A preferential flow leaching index - Semantic Scholar

Click Here

WATER RESOURCES RESEARCH, VOL. 45, W11405, doi:10.1029/2008WR007265, 2009

for

Full Article

A preferential flow leaching index Gavan Sean McGrath,1 Christoph Hinz,1 and Murugesu Sivapalan2,3,4 Received 5 July 2008; revised 20 July 2009; accepted 3 August 2009; published 5 November 2009.

[1] The experimental evidence suggests that for many chemicals surface runoff and rapid

preferential flow through the shallow unsaturated zone are significant pathways for transport to streams and groundwater. The signature of this is the episodic and pulsed leaching of these chemicals. The driver for this transport is the timing and magnitude of rainfall events which trigger rapid flow and the release of solute from a source zone, located near the soil surface. Based on these considerations we develop a conceptual model capable of reproducing many of the signatures of this rapid transport. This driver-source-trigger-signature framework forms the basis of the development of a new leaching index which describes the potential for rapid solute transport by preferential flow or surface runoff. This preferential flow (PF) index is based upon soil and chemical parameters as well as the timing and magnitude of rainfall and preferential flow events. The PF index suggests that a chemical’s potential to experience rapid transport increases as sorption strength increases, however, when an approximation to account for sorption kinetics is considered the PF index peaks at moderate sorption values. The model is sensitive to the timing and magnitude of rapid flow events, which may require existing data or infiltration models for their estimation. Citation: McGrath, G. S., C. Hinz, and M. Sivapalan (2009), A preferential flow leaching index, Water Resour. Res., 45, W11405, doi:10.1029/2008WR007265.

1. Introduction [2] The attenuation factor (AF) was derived by Rao et al. [1985] as a tool to aid prediction of the relative leaching potential of pesticides. It calculates what proportion of the applied chemical reaches groundwater, by assuming steady leaching of solutes through the unsaturated zone via plug flow. The AF was derived by calculating the time required for a chemical to be transported to a depth zx. According with the assumptions, this is regulated by the chemical’s sorption to the soil, assumed to be of the linear equilibrium type, the recharge rate, assumed to be steady, and the constant water content participating in solute transport. During transport the plug of chemical undergoes first order degradation which leads to the concentration changing with time as C ðt Þ ¼ C ð0Þ expðkb t Þ

ð1Þ

where C [M L3] is the solute concentration, kb [T1] the first order rate coefficient, and t denotes time. Combining this with the time required for transport to a depth zx leads to

1 School of Earth and Environment, University of Western Australia, Crawley, Australia. 2 Centre for Water Research, University of Western Australia, Crawley, Australia. 3 Departments of Geography and Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA. 4 Department of Water Management, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, Netherlands.

Copyright 2009 by the American Geophysical Union. 0043-1397/09/2008WR007265$09.00

the calculation of the proportion of the applied concentration which reaches groundwater, the AF, as given by C zx zx DqR AF ¼ ¼ exp kb i C ð0Þ

ð2Þ

where i [L T1] is the average rate of groundwater recharge, Dq [L3 L3] the volumetric water content involved in transport and R = 1 + rbKd/q [], the retardation factor, comprised of rb [M L3] the soil bulk density, q [L3 L3] the plug’s volumetric water content, and Kd [L3 M1] the distribution factor, governing the partitioning of chemical between solution and soil. 1.1. Limitations of the AF and Similar Indices [3] The AF is primarily used for relative measures of leaching risk [Rao et al., 1985]. For example, the PIRI risk tool [Kookana et al., 2005] uses AF to rank the susceptibility of a suite of pesticides to leaching and then this factor contributes to a number of other toxicity and management factors to quantify the vulnerability of streams and groundwater. While a number of refinements to the AF have been proposed [Loague et al., 1990, 1996; Paraiba and Spadotto, 2002; Stenemo et al., 2007], none have addressed its acknowledged [Rao et al., 1985] inability to account for rapid transport processes, such as preferential flow. [4] The experimental evidence indicates that it is the timing of significant rainfall events since pesticide application which exerts a strong control on when and to what extent pesticides are observed in receiving waters [Leonard, 1990; Flury, 1996; Domagalski et al., 1997; Bergamaschi et al., 2001; Kladivko et al., 2001; Louchart et al., 2001; Fortin et al., 2002; Scorza et al., 2004]. A number of simple models were developed to account for this rainfall variabil-

W11405

1 of 10

W11405

MCGRATH ET AL.: A PREFERENTIAL FLOW LEACHING INDEX

ity with a priori [Rao et al., 1976; Dayananda, 1982; Jury and Gruber, 1989; Giambelluca et al., 1996; Aylmore and Di, 2000] and a posterior [Stewart and Loague, 1999; Jury and Roth, 1990] predictions of leaching risk. One notable problem with these cited approaches is that they essentially consider flow only in the soil matrix and not through episodically activated rapid flow pathways [Jury and Roth, 1990]. For this reason the predictions from these methods, the AF, and other more complex models, based on a similar matrix-only flow assumption, are quite similar [Rao et al., 1988; Jury and Gruber, 1989; Aylmore and Di, 2000]. [5] Rainfall event timing and magnitude are significant controls on leaching because they influence the triggering of episodic fast flow processes such as surface runoff and preferential flow through the unsaturated zone [see the reviews of Leonard, 1990; Flury, 1996; Kladivko et al., 2001]. Preferential flow is now recognized as the dominant process for the transport of many pesticides to groundwater [Flury, 1996; Kladivko et al., 2001]. Models which do account for preferential flow and surface runoff are often more complex and usually require numerical simulation and significant parameterization [Jarvis et al., 1994]. However, the information required to operate these models is often unavailable at the initial phase of a risk assessment. Simple, physically based indices, like the AF, are attractive for initial risk screening because of their limited parameterization and the rapidity with which they can be applied. As we will later see, there is some similarity in the mechanisms for triggering surface runoff and preferential flow, as well as similar dynamics of pesticide transport. It would be useful therefore to have a simple index which describes the potential for rapid pesticide transport by a generic fast flow process. [6] In sections 1.2 –1.5 the evidence for how pesticides are transported to streams and groundwater is briefly reviewed. This will be presented within a driver-sourcetrigger-signature framework. We hypothesize that the dominant driver of pesticide transport is the highly variable and intermittent rainfall signal. The source of pesticides which are transported rapidly off site is often a thin layer of soil near the surface, the same location where rapid flow processes, such as surface runoff and preferential flow, are episodically initiated. The pulsed and episodic dynamics of pesticide leaching that we see is a result of the driversource-trigger conceptual model. Later in the paper we will evaluate how this simple conceptual model qualitatively reproduces a variety of the observed dynamics. These dynamics are the emergent patterns, the signatures, that reflect the underlying processes controlling pesticide leaching. This framework will ultimately lead us to develop a new, physically based leaching index. 1.2. The Driver [7] The timing and magnitude of rainfall events since pesticide application have been recognized as significant controls on pesticide transport at the plot [Flury, 1996], field [Leonard, 1990; Kladivko et al., 2001] and basin wide scales [Capel et al., 2001]. In particular, large storm events occurring shortly after pesticide application generate the largest losses of the chemical to streams and groundwater. At the catchment scale the mean annual pesticide load in streams, as a percentage of use, tends to stay the same with the change in contributing area [Capel et al., 2001]. This

W11405

scale invariance occurs despite strong spatial and temporal scaling of rainfall variability [Schertzer and Lovejoy, 1987]. Given the above evidence for the significance of individual rainfall events, this scaling behavior suggests that small space and timescale rainfall is relevant for the dynamics of pesticide transport at larger scales too. [8] Variations of rainfall intensity within a single rainfall event have also been shown to have a significant impact on the amount of chemical rapidly transported [Zhang et al., 1997; McGrath et al., 2008a]. It has also been found that the mean amount leached during an event, increased at low sorption strength before decreasing as sorption increased further [McGrath et al., 2008a]. Larsson and Jarvis [2000] modeled the impact of chemical properties on total leaching with and without preferential flow over multiple rainfall events. They found that the ratio of total leaching with preferential flow to total leaching without, peaked at intermediate levels of sorption. The AF or its matrix-only flow variants cannot reproduce this behavior. 1.3. The Source [9] Pesticides which persist in the near surface do so because they tend to strongly adsorb to the surface of clay minerals and organic particles. As a result, pesticides detected in soil cores, even a long time after application, are often located near the surface of the soil (see for example Flury et al. [1995]). This persistence near the soil surface places pesticides where rapid flow processes are initiated, making them available for rapid transport [Leonard, 1990; Allaire-Leung et al., 2000a, 2000b]. [10] Pesticides of widely varying sorption properties are often transported through the unsaturated zone to the same depth at the same time [Ghodrati and Jury, 1992; Flury, 1996; Lennartz, 1999; Elliott et al., 2000; Kladivko et al., 2001; Laabs et al., 2002; Fortin et al., 2002; Malone et al., 2004]. The amount of solute transported in an event however, tends to decrease as sorption increases [Flury, 1996; Laabs et al., 2002; Fortin et al., 2002; Leu et al., 2004; Malone et al., 2004]. Reichenberger et al. [2002] on the other hand suggested that the potential for a chemical to be transported to depth by preferential flow, as opposed to matrix transport, actually increased with increasing sorption strength. As we will later demonstrate, these last two observations are not necessarily contradictory. [11] Ahuja et al. [1981] demonstrated that it is only the top 10 mm of soil which contributes strongly sorbing solutes to surface runoff. Leonard [1990] summarized the evidence demonstrating the correlation between the concentration of solute in a thin surface layer prior to a rainfall event with the total amount of solute released to surface runoff. A thin near-surface mixing zone has also been incorporated into a number of preferential flow models [Jarvis et al., 1994; Steenhuis et al., 1994]. The link between the surface and preferential transport is further supported by the tendency for concentration peaks of successive rapid leaching episodes to decrease exponentially with time [Leonard, 1990; Domagalski et al., 1997; Lennartz et al., 1997; Renaud et al., 2004; Scorza et al., 2004] in a similar fashion to the exponential like loss of solutes from the near surface. [12] Incorporation of pesticides into the soil results in smaller amounts of leaching to groundwater and streams compared to surface applications [Leonard, 1990; Flury,

2 of 10

W11405


1996; Kladivko et al., 2001]. Similarly, smaller magnitude rainfall events occurring before a large event can assist the migration of chemical below the surface and reduce off-site chemical migration [Leonard, 1990; Kladivko et al., 2001]. The loss of solute from the near surface, between rapid flow events, therefore influences the amount of chemical available for rapid transport when they do occur. These loss processes include slow leaching, degradation, volatilization, kinetic sorption, and plant uptake, amongst others. [13] More recently, McGrath et al. [2008b] derived statistics of the persistence of chemicals in the source zone, subject to a random rainfall signal. It was assumed there that pesticide dissipation can be described by a piecewise continuous process, with continuous degradation between rainfall events and discrete losses during them. We will exploit this approach in this paper for the analytical derivation of a new leaching index. 1.4. The Trigger [14] Rapid preferential flow and surface runoff are triggered by particular rainfall events [Heppell et al., 2002] when either the soil is close to saturation or when the rainfall intensity is greater than the infiltration capacity at the surface [Beven and Germann, 1982]. When the hydraulic properties of the soil matrix are reduced, by sealing for example, pesticide transport by preferential flow can become more dominant [Heppell et al., 2004]. [15] The triggering of fast flow involves highly nonlinear, threshold processes. As a result, not every rainfall event will trigger surface runoff or preferential flow. The temporal structure of these episodic rapid flow events was quantified for simple model systems [McGrath et al., 2007; Struthers et al., 2007]. For example, McGrath et al. [2007] derived analytical expressions for the mean and variance of the time between successive rapid flow events triggered by thresholds in soil moisture storage and rainfall intensity. Events controlled by soil moisture storage were found to be temporally clustered, the degree of which depended upon the statistical structure of rainfall. [16] Therefore, pesticide transport occurs episodically with respect to rainfall events. Additionally, these fast flows are short-lived, pulsed, only occurring during or for a short period after a rainfall event. Because these rapid flows dominate off-site transport of many pesticides the signature of pesticide leaching we observe reflects the pulsed and episodic triggering of these fast flow processes. [17] In summary we hypothesize that the essentials for a conceptual model to capture pesticide leaching dynamics are: (a) a thin near-surface layer in which pesticides reside; (b) a rapid flow pathway connected from the soil surface to the receiving water; (c) pesticide mixing with low intensity rainfall and subsequent transport into slow flow pathways; and (d) the episodic triggering of rapid flow pathways and hence rapid pesticide transport triggered by significant rainfall events. 1.5. Outline [18] In the remainder of the paper we first aim to demonstrate with a simple driver-source-trigger conceptual model some qualitative agreement with the known signatures of pesticide leaching. Next, with this as justification we simplify the structure of rainfall and rapid flow event triggering to derive analytically a new leaching index. This

W11405

index describes the potential amount of solute rapidly leached, by a generic fast flow pathway such as preferential flow or surface runoff. This preferential flow (or rapid flow) leaching index is then briefly assessed.

2. Methods 2.1. Source Zone Mass Balance [19] The following model of the solute mass balance near the soil surface aims to be as consistent as possible with many of the assumptions used in the derivation of the AF. For that reason we neglect to account for more complex sorption, degradation and transport processes. In the spirit of the AF this is also consistent with the limited knowledge available at the time of an initial risk assessment. [20] We model here a thin layer near the soil surface containing pesticides with a concentration in the liquid phase given by C [M L3], which fully mixes with water from intermittent rainfall events [Leonard, 1990; Jarvis et al., 1994; Steenhuis et al., 1994; Zhang et al., 1997, 1999; McGrath et al., 2008b]. The near surface mixing layer is parameterized by a depth zl [L] and constant volumetric water content ql [L3 L3]. As with the AF we assume that pesticides undergo linear, equilibrium sorption and first order degradation with a rate coefficient kl [T1]. [21] There is general agreement that sorbed chemical is usually not bio available [Ogram et al., 1985]. From a modeling point of view however, it may be practicable to simulate degradation on the sorbed phase as a means to compensate for the exclusion of other processes, such as diffusion limited sorption/desorption, while still applying the instantaneous equilibrium assumption mathematically [Fomsgaard, 2004]. Therefore we will also consider the case when first order degradation occurs on the sorbed phase (where the concentration sorbed is Cs [M M1]) has a rate coefficient ks [T1]. In the application of the MACRO model [Jarvis et al., 1994] it is common practice to assume degradation rates are equal in both phases [Fomsgaard, 2004]. This is because it is usually difficult to distinguish between the two rates experimentally. We will therefore present two scenarios. The first describes the case where degradation is inversely proportion to sorption (i.e. ks = 0), while the second describes the case where degradation rates in both phases are equal and the effective degradation rate is independent of sorption. [22] A mass balance equation, describing the rate of change in the concentration of solute over time is thus zl ql R

dC ¼ kl zl ql C ks zl rb Cs Ciðt Þ dt

ð3Þ

where i(t) is the time variable rainfall intensity. This model only considers dissolved phase transport, however we acknowledge that colloidal and sediment bound transport can be important vectors too [Flury, 1996]. With equation (3) we assume explicitly that the water content in the source zone remains constant. We also implicitly assume that the temperature does not vary as well. These two state variables are actually likely to vary significantly in the source zone, which can strongly influence degradation, sorption and volatilization processes. Later we will suggest how to account for this variability within the leaching index if the

3 of 10


W11405

Table 1. Parameters Used in the Example Pesticide Simulations Parameter

Description

Value(s)

tb tr h a0 H Ix zl ql R kl ks m(0)

Mean interstorm duration Mean storm duration Mean storm depth bounded random cascade scaling intercept bounded random cascade scaling exponent infiltration capacity mixing cell depth porosity in mixing layer retardation factor solution phase degradation rate coefficient sorbed phase degradation rate coefficient applied pesticide mass

3.3 days 12 hours 1 mm 15 0.45 60 mm day1 10 mm 0.4 cm3cm3 1, 10 0.01 day1 0 day1 100 mg m2

data is available. This equation can be simplified to the more familiar form zl ql R

dC ¼ kb zl ql C CiðtÞ dt

ð4Þ

where kb = kl + ks (R 1). This is related to the chemical’s half-life via t1/2 = ln(2)/kb [T] which we will use later in a comparison of leaching indices. [23] In order to begin to assess the role of the timing and magnitude of rainfall events on leaching we assume that the duration of rainfall events is small in comparison to the time between events. This allows us to consider the loss of solute from the source zone to be a piecewise continuous process, with instantaneous leaching losses due to rainfall events and continuous losses due to degradation between storms [McGrath et al., 2008b]. Using the transformed variable x(t) = ln[C(t)/C(0)] the dimensionless concentration remaining just prior to a rainfall event is given by xðtb Þ ¼

kb tb R

ð5Þ

where tb the time till a rainfall event. The concentration remaining after a rainfall event is xðtb þ tr Þ ¼ xðtb Þ

h zl ql R

ð6Þ

where h = itr is the storm depth, i its average intensity and tr its duration. Given the assumption that tr tb then we effectively have a step change in concentration at t = tb, which is consistent with the intermittent nature of rainfall events. If a proportion f of that rainfall event generates rapid flow, then a conservative estimate of the mass rapidly transported (mp) can be calculated from mass balance considerations as ð1 f Þh mp ðtb þ tr Þ ¼ zl qRC ð0Þ exp xðtb Þ zl ql R h exp xðtb Þ zl q l R

ð7Þ

[24] Equation (7) describes the mass of chemical that is loaded to a rapid flow pathway. When more rain events

W11405

occur prior to the first event generating preferential flow then it should be evident that the form of this equation essentially remains unchanged. We will later demonstrate this when we derive a leaching index which accounts for numerous rainfall and preferential flow events. [25] When applied to preferential flow, for example, this equation has no depth limitation built in. Therefore, it should be considered to describe the loading of macropores, not the actual transport to groundwater. As a result it is applicable to surface runoff or for shallow preferential flow through the root zone. Acknowledging these limitations, this equation will be used later for numerical simulations as well as derivation of a rapid flow leaching index. 2.2. Simulation of Rapid Solute Transport [26] For the purpose of reproducing qualitatively the signatures of pesticide transport dynamics we conducted numerical simulations of the driver-source-trigger conceptual model. Fast flow processes such as surface runoff and preferential flow are often triggered by a soil water storage threshold or an infiltration excess threshold [Beven and Germann, 1982; Edwards et al., 1992, 1993]. Here we use a simple rainfall intensity threshold Ix [L T1] to partition rainfall between the soil matrix and preferential flow pathways. Episodic triggering is also expected of more complex descriptions of infiltration, so in this paper we adhere to a principle of minimalism. [27] For numerical simulations we consider that rainfall arrivals are described as a Poisson process, where the resulting time between events is exponentially distributed with a mean t b. Rain events are assumed to have a duration, exponentially distributed with a mean t r and a depth independently and exponentially distributed with a mean h. Based on this average rainfall intensity, a rainfall event is then disaggregated to a temporal resolution of 6 minutes. A bounded random cascade is used to generate the withinstorm rainfall variability using two variables a0 and H [Menabde and Sivapalan, 2000]. All parameters used in the simulation are summarized in Table 1. [28] Once the intensities have been calculated then the periods during an event where the rainfall intensities are greater than Ix are used to determine what proportion f of the storm’s rainfall will become preferential flow and what proportion will infiltrate into the slow soil matrix pathways (Figure 1). In order to follow the rationale of the solute mass balance set out above we now lump together the total event’s rainfall, considering it to be an instantaneous depth, as opposed to an intensity. The solute mass balance and the amount rapidly leached can then be accounted for using equations (5) through (7).

3. Qualitative Model Behavior [29] The simulations show a number of features consistent with observed transport in the field (Figure 2). First, because of the filtering of the rainfall signal by the rainfall intensity threshold to trigger preferential flow, rapid flow events occur episodically (Figure 2a). Pesticide transport that results from these rapid flow events also occurs as short-lived discrete events [Hyer et al., 2001; Fortin et al., 2002; Laabs et al., 2002] (Figure 2b). This is of course due to the model assumptions, but is consistent with the relatively short-lived nature of rapid flow events (see for

4 of 10

W11405


W11405

equation (6)) [Flury, 1996; Fortin et al., 2002; Laabs et al., 2002; Malone et al., 2004; Leu et al., 2004]. [32] The dynamics of this model, which essentially describes the episodic release of a chemical from near the soil surface to fast flow pathways, appears to be consistent

Figure 1. Example of rainfall filtering for preferential flow and solute loading simulation. (a) A single storm generated by a bounded random cascade. Rainfall above an infiltration capacity threshold of 2 mm/hr is partitioned to preferential flow. (b) A series of such storms now considered as instantaneous events for simulation with equation (3).

example Brown et al. [2000]; Laabs et al. [2002]; Leu et al. [2004]). The pulses of detectable pesticide concentrations can occur for long periods after application [Johnson et al., 2001; Louchart et al., 2001; Kjær et al., 2005] and tend to decay exponentially with time [Lennartz et al., 1997; Domagalski et al., 1997; Renaud et al., 2004; Scorza et al., 2004] (Figure 2b) due to the exponential-like loss of chemical from the source zone (not shown). [30] The cumulative mass of pesticide in leachate (Figure 2c) shows similar staircase like behavior as observed in lysimeter leaching experiments [Renaud et al., 2004; Scorza et al., 2004; Kjær et al., 2005]. This behavior is in contrast to the smooth, continuous breakthrough curves of more mobile solutes [Butters et al., 1989]. One quarter of one percent of the applied pesticide was rapidly leached. This is of a similar magnitude to typically reported losses [Leonard, 1990; Kladivko et al., 2001]. In contrast the AF often underpredicts the total mass of solute reaching groundwater. [31] For both a pesticide and a nonsorbing tracer it can be seen that the first preferential flow event since application contributed the largest leaching event [Leonard, 1990; Flury, 1996; Kladivko et al., 2001]. A tracer (R = 1) however, has a low potential for episodic leaching behavior to be observed (see Figure 2d), as it is only the first preferential flow event where any significant rapid leaching is observed. This is because of the potential for a significant amount of transport into the soil matrix before the first and between subsequent preferential flow events. Also, when two pesticides with contrasting sorption strengths are rapidly transported during a single event, the amount released to preferential flow is smaller when sorption is stronger (see

Figure 2. Simulated pesticide transport by a series of rainfall events. (a) Peak rainfall intensity during a storm illustrating the temporal triggering of infiltration excess with an infiltration capacity threshold of 60 mm/day. (b) Time series of pesticide (R = 10) concentration in preferential flow. (c) Cumulative amount of pesticide transported by preferential flow as a percentage of the mass applied. (d) Cumulative amount of a tracer (R = 1) transported by preferential flow as a percentage of the mass applied. Parameters used in the simulation are summarized in Table 1.

5 of 10

W11405


W11405

and xm denotes the dimensionless amount of chemical lost due to slow matrix leaching between preferential flow events, given by xm ¼ N

Figure 3. Description of the variables and the conceptual structure of rainfall used to derive the preferential flow leaching index equation (18). Time between rainfall events tb, the time between preferential flow events tp, the magnitude of the proportion of storm rainfall not generating preferential flow hm, and the magnitude of a preferential flow event hp.

with a number of signatures observed of pesticide transport. These dynamics cannot be reproduced by the processes embedded within the AF. This provides the motivation to use the driver-source-trigger concept to develop a physically based preferential leaching index, based upon chemical properties as well as the structure of rainfall and preferential flow events.

hm zl ql R

[35] When a preferential flow event happens on the Nth rainfall event we assume that following some initial slow leaching into the soil, the chemical is then released to preferential flow. The dimensionless amount released is thus given by xp ¼

hp zl ql R

[33] In this section we use the same mass balance approach to derive an estimate of the amount of solute which is lost to rapid flow on the basis of an idealized structure of rainfall and preferential flow event occurrence. This structure is shown in Figure 3. [34] We begin with the concentration of solute remaining in the source zone prior to the first rainfall event since application, given by

mþ N ¼ zl ql RC ð0Þ exp xb xm xp

where = tb is the time till the first rainfall event. Immediately following the first rainfall event the concentration remaining is

Therefore the proportion of the applied mass released to preferential flow at this time is

tb kb R

ð16Þ

ð10Þ

ð11Þ

1 X

exp j xb þ xm þ xp þ xp

j¼1

ð9Þ

where xb denotes the dimensionless amount of chemical lost due to degradation between preferential flow events, given by xb ¼ N

þ m N mN zl ql RC ð0Þ

When there are an infinite number of such N rainfalls and preferential flow event combinations the total proportion of the applied mass released to preferential flow is PF ¼

where hm is the depth of the rainfall event. At this point we consider that no preferential flow has occurred. It is evident therefore, that following N identical storm and interstorm periods without preferential flow, the concentration remaining is xðtN Þ ¼ xb xm

ð15Þ

ð8Þ

t 1

hm x t1þ ¼ x t1 zl ql R

ð14Þ

The mass of solute remaining after the preferential flow event is

PF1 ¼ kb tb x t1 ¼ R

ð13Þ

where hp is the magnitude of the preferential flow event. With a timescale between preferential flow events tp we can define N = tp/tb. Given that in practice this ratio of timescales may be estimated from a combination of sources we expect that N need not necessarily be an integer. At time tp, following N storm and interstorm periods, the mass of solute remaining at the soil surface prior to a preferential flow event is given by m N ¼ zl ql RC ð0Þ expðxb xm Þ

4. A Preferential Flow Leaching Index

ð12Þ

exp j xb þ xm þ xp

ð17Þ

Equation (17) simplifies to PF ¼

exp xp 1 exp xb þ xm þ xp 1

ð18Þ

This is the preferential flow leaching index. [36] For chemicals which do not degrade (xb = 0) and where all rainfall becomes preferential flow (xm = 0) then PF = 1. When no preferential flow occurs (xp = 0) then PF = 0. Equation (18) only describes the leaching potential by rapid flow processes. It does not consider the possibility of slower transport through the soil matrix. This can be seen for example, when there is no degradation (xb = 0), then

6 of 10

W11405


W11405

[39] From our results the proportional contribution to rapid leaching (PF1/PF) by the first rapid flow event (PF1), can be computed as PF1 ¼ 1 exp xb xm xp PF

ð19Þ

It can be seen that the contribution of the first rapid leaching event to overall rapid transport (equation (19)), decreases with increasing sorption (Figure 5). However, as the strength of sorption increases the amount of solute released during the first rapid flow event increases for weak sorption before decreasing again at larger sorption values (Figure 5a). It can be shown that in the case where degradation is inversely proportional to sorption (i.e. ks = 0) the peak occurs when x p ¼ xb þ xm exp xp 1

Figure 4. Contours of PF and PF1 as a function of the dimensionless variables xb, xm and xp, defined by equations (11), (12), and (13), respectively.

potentially all the chemical reaches the receiving water via fast and slow flow pathways. However, the value of PF can be less than one, depending upon the values of xp and xm. [37] It is commonly observed that the greatest amount of leaching occurs as a result of the first significant rainfall event following chemical application [Leonard, 1990; Kladivko et al., 2001]. In terms of the dimensionless parameters, the amount rapidly leached by the first preferential flow event (PF1) is largely independent of degradation and nonrapid flow generating rainfall when xb + xm < 0.1 (Figure 4), whereas the total amount rapidly transported (PF) decreases as degradation and transport in the soil matrix increase. As the contributions to losses from degradation and slow transport into the soil matrix increase further, the first rapid flow event tends to contribute a greater proportion of the total amount rapidly leached. This can be seen in Figure 4 by the merging of PF1 and PF contours. Additionally, the total amount rapidly transported tends to become independent of the structure of preferential flow events. [38] As the sorption strength increases (a proportional increase in R) PF increases reaching a plateau at strong sorption, indicating that more strongly sorbing solutes are more susceptible to preferential transport (Figure 5a). This is consistent with the evidence that preferential flow is a significant component of the transport of strongly sorbing solutes such as pesticides and some metals [Flury, 1996; Bundt et al., 2000; Kladivko et al., 2001]. Leaching experiments tend to suggest that the amount of pesticide transported during a leaching event decreases as sorption increases. The PF index on the other hand describes many leaching events and does not consider attenuation within preferential flow pathways which may lower the amount actually transported to depth.

ð20Þ

[40] For the case when degradation is independent of sorption (i.e. kl = ks), then rather than the PF reaching a plateau at strong sorption, it actually peaks at moderate R

Figure 5. The effect of sorption on the proportion of applied mass rapidly leached PF, the mass rapidly leached by the first event PF1, and the proportional contribution of the first rapid flow event PF1/PF. (a) The effective degradation rate is considered to be inversely proportional to sorption (used kl = 0.05 and ks = 0 day1). (b) The effective degradation rate is independent of sorption (used kl = 0.025 and ks = 0.025 day1). The following parameters were used for both Figures 5a and 5b: tp = 10 days, tb = 3 days, hm = 3 mm, hp = 5 mm, zl = 10 mm and ql = 0.4.

7 of 10

W11405


Figure 6. Comparison of PF (solid), PF1 (small dashed), and AF (large dashed lines) leaching indices, as a function of the retardation factor R and the degradation half-life t1/2 = ln(2)/kb (days1). The following parameters were used: tp = 5 days, tb = 2 days, hm = 1 mm, hp = 1 mm, zl = 10 mm, zx = 100 mm, ql = 0.4, Dq = 0.1 cm3cm3 and ks = 0 day1.

values and decreases gradually thereafter (see Figure 5b). The greater the degradation rate on the sorbed phase the smaller is the maximum PF. We can now show that the peak in leaching can potentially occur as a result of multiple rainfall events, due to preferential transport alone. Previously such a peak had only been demonstrated for loading within a single rainfall event [McGrath et al., 2008a] or over multiple events as a result of combined matrix and preferential transport [Larsson and Jarvis, 2000]. [41] This is therefore consistent with our previously argued mechanism for the occurrence of such a peak [McGrath et al., 2008a]. This peak occurs because of a balance between the amount of chemical retained near the surface at the time of rapid flow events and the amount that can be transported rapidly during each event [McGrath et al., 2008a]. Weakly sorbing and rapidly degrading solutes will tend to be readily lost from the source zone, either mobilized into the soil matrix or degraded by other means. Strongly sorbing chemicals on the other hand, will be retained in the source zone but only small amounts will be released during rapid flow events. The peak occurs where retention and release can maximize the loading of chemical to rapid flow pathways. [42] These results do not contradict the observations of irrigated experiments, which find that the relative ranking of the concentration of a number of solutes rapidly transported by preferential flow tends to be consistent with their relative mobility as measured by sorption [Flury, 1996]. In many of these single irrigation experiments, where chemicals have been applied to the soil, ponding is initiated rapidly and for

W11405

the duration of the irrigation. Under these circumstances tp = tb and hp is likely to be of a similar order of magnitude as hm. When this is the case PF1 tends to decrease with increasing R for all R. [43] In addition, the results resolve the apparent contradiction in observations noted in the review. Given a suite of solutes applied to soil, the more strongly sorbing chemicals will be retained more near the soil surface [Flury, 1996]. On a single event basis the amount of rapid transport decreases with increasing sorption [Flury, 1996], however over many such events it is the more strongly sorbing chemicals which will be more likely to have gotten to depth predominantly by preferential flow [Reichenberger et al., 2002]. [44] In comparison to AF (Figure 6), we generally expect a small proportion of preferential flow leaching and a large proportion of slow matrix leaching when sorption is weak (small R) and the degradation rate is small (large half-life t1/ 2). On the other hand the potential for significant amounts of rapid leaching and very small amounts of slow matrix leaching occurs when sorption is strong (large R) and degradation is fast (small t1/2). Given the differences between AF and PF we would expect the transport of many chemicals to be dominated by preferential flow in the system shown in Figure 6. When sorption is strong the differences between AF and both PF and PF1 are most pronounced. Finally, there are also regions of this phase space, particularly where sorption is weak and degradation slow, where the AF predicts greater leaching. Therefore a combination of slow and rapid flow leaching measures may be required to quantify the relative leaching potential. [45] The PF index does not account for attenuation of chemicals within preferential flow pathways or the soil matrix, it therefore should be remembered that it gives a measure of the potential for a chemical to be loaded to a fast flow pathway. For many strongly sorbing chemicals equation (18) provides estimates of this loading over the lifetime of the chemical, so while the PF index may be high the actual concentrations in pulsed leached events may be quite low. In comparison to the absolute values provided by the AF, the PF index gives much more conservative estimates of the leaching potential of many moderately to strongly sorbed chemicals.

5. Conclusions [46] In this paper we developed a new leaching index which describes the proportion of the applied chemical mass which is potentially mobilized from near the soil surface to rapid flow pathways such as surface runoff and preferential flow. The assumptions used include: instantaneous and complete mixing with discrete rainfall events; a constant near surface water content; linear equilibrium sorption; first order degradation (both in solution and sorbed); a periodic rainfall – preferential flow event occurrence; and importantly, no attenuation of solute during transport. The index should therefore be considered for application to the shallow unsaturated zone or to surface runoff. [47] Parameterization of this index at present requires further research. The most significant variables, currently not described in the literature are the frequency and magnitude of preferential flow events. The parameters tp, hm and hp however, could be estimated from existing infiltration models. The parameters hm and hp must also be constrained

8 of 10

W11405


by the amount of rainfall that occurs in a particular area, while the variable tb could be estimated from data as the mean time between rain events. As with the application of any such transport model, accounting for the spatial variability of model parameters is an area that would also require further research. [48] With the current approach there is the potential to explore the impact of the temporal variability of rainfall or the other state variables. For example seasonality in rainfall (and flow event) timing and magnitude can be introduced by exchanging sinusoidal terms with the various parameters making up the PF in equation (17). Alternatively, one could account for the variability in soil moisture and temperature in the source zone and their impact on sorption and degradation. The PF index is also limited by the fact that the triggering of rapid flow events has been abstracted, such that it is independent of the soil moisture used to calculate the solute mass balance. Further work is required to properly couple the two within the index. [49] Acknowledgments. We would like to acknowledge the financial support of the Australian Research Council, Water Corporation of Western Australia, and the Centre for Groundwater Studies. The authors would also like to thank Suresh Rao, Nandita Basu, and three other reviewers for their helpful comments. In particular we would like to thank Nick Jarvis for suggesting the modification to simulate sorbed degradation.

References Ahuja, L., A. Sharpley, M. Yamamoto, and R. Menzel (1981), The depth of rainfall-runoff-soil interactions as determined by 32P, Water Resour. Res., 17(4), 969 – 974, doi:10.1029/WR017i004p00969. Allaire-Leung, S. E., S. C. Gupta, and J. F. Moncrief (2000a), Water and solute movement in soil as influenced by macropore characteristics 1. Macropore continuity, J. Contam. Hydrol., 41(3 – 4), 283 – 301, doi:10.1016/S0169-7722(99)00079-0. Allaire-Leung, S. E., S. C. Gupta, and J. F. Moncrief (2000b), Water and solute movement in soil as influenced by macropore characteristics: 2. Macropore tortuosity, J. Contam. Hydrol., 41(3 – 4), 303 – 315, doi:10.1016/S0169-7722(99)00074-1. Aylmore, L. A. G., and H. J. Di (2000), Predicting the probabilities of groundwater contamination by pesticides under variable recharge, Aust. J. Soil Res., 38(3), 591 – 602, doi:10.1071/SR99060. Bergamaschi, B. A., K. M. Kuivila, and M. S. Fram (2001), Pesticides associated with suspended sediments entering San Francisco Bay following the first major storm of water year 1996, Estuaries, 24(3), 368 – 380, doi:10.2307/1353239. Beven, K., and P. Germann (1982), Macropores and water flow in soils, Water Resour. Res., 18, 1311 – 1325, doi:10.1029/WR018i005p01311. Brown, C. D., J. M. Hollis, R. J. Bettinson, and A. Walker (2000), Leaching of pesticides and a bromide tracer through lysimeters from five contrasting soils, Pest Manage. Sci., 56(1), 83 – 93, doi:10.1002/(SICI)15264998(200001)56:13.0.CO;2-8. Bundt, M., A. Albrecht, P. Froidevaux, P. Blaser, and H. Flu¨hler (2000), Impact of preferential flow on radionuclide distribution in soil, Environ. Sci. Technol., 34(18), 3895 – 3899, doi:10.1021/es9913636. Butters, G., W. A. Jury, and F. Ernst (1989), Field scale transport of bromide in an unsaturated soil: 1. Experimental methodology and results, Water Resour. Res., 25, 1575 – 1581, doi:10.1029/WR025i007p01575. Capel, P., S. Larson, and T. Winterstein (2001), The behavior of 39 pesticides in surface waters as a function of scale, Hydrol. Processes, 15, 1251 – 1269, doi:10.1002/hyp.212. Dayananda, P. W. A. (1982), A simple model for the path of solute in root zone of soil, Ecol. Model., 16, 81 – 84, doi:10.1016/0304-3800(82) 90001-1. Domagalski, J. L., N. M. Dubrovsky, and C. R. Kratzer (1997), Pesticides in the San Joaquin River, California: Inputs from dormant sprayed orchards, J. Environ. Qual., 26(2), 454 – 465. Edwards, W., M. Shipitalo, W. Dick, and L. Owen (1992), Rainfall intensity affects transport of water and chemicals through macropores in no-till soils, Soil Sci. Soc. Am. J., 57, 1560 – 1567.

W11405

Edwards, W., M. Shipitalo, L. Owens, and W. Dick (1993), Factors affecting preferential flow of water and atrazine through earthworm burrows under continuous no-till corn, J. Environ. Qual., 22, 453 – 457. Elliott, J. A., A. J. Cessna, W. Nicholaichuk, and L. C. Tollefson (2000), Leaching rates and preferential flow of selected herbicides through tilled and untilled soil, J. Environ. Qual., 29(5), 1650 – 1656. Flury, M. (1996), Experimental evidence of transport of pesticides through field soils—A review, J. Environ. Qual., 25(1), 25 – 45. Flury, M., J. Leuenberger, B. Studer, and H. Flu¨hler (1995), Transport of anions and herbicides in a loamy and a sandy field soil, Water Resour. Res., 31(4), 823 – 836, doi:10.1029/94WR02852. Fomsgaard, I. S. (2004), The influence of sorption on the degradation of pesticides and other chemicals in soil, Environmental Project 902 2004, Dan. Inst. of Agric. Sci., Dan. Environ. Protect. Agency, Copenhagen, Denmark. Fortin, J., E. Gagnon-Bertrand, L. Vezina, and M. Rompre (2002), Preferential bromide and pesticide movement to tile drains under different cropping practices, J. Environ. Qual., 31(6), 1940 – 1952. Ghodrati, M., and W. A. Jury (1992), A field-study of the effects of soil structure and irrigation method on preferential flow of pesticides in unsaturated soil, J. Contam. Hydrol., 11(1 – 2), 101 – 125, doi:10.1016/ 0169-7722(92)90036-E. Giambelluca, T. W., K. Loague, R. E. Green, and M. A. Nullet (1996), Uncertainty in recharge estimation: Impact on groundwater vulnerability assessments for the Pearl Harbor Basin, O’ahu, Hawaii, USA, J. Contam. Hydrol., 23(1 – 2), 85 – 112, doi:10.1016/0169-7722(95)00084-4. Heppell, C. M., F. Worrall, T. P. Burt, and R. J. Williams (2002), A classification of drainage and macropore flow in an agricultural catchment, Hydrol. Processes, 16(1), 27 – 46, doi:10.1002/hyp.282. Heppell, C. M., A. S. Chapman, V. J. Bidwell, G. Forrester, and A. A. Kilfeather (2004), A lysimeter experiment to investigate the effect of surface sealing on hydrology and pesticide loss from the reconstructed profile of a clay soil. 1. hydrological characteristics, Soil Use Manage., 20(4), 373 – 383, doi:10.1079/SUM2004278. Hyer, K. E., G. M. Hornberger, and J. S. Herman (2001), Processes controlling the episodic stream water transport of atrazine and other agrichemicals in an agricultural watershed, J. Hydrol., 254(1 – 4), 47 – 66, doi:10.1016/S0022-1694(01)00497-8. Jarvis, N. J., M. Stahli, L. Bergstrom, and H. Johnsson (1994), Simulation of dichlorprop and bentazon leaching in soils of contrasting texture using the MACRO model, J. Environ.l Sci. Health A, 29(6), 1255 – 1277, doi:10.1080/10934529409376106. Johnson, A. C., T. J. Besien, C. L. Bhardwaj, A. Dixon, D. C. Gooddy, A. H. Haria, and C. White (2001), Penetration of herbicides to groundwater in an unconfined chalk aquifer following normal soil applications, J. Contam. Hydrol., 53(1 – 2), 101 – 117, doi:10.1016/S0169-7722(01) 00139-5. Jury, W. A., and J. Gruber (1989), A stochastic analysis of the influence of soil and climatic variability on the estimate of pesticide groundwater pollution potential, Water Resour. Res., 25(12), 2465 – 2474, doi:10.1029/WR025i012p02465. Jury, W. A., and K. Roth (1990), Transfer Function and Solute Movement Through Soil: Theory and Applications, Birkhauser, Basel, Switzerland. Kjær, J., P. Olsen, M. Ullum, and R. Grant (2005), Leaching of glyphosate and amino-methylphosphonic acid from Danish agricultural field sites, J. Environ. Qual., 34, 608 – 620. Kladivko, E. J., L. C. Brown, and J. L. Baker (2001), Pesticide transport to subsurface tile drains in humid regions of north America, Crit. Rev. Environ. Sci. Technol., 31(1), 1 – 62, doi:10.1080/20016491089163. Kookana, R., R. Correll, and R. Miller (2005), Pesticide impact rating index: A pesticide risk indicator for water quality, Water Air Soil Pollut. Focus, 5, 45 – 65, doi:10.1007/s11267-005-7397-7. Laabs, V., W. Amelung, A. Pinto, and W. Zech (2002), Fate of pesticides in tropical soils of Brazil under field conditions, J. Environ. Qual., 31(1), 256 – 268. Larsson, M. H., and N. J. Jarvis (2000), Quantifying interactions between compound properties and macropore flow effects on pesticide leaching, Pest Manage. Sci., 56, 133 – 141. Lennartz, B. (1999), Variation of herbicide transport parameters within a single field and its relation to water flux and soil properties, Geoderma, 91(3 – 4), 327 – 345, doi:10.1016/S0016-7061(99)00008-7. Lennartz, B., X. Louchart, M. Voltz, and P. Andrieux (1997), Diuron and simazine losses to runoff water in Mediterranean vineyards, J. Environ. Qual., 26(6), 1493 – 1502. Leonard, R. (1990), Movement of pesticides into surface waters, in Pesticides in the Soil Environment: Processes, Impacts, and Modeling, edited by H. H. Cheng, pp. 303 – 349, Soil Sci. Soc. of Am., Madison, Wisc.

9 of 10

W11405


Leu, C., H. Singer, C. Stamm, S. Mu¨ller, and R. Schwartzenbach (2004), Variability of herbicide losses from 13 fields to surface water within a small catchment after a controlled herbicide application, Environ. Sci. Technol., 38, 3835 – 3841, doi:10.1021/es0499593. Loague, K., R. Green, T. Giambelluca, and T. Liang (1990), Impact of uncertainty in soil climatic and chemical information in a pesticide leaching assessment, J. Contam. Hydrol., 5, 171 – 194, doi:10.1016/01697722(90)90004-Z. Loague, K., R. L. Bernknopf, R. E. Green, and T. Giambelluca (1996), Uncertainty of groundwater vulnerability assessments for agricultural regions in Hawaii: Review, J. Environ. Qual., 25, 475 – 490. Louchart, X., M. Voltz, P. Andrieux, and R. Moussa (2001), Herbicide transport to surface waters at field and watershed scales in a Mediterranean vineyard area, J. Environ. Qual., 30(3), 982 – 991. Malone, R. W., J. Weatherington-Rice, M. J. Shipitalo, N. Fausey, L. W. Ma, L. R. Ahuja, R. D. Wauchope, and Q. L. Ma (2004), Herbicide leaching as affected by macropore flow and within-storm rainfall intensity variation: A RZWQM simulation, Pest Manage. Sci., 60(3), 277 – 285, doi:10.1002/ps.791PMid:15025239. McGrath, G. S., C. Hinz, and M. Sivapalan (2007), Temporal dynamics of hydrological threshold events, Hydrol. Earth Syst. Sci., 11, 923 – 938. McGrath, G. S., C. Hinz, and M. Sivapalan (2008a), Modeling the impact of within-storm variability of rainfall on the loading of solutes to preferential flow pathways, Eur. J. Soil Sci., 59, 24 – 33. McGrath, G. S., C. Hinz, and M. Sivapalan (2008b), Modeling the effect of rainfall intermittency on the variability of solute persistence at the soil surface, Water Resour. Res., 44, W09432, doi:10.1029/2007WR006652. Menabde, M., and M. Sivapalan (2000), Modeling of rainfall time series using bounded random cascades and Levy-stable distributions, Water Resour. Res., 36(11), 3293 – 3300, doi:10.1029/2000WR900197. Ogram, A. V., R. E. Jessup, L. T. Ou, and P. S. C. Rao (1985), Effects of sorption on biological degradation rates of (2,4-Dichlorophenoxy)acetic acid in soil, App. Environ. Micobiol., 49(3), 582 – 587. Paraiba, L. C., and C. A. Spadotto (2002), Soil temperature effect in calculating attenuation and retardation factors, Chemosphere, 48, 905 – 912, doi:10.1016/S0045-6535(02)00181-9PMid:12222785. Rao, P. S. C., and W. M. Alley (1993), Pesticides in Regional Groundwater Quality, edited by W. M. Alley, pp. 345 – 382, Van Nostrand Reinhold, New York. Rao, P. S. C., J. M. Davidson, and L. C. Hammond (1976), Estimation of nonreactive solute front locations in soils, in Proceedings of the Hazardous Waste Research Symposium, EPA-600/09-76-015, p. 235, U.S. Environ. Protect. Agency, Cincinnati, Ohio. Rao, P. S. C., A. G. Hornsby, and R. E. Jessup (1985), Indices for ranking the potential for pesticide contamination of groundwater, Soil Crop Sci. Soc. Fla. Proc., 44, 1 – 8.

W11405

Rao, P. S. C., R. E. Jessup, and J. M. Davidson (1988), Mass flow and dispersion, in Environmental Chemistry of Herbicides, edited by R. Grover, pp 21 – 43, CRC Press, Boca Raton, Fla. Reichenberger, S., W. Amelung, V. Laabs, A. Pinto, K. U. Totsche, and W. Zech (2002), Pesticide displacement along preferential flow pathways in a Brazilian oxisol, Geoderma, 110(1 – 2), 63 – 86, doi:10.1016/S00167061(02)00182-9. Renaud, F. G., C. D. Brown, C. J. Fryer, and A. Walker (2004), A lysimeter experiment to investigate temporal changes in the availability of pesticide residues for leaching, Environ. Pollut., 131(1), 81 – 91, doi:10.1016/j. envpol.2004.02.028. Schertzer, D., and S. Lovejoy (1987), Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes, J. Geophys. Res., 92, 9693 – 9714, doi:10.1029/JD092iD08p09693. Scorza, R. P., J. H. Smelt, J. J. T. I. Boesten, R. F. A. Hendriks, and S. E. A. T. M. van der Zee (2004), Preferential flow of bromide, bentazon, and imidacloprid in a Dutch clay soil, J. Environ. Qual., 33(4), 1473 – 1486. Steenhuis, T. S., J. Boll, G. Shalit, J. S. Selker, and I. A. Merwin (1994), A simple equation for predicting preferential flow solute concentrations, J. Environ. Qual., 23(5), 1058 – 1064. Stenemo, F., C. Ray, R. Yost, and S. Matsuda (2007), A screening tool for vulnerability assessment of pesticide leaching to groundwater for the islands of Hawaii, USA, Pest Manage. Sci., 63, 404 – 411, doi:10.1002/ ps.1345PMid:17315270. Stewart, I. T., and K. Loague (1999), A type transfer function approach for regional – scale pesticide leaching assessments, J. Environ. Qual., 28, 378 – 387. Struthers, I., M. Sivapalan, and C. Hinz (2007), Conceptual examination of climate – soil controls upon rainfall partitioning in an open-fractured soil II: Response to a population of storms, Adv. Water Resour., 30, 518 – 527, doi:10.1016/j.advwatres.2006.04.005. Zhang, X. C., L. D. Norton, and M. Hickman (1997), Rain pattern and soil moisture content effects on atrazine and metolachlor losses in runoff, J. Environ. Qual., 26(6), 1539 – 1547. Zhang, X., D. Norton, T. Lei, and M. Nearing (1999), Coupling mixing zone concept with convective-diffusion equation to predict chemical transfer to surface runoff, Trans. ASAE, 42, 987 – 994.

C. Hinz and G. S. McGrath, School of Earth and Environment, University of Western Australia, M087, 35 Stirling Highway, Crawley 6009, Australia. ([email protected]; [email protected]) M. Sivapalan, Department of Geography, University of Illinois at Urbana-Champaign, 220 Davenport Hall, 607 South Mathews Ave., Urbana, IL 61801 USA. ([email protected])

10 of 10