Due to the poor availability of freshwater, the practice of

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1 TECHNICAL REPORTS: ORGANIC TECHNICAL COMPOUNDS REPORTS IN THE ENVIRONMENT Modeling Concentration-Dependent Sorption Desorption Hysteresis of Atrazine in a Sandy Loam Soil Ihuaku Anagu,* Joachim Ingwersen, Yaron Drori, Benny Chefetz, and Thilo Streck Nonequilibrium sorption plays an active role in the transport of organic contaminants in soil. We applied a two-stage, onerate model (2S1R) and a new, nonlinear variant (2S1RN) of this model to examine the effects of wastewater irrigation on the sorption kinetics of atrazine (2-chloro-4-ethylamino-6- isopropylamino-1,3,5-triazine) in soil. The models were applied to previously published sorption desorption data sets, which showed pronounced deviations between sorption curves and desorption curves (sorption desorption hysteresis). Moreover, the slopes of the desorption curves decreased with decreasing concentration. Different treatments had been used, and two experimental time steps (2 and 14 d) were used. Treatments considered were lipid removal, fulvic and humic acid removal, and untreated soil. The 2S1R model was unable to reproduce the observed type of hysteresis, but the 2S1RN model, which assumes that the sorption desorption process follows a power function relationship, was able to reproduce the observed type of hysteresis. Visually, applying the new model improved the model fits in all test cases. Statistically, as tested by an extra sum of squares analysis, the new model performed significantly better in 50% of all test cases. According to an example simulation, the choice of the sorption model has a considerable impact on the prediction of atrazine transport in soil. Copyright 2011 by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America. All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. J. Environ. Qual. 40: (2011) doi: /jeq Posted online 3 Feb Received 28 June *Corresponding author (ihuakuo@yahoo.com). ASA, CSSA, SSSA 5585 Guilford Rd., Madison, WI USA Due to the poor availability of freshwater, the practice of using treated wastewater for irrigation is on the increase in some regions of the world. Long-term irrigation with wastewater affects soil properties and soil organic matter (SOM) (Gonzalez- Vila et al., 1995; Friedel et al., 2000). In addition, wastewater carries relatively high levels of dissolved organic matter (DOM). Nonequilibrium sorption is known to significantly affect the transport of organic chemicals in soils and their subsurface and has been an active area of research over the last two decades (Brusseau and Reid, 1991; Streck et al., 1995; Streck and Richter, 1999; Wehrhan et al., 2010). Drori et al. (2005) reported a higher sorption and lower desorption ability of freshwater-irrigated soils than wastewaterirrigated soils. Also, lipid removal was found to increase a soil s sorption affinity to atrazine and chlorotoluron (Drori et al., 2006). Lipids are the water-insoluble fraction of organic matter that can be removed from soils using nonpolar organic solvents. According to Stevenson (1994), lipids make up between 0.2 and 0.5% of the total SOM. Lipids are known to affect the sorption desorption behavior of hydrophobic organic compounds (Kohl and Rice, 1999; Kohl et al., 2000; Tremblay et al., 2005). Drori et al. (2008) reported that humins are strong sorbents and that their removal from soil increases sorption desorption nonsingularity (hysteresis). The soil humin fraction constitutes between 20 and 50% of the SOM (Stevenson, 1994; Rice, 2001; Yang et al., 2004; Nichols and Wright, 2006). Studies by Cameron and Klute (1977), Brusseau et al. (1989), Ball and Roberts (1991), and Kleineidam et al. (1999) revealed that the sorption of many organic chemicals occurs in two stages. The first is a fast sorption process that may take several minutes or hours; the second is a slower process that may take weeks, months, or even longer. Consequently, the most popular kinetic sorption model is the two-site or two-stage model, which divides the sorption sites into two domains (Brusseau and Rao, 1989; Miller and Pedit, 1992; Streck et al., 1995; Beigel and Di Pietro, 1999; Schlebaum et al., 1999; Altfelder et al., 1999; 2000; Kasteel et al., 2010; Wehrhan et al., 2010). It assumes that the sorption in one domain is always in equilibrium while I. Anagu, J. Ingwersen, and T. Streck, Institute of Soil Science and Land Evaluation, Biogeophysics section, Univ. of Hohenheim (310), Stuttgart, Germany; Y. Drori and B. Chefetz, Dep. of Soil and Water Sciences, Faculty of Agriculture, Food and Environment, The Hebrew Univ. of Jerusalem, P.O. Box 12, Rehovot 76100, Israel. Assigned to Associate Editor Myrna Simpson. Abbreviations: 2S1R, two-stage, one-rate sorption model; 2S1RN, two-stage, one-rate nonlinear sorption model; DOM, dissolved organic matter; SOM, soil organic matter; SSQ, sum of squares. 538

2 in the other it is kinetically controlled. In general, the sorption process is diffusion controlled (Brusseau et al., 1991), so that the rate parameter depends on the duration of the sorption experiment (Altfelder and Streck, 2006). Streck and Richter (1999) developed a simple expression that allows for temporal upscaling of the rate coefficient in two-stage or twosite models. Atrazine is of interest in this study because it is one of the most commonly used herbicides. Although it was banned in the European Union in 2004, it is widely used in other parts of the world. Gilliom et al. (2006) reported that over half of streams in the United States had pesticide concentrations above threshold values, with atrazine being one of the most frequently detected in surface water and groundwater. Atrazine is also widely used in Australia due to its effectiveness in weed control (Dixon and Clay, 2004). Its extensive use, combined with its moderate persistence in soil, has led to it being detected in surface water and groundwater (Meisner et al., 1992; Oliver et al., 2003; Guzella et al., 2006; Lewis et al., 2009). Gamerdinger et al. (1990), Ma and Selim (1994), Gaber et al. (1995), and Chen and Wagenet (1997) used different models to describe the nonequilibrium transport of atrazine in soil. Seol and Lee (2000) considered the effect of DOM in treated effluents on sorption of atrazine. Lesan and Bhandari (2003) and Bhandari and Lesan (2003) considered soils under different land uses (woodland and agricultural). Prata et al. (2003) compared the impact of two agricultural practices (no-till and conventional) on sorption desorption of organic chemicals. Schlebaum et al. (1999) used a combined linear-nonlinear rate limited sorption (RLS) (Jury and Roth, 1990) model to study the desorption kinetics of the slow-desorbing organic contaminant fraction in soil. Their model can be considered a two-site or two-stage model without the fast sorption sites. This study is based on data from the experiments of Drori et al. (2005, 2006, 2008). They investigated the effects of wastewater irrigation on the sorption desorption behavior of atrazine, chlorotoluron, and phenanthrene in soil under different treatments (lipid extraction, humic acid extraction, and fulvic acid extraction). This study takes the work of the last authors further by modeling and evaluating their sorption desorption data on atrazine. A characteristic of their data is a strong dependence of the slope of the desorption branches on the solution phase concentration. We show that this behavior can be better described by accounting for nonlinearity in the sorption process. This study, therefore, introduces a new model, which is an extension of the existing two-stage, one-rate model. The new model assumes that the slow sorption process follows a power function. It is explicitly stated here that this is not the same as assuming nonlinear (Freundlich) sorption at equilibrium. Materials and Methods Datasets Our study is based on three datasets, each having a freshwaterand a wastewater-irrigated component. These datasets are based on the experiments of Drori et al. (2005, 2006, 2008). The data of the untreated soils were collected by Drori et al. (2005). For the lipid-extracted soils, we used the 14-d sorption desorption data from a combined experiment of which only the 2-d data have been published (Drori et al., 2006). The sorption desorption data of the soils from which humic and fulvic acid had been removed were obtained from Drori et al. (2008). Soils Used as Sorbents Topsoils (Rhodoxeralf) were sampled from a citrus orchard in Basra, Israel. Soils were sampled from two neighboring plots, one irrigated with freshwater and the other with treated wastewater. Samples were collected from four locations in each plot and were taken from 3 to 30 cm depth after the 0- to 3-cm organic layer had been removed. The soils were air-dried, passed through a 2-mm sieve, and stored. The general properties of the soils are presented in Drori et al. (2005, 2006, 2008). In this study, we used the bulk soils, the lipid-extracted soils, and the alkaline-extracted soils. Lipids were extracted from soils by soxhlet extraction with benzene/methanol at a ratio of 3:1 for 16 h. The soils were dried at room temperature and later oven-dried at 65 C. Details of lipid extraction and characterization are presented in Drori et al. (2006). For humin isolation, a mild method of humin isolation, which involved alkaline extraction, was used (Swift, 1996). To obtain the alkaline-extracted soils, the bulk soils were treated to remove the humic and fulvic acids. Then the soils were washed with distilled water to reduce the electrical conductivity of the supernatant to <0.05 ds m 1 and to increase the ph to values higher than 5.5. Detailed information about the procedure is presented in Drori et al. (2008). Batch Sorption Desorption Experiments Aqueous solutions of atrazine (98% purity) (Agan Co., Ashdod, Israel) were prepared in a background solution containing 10 mmol L 1 CaCl 2 and 100 mg L 1 NaN 3 (Chefetz et al., 2006). Atrazine solutions were added to samples previously weighed into Teflon centrifuge tubes (Nalgene, Rochester, NY) with Teflon caps. Adsorption trails were performed using six initial concentrations of atrazine. These initial concentrations were different for each of the datasets. Equilibration periods considered were 2 and 14 d for the untreated soils, 14 d for the lipid-extracted soils, and 14 d for the alkaline-extracted soils. After agitation, the tubes were centrifuged, and 10 ml of the supernatant was removed for analysis and replaced with fresh background solution. The tubes were further agitated under the same conditions to carry out the desorption steps. Four sequential desorption steps were performed for the untreated soils, two steps were performed for the lipid-extracted soils, and three steps were performed for the alkaline-extracted soils. Desorption periods for the untreated and lipid-extracted soils were 2 d for the 2-d sorption period and 14 d for the 14-d sorption period. For the alkaline-extracted soils, desorption periods were 7 d. Atrazine was analyzed by high-performance liquid chromatography using a photodiode array detector at an absorbance of 222 nm. Experiments were conducted in triplicate. Measured concentrations were averaged over the replicates. Models The experimental data were analyzed by means of the twostage, one-rate model (2S1R) by Streck et al. (1995). Using a mass transfer approach, the authors derived the model from Anagu et al.: Sorption-Desorption Hysteresis of Atrazine 539

3 a diffusion hypothesis (Brusseau et al., 1991). The model is based on a nonlinear sorption isotherm and uses a linear (firstorder) approach for the sorption desorption kinetics. In the present study, the model was extended to account for nonlinear kinetics (2S1RN model). The 2S1R and 2S1RN models divide the sorbent into two domains. In domain 1, sorption is fast, so that equilibrium can be assumed: S 1 = kc m [1] In domain 2, sorption is assumed to be rate limited: α n ds ( S 2 1 S2) S1 S2 (1 f ) = d n t α S1 S2 S1 < S2 where S 1 and S 2 (mg kg 1 ) are the local sorbed phase concentrations in domains 1 and 2, respectively; C is the concentration of the dissolved chemical (mg L 1 ); k is the Freundlich coefficient (mg 1 m L m kg 1 ); and m is the Freundlich exponent. The parameter n describes the nonlinearity of the slow sorption process, f is the fraction of sorption sites in the fast domain, α is the sorption rate coefficient (mg 1 n kg n 1 d 1 ), and t is time. The total sorbed phase concentration of the chemical is given by: S = fs 1 + (1 f)s 2 [3] The popular 2S1R model is a special case of the 2S1RN model (n = 1). Figure 1 demonstrates the difference between the two models. The total mass of the chemical per unit mass of soil, C t (mg kg 1 ), is given by: θ Ct = C+ S [4] ρ where θ and ρ represent volume of water (L) and mass of soil (kg), respectively. The retardation factor, R, is an indicator for the transport of chemicals through soil. It expresses the transport velocity of a sorbing solute relative to that of a nonsorbing tracer. It is given by ρ ds R = 1+ θ dc [5] where, in the case of Freundlich equilibrium, ds m 1 = kmc [6] dc Assuming that sorption desorption hysteresis merely reflects sorption nonequilibrium (which is not always true; see Sander et al., 2005), the sorption rate coefficient (α) can be interpreted as a measure of hysteresis. The lower the α values, the stronger the hysteresis, and vice versa. The Freundlich coefficient, k, is a measure of sorption affinity. A high k value implies high affinity, whereas a low k value indicates the opposite. The Freundlich exponent, m, is a measure of the sorption linearity at equilibrium. The further it deviates from unity, the more nonlinear the equilibrium distribution. The symbol n is peculiar to the 2S1RN model and provides information about the nonlinearity in the sorption process (Fig. 1). [2] Fig. 1. Rate of sorption in the slow domain simulated with the twostage, one-rate (2S1R) and the two-stage, one-rate nonlinear (2S1RN) models as a function of driving force, the difference in concentrations of the different sorption domains. Note that S 1 = kc m (Eq. [1]). Parameter Estimation The parameters α, f, k, m, and n were estimated using the Levenberg-Marquardt algorithm (Press et al., 1992). Initial guesses were determined by a gridded search in the multidimensional parameter space. For the treated soils (lipid- and alkaline-extracted), log-transformed values were used in the parameter estimation because normal values gave bad fits during presimulations. In contrast, normal values were used for the untreated soils because log-transformed values gave bad fits. To determine whether the additional parameter in the 2S1RN model significantly improves the model performance, we applied an extra sum of squares (SSQ) analysis (Bates and Watts, 1988; Streck et al., 1995). Results and Discussion Presimulations showed that with both models and all data sets, the parameters f and k were highly correlated. One way to circumvent this problem would be to use a simpler model. We tried letting f = 0 (which turns the two-stage model into the simpler rate-limited sorption model [Jury and Roth, 1990]), but the model did not fit well to the data. This implies that fast sorption cannot be ignored. Another way is to assume a fixed value for f. Karickhoff and Morris (1985) found the fraction of the sorption sites in the fast domain, f, to be 0.5 for hydrophobic organic contaminants, whereas Brusseau et al. (1989) fixed f to a value of 0.5 in their study. Following these previous studies, we iteratively fixed f at different values between 0.05 and 0.5 and found the value 0.1 to be most suitable for our data. Hence, we fixed f to a value of 0.1 in all our simulations. In other words, we assumed that 10% of the sorption sites are fast sorbing. Untreated Soils Figure 2 shows the measured 2-d sorption desorption data of the untreated soils along with the fits of the 2S1R and of the 2S1RN models. The data exhibit significant sorption desorption hysteresis (i.e., nonsingularity). The term hysteresis is used 540 Journal of Environmental Quality Volume 40 March April 2011

4 Fig. 2. Measured and simulated sorption desorption data of atrazine on Rhodoxeralf topsoil irrigated with freshwater and treated wastewater, respectively. Sorption desorption time steps were 2 d. 2S1R, two-stage, one-rate; 2S1RN, two-stage, one-rate nonlinear. to describe the fact that adsorption and desorption curves do not coincide in a sorption experiment (Streck, 2003). The larger the difference in the slopes of sorption and desorption curves, the stronger the hysteresis, and vice versa. Both models assume fully reversible sorption. As demonstrated by Altfelder et al. (2000), measured sorption desorption hysteresis is often (but not always) an artifact due to incomplete equilibration. Hysteresis increases with decreasing initial concentrations. A similar observation was made previously by Gamst et al. (2001). The 2S1RN model is able to reproduce the effect, whereas the 2S1R model is not. Hence, the effect can be traced back to nonlinearity of the sorption process. This is not the same as nonlinearity in the sorption isotherm, which is a characteristic of both models. Assuming retarded intraparticle diffusion, Grathwohl (1998) suggested that, at lower solute concentrations, nonlinearity of sorption to SOM increases; this leads to slower diffusion, in turn increasing hysteresis. However, intraparticle diffusion plays a role in sediments that are typically low in organic matter. In surface soils, with typically high organic matter contents, sorption is likely to be dominated by intraorganic matter diffusion. Hence, retarded pore diffusion is probably not the reason for the observed dependency of nonlinearity on concentration. The measured 14-d sorption desorption isotherms of the untreated soils together with fits of the 2S1RN model are presented in Fig. 3. Sorption desorption hysteresis of the 14-d isotherms is more pronounced than that of the 2-d isotherms (i.e., the slopes of desorption curves were smaller for the 14-d sorption equilibration period). Parameter estimates and model statistics for the data of the untreated soils are presented in Table 1. Both models yield comparable estimates of the Fig. 3. Measured and simulated sorption desorption data of atrazine on Rhodoxeralf topsoil irrigated with freshwater and treated wastewater, respectively. Sorption desorption time steps were 14 d. 2S1R, two-stage, one-rate; 2S1RN, two-stage, one-rate nonlinear. Freundlich coefficient (k) and the Freundlich exponent (m). Estimates of the sorption rate coefficient (α) of the 2S1RN model are always higher than those obtained for the 2S1R model. This is to be expected because n, the second nonlinearity parameter of the 2S1RN model, is typically <1 (see Eq. [2] and [4]). The statistics demonstrate that both models produce sound fits. However, the 2S1R model was unable to reproduce the dependency of the slopes of the desorption curves on concentration (Fig. 2). Both models were unable to reproduce the sorption desorption data at the two different time scales with the same set of parameters (results not shown). This is probably because kinetic sorption of organic contaminants in soil reflects a diffusion process (Brusseau et al., 1991). Altfelder and Streck (2006) measured sorption and desorption of the herbicide chlorotoluron at different time scales (days to months). The data could only be modeled after extending the 2S1R model by an extra compartment for very slow sorption or, physically more appealing, by directly using a diffusion approach for slow sorption. With chlorotoluron (field data) and naphthalene (lab data), respectively, Streck and Richter (1999) and Gamst et al. (2001) also found the sorption rate parameter, α, to be sensitive to the time scale of the experiment. In numerical experiments, Young and Ball (1995, 1997) computed solute breakthrough through columns made up of identically sized spheres, in which sorption was governed by diffusion, and fitted the two-site model to the breakthrough curves. The rate parameter decreased with experimental time until it reached an asymptotic value (termed Glückauf approximation). It can be shown that early in the sorption process the rate parameter decreases with the square Anagu et al.: Sorption-Desorption Hysteresis of Atrazine 541

5 root of time, which can be used for temporal upscaling (Streck and Richter, 1999). Our estimates of the rate parameter α approximately follow this relationship. The ratios of α values estimated from the 2-d and 14-d data sets, respectively, range from 1.8 to 4.1, while the theoretical value is 14 / 2 = 2.6. The scaling relationship of Streck and Richter (1999) is based on simplifying assumptions (semi-infinite geometry of sorbents, constant solute concentration); for our sorption desorption experiments, it therefore represents an approximation. The relationship was developed for the 2S1R model but is applicable to the 2S1RN model as well, provided that the solute concentrations in the experiments with different time steps are not too different. Sorption affinity (k values) was less for the wastewaterirrigated soils than for the freshwater-irrigated soils. Sorption affinity decreased by 24 and 3% (2S1RN model; Table 1) for Table 1. Parameter estimates obtained from fitting the two models to the untreated soils. Sum of squares Parameter Approximate Estimate t ratio SE 2-d sorption/two-stage, one-rate Correlation matrix α k m n Freshwater α k m R# 3.30 Wastewater α k m R d sorption/two-stage, one-rate nonlinear Freshwater α k m n R 3.37 Wastewater α k m n R d sorption/two-stage, one-rate Freshwater α k m R 2.76 Wastewater α k m R d sorption/two-stage, one-rate nonlinear Freshwater α k m n R 2.88 Wastewater α k m n R 2.60 Parameter estimation was carried out with normal (not log-transformed) values. Sorption rate parameter (mg 1 n kg n 1 d 1 ). Freundlich coefficient (mg 1 m L m kg 1 ). Freundlich exponent. # Retardation factor computed at the median solution phase concentration (C) of each data set. Parameter representing nonlinearity in the sorption process. 542 Journal of Environmental Quality Volume 40 March April 2011

6 the 2-d and 14-d equilibration periods, respectively, as a result of wastewater irrigation. Graber et al. (1995) attributed this phenomenon to the presence of higher DOM in the wastewater-irrigated soils. They suggested that the high level of DOM keeps the solute in solution. Seol and Lee (2000) reported a similar finding in their study of the effects of DOM in treated effluents on the sorption of atrazine and prometryn by soils. They observed that very high DOM levels were needed to significantly reduce triazine herbicide sorption to soil. In contrast, Drori et al. (2005) concluded that the higher sorption affinity in freshwater-irrigated soils results from a higher sorption affinity of atrazine to the solid-phase SOM. Because of the lower sorption affinity, the retardation factor, R, is lower in the wastewater-irrigated soil as well. In principle, this implies that wastewater irrigation increases the transport velocity of atrazine. However, if the lower sorption is due to increased DOM concentration, a complete picture could only be drawn if transport, sorption, and transformation of DOM were known in a given soil. Based on approximate standard errors (Table 1), there were no significant differences (at P = 0.95) in m values between freshwater- and wastewater-irrigated soils and with experimental time. Sharer et al. (2003) reported a similar finding. Increasing nonlinearity with time has been reported by Weber and Huang (1996), Young and Ball (1999), Lesan and Bhandari (2003), and Altfelder and Streck (2006). Our results are also not in agreement with the dual-mode sorption mechanism as proposed by Xing and Pignatello (1996). They conjectured that organic sorbents are made up of rubbery regions, where sorption is due to partitioning and is linear in nature, and of glassy regions, where sorption occurs by hole-filling mechanisms and is nonlinear. Assuming that the glassy regions are located in the interior of the sorbent, sorption nonlinearity is expected to increase with time. Drori et al. (2005) concluded that the above mechanism does not govern atrazine sorption in the soils used for this study. Lipid-Extracted Soils Based on the parameter estimates, the effect of lipid removal was higher with the freshwater-irrigated than with the wastewater-irrigated soils (Fig. 4; Table 2). This reflects the differences in the composition of lipids in the two soils because the lipid extract from the freshwater-irrigated soils is composed of aromatics, double bonds, ester, ether, and methyl moieties, whereas the extract from the wastewater-irrigated soils consists mainly of straight paraffinic chains (Drori et al., 2006). These authors conjectured that more polar-extractable compounds can compete successfully with polar solutes like atrazine for specific binding sites in the SOM. Because the experimental time steps for the treated soils were 14 d, comparisons between treated and untreated soils are made using the 14-d data of the untreated soils. Sorption affinity, k, increased as a result of lipid extraction for the freshwater- and wastewater-irrigated soils (Table 2). Sorption nonlinearity increased as a result of lipid extraction for both soils. Drori et al. (2006) suggested that those binding sites having a higher affinity for atrazine may have been occupied by lipids. Fig. 4. Measured and simulated sorption desorption data of atrazine on lipid-extracted (upper panel) and alkaline-extracted (lower panel) Rhodoxeralf topsoil. Soils had been irrigated with freshwater and treated wastewater, respectively. Sorption desorption time steps were 14 d. Simulations were performed with the two-stage, one-rate nonlinear model. Alkaline-Extracted Soils The lower part of Fig. 4 shows the results of fitting the 2S1RN model to the measured data of the alkaline-extracted soils. The parameter estimates are listed in Table 3. The trend of lower sorption affinity for the wastewater- versus freshwater-irrigated soils was repeated. The sorption rate parameter, α, was higher in the wastewater-irrigated soil. Nonlinearity was also higher in that soil. In the case of freshwater irrigation, sorption increased after alkaline extraction, but it decreased in the case of wastewater irrigation. This is probably because the humin content was higher in the freshwater-irrigated soils (Drori et al., 2008). An increase in sorption as a result of humin (fulvic and humic acid) isolation has also been reported by Gunasekara and Xing (2003), Kang and Xing (2005), Oren and Chefetz (2005), and Bonin and Simpson (2007). Furthermore, nonlinearity increased as a consequence of alkaline extraction. The higher degree of isotherm nonlinearity has been attributed to the more condensed and glassy structure of the organic matter making up the humin fraction (Huang and Weber, 1997; Simpson et al., 2007). The sorption rate parameter, α, shows no consistent trend. This combination of increased sorption and isotherm nonlinearity as a result of humin isolation suggests that humin is a natural sorbent for hydrophobic organic compounds in soil (Chefetz et al., 2000; Xing, 2001). Therefore, removal of humic and fulvic acids increases sorption and subsequently decreases transport of atrazine in soils irrigated with freshwater. Comparison of the Models Table 4 compares the parameter estimates of the two models in form of a Boolean table. The data show that wastewater Anagu et al.: Sorption-Desorption Hysteresis of Atrazine 543

7 irrigation typically led to a decrease in parameter values; that is, sorption in soil irrigated with wastewater is weaker, slower, and less linear compared with freshwater irrigation. Extra Sum of Squares Analysis Whether the application of the more complex model (2S1RN) is justified from a statistical point of view was tested by an extra SSQ analysis (Table 5). Because the 2S1R model is nested in the 2S1RN model, the SSQ of the 2S1RN model must be equal to or smaller than that of the 2S1R model. The extra SSQ principle allows a comparison of models in which one is nested in the other. The F ratio, computed in the process, is used to determine whether there is a statistically significant improvement (at α = 0.05) in the estimates as a result of the additional variable (in this case, n). Both models are nonlinear, so our analysis yields only approximate Table 2. Parameter estimates obtained from fitting the two models to the lipid-extracted soils. Sum of squares Parameter Approximate Estimate t ratio SE 14-d sorption/two-stage, one-rate Correlation matrix α k m n Freshwater α k m Wastewater α k m d sorption/two-stage, one-rate nonlinear Freshwater α k m n# Wastewater α k m n Parameter estimation was carried out with log-transformed values. Sorption rate parameter (mg 1 n kg n 1 d 1 ). Freundlich coefficient (mg 1 m L m kg 1 ). Freundlich exponent. # Parameter representing nonlinearity in the sorption process. Table 3. Parameter estimates obtained from fitting the two models to the alkaline-extracted soils. Sum of squares Parameter Approximate Estimate t ratio SE 14-d sorption/two-stage, one-rate Correlation matrix α k m n Freshwater α k m Wastewater α k m d sorption/two-stage, one-rate nonlinear Freshwater α k m n# Wastewater α k m n Parameter estimation was carried out with log-transformed values. Sorption rate parameter (mg 1 n kg n 1 d 1 ). Freundlich coefficient (mg 1 m L m kg 1 ). Freundlich exponent. # Parameter representing nonlinearity in the sorption process. 544 Journal of Environmental Quality Volume 40 March April 2011

8 results. The F ratio is at least 2 in all cases, but only in half of the cases is the decrease of SSQ statistically significant. The improvement of the 2S1RN over the 2S1R model was systematically significant for the 2-d sorption equilibration period and not for the 14-d period. An explanation could be that the importance of sorption kinetics decreases as equilibrium is approached. It could also be attributed to air-drying and rewetting cycles, as reported by Altfelder et al. (1999). Table 4. Summary of trend of parameter estimates. Untreated Lipid-extracted Alkaline-extracted Treatment time step 2 d 14 d 14 d 14 d model 2S1RN 2S1R 2S1RN 2S1R 2S1RN 2S1R 2S1RN 2S1R k (W ) < k (F ) yes yes yes yes yes yes yes yes α (W) < α (F) no no yes yes no yes no no m (W) < m(f) yes yes yes yes yes yes no no n (W) < n (F) yes yes yes yes Two-stage, one-rate nonlinear. Two-stage, one-rate. Wastewater-irrigated. Freshwater-irrigated. Table 5. Extra sum of squares analysis. Sum of squares Degrees of freedom Mean square F ratio Significance Untreated soils Wastewater 2 d Extra S1RN yes 2S1R Freshwater 2 d Extra S1RN yes 2S1R Freshwater 14 d Extra S1RN no 2S1R Wastewater 14 d Extra S1RN no 2S1R Lipid-extracted soils Freshwater 14 d Extra S1RN yes 2S1R Wastewater 14 d Extra S1RN no 2S1R Alkaline-extracted soils Freshwater Extra d 2S1RN no 2S1R Wastewater 14 d Extra S1RN yes 2S1R Difference between the sums of squares of the models. Two-stage, one-rate nonlinear. Two-stage, one rate. Anagu et al.: Sorption-Desorption Hysteresis of Atrazine 545

9 They explained that air-drying of soils and subsequent rewetting before experiments changes sorbent properties only in the short-term and that the properties are re-established over a longer period (weeks). Transport Simulations To demonstrate that the nonlinearity in the sorption kinetics may be relevant in field situations, we linked the respective sorption equations with the convection-dispersion equation to simulate atrazine transport in soil (Streck et al., 1995). The simulations were performed with parameter estimates obtained from the freshwater-irrigated, 2-d sorption equilibration data of the untreated soils (Table 2; Fig. 2). Figure 5 shows that application of the 2S1R model and the 2S1RN model yield very different predictions of atrazine displacement in soil. However, due to the unavailability of measured transport data of atrazine, a decision on which model represents the real situation is not possible. Conclusions Because the 2S1R model was unable to simulate the phenomenon that the slopes of desorption branches decreased with decreasing concentration, we set up a nonlinear variant of the 2S1R model, the 2S1RN model. Visually, the new model improved model fits in all test cases. Statistically, as tested by extra SSQ analysis, the new model performed significantly better in 50% of all test cases. We recommend applying the 2S1RN model to sorption desorption data ( sorption desorption isotherms ) when the slopes of desorption curves noticeably decrease with decreasing concentration. However, a comparison of the 2S1R and the 2S1RN model with measured column or field data or by means of a sensitivity analysis remains to be done. Regarding the effect of wastewater irrigation, sorption of atrazine to soil is typically weaker, slower, and less linear than in soil irrigated with freshwater. 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