Estimation of stochastic colored noise signal driving DNAPLs degradation kinetics in the natural water environment

Chemosphere 119 (2015) 130–136

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Chemosphere journal homepage: www.elsevier.com/locate/chemosphere

Estimation of stochastic colored noise signal driving DNAPLs degradation kinetics in the natural water environment L. He ⇑, H. Lu School of Renewable Energy, North China Electric Power University, Beijing 102206, China

h i g h l i g h t s  We proposed an integrated numerical-simulation and statistical-inference method.  The method is used to identify colored noises driving DNAPL degradation kinetics.  Colored noise has a significant impact on DNAPL degradation.  The more the repeated experiments, the higher the estimation accuracy.  The larger the true value, the higher the estimation accuracy.

a r t i c l e

i n f o

Article history: Received 20 June 2013 Received in revised form 4 May 2014 Accepted 23 May 2014 Available online 26 June 2014 Handling Editor: X. Cao Keywords: DNAPLs Degradation kinetics Colored noise signal Noise estimation Stochastic process

a b s t r a c t Little attention has been devoted to the characterization of colored noise in stochastic modeling systems. This study aims to propose an integrated numerical-simulation and statistical-inference method for the characterization of individual and mixed colored noises driving the DNAPL degradation kinetics. Through the method, the properties of colored noise (i.e. intensity and time correlation) can be identified statistically. Results for the estimations indicate that the method is useful for identifying the colored noise since the regression equations have high R square values and most of the relative errors of the estimates are below 40%. It is also found that (i) the more the repeated experiments, the higher the estimation accuracy; (ii) the larger the true value, the higher the estimation accuracy; (iii) a large number of statistical samples does not always imply high estimation accuracy. Moreover, the increase in both number of samples and interval of sampling is not helpful in enhancing the estimation accuracy. Results from the estimation of the mixed multiplicative colored-noise also show that the estimates can be regarded to be acceptable. Future studies will be needed for estimation of other types of mixed additive and multiplicative colored noises. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Dense nonaqueous phase liquids (DNAPLs) can migrate to substantial depths below the water table and slowly dissolve into flowing groundwater when they are released to the subsurface. Some of dissolved chlorinated compounds, like trichloroethene (TCE) and tetrachloroethene (PCE), can pose a risk for drinking water sources as they can be transported to groundwater (Laturnus, 2003). Many experimental and numerical techniques have been employed for investigating the degradation of these chlorinated compounds in the natural water environment

⇑ Corresponding author at: School of Renewable Energy, North China Electric Power University, Beijing 102206, China. Tel.: +86 (10) 6177 2416. E-mail address: [email protected] (L. He). http://dx.doi.org/10.1016/j.chemosphere.2014.05.061 0045-6535/Ó 2014 Elsevier Ltd. All rights reserved.

(Hossain, 2006; de Zorzi et al., 2008; He et al., 2013). For instance, Gerritse et al. (1995) investigated the degradation of PCE by combining the metabolic abilities of anaerobic bacteria, capable of reductive dechlorination of PCE, with those of aerobic methanotrophic bacteria, capable of co-metabolic degradation of the lesschlorinated ethenes formed by reductive dechlorination of PCE. Bjerg et al. (1999) examined the fate of seven aromatic and four chlorinated aliphatic compounds using in situ microcosm and laboratory batch experiments performed at six distances along a flow line in the anaerobic leachate plume downgradient of the Grindsted Landfill, Denmark. The results suggested that laboratory batch experiments could be a useful tool for determining the degradability of mono aromatic hydrocarbons and chlorinated aliphatic hydrocarbons under the natural attenuation (strongly anaerobic) conditions. Yan and Schwartz (1999) used a simple and quick approach to estimate permanganate consumption by other organic

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compounds for field applications; the TCE degradation rate was also predicted in the study system involving PCE, TCE, and three isomers of dichloroethylenes (DCEs). The modeling results suggested that the effect of autocatalysis by MnO2 on TCE degradation is significant when the system contains high concentration levels of MnO4 and total organic carbon. With regards to modeling studies on DNAPL degradation kinetics, very few of them attempted to address the resonance of their modeling results to potentially existing colored noise (Hernandez-Machado et al., 1991; Angulo et al., 2008; Durdu, 2010). Usually, colored noise can have effects on stochastic resonance in physical, chemical and biological and systems (Castro et al., 1995; Stijnen and Heemink, 2003). A number of studies have ever been undertaken to use colored noise driven models for understanding the impacts of colored noise and seeking ways of mitigating these impacts (He et al., 2010a, b). Kim et al. (1997) investigated noise-induced phase transitions in soft Ising spins, which have continuous values with a fluctuating interaction within the framework of the mean-field scheme. The results implied that the interplay of the fluctuating interaction and an additive noise leads to a reentrant transition, triple transitions, and a softening of the order parameter, presenting a weak order in the order phase. Nozaki et al. (1999) performed a numerical experiment to demonstrate that the optimal noise intensity is the lowest and the output signal-to-noise ratio the highest for conventional white noise; meanwhile, under certain circumstances, 1/f noise can be better than white noise for enhancing the response of a neuron to a weak signal. Zhong and Xin (2001) compared the effects of colored noise with finite correlation time with those of white noise without any time correlation through a chemical model system. It was found that the correlation time of noise could affect the peak value of internal stochastic resonance and the location of the optimal noise intensity for resonance behavior. Zhu et al. (2002) investigated a modified Oregonator model subject to exponential Gaussian colored noise. The results revealed that the colored noise can weaken explicit internal signal stochastic resonance (EISSR), and the maximum effect of EISSR can be shifted to lower noise intensity with the increment of the correlation time. The signal-to-noise ratio of the noise was also found to have the resonance behavior with the variation of the correlation time as the noise intensity is fixed. Charles et al. (2009) simulated the advection and diffusion of pollutants in shallow waters based on a set of stochastic differential equations. Results from the case study revealed that the colored noise can address the short-term correlated turbulent fluid flow velocity of particles in the water. In these studies, a prerequisite assumption is that the properties of the colored noise are completely known prior to the use of the models. In fact, these properties usually need to be identified through noise characterization based on experimental, simulation and/or statistical approaches. Outputs from the noise characterization include reorganization of noise types (white, colored, or mixed), estimation of noise parameters (such as intensities and correlation times), and identification of the correlations between different noises. Regretfully, very little attention was devoted to the characterization of colored noise in practical stochastic modeling systems. This study thus aims to propose an integrated numerical-simulation and statistical-inference method for the characterization of individual and mixed colored noises based on observed data. This work will present a method for characterization of colored noise driving the DNAPL degradation kinetics. Through the method, the properties of colored noise (i.e. intensity and time correlation) will be identified statistically. The performance of the method for noise characterization will also be analyzed.

2. Materials and methods Generally, PCE degradation takes the pathway of from PCE to TCE, then to DCE, and finally to vinyl chloride (VC). In terms of the operator splitting procedure, the degradation kinetics can be represented through the following four differential equations (Alvarez and Illman, 2006):

dC PCE =dt ¼ kPCE C PCE þ SPCE

ð1Þ

dC TCE =dt ¼ yTCE=PCE kPCE C PCE  kTCE C TCE þ STCE

ð2Þ

dC DCE =dt ¼ yDCE=TCE kTCE C TCE  kDCE C DCE þ SDCE

ð3Þ

dC VC =dt ¼ yVC=DCE kDCE C DCE  kVC C VC þ SVC

ð4Þ

where CPCE, CTCE, CDCE and CVC are concentrations of PCE, TCE, DCE and VC, respectively; kPCE, kTCE, kDCE, and kVC are anaerobic constants for PCE, TCE, DCE and VC, respectively; yTCE/PCE, yDCE/TCE, and yVC/DCE are TCE/PCE, DCE/TCE, and VC/DCE stoichiometric yield constants, respectively; SPCE, STCE, SDCE, and SVC are sink/source terms for PCE, TCE, DCE and VC, respectively. Note that these coupled differential equations only address the natural degradation of DNAPL compounds temporally, yet ignore other processes such as sorption, advection, dispersion, and diffusion in the subsurface. Despite the simplifications, more processes can be directly incorporated into the equations if desired. When the model is driven by colored noise, the equations need to be transformed to the following stochastic differential equations: v

ð5Þ

v

ð6Þ

v

ð7Þ

dC PCE =dt ¼ kPCE C vPCE þ SPCE þ v PCE ðtÞ dC TCE =dt ¼ yTCE=PCE kPCE C vPCE  kTCE C vTCE þ STCE þ v TCE ðtÞ dC DCE =dt ¼ yDCE=TCE kTCE C vTCE  kDCE C vDCE þ SDCE þ v DCE ðtÞ v

dC VC =dt ¼ yVC=DCE kDCE C vDCE  kVC C vVC þ SVC þ v VC ðtÞ v

v

v

ð8Þ

v

where C PCE , C TCE , C DCE and C VC are concentrations of PCE, TCE, DCE and VC driven by colored noise v(t), respectively; vPCE(t), vTCE(t), vDCE(t) and vVC(t) are colored noises added in the models for PCE, TCE, DCE and VC, respectively. Here, the colored noise, v(t), is assumed to (a) be an Ornstein–Uhlenbeck process with a zero mean and an exponential correlation function, and (b) have no correlations to noises in other differential equations. In terms of the assumptions, v(t) has the properties of

< mðtÞ >¼ 0

ð9Þ

< v ðtÞv ðt þ DtÞ >¼ Dk expðkDtÞ

ð10Þ

where D represents the intensity of the colored noise, and k is a time constant whose inverse (k1) represents the correlation time of the noise. Due to the existence of colored noise, C vPCE , C vTCE , C vDCE and C vVC computed through solving Eqs. (5)–(8) also present stochastic properties. Their statistical prosperities including means, deviations and probability density functions (PDFs) need to be resolved by solving a couple of Liouville equations associated with Eqs. (5)–(8). However, a numerical algorithm is more generally used in consideration of the difficulty in obtaining the analytical solutions. The Box– Mueller algorithm is therefore used to computationally solve the equations (Fox et al., 1988), for which Eqs. (5)–(8) should be approximated by a set of difference equations:

C vPCE ðt þ DtÞ ¼ C vPCE ðtÞ þ ½kPCE C vPCE ðtÞ þ SPCE ðtÞ  Dt þ v PCE ðt þ DtÞ ð11Þ C vTCE ðt þ DtÞ ¼ C vTCE ðtÞ þ ½yTCE=PCE kPCE C vPCE ðtÞ  kTCE C vTCE ðtÞ þ STCE ðtÞ  Dt þ v TCE ðt þ DtÞ

ð12Þ

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C vDCE ðt þ DtÞ ¼ C vDCE ðtÞ þ ½yDCE=TCE kTCE C vTCE ðtÞ  kDCE C vDCE ðtÞ þ SDCE ðtÞ  Dt þ v DCE ðt þ DtÞ

ð13Þ

C vVC ðt þ DtÞ ¼ C vVC ðtÞ þ ½yVC=DCE kDCE C vDCE ðtÞ  kVC C vVC ðtÞ þ SVC ðtÞ  Dt þ v VC ðt þ DtÞ

ð14Þ

The detailed procedures of the algorithm are shown as follow: [Step 1] Input the initial concentrations for the four compounds: CPCE(0), CTCE(0), CDCE(0), and CVC(0), and set a time step of Dt. [Step 2] Set t = 0. [Step 3] At time t + Dt, use the Box–Mueller algorithm (Fox et al., 1988) to generate four random numbers, v 0PCE ðt þ DtÞ; v 0TCE ðt þ DtÞ; v 0DCE ðt þ DtÞ; and v 0VC ðt þ DtÞ; which form one set of realizations of the colored noises. [Step 4] Calculate the concentrations of the four compounds sequentially based on Eqs. (11)–(14). [Step 5] Set t = t + Dt. [Step 6] Repeat Steps (2) to (5) for N times. To estimate parameters k and D for the colored noise, the natural logarithm of formula (10) is taken for both sides, yielding

Y ¼ aX þ b

ð15Þ

where

Y ¼ ln < v ðtÞv ðt þ DtÞ >

ð16Þ

X ¼ Dt

ð17Þ

a ¼ lnðDkÞ

ð18Þ

b ¼ k

ð19Þ

The estimation needs to use a set of statistical samples, which consist of X (i.e. Dt) and Y, where Y can be obtained by Eq. (16). When a substantial number of statistical samples (X, Y) are prepared under varied t and Dt levels, linear regression can be performed for estimation of k and D. 3. Results In demonstration of the method, VC is selected for the detailed result analysis. Other compounds are not discussed because the findings from this case study are similar. The constants input to the DNAPLs degradation kinetics model is shown in Table S1 in the Supplementary Information. Fig. 1 presents the variation of VC concentrations driven by colored noise with varied k and D levels. A total of 8 scenarios are shown in the figure, with each on representing one realization under a given k and D level. It is obvious that the variation tendencies of VC do not change in a whole no matter how D and k vary. Despite different k and D levels, the VC concentrations almost keep increasing from days 0 to approximately 1500 and then begin to decrease. This tendency is particularly clear when D and k have rather low levels. Nevertheless, the signals obtained through the colored-noise-driven model become increasingly unstable with enhancing D and k levels. When k and D are rather low (0.005 d1 and 0.0025, respectively), the curves are rather smooth under the 8 scenarios, showing that the variation tendency of VC concentrations can be captured under the impact of colored noise. When k and D increase by 100 times, the signal representing VC concentrations becomes undulant, fluctuating up and down the curve depicting the original signal. This indicates that a k level of 0.05 d1and a D level of 0.25 have a significant impact on VC concentrations, since there is difficulty in capturing the variation tendency with ease. Particularly in this

situation, it is necessary to estimate k and D levels for analyzing the colored noise effect quantitatively. Fig. 2 presents a set of statistical samples describing the relationships between the logarithm of expected value of covariance of the colored noise (i.e. ln < v ðtÞv ðt þ DtÞ >) and time interval (i.e. Dt). Each subfigure represents the samples obtained from one group of signal as shown in Fig. 1. In each subfigure, the statistical samples are used to output regression equations. It is shown that the R square coefficients are much high, with the lowest and highest ones being 0.8066 and 0.9934, respectively. Therefore, they slope and intercept of each regression equation can be used to estimate k and D levels in terms of Eq. (11). The figure also reveals that even if the original signal is polluted by colored noise, the regression method can be used to identify the characteristics of the colored noise since the regression equations have high R square values. Fig. 3 exhibits the estimates of k and D based on the 8 groups of signals shown in Fig. 1. The true values are represented as red star, and each estimate for (k, D) under one group of signal is depicted as a point. In scenario 1 (Fig. 1a), the true k and D levels are set to be 0.005 d1 and 0.0025, respectively. All the points obtained based on the 8 groups of polluted signals are below the true one, indicating that the estimates for D are all lower than the true level. The lowest and highest relative errors of the estimates for D are 12.6% and 99.0%, respectively, occurring at points (0.0058 d1, 0.0022) and (0.0052 d1, 0.00024). By contrast, the best estimates for k occur at points (0.0051 d1, 0.0014) and (0.0051 d1, 0.0004), with the relative errors being 2.0%. The worst estimate occur at point (0.002 d1, 0.00003), with the relative error being 60.0%. In Fig. 3b, the k and D levels are assumed to be 0.5 d1 and 0.0025, respectively. The points depicting the k and D estimates are rather close to that representing the true values. The most satisfactory estimates occur at points (0.462 d1, 0.003) and (0.489 d1, 0.0017). Their relative errors for (k, D) are (7.6, 20)% and (2.2, 30.4)%, respectively. In comparison, the least acceptable estimates occur at points (0.71 d1, 0.001), whose relative errors for (k, D) are (42.0, 60.0)%. This shows that the impact of colored noise can hardly be ignored since it has significant influence on the accuracy of the estimates. In general, the estimates for k as shown in Fig. 2(b) are acceptable, with the lowest and highest relative errors being 2.0% and 42.0%, respectively; by contrast, the estimates for D are rather high compared to D, with the lowest relatively error being 20.0% and the highest one approximately 60.0%. Fig. 3(c) shows the estimates for k and D based on the signals obtained where the true values of k and D are 0.005 d1 and 0.25, respectively. The most satisfactory estimate for this scenario occurs at point (0.0051 d1, 0.31), whose relative errors are (2.0, 24.0)%. The best and worst estimates for k occur at points (0.0051 d1, 0.31) and (0.0012 d1, 0.247), whose relative errors are 2.0% and 75.4%. The best and worst estimates for D occur at points (0.0012 d1, 0.247) and (0.0048 d1, 0.0427), whose relative errors are 1.2% and 70.8%, respectively. Fig. 3(d) presents the estimates for k and D based on the signals obtained where the true values of k and D are 0.5 d1 and 0.25, respectively. The best estimate for (k, D) occurs at point (0.496 d1, 0.203), with the relative errors of (0.8, 18.8)%. The most unsatisfactory point occurs at point (0.268 d1, 0.361), whose relative errors are both larger than 40.0%. In sum, the obtained estimates for k and D can be acceptable though the maximum relative estimation error reaches as high as approximately 100% (note that most of the relative errors are below 40%). This demonstrates the practicability of the proposed method for estimation of individual colored noise driving the degradation kinetic model. Estimation based on an individual group of signal could underestimate or overestimate the colored noise due to randomness of

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Fig. 1. Variation of VC concentrations driven by colored noises with increase of D and k.

Fig. 2. Regression equations of Y (vertical axis) vs. X (horizontal axis).

sampling. The method is therefore used based on multiple groups of signals for estimation of colored noise. This is helpful for investigating whether the average of multiple estimation results obtained from repeated numerical experiments can improve the estimation accuracy or not. Each of the repeated numerical experiments means that the model is solved numerically based on once Monte Carlo sampling and then outputs one realization of the

signal representing VC concentrations. Fig. 4 presents the comparisons of average estimates for k and D from repeated numerical experiments. Fig. 4(a) exhibits the scenario where the true k and D values are set to be 0.005 d1 and 0.0025, respectively. In this scenario, the estimates for k are quite accurate, with the relative errors in the range of 0.60–4.4%; by contrast, the estimates of D are not as

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Fig. 3. Estimates of k and D based on the signals show in Fig. 1, where the horizontal and vertical axes represent k and D, respectively, and the red star represents true value.

Fig. 4. Averages of estimates for k and D under multiple groups of signals.

satisfactory as k when a small number of samples are used. For example, when 8 samples are used, the average relative error is 68.95%; this can be reduced to 4.00% and 10.48%, respectively, with

the samples increasing to 200 and 500, respectively. Fig. 4(b) shows another scenario where the true k and D values both increase by 100 times compared to Fig. 4(a). It is found that the errors of average estimates are significantly decreased, with the highest relative errors for k and D being 6.33% and 6.88%, respectively; the lowest relative errors are 0.20% and 0.48%, respectively. Note that the lowest estimation error does not always correspond to the larges statistical samples. For example, the average relative error is 4.00% when 200 statistical samples are used; however, the error eventually rises to 10.48% with the statistical samples increasing to 500. In general, by comparing the two subfigures, it can be concluded that (i) the more the repeated experiments, the higher the estimation accuracy; (ii) the larger the true value, the higher the estimation accuracy; (iii) a large number of statistical samples does not always imply high estimation accuracy. Fig. 5 shows the movement of estimated point (k, D) to the true point (0.005 d1, 0.0025) with increasing in number of samples and interval of sampling. In Fig. 5(a), The ‘X runs’ means the preceding X samples are used for estimation of the colored noise (X represents 20, 50, 100, and 200). For example, for a group of signal taken from 0 to 500 d, if a statistical sample is taken every one day, then a total of 500 samples are generated. Thus, X equal to 20 means the preceding 20 samples are used for estimation of the colored noise, while the following ones are disregarded. As shown in Fig. 5(a), when the number of samples is low (e.g., 20, 50, 100), the estimates of (k, D) are rather far away from the true point (marked as red star), indicating that the estimation accuracy is not satisfactory. When the number of samples increases to 200, the point begin to move close to the true one; however, it is still far away from the true point than some other ones such as point (0.0058 d1, 0.0022) (marked as yellow diamond). Fig. 5(b) is obtained based on different intervals of sampling. ‘DT = X d’ means that the statistical samples are taken every X days and all the obtained samples are input to create the regression equations for estimation of colored noise (X represents 1, 10, 50, 100, and 200). As shown in Fig. 5(b), when DT = 1, 100 and 200 d, the estimates of (k, D) are far away from the true point. In comparison, they are closer to the true point when DT = 50 d, though not as close as point (0.0058 d1, 0.0022). In sum, the increase in both number of samples and interval of sampling is not helpful in enhancing the estimation accuracy. Therefore, a potential way to enhance the estimation accuracy may depend on the improvement of the current method. The abovementioned section shows the process of the estimation of an individual colored noise driving the DNAPL kinetics model. As a matter of fact, many models could be driven by mixed noises. The mixed noise may be generated by additive or multiplicative noises. Table S2 in the Supplementary Information exhibits various types of mixed white and/or colored noises. The property and time correlation of each type of mixed noise is also shown in the table. Note that the detailed derivation of time correlation is not shown here since it is straightforward. This section further discusses the estimation performance for mixed multiplicative colored-noise using the proposed method. The estimation of mixed additive colored-noise is not included in this study because of the failure of the method. This will be the major subject of our future study aiming to develop a new method which accommodates more types of mixed colored and/or white noises. Fig. 6 compares the estimated intensity and correlation time of the multiplicative colored noise with the true ones of the noise. Fig. 6(a) shows the estimates when k1, k2, D1, and D2 are 0.005 d1, 0.01 d1, 0.005, and 0.0025, respectively. The results show that k1, D1, D2 and are 38%, 34%, and 56% less than the true value, respectively, whereas k2 is 54% larger than the true value. Fig. 6(b) shows the estimates when k1, k2, D1, and D2 are all increased by 10 times compared to Fig. 6(a). For this scenario,

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Fig. 5. Variations of estimates with sampling times and sampling intervals, where the horizontal and vertical axes represent k and D, respectively, and the red star represents true values. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 6. Estimates of mixed colored noises.

the estimates are rather better than the 1st scenario. The estimated k1, k2, and D2 are 20.8%, 8.0%, and 38.0% less than the true value, respectively, whereas D1 is 34.0% larger than the true value. From both the subfigures, the estimates of the mixed multiplicative colored-noise are regarded to be acceptable, though the largest relative error is higher than 50%.

(0.0025 d1 and 0.5), (0.25 d1 and 0.005), and (0.25 d1 and 0.5), respectively. Results for the estimations indicate that the method is useful for identifying the colored noise since the regression equations have high R square values and most of the relative errors of the estimates are below 40%. It is also found that (i) the more the repeated experiments, the higher the estimation accuracy; (ii) the larger the true value, the higher the estimation accuracy; (iii) a large number of statistical samples does not always imply high estimation accuracy. Moreover, the increase in both number of samples and interval of sampling is not helpful in enhancing the estimation accuracy. Therefore, a potential way to enhance the estimation accuracy may depend on the improvement of the current method. Estimation of the mixed multiplicative colored-noise is also performed. Results showed that the estimates can be regarded to be acceptable, though the largest relative error is higher than 50%. To estimate the colored noise, model (5)–(8) should be computationally solved at first. Fox et al. (1988) ever proposed the Box– Mueller algorithm to numerically solve a type of stochastic differential model driven by the Ornstein–Uhlenbeck process. Later on, other researchers (Zhong and Xin, 2001; Zhu et al., 2002; Stijnen and Heemink, 2003) followed his work, attempting to use the algorithm to solve a wider range of colored-noise-driven stochastic problems. Similarly, we selected this algorithm because it has been proven to be faster, more accurate and more useful for larger step sizes thank old algorithms (Fox et al., 1988). The proposed estimation method is useful when colored noise with exponential correlation functions is driving force of a model. For the exponential correlation functions, logarithms can be adopted to transform the nonlinear regression equations to the linear ones. However, many of the colored noise may have other types of correlation functions, thus causing the failure of the method to work. Other methods such as spectral analysis may be a useful tool for addressing these issues. This will be involved in future studies where other types of colored noises need to be identified.

4. Conclusions and discussion

Acknowledgements

A DNAPLs degradation kinetic model is investigated, which consists of four differential equations depicting the degradation procedures from PCE to TCE, then to DCE, and finally to VC. A type of colored noise, assumed to be an Ornstein–Uhlenbeck process with a zero mean and an exponential correlation function, is added to drive the model. For estimation of colored noise, an integrated numerical-simulation and statistical-inference method is proposed, through which the intensity and time correlation can be identified statistically. A total of 8 groups of signals representing VC concentrations are used for estimation of the colored noise under four scenarios. The four scenarios assume the original levels of time correlation (k) and intensity (D) are (0.0025 d1 and 0.005),

This research was supported by the China National Funds for Excellent Young Scientists (51222906), National Natural Science Foundation of China (41271540), Program for New Century Excellent Talents in University of China (NCET-11-0632), and Fundamental Research Funds for the Central Universities.

Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.chemosphere. 2014.05.061.

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