and calculated (hm) model parameters
and the Pearson’s correlation coefﬁcient (R2) values. In general themodel provided a reasonable description of the experimental data
(R2 > 0.90). Calculated values of hm = hT  him were always less than
0.09 cm, reﬂecting the small height of the water in the runoff layer.
In contrast, values of him were always much larger (1–3.09 cm)
than hm, and provided an indication of the depth of the storage
zone in the sand that contributed to exchange and/or the extent
of physical nonequilibrium in the runoff layer. The amount of
exchange with the sand and/or the extent of physical nonequilibrium in the runoff water layer depended on the values of hT, him,
and a. In general, values of hT, him, and a tended to increase withincreasing chamber slope because of enhanced exchange and/or
physical nonequilibrium. The increase in a with increasing slope
indicates a greater rate of diffusive mass transfer between the runoff water and the stagnant zone.
Even though the transient storage model provides a reasonable ﬁt of the experimental data, the ﬁtted model parameters
were not always realistic. For example, the Manning equationof overland ﬂow predicts that the value of hm should decrease
with the chamber slope, whereas the opposite trend was sometimes observed (Table 2). Furthermore, values of a were high(ranging from 0.19 to 0.54 min1), which were not consistent
with a slow diffusion controlled exchange process. In addition,
the transient storage model sometimes did not fully capture thetailing behavior in the runoff BTCs (Figs. 3 and 4). Advective
exchange between the runoff layer and the subsurface was notconsidered in the transient storage model because of steady-statewater ﬂow conditions in the chamber. Consequently, the transient storage model does not account for important exchange
processes in the sand, such as inﬁltration, transport, retention,
release, and exﬁltration.

To improve our understanding of the runoff transport andexchange processes for the tracer we employed a model that
accounted for the full coupling between runoff water and the subsurface. Fig. 6 shows the cumulative amount of tracer that crosses
the total surface of the sand layer (Fig. 6a), and the top (Fig. 6b),
middle (Fig. 6c), and bottom (Fig. 6d) third of the surface of thesand layer as a function of time when the chamber slope was
5.6%, 8.6%, and 11.8%. Simulation results indicate that tracer
exchange with the sand layer was dominated by advection which
varied with the slope and the distance along the slope.
Inﬁltration occurred mainly upslope, and initially served as a sink
for the tracer (negative values), whereas exﬁltration mainly
occurred downslope and it served as a delayed tracer source tothe runoff layer. The contribution of inﬁltration and exﬁltrationon the runoff BTC depended on the chamber slope and the transport of the tracer through the sand layer downslope. Indeed, higher
slopes (elevations) increase the inﬂuence of gravity on water ﬂow,
which tended to produce greater inﬁltration upslope and transportof the tracer to deeper depths in the sand. Consequently, inﬁltration and exﬁltration played an important role in exchange between
runoff water and the sand layer at higher slopes, and were partially
responsible for the observed differences in the runoff BTC shapes
shown in Fig. 2.
The use of the fully coupled model to study exchange process at
the interface of runoff water and the sand surface has some significant advantages over the transient storage model. Exchange processes between runoff water and the surface of natural soils arecomplex, and are expected to depend on the surface topography,
obstruction and depression storage, the initial soil water status,
soil hydraulic properties, subsurface heterogeneity, and preferential ﬂow pathways (Bradford et al., 2013). The roles of advective
and diffusive exchange across the soil surface are likely to changewith these surface and soil properties, and the use of the fully coupled model is potentially an important tool to help understand theinﬂuence of these various factors. However, use of the fully coupled model requires knowledge of many additional parameter values (e.g., conductivities and dispersivities in the sand and runoff
layers) than the transient storage model.
A more signiﬁcant limitation of the transient storage and fully
coupled models arises from the conceptual description of waterﬂow in the runoff layer. In particular, water ﬂow in the runoff layer
is implicitly assumed in diffusion and kinematic wave equations tooccur as sheet ﬂow; e.g., a thin, continuous ﬁlm over the smoothsoil surface. In reality, erosion at the soil surface is complex, andis well known to produce concentrated water ﬂow and transport
in rills and rivulets (Dunne et al., 1991; Darboux and Huang,
2005; Thompson et al., 2010). Similarly, we observed enhanced
water ﬂow in small rivulets in our runoff chamber experiments.
This deviation from sheet ﬂow can produce preferential ﬂow pathways and incomplete mixing of the tracer in the runoff layer. Bothof these factors are presently not accounted for in the fully coupledmodel, and may produce signiﬁcant deviations in observed andsimulated transport. For example, Fig. 7 presents observed andsimulated tracer BTCs in the runoff efﬂuent when the chamber
slope was 11.8%. Note that the fully coupled model overestimates
the arrival time of the runoff BTC, and underestimates the amountof concentration tailing. These observations suggest that physicalnonequilibrium ﬂow and transport processes were signiﬁcantly
contributing to behavior in the runoff layer as a result of nonuniform water ﬂow and incomplete mixing, and that transport models
need to account for such processes. We did not attempt to simulate
the transport, retention, and release of D21g in the chamber experiments using the fully coupled model due to this limitation. Itshould be mentioned that a number of ﬂow and transport models

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S.A. Bradford et al. / Journal of Hydrology 525 (2015) 760–768

Fig. 6. The simulated cumulative amount of tracer mass that is transferred across the total sand surface (a), the top third of the sand surface (b), the middle third of the sandsurface (c), and the bottom third of the sand surface (d) when the chamber slope was 5.6%, 8.6%, and 11.8%. A negative mass indicates that the tracer has moved into the sand,and a positive mass indicates that the tracer has entered the runoff layer.

4. Summary and conclusions

Fig. 7. Observed and simulated runoff breakthrough curves for a 100 mM NaCl
tracer when the runoff chamber slope was 11.8%. The simulations where obtainedusing the fully coupled model (Eqs. (3) and (4)) and ﬁtted values of Ks = 0.108 and6000 cm min1 for the sand and runoff layers, respectively.

have been developed to describe physical nonequilibrium processes in porous media (e.g., Jarvis, 2007; Šimůnek and van
Genuchten, 2008; Köhne et al., 2009). It is possible that these models may be extended to account for similar physical nonequilibrium processes in the runoff layer, but such an undertaking isbeyond the scope of this paper.

Experimental and numerical modeling studies were initiatedto study the effects of solution IS and chamber slope on thetransport, retention, and release of E. coli D21g in runoff water.
Complimentary conservative tracer studies revealed the importance of exchange with the sand and/or physical nonequilibriumin the runoff layer. In particular, the peak efﬂuent concentrationand the amount of concentration tailing in the runoff BTC werestrongly dependent on the amount of water inﬁltration and exﬁltration. Lower peak concentrations and greater amounts of concentration tailing in the runoff BTC were associated with greater
amounts of inﬁltration, exﬁltration, and physical nonequilibrium(e.g., ﬂow in small rivulets and incomplete mixing) that occurredwith increasing runoff chamber slope. Inﬁltration primarily
occurred upslope, whereas exﬁltration mainly happened
downslope.
In addition to inﬁltration and exﬁltration, the transport of E. coli
D21g was also sensitive to the solution IS because of its inﬂuenceon cell retention. The runoff BTC for D21g was very similar to thatof the conservative tracer when the IS was low (1 mM NaCl)because cell retention was highly unfavorable. In this case, theamount of inﬁltration, exﬁltration, and physical nonequilibrium
controlled the runoff BTC shape. Conversely, cell retention in thesand increased under high IS (100 mM NaCl) conditions due toelimination of the energy barrier to attachment. Enhanced cellretention tended to lower the peak efﬂuent concentration and to
drastically reduce the amount of concentration tailing in the runoff

S.A. Bradford et al. / Journal of Hydrology 525 (2015) 760–768

BTC of D21g in comparison to the conservative tracer.
Consequently, cell retention may mask the inﬂuence of various
exchange and/or physical nonequilibrium processes that occur at
the interface of runoff water and soil.
Retained cells could be released back into the runoff water
when the IS of the runoff water was decreased and the diffuse double layer was expanded. The amount and rate of cell release fromthe sand layer depended upon the initial distribution of retained
cells, the amounts of inﬁltration and exﬁltration (the chamber
slope), the rate of transport through the sand layer, and the extent
of physical nonequilibrium.
The transient storage model is commonly used to describetransport and diffusive exchange of solutes and microbes in runoff
water. This model provided a good description of the runoff BTCs,
but model parameters were not always physically realistic.
Simulations from a fully coupled ﬂow and transport model provided valuable insight on advective and diffusive exchange processes at the interface of runoff water and the sand surface.
However, the coupled model did not provide an adequate description of the runoff BTCs. This discrepancy, and experimental evidence (e.g., ﬂow in small rivulets), indicates that physicalnonequilibrium processes were occurring in the runoff layer andthat the model assumption of sheet ﬂow was violated.
Acknowledgments
This research was supported by the 214 Manure and ByproductUtilization Project of the USDA–ARS. Mention of trade names andcompany names in this manuscript does not imply any endorsement or preferential treatment by the USDA.
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