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Pesticide washoff from concrete surfaces: Literature reviewand a new modeling approach

Yuzhou Luo a,*, Frank Spurlock a, Weiying Jiang a,b, Brant C. Jorgenson c,Thomas M. Young d, Jay Gan b, Sheryl Gill a, Kean S. Goh a

aDepartment of Pesticide Regulation, California Environmental Protection Agency, Sacramento, CA 95812, USAbDepartment of Environmental Sciences, University of California, Riverside, CA 92521, USAcAgricultural and Environmental Chemistry Gradate Group, University of California, Davis, CA 95616, USAdDepartment of Civil and Environmental Engineering, University of California, Davis, CA 95616, USA

a r t i c l e i n f o

Article history:

Received 5 October 2012

Received in revised form

11 March 2013

Accepted 13 March 2013

Available online 26 March 2013

Keywords:

Concrete

Model

Pesticide

Urban

Washoff

* Corresponding author. Tel.: þ1 916 445 209E-mail address: yluo@cdpr.ca.gov (Y. Luo

0043-1354/$ e see front matter ª 2013 Elsevhttp://dx.doi.org/10.1016/j.watres.2013.03.032

a b s t r a c t

Use of pesticides over impervious surfaces like concrete and subsequent washoff and

offsite transport significantly contribute to pesticide detection and aquatic toxicity in

urban watersheds. This paper presents a comprehensive study on pesticide washoff from

concrete surfaces, including reviews of reported experiments and existing models, devel-

opment of a new model, and its application to controlled experimental conditions. The

existing modeling approaches, mainly the exponential function and power-law function,

have limitations in explaining pesticide washoff processes characterized from experi-

mental data. Here we develop a mathematical and conceptual framework for pesticide

washoff from concrete surfaces. The new modeling approach was designed to characterize

pesticide buildup and washoff processes on concrete surfaces, including the time-

dependence of the washoff potential after application and the dynamics in pesticide

washoff during a runoff event. One benefit is the ability to integrate and quantify multiple

processes that influence pesticide washoff over concrete surfaces, including product

formulation, aging effects, multiple applications, and rainfall duration and intensity. The

model was applied to experimental configurations in two independent studies, and satis-

factorily simulated the measured temporal variations of pesticide washoff loads from

concrete surfaces for the five selected pyrethroids in 15 runoff events. Results suggested

that, with appropriate parameterization and modeling scenarios, the model can be used to

predict washoff potentials of pesticide products from concrete surfaces, and support

pesticide risk assessments in urban environmental settings.

ª 2013 Elsevier Ltd. All rights reserved.

1. Introduction and Lydy, 2009, 2005; Weston and Lydy, 2010, 2012). With the

Environmental monitoring studies have shown that urban

pesticide applications result in potentially toxic surface water

runoff in California and other States (Amweg et al., 2006; Ding

et al., 2010; Hintzen et al., 2009; Holmes et al., 2008; Weston

0; fax: þ1 916 445 4405.).ier Ltd. All rights reserved

discontinued residential use of organochlorines and some

organophosphates, use of replacement insecticides such as

synthetic pyrethroids and fipronil has increased in recent

years (Epstein and Bassein, 2003). Pesticide applications on

impervious surfaces like concrete have been considered as an

.

wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 3 1 6 3e3 1 7 23164

important source of surface water contamination in urban

areas. Formore effectivemitigation strategies to protect urban

aquatic environment, research is needed to improve under-

standing and prediction of pesticide washoff mechanisms

over impervious surfaces.

Three major components are involved in pesticide gener-

ation and transport in an urban environment: stormwater

hydrology, pesticide washoff from the landscape into the

overland flow, and pesticide transport along urban landscape

and storm drainage system (Moran and TenBrook, 2011).

While stormwater management and water quality in the

receiving water bodies of urban watersheds have been widely

investigated, few studies were developed to characterize

pesticide washoff from components of the urban landscape,

especially from impervious surfaces. Pesticidewashoff, which

determines the mass of pesticide available for subsequent

transport during a storm event, is required for accurate urban

pesticide modeling and evaluation. The reliability of pesticide

risk assessment and associated regulation and mitigation

practices at the urban watershed scale significantly hinges on

the accuracy of the initial predictions. Currently, limited

information is available to support specification of this

component.

This study develops a mathematic model for pesticide

release from concrete surfaces based on the considerations of

physicochemical processes and observed characteristics from

pesticide washoff experiments. The procedure applied in this

study consists of three steps: [1] experimental data charac-

terization, [2] model development, and [3] model evaluation

(calibration and validation). Published experiments for pesti-

cide washoff from concrete surfaces were first reviewed. The

experimental results were investigated and summarized with

their implications for further model development. Finally a

novel modeling approach was developed to characterize the

dynamics in pesticide washoff during a runoff event, and the

time-dependence of the washoff potential after application.

Case studies for model evaluation were performed based on

the published experimental data.

Fig. 1 e Example of pesticide washoff profiles from

concrete surfaces, generated from reported data of single

washoff experiments at 1 day after application (Jorgenson

and Young, 2010; Thuyet et al., 2012). Pesticides were

formulated as EC (micro-emulsion) or SC (suspension

concentrate).

2. Materials and methods

2.1. Characterization of pesticide washoff from concretesurfaces

Most studies on pesticide washoff from hard surfaces are

small-scale experiments, such as those on concrete cubes and

slabs, with pesticide spikes and simulated rainfall. Runoff

water samples are analyzed for pesticides (active ingredients

and/or degradates) to estimate release rate and persistence for

off-site transport. The amount of pesticide available to runoff

extraction is defined as “washoff potential”,MP(t) (kg/m2, or user-

defined unit of mass/area), at a given time after application

(referred as “incubation time” or “set time”). Washoff potential

is unlikely to be directly measured; instead, it’s operationally

indicated by “washoff load”, i.e., cumulative mass of pesticide

released to water over the duration of a rainfall event, MW

(mass/area). Washoff load is determined by experiments with

flowingwater (runoff induced by natural or artificial rainfall) or

static water (immersion test for a given equilibrating period).

According to the experimental settings, washoff load can be

measured at certain time intervals during a washoff event,

MW(t), or only at the end of the event as “total washoff load”.

For the former case, washoff load is usually plotted with cu-

mulative time or runoff, referred as a “washoff profile”

(Jorgenson and Young, 2010) or “load characteristic curve”

(Alley, 1981) for a pesticide in a given experimental configu-

ration. Fig. 1 illustrates reportedwashoff profiles from concrete

surfaces in controlled washoff experiments for pesticides with

a wide range of chemical properties (logKOW ¼ 0.6e6.9).

Table 1 summarizes experiments of pesticidewashoff from

concrete surfaces reported in the literature. Pesticide washoff

from concrete surfaces has been studied since the 1990s, with

early studies focused on herbicide washoff from highways

and railways. For example, Shepherd and Heather (1999)

investigated six herbicides (glyphosate, isoxaben, oryzalin,

oxadiazon, diuron and atrazine) from concrete and other two

surface types (asphalt and ballast). Normalized by application

rate and rainfall volume, the highest pesticide concentrations

and total mass in runoff were generally observed for concrete,

followed by asphalt then ballast. In addition, the majority of

pesticide washoff from concrete occurred in the early stages

of a rainfall event. In contrast, pesticide runoff from asphalt

yielded a more constant steady pesticide release rate. The

dependence of pesticide washoff loads on incubation time

(the interval between pesticide application and the first rain-

fall event) and rainfall duration (while rainfall intensity was

fixed value) were tested. Results showed that herbicide

washoff load was mainly affected by rainfall duration, while

incubation time up to 7 days had little effect. The experi-

mental results were used to develop a first-tier model for

Table 1 e Summary of pesticide washoff experiments on concrete surfaces.

Studya Pesticides Rainfall intensityb Rainfall durationb Incubation period

[1] Atrazine, diuron, glyphosate, isoxaben, oryzalin,

oxadiazon

Not reported Rainfall depth: 5e15 mm 6e168 h

[2] Diflufenican, diuron, glyphosate 60 mm/h 3 min 0, 48, 168 h

[3] Atrazine, diuron, fluoranthene, phenanthrene,

oryzalin, isoxaben, dichlorophen, isoproturon

Release to 250 ml water 10 s, 1 h, 24 h, 48e144 h 24 h

[4] Bifenthrin, lambda-cyhalothrin, cyfluthrin,

fipronil, permethrin

Release to 30 ml CaCl2 solution 10 min 0e112 d

[5] Bifenthrin, lambda-cyhalothrin, beta-cyfluthrin,

esfenvalerate

25 or 50 mm/h 1 h 1.5 h, 1 and 7 d

[6] Permethrin Release to water

containing 0.1 g of Tenax beads

1e300 h 0, 1, 7 d

[7] Fipronil, imidacloprid 25 mm/h 1 h 1.5 h, 1 d and 7 d

[8] Bifenthrin, permethrin 26.2 mm/h 15 min 1e221dc

Notes:

a References: [1] (Shepherd and Heather, 1999); [2] (Spanoghe et al., 2005); [3] (Ramwell, 2005); [4] (Jiang et al., 2010); [5] (Jorgenson and Young,

2010); [6] (Jiang et al., 2011); [7] (Thuyet et al., 2012); and [8] (Jiang et al., 2012).

b For desorption experiments, water volume and equilibrating period are listed.

c 1e89 d for simulated rain, and 1e221 d for natural rain.

wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 3 1 6 3e3 1 7 2 3165

predicting pesticide washoff from hard surfaces (DEFRA,

1999).

Since 2005, California Department of Pesticide Regulation

(CDPR) has sponsored a series of studies on insecticides (espe-

cially pyrethroids and fipronil) washoff from concrete surfaces

(http://www.cdpr.ca.gov/docs/emon/surfwtr/contracts.htm).

In these studies, experiments were conducted mainly for the

following two objectives: [1] to determine the washoff poten-

tials of pesticides after a certain incubation period; and [2] to

characterize the dynamicsofpesticidewashoff during a rainfall

event. In addition, the effects of product formulation, applica-

tion rate, rainfall intensity, and concrete surface condition on

pesticide washoff were also tested. The following paragraphs

review the experimental settings and results. Details of those

studies have been documented in their original papers (Jiang

et al., 2011, 2012, 2010; Jorgenson and Young, 2010; Thuyet

et al., 2012).

Jorgenson and Young (2010) reported the washoff profiles

for four pyrethroids (bifenthrin, beta-cyfluthrin, lambda-

cyhalothrin, and esfenvalerate) in commercial formulations

during 1-hour runoff period (study [5], Table 1). While all

resultant washoff profiles displayed rapid initial washoff

(Fig. 1), the authors further categorized the washoff profiles

into “type A” (“a steep dissipation rate followed by a more

steady rate”, e.g., bifenthrin and b-cyfluthrin in Fig. 1) and

“type B” (“relatively steady dissipation rate over the duration

of the experiment”). Study results indicated that the type of

washoff profile and total washoff load of a pesticide were

dependent on the incubation time and the product formula-

tion, especially the existence of surfactant component. For

example, washoff profile of neat bifenthrin followed the type-

B profile, and the total washoff loads (normalized by the

application rate) for 1.5 h incubation time and 1 h washoff at

25 mm/h were reported as 0.25%. With the existence of sur-

factant, however, bifenthrin showed type-A profile and

significantly higher total washoff load: 0.86% for bifenthrin &

LAS (linear alkylbenzenesulfonate surfactant) neat grade;

1.5% for 2009 bifenthrin CE (emulsifiable concentrate); and

5.0% for 2007 bifenthrin CE. Strong linearity was observed for

relatively soluble chemicals such as imidacloprid and fipronil.

This finding was in agreement with the leaching test result of

biocides from facades in which linear regression was applied

to the cumulative emission of diuron and terbutryn vs. cu-

mulative runoff (Burkhardt et al., 2012). In addition, the tran-

sition of type-A to B was observed with increased incubation

time, repeated washings, or their combinations. This was

confirmed by similar experiments for imidacloprid and fipro-

nil (Thuyet et al., 2012), in which washoff profile for the first

washing at 1 day after application (DAA) generally followed a

power-law function, while the second and thirdwashings (at 7

and 14DAA) displayed more linear washoff profiles.

In order to determine the dependence of total washoff load

on the incubation time, Jiang et al. (2010) developed a bench-

scale study for measuring pesticide desorbed from concrete

disks at 0-112DAA. Concrete disks were spiked with pyre-

throids (bifenthrin, cyfluthrin, lambda-cyhalothrin, and

permethrin) and fipronil in commercial formulations, and

equilibrated with 30 ml water for 10 min. The released pesti-

cides from concrete disks immediately after applications were

4.3% (lambda-cyhalothrin) e 35.9% (fipronil) of the initially

spiked amounts. Except for permethrin (which showed a first-

order kinetic release process for the entire study period), the

total washoff load was significantly reduced with incubation

time by following a fast stage (0-7DAA) and a slow stage (14-

112DAA). Experimental results also indicated the prolonged

availability of pesticides from concrete surfaces. A 42DAA

with 14 repeated washing events bifenthrin was still detected

at levels sufficiently high to cause mortality to aquatic in-

vertebrates (Jiang et al., 2010). The time-dependence of total

washoff loads was also confirmed by the follow-up study

(study [8], Table 1) with bifenthrin and permethrin as test

agents for up to 221DAA under simulated and natural rainfalls

(Jiang et al., 2012). These findings indicate that a dissipation

model with a decreasing rate constant provides a more real-

istic representation of the dynamics in pesticide washoff po-

tential from concrete than a simple first-order model.

wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 3 1 6 3e3 1 7 23166

There is strong evidence for the existence of an immobile

pool in which pesticide cannot be extracted by runoff. For

pesticides such as bifenthrin, only a small portion of applied

amount can be recovered by washing even with a short in-

cubation period. For freshly spiked (1.5 h after application)

bifenthrin in commercial liquid formulation, only 1.5e5.0%

of applied amount were recovered by 60 min washing at

25 mm/h rainfall (Jorgenson and Young, 2010). At 1DAA, 1.0%

and 1.4% of applied bifenthrin were recovered by 15 min and

60 min washings at the similar rainfall intensity, respectively

(Jiang et al., 2012; Jorgenson and Young, 2010). The resultant

type-A washoff profile indicated that further washing may

not significantly increase the washoff load. Furthermore, for

freshly spiked 14C-permethrin about 20% 14C-residue

remained on concrete after 300-hour washing, and the

retention ratio apparently increased with incubation time,

indicating a continuous transfer of pesticide and its degra-

dates into the immobile pool by transport to domains inac-

cessible to runoff, or irreversible adsorption (Jiang et al.,

2011).

Fig. 2 illustrates total washoff loads of pesticides vs. their

KOW for the studies reviewed. Only experimental data with

incubation periods of 0e2 days were selected for consistency.

It’s noteworthy that pesticide formulations, rainfall duration

(contact time with water) and intensity, and surface condi-

tions varied among the studies. For pesticides with moderate

KOW values (atrazine, diuron, diflufenican, and fipronil), there

is a generally decreasing trend of total washoff loads with the

KOW, consistent to the relationship observed for biocide

leaching from building materials (Schoknecht et al., 2009,

2012). Previous studies tested herbicides with a wide range

of physicochemical properties for their washoff potentials

under various conditions of hard surface, suggesting a weak

relationship between experimentally derived adsorption co-

efficients and their KOC or KOW (Ramwell, 2005; Spanoghe et al.,

2005). For the subset of data available for pyrethroids, how-

ever, no linear association between total washoff load and

Fig. 2 e Relationship between pesticide KOW and total washoff

Table 1. KOW values were taken from the FOOTPRINT database

KOW is observed with statistical significance (Fig. 2). Further

washoff studies with uniform experimental settings are

needed for pyrethroids, either applied as formulated products

or neat chemicals, to characterize the dependence of total

washoff loads on chemical properties.

Based on the studies reviewed, general conclusionsmay be

drawn for pesticide washoff from concrete surfaces:

[1] Under similar experimental conditions, the washoff loads

of pesticides are weakly associated with their physico-

chemical properties, andmore significantly affected by the

formulation, especially by the surfactant components.

Therefore, washoff model parameters should be deter-

mined at product level, rather than for the pesticide active

ingredient.

[2] Washoff profiles are generally characterized by a steep

initial dissipation rate followed by amore steady rate. This

could be caused by an increased resistance of pesticide

desorption with the increase of the extraction depth of

concrete surface, or with the decrease of remaining

pesticide available for extraction. In either case, a time-

dependent release rate should be utilized in simulating

pesticide washoff from concrete surfaces.

[3] In most cases, only a small percent of applied pesticide can

be extracted from concrete surfaces even within a short

incubation period (e.g., 1 day). In addition to pesticide

degradation, the “loss” of washoff potential may be asso-

ciated with transport to inaccessible domains in the con-

crete matrix, called irreversible adsorption (Jiang et al.,

2011). Similar to the dynamics of washoff profile, the

decline of washoff potential can be described by an initially

high but decreasing rate constant with incubation time.

2.2. Model development

Knowledge about pesticide washoff processes from hard

surfaces is less detailed compared to those from bare or

load from concrete surfaces, based on reviewed studies in

(FOOTPRINT, 2012).

Fig. 3 e The four-pool conceptual model for pesticide

buildup and washoff on concrete surfaces.

wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 3 1 6 3e3 1 7 2 3167

vegetated soils. Desorption and diffusion are the dominant

transport mechanisms for dissolved portion of the released

mass. Transport of pesticides in particulate phase is asso-

ciated with particle detachment and resuspension under the

interaction between concrete surface and flowing water. It’s

very difficult to individually simulate those processes in

modeling pesticide washoff, and models were usually

designed to simulate the overall dynamics and variability in

the observed washoff loads. Most of the existing modeling

efforts for pollutant transport from hard surfaces were

based on empirical equations (mainly exponential or power-

law functions). More information on those functions and

their applications was provided in the Supplementary

Materials.

There are several difficulties in using exponential or

power-law functions for washoff prediction to reproduce the

measured data. Initially, a more accurate “buildup” repre-

sentation is required to describe the time-dependence of

pesticide washoff potential during antecedent dry periods,

where degradation and applications may occur. Secondly,

experimental results indicated nonlinear associations be-

tween the washoff potential and the incubation time and

runoff duration, suggesting that the model coefficients in

exponential or power-law functions are not constants within

a storm event or between storms, even with the same

controlled rainfall intensity. For example, the exponential

functionwas utilized by Jiang et al. (2011) to predict sequential

desorption of 14C-permethrin from concrete cubes. They

found that a multiple-stage exponential model was required

to fully capture thewashoff profile characterized by initial fast

release. Similarly, bi-phasic exponential functions were used

to describe two types of dynamics of a fast diffusion followed

by a slow diffusion formodeling biocide leaching from facades

(Schoknecht et al., 2009, 2012; Wittmer et al., 2011). In addi-

tion, Thuyet et al. (2012) used the power-law function to fit

washoff profiles of imidacloprid from concrete surfaces. The

results suggested that the regression coefficients have to be

calibrated separately for each of the washoff profiles with

various incubation periods. Similarly, simple exponential or

power-law functions cannot simulate the time-variable rate

constants in the dissipation of washoff potential and associ-

ated irreversible adsorption of pesticide in concrete matrix.

A semi-mechanistic modeling approach was developed in

this study to characterize pesticide washoff profiles from

concrete surfaces based on the knowledge gained from the

results of experimental data analysis. Once applied to con-

crete surfaces, pesticide (the active ingredient and its degra-

dates) is assumed to be distributed into four theoretical pools

in the concrete or in the runoff water (Fig. 3), [1] “washoff

potential” or the portion of the pesticide remaining in con-

crete and available for washoff,MP(t), [2] “washoff load” or the

pesticide mass measured in the runoff water, MW(t), [3] the

portion of the degradates available for washoff, and [4] the

combination of the pesticide and its degradates retained in

the concrete and not available to water extraction. Pools [1]

and [2] are included as the simulation domain in this study,

while both processes of the degradation and irreversible

adsorption are considered as sink. Pool [3] is separately

defined for further model development to simulate degradate

transport.

2.3. Pesticide buildup in the concrete surface betweenrunoff events

During the dry period between runoff events, pesticide

washoff potential is determined by new applications (MA,

mass/area), transformation to degradates, and irreversible

adsorption. The latter two items can be aggregated and

simulated by first-order kinetics with time-variable rate con-

stant as suggested by the experimental results,

MPðtÞ ¼ MPð0Þexp½�KðtÞ$t� þMAðtÞ (1)

where K (d�1) is the rate constant of the overall loss of pesti-

cide active ingredient by degradation and irreversible

adsorption, t ¼ 0 is defined the beginning of the dry period,

usually immediately after an application (for first flush or

single washoff) or after the last runoff event (for repeated

washoff). As summarized in the implications from experi-

ment review, the rate at which washoff potential declines

decreases over time. To reflect this, a simple function was

applied to relate K to themass of remaining washoff potential,

KðtÞ ¼ Kð0Þ MPðtÞMPð0Þ (2)

2.4. Pesticide washoff in a single runoff event

The overall transport flux from pesticide in concrete matrix

(pool [1]) to the flowing water ([2]) was predicted by a dynamic

diffusion-type process, which mathematically simulate the

integrate effects of individual transport processes involved in

pesticide washoff. Previous studies (Ozdemir and Floros, 2001;

Schoknecht et al., 2012; Wittmer et al., 2011) indicated that

non-Fickian diffusion mechanism could be used to model the

time-variable release rates of a chemical, which was consis-

tent to the observed dynamics from pesticide washoff exper-

iments. In this study, pesticide washoff from concrete

surfaces during a runoff event was formulated based on Fick’s

second law with time-variable diffusivity, D(t) (m2/s),

vCvt

¼ DðtÞ v2Cvz2

(3)

wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 3 1 6 3e3 1 7 23168

where z is the coordinate measured in the direction of

pesticide release, C (kg/m3), as a function of t and z, is the

pesticide concentration in the concrete subject to washing by

overland flow. Eq. (3) uses the convention that the beginning

of the runoff event corresponds to t ¼ 0. This is in contrast to

the different time scale used to describe pesticide buildup

simulation in Eq. (1). The duration of a runoff event is

generally much smaller than the incubation time. Therefore,

pesticide buildup and washoff are simulated as independent

processes (with different origins of the simulation time) in

this study. It’s noteworthy that (3) is also in the form of a

generic equation for simulating other physical processes such

as 1-D heat transfer.The partial differential equation in (3) can

be rearranged in the form of a 1-dimensional heat transfer

equation, by introducing a transformation of dimensionless

time T,

vCvT

¼ l2v2Cvz2

; (4)

where

vTvt

¼ DðtÞl2

¼ pDðtÞ; or T ¼Z t

0

�pDðtÞ

�dt (5)

with l (m) denoting the equivalent thickness of pool [1] con-

taining pesticide potentially available to water extraction. A

similar concept of equivalent thickness has been applied to

simulating pesticide extraction by surface runoff over top soil

layers (Luo and Zhang, 2011; Neitsch et al., 2011). Although the

thickness cannot be physically measured, it can be calibrated

together with D(t) as one model input parameter ( pD(t) ¼ D(t)/

l2, s�1). The initial concentration (C0) was calculated from the

total mass of pesticide potentially available for washoff

immediately before the washoff event, while boundary con-

ditions were defined at the watereconcrete interface,

Initial condition:

Cðt ¼ 0Þ ¼ C0 @0 < z < l;T ¼ 0 (6)

Boundary conditions:

vCdz

¼ 0 @ z ¼ 0;T > 0

C ¼ 0 @ z ¼ l;T > 0

(7)

An analytical solution to equations and conditions in (4)e(7)

is given by Crank (1980),

CC0

¼ 4p

XNm¼0

exph� ð2mþ 1Þ2p2T

ið2mþ 1Þ2 (8)

The pesticide washoff potential remaining in the concrete,

MP(t), is the integration of the concentration profile between

z ¼ 0 to l. The washoff load as a percent of the washoff po-

tential (F ) is calculated as,

F ¼ 1� MPðtÞMPð0Þ ¼ 1� 8

p2

XNm¼0

exph� ð2mþ 1Þ2p2T

ið2mþ 1Þ2 (9)

Eq. (9) can be approximated with a maximum error of 0.3%

(Liu, 1993; Liu and Simpson, 1997),

F ¼

8>>><>>>:

ffiffiffiffiffiffi4T

p

r; F � 0:52

1� 8p2

exp

��p2T

4

�; F > 0:52

(10)

Similar to the adjustment of the rate constant for overall

loss in Eq. (2), pD is assumed to be linearly related to the

washoff potential. Mass-based adjustment of diffusivity was

also used in previous modeling studies (Korsmeyer and

Peppas, 1981; Ozdemir and Floros, 2001). In addition, a

power-law function is introduced to reflect the decreasing

trend on pesticide release rate from concrete with runoff

duration (with exponent s > 0),

pDðtÞ ¼ pDð0Þt�s (11)

Eqs. (1) and (9) established a semi-mechanistic simulation

for pesticide washoff from concrete surfaces. Time depen-

dence of the overall decay rate constant (K ) and the diffusion

parameter ( pD) in Eqs. (2) and (11) were selected in this study

based on previous studies and the characteristics of washoff

profiles from controlled runoff studies. The assumptions

applied in the model, which provide a conservative estimate

of pesticide release from concrete surfaces, were summarized

as follows:

[1] During a washoff event, dissipation of pesticide washoff

potential is dominated by the transfer flux into the over-

lying water column, while degradation and irreversible

adsorption fluxes are negligible. This is justified by the fact

that the duration of a washoff event was significantly

shorter than the typical incubation time after application.

The overall loss to degradation and irreversible adsorption

is considered between washoff events by Eq. (1).

[2] At the watereconcrete interface (z ¼ l ), a general form of

pesticide transfer across the interface could be written as,

DðtÞ vCvz

¼ �SðC� CeÞ @ z ¼ l;T > 0 (12)

where Ce is the concentration in equilibrium with the water-

side concentration of pesticide, and S is the pesticide release

coefficient at the watereconcrete interface. In this study,

conservative assumptions of (Ce ¼ 0) and (S ¼ N) were applied

to maximize the transport flux across the interface. This im-

plies that all pesticide in the layer of z ¼ l will be immediately

released into runoff water, i.e., C(z ¼ l ) ¼ 0 as the second

boundary condition in Eq. (7). This condition could be refined

by introducing a rainfall intensity dependent release coeffi-

cient (Wittmer et al., 2011).

[3] At the end of a runoff event, remaining washoff potential

will be redistributed to a uniform concentration profile.

The three model parameters of decay rate constant (K ),

diffusion parameter ( pD), and the exponent s have physical

meanings related to pesticide buildup and washoff mecha-

nisms. K quantifies the transfer rate of pesticide from pool [1]

to pools [3] and [4] during the dry period (Fig. 3). At a given time

step, the half-life of the washoff potential is ln2/K. Since K

varies with time in this study, however, the effective half-life

should be calculated based on the specific time dependence.

wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 3 1 6 3e3 1 7 2 3169

The auxiliary variable pD is the inverse of a characteristic time

for pesticide release from the domain 0 < z < l to runoff water

at the given time step (Fig. 3). With a unit of s�1, pD can be also

related to the corresponding effective half-life based on the

washoff potential in Eq. (10) and the time dependence of pD in

Eq. (5). It is worth noting that the calculated half-life may be

much longer than the typical runoff duration, especially for

hydrophobic chemicals; in this case only a small portion of

applied pesticide will be collected in the runoff water.

3. Case study and discussion

To implement the model equations in (1) and (9), the three

parameters of initial decay rate constant K(0), initial diffusion

parameter pD(0), and the exponent s need to be determined for

particular pesticide products and environmental settings. In

this study, an incubation period of at least 1 day was selected

for themodel parameterization. Sprayed pesticide is assumed

to be fully incorporated with the concrete surface after the

incubation period of 1 day. In addition, a set time of 1 day also

provides most protective estimation of pesticide washoff

under real field conditions, since it’s unusual to apply pesti-

cide on urban landscapes within 1 day of a storm event.

Experimental data for model evaluation was taken from

two independent studies of [5] (Jorgenson and Young, 2010)

and [8] (Jiang et al., 2012) as summarized in Table 1. Study [5]

was designed to characterize the washoff profiles of bifen-

thrin, beta-cyfluthrin, lambda-cyhalothrin, and esfenvalerate,

while study [8] for the time dependence of washoff potentials

of bifenthrin and permethrin with incubation durations. The

studies include experiments withmultiple rainfall conditions,

formulations, surface conditions, and repeated washoff

events. In this study, model testing was performed only for

the reported data for commercial formulations during single

washoff events (or “first flush” after treatment) with about

25 mm/h simulated rainfall. For beta-cyfluthrin, lambda-

cyhalothrin and esfenvalerate, model parameters were

Table 2 e Calibrated model parameters and model performanc

Pesticide products Model parameters

pD(0), s�1 K(0), d�1 s

Study [5]

Bifenthrinb 4.78 � 10�7 0.083 0.748

Beta-cyfluthrin 1.49 � 10�4 0.139 1.013

Lambda-cyhalothrin 1.97 � 10�6 1.528 0.000

Esfenvalerate 3.46 � 10�8 0.054 0.000

Study [8]

Bifenthrin 9.32 � 10�7 0.437 1.124

Permethrinc 4.61 � 10�6 0.392 1.437

Notes:

a The NasheSutcliffe coefficient (NS) and the coefficient of the variance of

measured from the experimental replicates. For beta-cyfluthrin, lambda-c

experiments conducted at 1DAA and validated at 7DAA. For other pesticid

b For bifenthrin in study [5], only the washoff profile at 1DAA was meas

c For permethrin, cis-permethrin and trans-permethrin were reported se

calibratedwith experiments conducted at 1DAA and validated

at 7DAA. For other pesticide products, no validations were

performed due to the data limitation.

For each pesticide product, the model parameters were

estimated by global optimization with the shuffled complex

evolution (SCE-UA) method (Duan et al., 1992). The objective

function to be minimized was defined as the coefficient of

variation (CV) of RMSE (i.e., RMSE normalized by the mean of

observations) between the predicted and observed washoff

loads. Parameter optimization was stopped when the change

of the objective function for the last 10 evolution loops was

less than 0.1%. The initial range of input parameters were

pD(0) ¼ [1 � 10�8, 1 � 10�3], K(0) ¼ [0.01, 10], and s ¼ [0, 2].

Calibrated model parameters and the minimized CV[RMSE]

are listed in Table 2. The NasheSutcliffe (NS) coefficient was

also reported for evaluating model performance. Modeling

results are illustrated aswashoff profiles for study [5] (Fig. 4) or

as total washoff loads for study [8] (Fig. 5).

With appropriate calibration the proposed model was

capable of describing temporal variations in the reported

washoff processes. In the model calibration, the resultant CV

[RMSE] ranged from 2.1 to 17.6%, and Nash-Sutcliffe co-

efficients from 0.981 to 0.998. Larger errors were observed in

the model applications to study [8], in which total washoff

loads were measured for up to 89DAA and across three orders

of magnitude (Fig. 5). Furthermore, in each runoff event of

study [8] only the total washoff load but not the washoff

profile was reported. Prediction capability could be improved

with time series data of washoff amounts during a runoff

event. Better model performance, with average CV[RMSE] of

3.0% for calibration and 4.8% for validation, was derived with

data in study [5], in whichwashoff profiles for runoff events at

two different incubation periods (except for bifenthrin) were

applied in the model calibration.

The parameter K(0) presents the initial pesticide loss rate

immediately after application. As discussed previously,

pesticide loss in this study referred to the portion of pesticide

becoming unavailable to water extraction by the two major

e.

Model performancea

Calibration Validation

CV[RMSE] NS CV[RMSE] NS

0.021 0.997 e e

0.021 0.996 0.051 0.980

0.026 0.998 0.056 0.990

0.051 0.992 0.036 0.995

0.077 0.997 e e

0.176 0.981 e e

RMSE are calculated based on the averagewashoff loads of pesticides

yhalothrin and esfenvalerate, model parameters were calibrated with

e products, no validations were performed due to the data limitation.

ured.

parately. Their summation was used in the model evaluation.

Fig. 4 e Predicted washoff profiles for (a) bifenthrin, (b) b-cyfluthrin, (c) l-cyhalothrin, and (d) esfenvalerate, in comparison

with observed data (Jorgenson and Young, 2010). DAA [ days after application.

Fig. 5 e Predicted total washoff loads (normalized by the

corresponding application rates) vs. incubation period for

bifenthrin and permethrin, in comparison with observed

data (Jiang et al., 2012). The error bars indicate the standard

deviations of the measurements.

wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 3 1 6 3e3 1 7 23170

processes of transformation and irreversible adsorption

(Fig. 3). Once applied to concrete surface, a significant amount

of pesticide would immediately become unavailable for

transferring into runoff, suggested by the initial decay half-

lives of 0.45e12.8 days. At the same time, the effective rate

constant, K(t), would be reduced with less washoff potential

according to Eq. (2). This suggested a “long tail” (or high

persistence) in the plot of total washoff loads with incubation

time as demonstrated in Fig. 5. The extended availability of

pesticide has been experimentally demonstrated, where

bifenthrin and permethrin were detectable in runoff water at

221DAA (Jiang et al., 2012).

The exponent s is an indicator for the shape of washoff

profile. Large s (for bifenthrin, beta-cyfluthrin, and permethrin

in this study) indicates a type-A profile (“a steep dissipation

rate followed by a more steady rate”), while small s (lambda-

cyhalothrin and esfenvalerate) suggests a type-B profile

(“relatively steady dissipation rate over the duration of the

experiment”) (Jorgenson and Young, 2010). This finding was

consistent to the reported profiles based on experiments

(Fig. 1).

The initial diffusivity of pesticide in the system of concrete

and penetrated water can be calculated by Eq. (5) with

calibrated pD(0) value in Table 2. If an interaction depth, l in Eq.

(5), in the magnitude of mm is assumed, the estimated

initial diffusivities are in the range of 10�6e10�4 cm2/s. The

values are comparable to or larger than the diffusivities of

the selected pesticides in water as estimated by the SPARC

wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 3 1 6 3e3 1 7 2 3171

calculator (http://archemcalc.com/sparc). The effective diffu-

sivity of a pesticide could be significantly improved by other

components in the product formulation, especially for the

period immediately after application (Jorgenson and Young,

2010). In addition, for pesticides associated with type-A

washoff profile (with a large s value) the initial diffusivity

will decrease quickly during the runoff process as suggested

by Eq. (11).

4. Summary and suggestions

A semi-mechanistic model was developed here for the pre-

diction of pesticide washoff from concrete surfaces. First-

order kinetics and Fick’s second law, with time-dependent

decay rate constant and diffusivity, were utilized in the

model simulation to describe pesticide buildup and washoff

processes, respectively. With three parameters of initial

decay rate constant (K ), initial diffusion parameter ( pD), and

the exponent s, the model is able to simulate both the

pesticide washoff profile during a runoff event and the

temporal variation of washoff potential at a given incubation

period. In a case study, the model was applied to the

measured data of pesticide washoff from concrete surfaces,

and successfully captured the reported washoff profiles and

washoff loads for the five selected pyrethroids in 15 runoff

events (with at least two replicates for each event). Cali-

brated models generated average CV[RMSE] of 6.58% and

average NS of 0.992 in comparison to the averages of re-

ported washoff loads.

Values of model parameters are mainly associated with

pesticide product, concrete property, and weather condition.

Therefore, two research efforts are required for model

application to local conditions, [1] washoff experiments for a

pesticide product, and [2] development of modeling sce-

narios. As suggested in the case study, at least two washoff

profiles, one at 1DAA and the other later, are needed for

accurate estimation of model parameters. Additional wash-

off experiments with longer incubation time would be useful

for further evaluating the time dependences of decay rate

constant and diffusion parameter. Most of the available data

were measured using prescribed rainfall intensity and

duration, which could be associated with the actual weather

condition in the study area. For example, 25 mm h�1 rainfall

of 60 min duration used in studies [5] and [7] (Table 1) reflects

a 1-year recurrence interval in Raleigh, North Carolina to 5

years in Sacramento, California (Jacobson, 2011). Other

weather conditions such as ambient temperature and solar

radiation could be also influential factors in pesticide

washoff. Previous study indicated that higher temperature

and direct solar radiation enhance the release of biocides

from construction materials (Burkhardt et al., 2012, 2008).

Therefore, modeling scenarios with a typical rainfall pattern

and concrete surface condition could be developed as

guidelines for the washoff experiments and model applica-

tions. Based on appropriate modeling scenarios and cali-

brated parameters, the model developed in this study is

anticipated to provide reasonable estimation of pesticide

washoff to support risk assessment in urban environmental

settings.

Appendix A. Supplementary data

Supplementary data related to this article can be found at

http://dx.doi.org/10.1016/j.watres.2013.03.032.

r e f e r e n c e s

Alley, W.M., 1981. Estimation of impervious-area washoffparameters. Water Resource Research 17 (4), 1161e1166.

Amweg, E.L., Weston, D.P., You, J., Lydy, M.J., 2006. Pyrethroidinsecticides and sediment toxicity in urban creeks fromCalifornia and Tennessee. Environmental Science &Technology 40 (5), 1700e1706.

Burkhardt, M., Zuleeg, S., Vonbank, R., Bester, K., Carmeliet, J.,Boller, M., Wangler, T., 2012. Leaching of biocides fromFacades under natural weather conditions. EnvironmentalScience & Technology 46 (10), 5497e5503.

Burkhardt, M., Zuleeg, S., Vonbank, R., Simmler, H., Lamani, X.,Bester, K., Boller, M., 2008. Biocides in facades runoff andstorm water of urban areas. 11th International Conference onUrban Drainage, Edinburgh, Scotland, UK.

Crank, J., 1980. The Mathematics of Diffusion. Oxford UniversityPress, USA.

DEFRA, 1999. The Development of Scenarios and Models forPredicting Losses of Herbicides from Hard Surfaces. UKDepartment for Environment Food and Rurual Affairs, SoilSurvey and Land Research Centre, London, UK. PL0520. http://randd.defra.gov.uk/Document.aspx?Document¼PL0520_1325_FRP.doc.

Ding, Y., Harwood, A.D., Foslund, H.M., Lydy, M.J., 2010.Distribution and toxicity of sediment-associated pesticides inurban and agricultural waterways from Illinois. USAEnvironmental Toxicology and Chemistry 29 (1), 149e157.

Duan, Q., Sorooshian, S., Gupta, V., 1992. Effective and efficientglobal optimization for conceptual rainfall-runoff models.Water Resources Research 28 (4), 1015e1031.

Epstein, L., Bassein, S., 2003. Patterns of pesticide use in Californiaand the implications for strategies for reduction of pesticides.Annual Review of Phytopathology 41, 351e375.

FOOTPRINT, 2012. The FOOTPRINT Pesticide Properties Database.The Agriculture & Environment Research Unit (AERU) at theUniversity of Hertfordshire, Hatfield, Herts, UK. http://sitem.herts.ac.uk/aeru/footprint/en/index.htm (accessed 5/2012).

Hintzen, E.P., Lydy, M.J., Belden, J.B., 2009. Occurrence andpotential toxicity of pyrethroids and other insecticides in bedsediments of urban streams in central Texas. EnvironmentalPollution 157 (1), 110e116.

Holmes, R.W., Anderson, B.S., Phillips, B.M., Hunt, J.W.,Crane, D.B., Mekebri, A., Connor, V., 2008. Statewideinvestigation of the role of pyrethroid pesticides in sedimenttoxicity in California’s urban waterways. EnvironmentalScience & Technology 42 (18), 7003e7009.

Jacobson, C.R., 2011. Identification and quantification of thehydrological impacts of imperviousness in urban catchments: areview. Journal ofEnvironmentalManagement92 (6), 1438e1448.

Jiang, W., Gan, J., Haver, D., 2011. Sorption and desorption ofpyrethroid insecticide permethrin on concrete. EnvironmentalScience & Technology 45 (2), 602e607.

Jiang, W., Haver, D., Rust, M., Gan, J., 2012. Runoff of pyrethroidinsecticides from concrete surfaces following simulated andnatural rainfalls. Water Research 46 (3), 645e652.

Jiang, W., Lin, K., Haver, D., Qin, S., Ayre, G., Spurlock, F., Gan, J.,2010. Wash-off potential of urban use insecticides on concretesurfaces. Environmental Toxicology and Chemistry 29 (6),1203e1208.

wat e r r e s e a r c h 4 7 ( 2 0 1 3 ) 3 1 6 3e3 1 7 23172

Jorgenson, B.C., Young, T.M., 2010. Formulation effects and theoff-target transport of pyrethroid insecticides from urban hardsurfaces. Environmental Science & Technology 44 (13),4951e4957.

Korsmeyer, R.W., Peppas, N.A., 1981. Effect of the morphology ofhydrophilic polymeric matrices on the diffusion and release ofwater soluble drugs. Journal of Membrane Science 9 (3),211e227.

Liu, J.Y., 1993. Mathematical relationship between desorption andsorption solutions. Drying Technology 11 (5), 961e975.

Liu, J.Y., Simpson, W.T., 1997. Solutions of diffusion equationwith constant diffusion and surface emission coefficients.Drying Technology 15 (10), 2459e2477.

Luo, Y., Zhang, M., 2011. Environmental modeling and exposureassessment of sediment-associated pyrethroids in anagricultural watershed. PLoS ONE 6 (1), e15794.

Moran, K.D., TenBrook, P.L., 2011. Modeling approaches forpesticide exposure assessment in rice paddies. In: Goh, K.,Bret, B., Potter, T., Gan, J. (Eds.), Sources of PyrethroidInsecticides in California’s Urban Watersheds: a ConceptualModel. American Chemical Society, pp. 287e308.

Neitsch, S.L., Arnold, J.G., Kiniry, J.R., Williams, J.R., 2011. Soil andWater Assessment Tool, Theotetical Documentation, Verison2009. Texas A&M University System, College Station, TX.Texas Water Resources Institute Technical Report No. 406.http://swatmodel.tamu.edu/.

Ozdemir, M., Floros, J.D., 2001. Analysis and modeling ofpotassium sorbate diffusion through edible whey proteinfilms. Journal of Food Engineering 47 (2), 149e155.

Ramwell, C.T., 2005. Herbicide sorption to concrete and asphalt.Pest Management Science 61 (2), 144e150.

Schoknecht, U., Gruycheva, J., Mathies, H., Bergmann, H.,Burkhardt, M., 2009. Leaching of biocides used in Facade

coatings under laboratory test conditions. EnvironmentalScience & Technology 43 (24), 9321e9328.

Schoknecht, U., Topfer, A., Uhlig, S., Baldauf, H., 2012.Chacracterisation of Leaching of Biocidal Active Substances ofMain Group 2 ’Preservatives’ from Different Materials underWeathering Conditions. Federal Environment Agency(Umweltbundesamt), Dessau-Roßlau, Germany.

Shepherd, A.J., Heather, A.I.J., 1999. Factors affecting the loss of sixherbicides from hard surfaces. In: Conference ProceedingsBrightonConferenceWeeds. BritishCropProtectionCouncil, UK.

Spanoghe, P., Claeys, J., Pinoy, L., Steurbaut, W., 2005.Rainfastness and adsorption of herbicides on hard surfaces.Pest Management Science 61 (8), 793e798.

Thuyet, D.Q., Jorgenson, B.C., Wissel-Tyson, C., Watanabe, H.,Young, T.M., 2012. Wash off of imidacloprid and fipronil fromturf and concrete surfaces using simulated rainfall. Science ofThe Total Environment 414 (1), 515e524.

Weston, D.P., Holmes, R.W., Lydy, M.J., 2009. Residential runoff asa source of pyrethroid pesticides to urban creeks.Environmental Pollution 157 (1), 287e294.

Weston, D.P., Holmes, R.W., You, J., Lydy, M.J., 2005. Aquatictoxicity due to residential use of pyrethroid insecticides.Environmental Science & Technology 39 (24), 9778e9784.

Weston, D.P., Lydy, M.J., 2010. Urban and agricultural sources ofpyrethroid insecticides to the Sacramento-San Joaquin Deltaof California. Environmental Science & Technology 44 (5),1833e1840.

Weston, D.P., Lydy, M.J., 2012. Stormwater input of pyrethroidinsecticides to an urban river. Environmental Toxicology andChemistry 31 (7), 1579e1586.

Wittmer, I.K., Scheidegger, R., Stamm, C., Gujer, W., Bader, H.-P.,2011. Modelling biocide leaching from facades. WaterResearch 45 (11), 3453e3460.