domain: math info

text:
Mariem Ellouze

Jean-Pierre Gauchi

Jean-Christophe Augustin

Global Sensitivity Analysis Applied to a Contamination Assessment Model of Listeria monocytogenes in Cold Smoked Salmon at Consumption

Keywords: Listeria monocytogenes, quantitative microbial risk assessment, sensitivity analysis

In this study, a variance-based global sensitivity analysis method was first applied to a contamination assessment model of Listeria monocytogenes in cold smoked vacuum packed salmon at consumption. The impact of the choice of the modeling approach (populational or cellular) of the primary and secondary models as well as the effect of their associated input factors on the final contamination level was investigated. Results provided a subset of important factors, including the food water activity, its storage temperature, and duration in the domestic refrigerator. A refined sensitivity analysis was then performed to rank the important factors, tested over narrower ranges of variation corresponding to their current distributions, using three techniques: ANOVA, Spearman correlation coefficient, and partial least squares regression. Finally, the refined sensitivity analysis was used to rank the important factors.

INTRODUCTION

Over the last years, quantitative microbial risk assessment (QMRA) has become an important tool for food safety, however criticized as an extremely data hungry and time consuming method. [START_REF] Havelaar | Challenges of quantitative microbial risk assessment at EU level[END_REF] In fact, simple and deterministic approaches are now put aside and a large variety of complexities can be found with very extensive and stochastic models. Indeed, it can be tempting to include every phenomenon that could be of relevance, but this could lead to overparameterized models. [START_REF] Zwietering | Quantitative risk assessment: Is more complex always better?-Simple is not stupid and complex is not always more correct[END_REF] Sensitivity analysis (SA) can help solve this issue by eliminating the less influential factors. SA is defined as the study of how the out-put uncertainty of a model can be apportioned to different sources of uncertainty in the model input. [START_REF] Saltelli | Sensitivity analysis for importance assessment[END_REF] Several SA methods have been previously used in QMRA (e.g., ANOVA, Spearman correlation coefficient) [START_REF] Frey | Identification and review of sensitivity analysis methods[END_REF][START_REF] Membr É | Use of sensitivity analysis to aid interpretation of a probabilistic Bacillus cereus spore lag time model applied to heat-treated chilled foods (REPFEDs)[END_REF] but these methods seem to be poorly adapted to complex and nonlinear models like those encountered in QMRA. Variance-based methods are commonly recognized in the statistical field and have been previously used in several scientific areas (e.g., ecology, chemistry, agronomy). Their application to microbiological modeling issues will represent a major breakthrough in QMRA. These methods proved to be useful to explore models over different combinations of input values to study how the variance of the output depends on the inputs and can be decomposed accordingly. [START_REF] Saltelli | Global Sensitivity Analysis: The Primer[END_REF] The variance was chosen as a summary measure of the variability in order to exploit its statistical properties. In fact, variance-based methods are model independent as the sensitivity measure is model free and make it possible to appreciate the nonlinear interactions between factors, 1 0272-4332/10/0100-0001$22.00/1 C 2010 Society for Risk Analysis which is not the case, for example, for the ANOVA, where a linear relationship between the inputs and the output is assumed. Let us consider a model f , its response Y, and its factors X i , with Y = f (X 1 , X 2 , . . . , X k ). Sensitivity indices are related to the decomposition of Y into terms related either to each X i taken singularly (first-order indices) or to the cooperative effects of more than one X i (total indices). [START_REF] Saltelli | Making best use of model evaluations to compute sensitivity indices[END_REF] The variance-based methods were first employed by chemists in the early 1970s, [START_REF] Cukier | Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients[END_REF] who proposed conditional variances for a sensitivity analysis based on first-order effects only. Their method FAST (Fourrier amplitude sensitivity test) had limited success mainly because of the difficulty in encoding it. [START_REF] Saltelli | Global Sensitivity Analysis: The Primer[END_REF] Sobol [START_REF] Sobol | Global sensitivity indices for non linear mathematical models and their Monte Carlo estimtes[END_REF] was inspired by these works and proposed a straightforward Monte-Carlo-based implementation of the concept, capable of computing sensitivity measures for arbitrary groups of factors. Several methods are now available to compute these indices [START_REF]Sensitivity Analysis[END_REF] but we chose the Saltelli variance-based method [START_REF] Saltelli | Making best use of model evaluations to compute sensitivity indices[END_REF] because it requires less simulations compared to other methods.

The aim of this study was to use this method to perform a SA applied to a contamination assessment model of Listeria monocytogenes in cold smoked vacuum packed salmon to identify the subset of the inputs that substantially impact the concentration of the pathogen at consumption. A refined sensitivity analysis was then performed on these important factors to rank them according to their impact on salmon contamination.

MATERIALS AND METHODS

The Contamination Assessment Model: L. monocytogenes in Cold Smoked Salmon

The model used in this study is a contamination assessment model for L. monocytogenes in cold smoked vacuum packed salmon. It evaluates the pathogen contamination of portions at the end of the food shelf life assuming an initial contamination level below 20 cells per portion.

The model is presented in Fig. 1 and is composed of a secondary model, which calculates the effects of the environmental conditions (pH, temperature, and water activity) on the maximum growth rate, μ max , and a primary model, which computes the final contamination level, Y, given the secondary model output (μ max ), the initial contamination level x 0 , and the initial physiological state of the microorganisms K. Two approaches were considered. The first and com-monly used approach is a populational approach in which all the contaminating cells located in a particular food portion are supposed to have the same initial physiological state K and their growth is modeled globally. The second approach is a cellular approach in which each cell contaminating a portion is characterized by a specific physiological state k i , which is deduced from the populational physiological state K by sampling in an extreme value type II distribution EVII(a,b): [START_REF] Guillier | Modelling the individual cell lag time distributions of Listeria monocytogenes as a function of the physiological state and the growth conditions[END_REF][START_REF] Guillier | Erratum to "Modelling the individual cell lag time distributions of Listeria monocytogenes as a function of the physiological state and the growth conditions[END_REF]

a = E [k] - 1.1642 0.3658 • S [k] and b = S [k] 0.3658 , (1)
with The growth of each cell was thus modeled individually and the final contamination level was estimated as the sum of the population density reached at consumption time by each cell of the initial inoculum.

S[k] = exp (1.004 • ln (E [k]) -0.447) and ln(E[k]) = 0.0103 • ln(K) 5 + 0.0065 • ln(K) 4 - 0.039 • ln(K) 3 + 0.0586 • ln(K) 2 + 1.1941 • ln(K) + 0.1549,
The tested primary models were those of Rosso et al. [START_REF] Rosso | Differential growth of Listeria monocytogenes at 4 and 8 • C: Consequences for the shelf life of chilled products[END_REF] (Equation ( 2)) and Baranyi and Roberts [START_REF] Baranyi | A dynamic approach to predicting bacterial growth in food[END_REF] (Equation ( 3)).

ln x = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ln x 0 , t ≤ K μ max ln x max -ln 1 + x max x 0 -1 t > K μ max exp (-μ max (t -K/μ max )) , (2)
ln x = ln x max -ln 1+ x max x 0 -1 exp (-μ max A(t)) (3)
with

A(t) = t + 1 μ max ln(exp(-μ max t) + exp(-K) -exp(-K -μ max t))
where x (CFU) is the bacterial density at the time t (h), x 0 (CFU) the initial bacterial density, x max (CFU) the maximum bacterial density, μ max (h -1 ) the maximum specific growth rate, and K the physiological state of L. monocytogenes.

A multiplicative type model based on the gamma concept [START_REF] Zuliani | Growth rate and growth probability of Listeria monocytogenes in dairy, meat and seafood products in suboptimal conditions[END_REF] was used as a secondary model to describe the effects of temperature, T, pH, and water activity, aw, on μ max . The temperature and pH effects were modeled by cardinal type models [START_REF] Rosso | Convenient model to describe the combined effects of temperature and pH on microbial growth[END_REF] while the water activity effect was modeled either by a cardinal type or a square root type model. [START_REF] Ratkowsky | Relationship between temperature and growth rate of bacterial cultures[END_REF] Finally, the effect of taking the interactions into account was investigated using the interaction terms presented in Augustin et al. [START_REF] Zuliani | Growth rate and growth probability of Listeria monocytogenes in dairy, meat and seafood products in suboptimal conditions[END_REF] μ max = μ opt .CM 2 (T).CM 1 (pH).

⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ SR(aw) SR(aw)γ int CM 1 CM 1 (aw)γ int (4) with CM n (X) = 0 X ≤ X min (X -X max )(X -X min ) n (X opt -X min ) n-1 (X opt -X min )(X -X opt ) -(X opt -X max )(X opt + X min -nX) X min < X < X max 0 X ≥ X max (5) SR(aw) = ⎧ ⎪ ⎨ ⎪ ⎩ 0, X ≤ X min X -X min X opt -X min , X min < X ≤ X opt ( 6
)
γ int = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 1, 2(1 -ψ), 0, ψ ≤ 0.5 0.5 < ψ < 1 ψ ≥ 1 ψ = i ϕ(i) 2 j#1 (1 -ϕ( j)) ϕ(X) = X opt -X X opt -X min 3 , (7)
where X min , X opt , and X max are the cardinal values of L. monocytogenes, μ opt is the optimal value of the maximum specific growth rate μ max (h -1 ) when X = X opt , and n is a shape parameter (n = 2 for T and n = 1 for pH and aw).

The parameters of these models were allowed to vary according to their respective ranges presented in Table I. The range of the physiological parameter, K, the increase in the L. monocytogenes population represented by the growth yield, Gy (x max in Equations (2) and (3) is equal to x 0 10 Gy ), the optimum specific growth rate in cold smoked salmon, μ opt , and the physicochemical characteristics of the food, pH and aw, were obtained directly from experimental data and corresponded to the minimum and maximum observed values. The range of variation of the cardinal values for temperature, pH, and aw corresponded to the 1st and 99th percentiles of the distributions kindly provided by the Sym'Previus program. Finally, the range of variation of the distribution chain parameters was obtained from a French study on the temperatures encountered by cold smoked salmon in the distribution chain. [START_REF] Morelli | Evolution des temp ératures du saumon fum é au cours des circuits logistiques[END_REF] To run the contamination assessment model, the differential forms of the primary models were solved numerically with the Runge-Kutta method using the ode23 function of the Matlab software v7.3.0 (The MathWorks Inc., Natick, MA, USA).

Global Sensitivity Analysis

The Saltelli [START_REF] Saltelli | Making best use of model evaluations to compute sensitivity indices[END_REF] method is based on a numerical procedure for computing the full set of first-order indices, S i , and total effect indices, St i , for all the factors i (i = 1, . . . , k) of the studied model.

In this method, two matrices A and B of N lines corresponding to the N simulation runs and k columns corresponding to the k studied factors are first filled with numbers provided by a spacefilling design, for instance, a Latin hypercube sampling (LHS) was used in this study [START_REF] Mckay | A comparison of three methods for selecting values of input variables in the analysis of output from a computer code[END_REF] with respect to the range of variation of each factor. Then, k matrices C i , i = 1, . . . , k, containing all the columns of B but the column i, which is replaced by the i th column of matrice A, are generated and the contamination assessment model is run on each row of the k + 2 matrices to provide k + 2 vectors Y A , Y B , and Y Ci . First-order and total effect indices are then calculated with the following formula: [START_REF] Saltelli | Making best use of model evaluations to compute sensitivity indices[END_REF]

S i = 1 N N u=1 Y (u) A Y (u) C i -g 0 1 N N u=1 Y (u) A Y (u) A -f 2 0 (8) St i = 1 - 1 N N u=1 Y (u) B Y (u) C i -f 2 0 1 N N u=1 Y (u) A Y (u) A -f 2 0 (9) with f 0 1 N N u=1 Y (u) A g 0 1 N N u=1 Y (u) A Y (u) B . ( 10
)
The bootstrap method [START_REF] Efron | An Introduction to the Bootstrap[END_REF] was used to assess the confidence intervals of these indices through reliable estimates without additional computational effort. [START_REF] Archer | Sensitivity measures, ANOVA-like techniques and the use of bootstrap[END_REF] In fact, values obtained for the response vectors were sampled with replacement for 10 4 bootstrap replicates and for each replicate, the indices S i and St i were calculated, leading to a bootstrap estimate of the distribution of the sensitivity indices. Finally, the 95% confidence intervals of the indices were defined using the 2.5th and 97.5th percentiles [START_REF] Archer | Sensitivity measures, ANOVA-like techniques and the use of bootstrap[END_REF] and were used to indentify the most important factors as the inputs for which total effect indices were significantly different from 0.

In this study, the effects of k = 26 factors (23 quantitative and 3 qualitative factors) were investigated (Table I) using N = 5 × 10 4 simulation runs.

Moreover, the effects of the choice of the model response as well as the number of the simulation runs (LHS size) on the SA results were investigated by repeating the analysis while applying the following changes. To investigate the effects of the choices of the model response, the results were first expressed in log CFU and then without the log transformation (in CFU). Finally, to study the effect of the LHS size, results obtained with the initial LHS size N = 5 × 10 4 simulations were compared to those obtained with 10 4 runs LHS.

Refined Sensitivity Analysis

The refined sensitivity analysis is also a global sensitivity analysis but its principle is different from that used in the variance-decomposition-based methods. The objective of the refined sensitivity method is to rank the factors that were identified as important factors by the SA.

These factors were therefore sampled in their marginal distributions presented in Table III while noninfluential factors were fixed to the median values of their respective ranges of variations presented in Table I. The contamination assessment model was then run on 10 4 simulations.

The distribution of the output was analyzed according to three methods: ANOVA, Spearman correlation coefficient (SCC), and partial least squares regression (PLSR). To perform the ANOVA, the values of the factors were transformed into 11 classes according to their respective 10th percentiles before performing the analysis using the anovan function of the Matlab software. The obtained p-values and F statistics were used to rank the factors. The SCC analysis was performed using the corr function of the Matlab software and the absolute value of the correlation coefficients were used to rank the factors. The PLSR was performed using the SIMCA-P9.0 software (UMETRICS AB, Umea, Sweden, www.umetrics.com). PLSR is a powerful method, well known in the chemometrics field [START_REF] Wold | PLS Regression: A basic tool of chemometrics[END_REF] for its numerous advantages, which are fully described in the literature. [START_REF] Schwob | Two efficient sensitivity analysis methods to address factor prioritization in the context of structural computations[END_REF][START_REF] Tenenhaus | La r égression PLS, th éorie et pratique[END_REF][START_REF] Tenenhaus | R égression PLS et applications[END_REF] The PLSR provides variable influence in projection (VIP) statistics, which were used to calculate PLSR-based sensitivity indices SI-VIP k for each factor k, using the following formula:

SI -VIP k = 100 VIP 2 k p , ( 11
)
where p is the total number of factors and their twofactor interactions (here p = 65). These PLS-based indices were first proposed in Schwob et al., [START_REF] Schwob | Two efficient sensitivity analysis methods to address factor prioritization in the context of structural computations[END_REF] who provided a complete description of the method. A full definition of VIP needs a brief recall on PLSR, which is given in the Appendix. This method is only applicable when the ranges of variation of the inputs are narrow. This is typically the case in the refined sensitivity analysis where important factors identified by the global SA are sampled among their respective distribution.

The important factors were thus finally ranked based on the refined sensitivity analysis indices.

RESULTS

Sensitivity Analysis

The SA results obtained after a log transformation of the bacterial contamination are depicted in Table II where the first order and total effect indices of the factors are presented with their confidence bootstrap intervals.

The 26 factors were ranked according to their total effect indices obtained with 5 × 10 4 runs LHS. Based on their confidence intervals, 10 factors composed the subset of important factors, namely, the salmon water activity, aw, the temperature, TR, and duration, dR, of the storage in the domestic refrigerator, the initial physiological state, K, the optimum growth rate, μ opt , the minimum water activity for growth, aw min , the minimum temperature for growth, T min , the initial contamination level, x 0 , and the temperature, TM, and the duration, dM, of the storage at retail. Besides, the parameters dR, T min , x 0 , dM, and TM were previously identified by Pouillot et al. [START_REF] Pouillot | Quantitative risk assessment of Listeria monocytogenes in French cold-smoked salmon: I. Quantitative exposure assessment[END_REF] in the top 5 of the most important factors influencing the exposure assessment model of L. monocytogenes in cold smoked salmon.

The values of the indices obtained with the 10 4 runs LHS were very similar to those obtained with 5 × 10 4 runs LHS. For example, for the factor aw, St i values of 0.50 and 0.49 and S i values of 0.31 and 0.29 were obtained for the 5 × 10 4 runs LHS and the 10 4 runs LHS, respectively. However, larger confidence intervals were obtained with the 10 4 runs LHS, especially for the total effect indices, which mean that if the analysis was based on the 10 4 LHS design, the factors μ opt , aw min , TM, dM, T min , and x 0 would not have been identified as important factors.

To study the effect of the type of response on the results, the SA was also performed directly on the bacterial contamination without applying the log transformation. Fig. 2 presents the subsets of important inputs when the SA was performed on the bacterial contamination or on the log of the bacterial contamination for 5 × 10 4 runs LHS. Fig. 2 shows that the subset of important factors was different in case the log transformation was applied to the model response before the SA was performed. In fact, when applying the SA directly to the L. monocytogenes contamination (in CFU) (Fig. 2a), the growth yield, Gy, appeared to be the most important factor (St i = 0.61) while it was not identified in the subset of important factors when applying the SA to the log of the L. monocytogenes contamination (in log CFU) (Fig. 2b). Besides, the factor aw min was part of the subset of important factors only when considering the log of the bacterial contamination. Thus, the identification of the most important factors relies both on the LHS size and on the choice of the model response.

Refined Sensitivity Analysis

Table III presents the values assigned to nonimportant factors and the distributions associated with the most influent factors used in the refined sensitivity analysis applied to the log of the bacterial contamination.

The results of the ANOVA proved that all the tested factors had significant impact on the log of the response as all the p-values were inferior to the 0.05 threshold. The F-statistic was then used to rank the factors. The rankings obtained by the ANOVA, the SCC, and the PLSR are depicted in Table IV, which shows close rankings of the factors whatever the method used. Thus, the five most important factors are the domestic refrigerator storage duration, dR, and temperature, dT, the physiological parameter, K, the optimum growth rate, μ opt , and the duration of the storage at retail, dM. Moreover, we noticed that the ranking obtained using the ANOVA method was very close to that obtained with PLSR. The results of the PLSR are depicted in Fig. 3 where the sensitivity indices SI-VIP of the studied factors (simple and quadratic effects) and their interactions are presented. These PLSR-based sensitivity indices represent the major advantage of the PLSR method as the assessment of the effects of the interactions between factors is not possible with the two other methods. The most important interaction was obtained between the temperature, TR, and the duration, dR, of the domestic storage in the refrigerator and this interaction was ranked at the 6th position in the PLSR refined sensitivity analysis, while the interaction between the duration and temperature of the storage at retail was ranked at the 9th position, before the factors T min , aw min , and x 0 , and followed by the interactions involving factors K and μ opt .

DISCUSSION

Total effect indices and first-order indices are especially powerful when performing SA in case of nonadditive and nonlinear models, [START_REF] Archer | Sensitivity measures, ANOVA-like techniques and the use of bootstrap[END_REF] such as the contamination assessment model used in this study. In fact, as shown in Table II, the sum of the first-order indices (S i ), which account for the individual contribution of each factor into the variance of the output, is less than 1 (0.77), which means that the variance of the output cannot be only explained by the sum of the individual effects of each factor but is also attributed to the effects of interactions and the use of the variance-based sensitivity analysis is therefore fully justified. This is also confirmed by the relatively important difference observed between the St i and the S i for all the important factors. For example, for the cold smoked salmon aw, the difference between the St i (0.5) and the S i (0.3) flags an important role of interactions. The factors temperature, TR, and duration, dR, of the domestic refrigerator storage were also identified as influential factors. The importance of the consumer link in the cold chain was previously reported [START_REF] Pouillot | Quantitative risk assessment of Listeria monocytogenes in French cold-smoked salmon: I. Quantitative exposure assessment[END_REF] and this study quantitatively confirms this observation. Besides, the factors μ opt , T min , and x 0 , also identified as important factors in this study, were previously ranked among important factors impacting the response of similar models in the same food product. [START_REF] Pouillot | Quantitative risk assessment of Listeria monocytogenes in French cold-smoked salmon: I. Quantitative exposure assessment[END_REF] The modeling approach choice (cellular or populational) was ranked among the less important factors in the framework of this contamination assessment. The same result was also observed in a previous study made for L. monocytogenes in p ât é stored at 7 • C. [START_REF] Franc ¸ois | Risk Assessment of Listeria monocytogenes: Impact of individual cell variability on the exposure assessment step[END_REF] Unlike the authors of that study, who used a very small range of variation for the cellular physiological states k i and studied a unique temperature for growth (7 • C), our work explored a larger range of variations for k i and tested several storage scenarios with different temperatures. Yet both analyses came out with the same conclusion. However, the lack of significant impact of the modeling approach in these two cases must not be extrapolated to all situations. In fact, in some exposure assessment models, it could indeed have an important effect. Moreover, the SA showed that the initial physiological state of the cells, K, was twice as important as x 0 . However, this factor is scarcely used in QMRA, leading to fail safe but incorrect predictions. We therefore recommend a better characterization of this factor to improve model predictions.

All of these factors were also identified as important factors when the response model was changed, considering the bacterial contamination without ap-plying the log transformation. However, a new factor, the growth yield, Gy, was added to the list of important factors. Moreover, the values of the indices were changed and the contribution of the first-order indices was less important, relating an increased effect of the interactions. It seems therefore crucial to identify the most appropriate model response before applying the SA. In the case of risk assessment, for example, where the prevalence and the number of cells are of paramount importance, especially for the dose-response model, it may be more relevant to consider the final cell number when applying the SA. In this case, the SA will identify factors influencing high and risky final contaminations. However, when contamination assessment models are used to estimate the probability to exceed low contamination thresholds (e.g., 100 CFU/g in the case of L. monocytogenes to fulfill the EU regulation regarding the ready-to-eat foods allowing the growth of the pathogen [START_REF]/2005 of 15 November 2005 on microbiological criteria for foodstuffs[END_REF] ), the log transformation will give more importance to low contamination levels and SA will more accurately identify factors influencing these low contamination levels.

In this framework, the effect of the LHS size was also investigated. When the analysis was performed on 10 4 runs LHS, the calculated indices were almost the same as those calculated with 5 × 10 4 runs LHS but the confidence intervals of the total effect indices, which are used to decide whether the studied factor is influential or not, were wider compared to those obtained with 5 × 10 4 runs LHS (Table II). On the contrary, the confidence intervals of the first-order effects were not drastically changed. This is, for example, typically the case for the factor μ opt ; the confidence interval for its total effect indice was estimated to be [-0.03, 0.16] instead of [0.03, 0.11] when using the 5 × 10 4 runs LHS, while its first-order indice confidence interval was estimated to be [0.02, 0.05] when using the 10 4 runs LHS and to be [0.03, 0.04] when using the 5 × 10 4 runs LHS. Thus, when comparing the lower confidence bound of the first effect indice to the total indice, we observed that the S i -bound was superior to the St i -bound, which is by definition impossible since the total effect St i is the sum of the first-order effect S i plus the interactions effects. This result is incoherent and proves that the LHS size was not appropriate. In fact, when the space filling design is sparse, the estimates of the main effect contribution of each input factor to the variance of the output remains possible and the confidence interval of the first-order indices are not affected; however, the effects of the interactions are poorly assessed, leading to large confidence intervals for the total effect indices and most of the factors that were identified as important factors (because their confidence interval was significantly different from 0) were consequently retrieved from the subset of influential factors. Clear decision rules to determine the optimum number of simulations for a given model are unfortunately not available in the literature (few hundreds to few thousands). We therefore propose to test the coherence between the confidence intervals of the total effects to those of the firstorder effects to check if the number of simulations is appropriate.

The refined sensitivity analysis provided a ranking of the important factors (identified by the global sensitivity analysis) when sampled in their marginal distributions. Just like the observation made in the SA results, the duration, dR, and the temperature, TR, of the storage at the domestic refrigerator were identified as major factors as well as the optimum growth rate, μ opt , and the physiological state, K. However, the aw was ranked 7th after the effect of the interaction between the duration and the temperature of the storage at the refrigerator. This observation confirms the complementarity between the SA and the refined sensitivity analysis. In the former analysis, numerous factors with large ranges of variations are used and the method is able to iden-tify a group of important factors and provide a primary ranking, while in the latter analysis, a ranking of these factors is proposed using a narrower range of variation for the subset of the identified important factors.

In this study, three refined sensitivity analysis methods were used and the PLSR was introduced and compared to commonly used ANOVA and SCC. The three methods provided similar results, which proves that the PLSR can be used efficiently in QMRA. Moreover, the PLSR provided PLSR-based sensitivity indices expressed in percentages. These are very easy to interpret and account for simple and quadratic effects of the factors and their interactions. For example, if we sum the simple and the quadratic effect of the duration of the domestic storage, dR, we can explain 23% of the response. Similarly the parameter K explains 13% of the variability of the response. Thus the variability of the top five factors is responsible for 74% of the variability of the response. More interestingly, this method made it possible to appreciate the effects of the interactions, which explain 16% of the model response, with the interaction between the duration, dR, and the temperature, TR, of the domestic storage being the most important (5% of the response).

CONCLUSION

The aim of this article was to apply the Saltelli global, variance-based sensitivity analysis method [START_REF] Saltelli | Making best use of model evaluations to compute sensitivity indices[END_REF] to a contamination assessment model involving quantitative and qualitative factors through the example of L. monocytogenes in cold smoked vacuum packed salmon. This method computed first-order indices and total effect indices for each of the factors and made it possible to identify a subset of 10 factors out of 26 as important factors. A refined sensitivity analysis was further performed using the PLSR innovative method. After sampling the important factors in their marginal distribution, a ranking of the most important factors was proposed using PLSR-based indices, taking into account simple and quadratic effects of the factors as well as their interactions with other factors.

The application of the presented global SA and refined sensitivity analysis to other models especially more complex QMRA models is worth conducting to try to simplify them and thus reduce data acquisition costs and provide an efficient tool to orientate risk management decisions and evaluate risk mitigation scenarios.

APPENDIX: A BRIEF PRESENTATION OF THE PLSR METHOD

PLSR is a regression method based on an iterative algorithm. As all other regression methods it provides a regression equation to relate several explanatory factors to a response. However, among many advantages, one of its major advantages is its ability to deal properly with correlated variables. Indeed, and since it is based on a tricky use of partial covariances, it can provide, even with this type of variables, several statistics (regression coefficients, VIP, . . . ) that can be used, for instance, for measuring the factor effects on the response uncertainty.

Its principle is to construct PLS components, referred to as t h , which are linear combinations of the original factors with their relative weights w hj . The originality of PLSR is that these weights take into account the response itself. The right number H of PLS components is given by means of a specific crossvalidation test.

Let us define the redundancy between the response Y and a t h component by: Rd(Y, t h ) = cor 2 (Y, t h ) and between the response Y and a set of several t h by: Rd(Y, t h1 , . . . , t H ) =

  where E[k] and S[k] are the expected value and standard deviation of k, respectively.

  (h) Duration of storage at retail 2-288 TM ( • C) Temperature of storage at retail 2-9 dV (h) Duration of the journey back home 0.1-2.5 TV ( • C) Temperature of the journey back home 6-20 dR (h) Duration of the storage in the refrigerator 0-336 TR ( • C) Temperature of the storage in the refrigerator 2

Fig. 2 .

 2 Fig. 2. Indices S i (black bars) and St i (white bars) obtained for the sensitivity analysis when applied to (a) the bacterial contamination or (b) the log of the bacterial contamination using a 5 × 10 4 runs LHS.

5 T

 5 Gy (log CFU) Increase in the L. monocytogenes population opt ( • C) L. monocytogenes optimum temperature for growth 38.0 T max ( • C) or SR effect of the aw with and without interactions SR without interactions Approach Populational or cellular Populational a N(m, s), normal distribution with expected value m and standard deviation s; PT(m, a,b), Poisson distribution with expected value m truncated on [a,b]; NT(m, s, a,b), normal distribution with expected value m and standard deviation s truncated on [a,b]; E(m), exponential distribution with expected value m.

Fig. 3 .

 3 Fig. 3. VIP-based sensitivity indices associated with the quadratic (white bars) and simple (black bars) effects of the important factors and their interactions. Interactions with uncertainty indices <0.5% were gathered under the item "others."

  Y, t h ).Then we can define the VIP as:VIP Hk = p Rd(Y, t 1 , . . . , t H )

  Diagram of interactions between factors, models, and approaches used in the global sensitivity analysis of the contamination assessment model of L. monocytogenes in cold smoked salmon.

				Modeling approach
		Populational approach				Cellular approach
	dTEP, TTEP			pH	x0 times
	dC, dM, TM TC dV, TV dR, TR dD, Td	CM2(T)	Secondary model SR(aw) CM1(pH) CM1(aw) γint=1 γint=0	aw µopt Tmin, Topt, Tmax pHmin awmin	dTEP, TTEP dC, TC dM, TM dV, TV dR, TR dD, Td	CM2(T)	Secondary model SR(aw) CM1(pH) CM1(aw) γint=1 γint=0	pH aw µopt Tmin, Topt, Tmax pHmin awmin
			µmax				µmax
			Primary model				Primary model
		Baranyi & Roberts (1994) Rosso (1995)	Gy K x0		Baranyi & Roberts (1994) Rosso (1995)	ki=f(K) Gy x0=1
							Yi
			Response: log Y				Response: log Y i
	Fig. 1.

Table I .

 I Identification

	Factors	Description	Range
	Microbiological parameters
	K	Physiological state of L. monocytogenes	0-8
	x 0 (CFU)	Initial contamination level	1-20
	Gy (log CFU)	Growth yield of the L. monocytogenes population	4-6
	μ opt (h -1 )	Optimum specific growth rate of L. monocytogenes	0.60-1.30
		in cold smoked salmon
	pH	Cold smoked salmon pH	5.3-6.3
	aw	Cold smoked salmon aw	0.925-0.995
	T min ( • C)	L. monocytogenes minimum temperature for	-2.8-0.6
		growth
	T opt ( • C) T max ( • C)	L. monocytogenes optimum temperature for growth L. monocytogenes maximum temperature for	36.4-40.0 40.5-46.1
		growth
	pH min	L. monocytogenes minimum pH for growth	3.9-4.5
	aw min	L. monocytogenes minimum aw for growth	0.901-0.943
	Distribution chain parameters dTEP (h) Duration of transport and storage TTEP ( • C) Temperature of transport and storage dC (h) Duration of storage in cold rooms	4-96 -2-7 0-48	and Range of Variations of the Contamination Assessment Model Parameters
	TC ( • C)	Temperature of storage in cold rooms	1-7
	dM

Table II .

 II Estimates of the First-Order (S i ) and Total Effect (St i ) Indices of the Sensitivity Analysis and Their Bootstrap 95% Confidence Intervals Obtained on the Log of the Bacterial Contamination with Different LHS Sizes (N = 5 × 10 4 and N = 10 4 )

		N = 5 × 10 4		N = 10 4
	Factors	St i	S i	St i	S i
	aw	0.50 [0.47, 0.54]	0.31 [0.30, 0.32]	0.49 [0.41, 0.57]	0.29 [0.26, 0.31]
	TR	0.15 [0.11, 0.19]	0.06 [0.05, 0.07]	0.19 [0.10, 0.28]	0.10 [0.08, 0.12]
	dR	0.12 [0.08, 0.16]	0.05 [0.05, 0.06]	0.16 [0.07, 0.25]	0.08 [0.06, 0.10]
	K	0.07 [0.03, 0.12]	0.03 [0.03, 0.04]	0.09 [0.03, 0.22]	0.05 [0.04, 0.07]
	μ opt	0.07 [0.03, 0.11]	0.01 [0.01, 0.02]	0.06 [-0.03, 0.16]	0.03 [0.02, 0.05]
	aw min	0.06 [0.02, 0.10]	0.02 [0.02, 0.03]	0.06 [-0.03, 0.16]	0.01 [0.00, 0.02]
	T min	0.06 [0.01, 0.10]	0.02 [0.02, 0.03]	0.05 [-0.05, 0.14]	0.03 [0.01, 0.04]
	x 0	0.05 [0.01, 0.10]	0.04 [0.04, 0.05]	0.05 [-0.05, 0.14]	0.03 [0.02, 0.04]
	TM	0.05 [0.01, 0.09]	0.02 [0.01, 0.02]	0.04 [-0.05, 0.14]	0.02 [0.01, 0.04]
	dM	0.05 [0.01, 0.09]	0.02 [0.01, 0.02]	0.05 [-0.05, 0.15]	0.02 [0.01, 0.03]
	pH	0.04 [0.00, 0.08]	0.02 [0.01, 0.02]	0.05 [-0.05, 0.14]	0.01 [0.00, 0.02]
	T opt	0.02 [-0.02, 0.07]	0.01 [0.00, 0.01]	0.01 [-0.09, 0.11]	0.00 [-0.01, 0.01]
	Gy	0.02 [-0.03, 0.06]	0.00 [0.00, 0.00]	0.01 [-0.09, 0.10]	0.00 [-0.01, 0.00]
	T max	0.01 [-0.03, 0.06]	0.00 [0.00, 0.01]	0.00 [-0.10, 0.09]	0.01 [0.00, 0.01]
	dD	0.01 [-0.03, 0.06]	0.00 [0.00, 0.00]	0.01 [-0.09, 0.10]	0.00 [0.00, 0.01]
	TD	0.01 [-0.03, 0.05]	0.00 [0.00, 0.00]	0.00 [-0.10, 0.10]	0.00 [0.00, 0.01]
	pH min	0.01 [-0.03, 0.05]	0.00 [0.00, 0.00]	0.00 [-0.10, 0.09]	0.00 [0.00, 0.00]
	TTEP	0.01 [-0.04, 0.05]	0.00 [0.00, 0.00]	0.00 [-0.09, 0.10]	0.00 [-0.01, 0.00]
	TC	0.01 [-0.04, 0.05]	0.00 [0.00, 0.00]	0.00 [-0.10, 0.09]	0.00 [0.00, 0.00]
	dC	0.01 [-0.04, 0.05]	0.00 [0.00, 0.00]	0.00 [-0.10, 0.09]	0.00 [0.00, 0.00]
	dTEP	0.01 [-0.04, 0.05]	0.00 [0.00, 0.00]	0.00 [-0.10, 0.09]	0.00 [0.00, 0.00]
	Approach	0.01 [-0.04, 0.05]	0.00 [0.00, 0.00]	0.01 [-0.09, 0.11]	0.00 [-0.01, 0.00]
	TV	0.01 [-0.04, 0.05]	0.00 [0.00, 0.00]	-0.01 [-0.10, 0.09]	0.00 [0.00, 0.00]
	dV	0.01 [-0.04, 0.05]	0.00 [0.00, 0.00]	-0.01 [-0.10, 0.09]	0.00 [0.00, 0.00]
	Primary models	0.01 [-0.04, 0.05]	0.00 [0.00, 0.00]	-0.01 [-0.11, 0.09]	0.00 [0.00, 0.00]
	Secondary models	0.01 [-0.04, 0.05]	0.00 [0.00, 0.00]	0.01 [-0.08, 0.11]	0.00 [-0.01, 0.01]

Table III .

 III Parameter Distributions and Fixed Values Used in the Refined Sensitivity Analysis Applied to the Log of the Bacterial Contamination

	Factors	Description	Distribution/Value a
	Uncertainty factors
	log K	Physiological state of L. monocytogenes	N(0.67, 1.23)
	x 0 (CFU) μ opt (h -1 )	Initial contamination level Optimum specific growth rate	PT(10,1, ∞) NT(0.924, 0.286, 0, ∞)
	aw	Cold smoked salmon aw	N(0.960, 0.006)
	T min ( • C)	L. monocytogenes minimum	N(-1.08, 0.72)
		temperature for growth
	aw min	L. monocytogenes minimum aw for	N(0.922, 0.009)
		growth
	dM (h)	Duration of storage at retail	E(120)
	TM

Table IV .

 IV Ranking of the Contamination Assessment Model Factors Using the ANOVA, SCC, and PLSR Refined Sensitivity Analyses Applied on the Log of the Bacterial Contamination

	Factors	ANOVA	SCR	PLSR
	dR	1	2	1
	K	2	1	3
	TR	3	5	4
	μ opt	4	3	5
	dM	5	4	2
	TM	6	8	7
	aw	7	7	6
	T min	8	9	8
	aw min	9	1 0	9
	x 0	10	6	10

Unit é MASQ, Ecole Nationale V ét érinaire d'Alfort, Maisons-Alfort Cedex, France.

[START_REF] Zwietering | Quantitative risk assessment: Is more complex always better?-Simple is not stupid and complex is not always more correct[END_REF] Unit é MIA (UR341), INRA, Jouy en Josas, France

.[START_REF] Saltelli | Sensitivity analysis for importance assessment[END_REF] CRYOLOG SA, Nantes, France. * Address correspondence to Mariem Ellouze, 7, Avenue du G én éral de Gaulle, P ôle HQSA, Maisons Alfort 94700, France; mellouze@vet-alfort.fr.

ACKNOWLEDGMENTS

The French program of predictive microbiology Sym'Previus is gratefully acknowledged for providing the cardinal values of L. monocytogenes. The authors also thank the Cemagref (Centre National du Machinisme Agricole, du G énie Rural, des Eaux et For êts) and the ANIA (Association Nationale des Industries Agro-alimentaires) for providing time temperature profiles.


domain: sdv sde

text:
Nicolas Perdrial
email: perdrial@illite.u-strasbg.fr

Nicole Liewig
email: nicole.liewig@c-strasbourg.fr

New technique for in situ sampling of particulate matter and colloids in soil and atmospheric fallout

Keywords: In situ monitoring, Lysimeter, Vadose zone, Infiltration water, Analytical electron microscopy

This note describes a new technique for in situ sampling of fine particulate matter (PM) including colloids in natural environments. The technique is based on a microlysimeter which is easy to move between field and laboratory and can be routinely used for in situ monitoring. The design of the device aims at limiting bias and artefacts encountered with current sampling methods based on successive field collection of liquid samples, transport, storage and filtration in the laboratory. Samples are directly collected on transmission electron microscopy (TEM) grids, thus totally eliminating the modifications classically due to handling of samples from collection to analysis. Detailed physical and chemical microscopic studies of individual particles can then be performed in order to fully characterize PM in natural media such as soil solutions, atmospheric fallout, rainfall and any aquatic system. This technique can be applied in a number of research fields, such as the characterization and determination of pollution vectors, the tracing of sources of emissions, or investigations on particle interactions.

Introduction

In the last 20 years, the role of particulate matter (PM) including colloids in pollutant transfer has gained increasing attention in soil and groundwater studies [START_REF] Mcdowell-Boyer | Particle transport through porous media[END_REF][START_REF] Mccarthy | Subsurface transport of contaminants; mobile colloids in the subsurface environments may alter the transport of contaminants[END_REF][START_REF] Crossan | Assessment of the distribution of pesticides on soil particle fractions in simulated irrigation run-off using centrifugal SPLITT fractionation and ELISA[END_REF][START_REF] Mcgechan | Transport of particulate and colloid-sorbed contaminants through soil. Part I: General principles[END_REF][START_REF] Citeau | Investigation of physico-chemical features of soil colloidal suspensions[END_REF]. It has been shown that both the abundance of PM and the nature of contaminants have a strong influence on pollution transfer and transport in porous media [START_REF] Roy | Chemical factors influencing colloid-facilitated transport of contaminants in porous media[END_REF][START_REF] Mccarthy | Colloid transport in the subsurface: past, present and future challenges[END_REF]. In 1986, McDowell-Boyer et al. [START_REF] Mcdowell-Boyer | Particle transport through porous media[END_REF] deplored the fact that most studies on natural systems had been carried out without paying attention to particulate components and advocated looking into the fundamental phenomena and mechanisms involved. Some of the processes controlling PM transfer were individually and independently explored, but a great majority of the studies performed during the last two decades did not involve natural systems. Because of their complexity and of sampling difficulties, it is impossible to investigate the whole range of matter and processes involved. Chen and Buffle [START_REF] Chen | Physicochemical and microbial preservation of colloid characteristics of natural water samples I: experimental conditions[END_REF] have pointed out the importance of the physical and chemical characterization of colloids and the challenge in sampling without drastically altering the nature and properties of colloidal material.

Numerous sampling devices already exist for sampling PM in the soil system. These devices, consisting in sampling soil water prior to filtration for PM study, can be separated in two types: tension lysimeters and zero-tension lysimeters. Tension lysimeters are: (i) tension plate lysimeters developed in the 1960s [9, cited in 10], consisting on applying a negative tension onto the plate to create a permanent drainage of water, and (ii) porous cup used since the 1940s [START_REF] Wallihan | An improvement in lysimeter design[END_REF] consisting on applying a suction force to aspire soil water. Those sampling devices avoid air-water interface but it seems that sampling of PM by filtration of previously pumped groundwater can introduce artefacts due to high pumping rates or alteration in chemical and physical properties [START_REF] Puls | Acquisition of representative ground water quality samples for metals[END_REF][START_REF] Domange | Effect of ceramic cups ageing on the capacity to assess pesticide concentration[END_REF]. Zero-tension lysimeters are of four types: (i) lysimeters sensus stricto [14, cited in 15]; (ii) plate lysimeters [16, cited in 17]; (iii) gutter lysimeters [START_REF] Boerner | An inexpensive, tension-free lysimeter for use in sandy soils[END_REF][START_REF] Haines | Soil solution nutrient concentrations sampled with tension and zero-tension lysimeters: report of discrepancies[END_REF], and (iv) wicks lysimeters [START_REF] Brown | Development of a capillary wick unsaturated zonepore water sampler[END_REF]. These devices are all based on the same principle: sampling gravitational water. However, the validity of information given by such devices has been often discussed and it is today accepted that: (i) a soil-air interface is artificially created into the soil [START_REF] Cole | Tension lysimeter studies of ion and moisture movement in glacial till and coral atoll soils[END_REF][START_REF] Giesler | Comparison of soil solution chemistry assessment using zero-tension lysimeters or centrifugation[END_REF][START_REF] Richards | Observations on moisture conditions in lysimeters: II[END_REF][START_REF] Colman | A laboratory study of lysimeter drainage under controlled soil moisture tension[END_REF], and (ii) a contamination from vessels, or coagulation and microbial changes during storage is possible [START_REF] Chen | Physicochemical and microbial preservation of colloid characteristics of natural water samples I: experimental conditions[END_REF]. Moreover, none of these devices have been designed to sample directly PM and colloids for individual particle investigation.

Based on the recent review paper of McCarthy and McKay [START_REF] Mccarthy | Colloid transport in the subsurface: past, present and future challenges[END_REF], it appears that the sampling of colloids/PM in the vadose zone as well as in saturated groundwater is a key challenge that needs to be addressed properly. Moreover, characterizing the atmospheric input of PM on soil surface is of prime interest in PM studies [START_REF] Pósfai | Aerosol bacteria over the Southern Ocean during ACE-1[END_REF][START_REF] Ndzangou | Anthropogenic Pb accumulation in forest soils from Lake Clair watershed: Duchesnay experimental forest (Québec, Canada)[END_REF]. It is therefore important to develop techniques that enable the characterization of individual PM present in atmospheric deposits and in gravitational water in a state as close as possible to natural conditions.

We propose here a new sampling method minimizing disturbances to the nature and organisation of the PM fraction in order to better investigate the characteristics and/or evolution of such material by analytical transmission or scanning electron microscopy (TEM, SEM).

Sampling device

Basic principle of the device

The basic principle of the field device consists in real time filtration of percolating water by lysimetry. The microlysimeter used for that purpose is a filtration box filled with inert sand and placed in contact with the soil at the desired sampling depth. The particle collector consists in TEM grids inserted in the sand bed and intercepting the PM by simple gravitational deposition.

The vertical flow of infiltrating water is isolated from lateral flow by confining the soil column in a PVC tube. A stopper fit to the bottom of the tube and drilled with holes allows the drainage of the soil solution. The microlysimeters can be replaced regularly for periodic monitoring. An adapted handling device allows lifting and dropping the tube with no further perturbation of the soil column confined inside the tube.

Microlysimeter

The essential part of the device is the microlysimeter (Fig. 1a). The container is a two stage Millipore © filtration cell for fluid analyses with a 4.5 cm internal diameter. In order to facilitate the inflow of water, the cover and the bottom of the box are drilled with holes. At the lower stage of the box a rigid I-Vyon ® filter is placed under a plastic basket containing carbon coated Cu and Ti TEM grids. This Vyon-type filter with a pore size of 80 m constitutes a support for the whole device. Grids are embedded in pure inert silica sand (diameter: 100-200 m). A cellulose nitrate filtration membrane is mounted over the sand bed and clamped between the two stages of the filtration cell. The membrane is covered with sand so as to fill completely the upper stage of the cell topped with a nylon filter (pore size: 100 m). This assembly is functioning as a lysimeter. The soil solution collected at the upper stage of the cell is filtered through the cellulose membrane (i.e., at 5 m), which allows the collection on the underlying grids of all the size fractions of PM from nanoparticles to the size of the porosity of the selected membrane. We recommend a rather large porosity of the membrane to keep it free of clogging and avoid the bias due to the interaction of PM with the pore edges that may occur with too small pore diameters. The design of the device is avoiding any air interface with a continuum of porosity due to the sand filling. The nylon filter has a rather large porosity (100 m), assumed to be close to the soil porosity and then let any PM and colloids reach the cellulose membrane, which is the truly restricting size filter. However, depending on the sampled environment and sampled objects, any other filter porosity can be adapted to the device. The use of a cellulose nitrate membrane as described below allows micro-biological analysis of the filter and SEM observation.

Field device

The field device (Fig. 1b) is based on PVC tubes driven vertically into the soil. The PVC tubes have an internal diameter of 12.7 cm and their length is adapted to the soil depth selected for a given study. This device may be used either to study a complete soil column, or various depths selected according to specific study criteria such as differentiated soil horizons, mod- ifications in porosity, or biological zonings. It is recommended to let the field device settle for a period to allow the sealing of cracks generated during the introduction of the tube in the soil. After the settling period, the tube is pulled out, the bottom stopper is removed, the particle collector is placed at the bottom of the soil column and the tube dropped back in place. To remove the particle collector and replace it with another one for monitoring purposes, the protocol is exactly the same.

In addition to the set of PVC tubes equipped with microlysimeters, a 500 mL filtration box is used at the surface of the soil, based on the same filtration principle than the particle collector device fitted to the soil columns. The filtration box is designed to filter rainwater and collect the atmospheric inputs.

According to the sampling intervals, the particle collector is recovered and dismantled in the laboratory under a glove box to avoid dust and bacterial contamination. Grids are washed with 20 L of purified and sterilized water to eliminate excess soil solution and avoid precipitation of dissolved matter. Observation of aggregates and organic particles proves that this washing is not affecting the particles integrity; however, the loss of a small amount of particles is possible. Then the grids are air dried prior to analysis in the microscope.

Discussion

As the device placed directly inside the soil is of very small size (a few centimeters), its effect on the hydrologic properties is equivalent to that of a small pebble, and as the TEM grid is 3 mm in diameter its effect is equivalent to that of a large sand grain. This does not significantly modify the drainage, the pH, or the temperature of the soil solution near the device. The grid can be considered as similar to an inert soil component or pore wall on which PM are collected by simple deposition. The TEM grids loaded with PM allow: (i) performing all analytical TEM techniques such as microanalysis (EDS), high resolution images (HRTEM), microdiffraction (SAED), providing chemical composition and physical characterization, as well as permitting image analysis for size distribution or shape studies (Fig. 2); (ii) performing additional observations by scanning electron microscopy such as SEM or ESEM investigations on grids or on filters; (iii) storing them in a dry state for months/years without altering particle characteristics.

The examination of sampling grids with TEM shows the presence of different types of colloidal PM and their assemblages in the field conditions. Samples from soil solutions and atmospheric fallout are representative of both mineral and biological components that are known to exist as PM in natural environments [START_REF] Mccarthy | Colloid transport in the subsurface: past, present and future challenges[END_REF][START_REF] Wagner | Use of porous ceramic cups to sample soil water within the profile[END_REF]. Moreover, it appears clearly that naturally occurring aggregates remain undisturbed by applying this technique (Fig. 3). Such aggregates are usually not studied in natural environments because of disaggregation caused by the tension applied during sampling and/or centrifugation of water to concentrate PM. Whereas aggregation processes, investigated in laboratory experiments, had been recently shown to be an important mechanism of PM and colloid-facilitated transport in soils [START_REF] Aurell | Coagulation of kaolinite colloids in high carbonate strength water[END_REF][START_REF] Alvarez-Puebla | Effect of pH on the aggregation of a gray humic acid in colloidal and solid state[END_REF][START_REF] Itami | Charge characteristics and related dispersion/flocculation behavior of soil colloids as the cause of turbidity[END_REF][START_REF] Majzik | Interaction between humic acid and montmorillonite in the presence of calcium ions II. Colloidal interactions: charge state, dispersing and/or aggregation of particles in suspension[END_REF].

One of the potential biases of the method is the installation of the field device. The field device is settled following the same protocol as conventional lysimeter settling. It has been shown that this settling is modifying the flow on the sidewall of the tube [START_REF] Corwin | Evaluation of a simple lysimeter-design modification to minimize sidewall flow[END_REF]. Since these authors highlighted the fact that the flow is not modified in the center of the tube; we assume that it is the same here. Moreover, we recommend to perform the first driving of the field device in a wet season and wait at least one month prior to sampling in order to let the soil heal up and eliminate possible discharge of PM due to the installation of the device. Another possible inconvenient is the difference in capillary pressure between the soil and the microlysimeter due to a difference of porosity. However, the diameter of the sand (100-200 m) is assumed to be inferior or similar to the soil porosity, then no barrier is created and the capillary force is normal or slightly positive. The size of the sand has to be selected according to the average porosity of the soil and a mixing of two or three different sand sizes is recommended in the upper part of the microlysimeter. A smaller diameter has to be selected for the lower part to create a slight positive capillary pressure and avoid a barrier due to the rather small porosity of the membrane.

Conclusion

To conclude, it appears that the design of this field device is a great step forward in the in situ monitoring and physicochemical characterization of individual PM from atmospheric input to soil solution. The sampling intervals are easy to adjust to the investigated subject, the device can be used indifferently for a short event (rain, storm), for a period of a week, for a month or a season. However, the tests performed with our device have shown that for soil nanoparticles a period of more than 2 to 3 months is not recommended because of problems such as clogging of the membrane as well as the overloading of PM on the grids.

Fig. 1 .

 1 Fig. 1. Description of the sampling device. (a) Assemblage of the microlysimeter. (b) Cross section of the field installation for sampling PM in soil infiltration water.

Fig. 2 .

 2 Fig. 2. Example of characterization of individual particles by analytical electron microscopy. (a) TEM micrograph of a cadmium-rich PM present in infiltration water of a tillage soil. Scale bar: 0.2 m. (b) Microdiffraction pattern of particle arrowed on (a). (c) Energy dispersive X-ray analysis of the particle arrowed on (a). C peak is due to the carbon coating of the grid and to the presence of organic matter. Cu peak is due to the copper grid.

Fig. 3 .

 3 Fig. 3. Examples of naturally occurring aggregates. (a) TEM micrographs of atmospheric PM. MO: organic matter; C: individual clay particle; B: bacteria associated with clays. (b) TEM micrograph of soil infiltrating water PM. Ox: metal oxide; B: bacteria associated with minerals; C: weathered clay. Scale bar: 1 m.

Acknowledgements

A Ph.D. fellowship to Nicolas Perdrial by the French Ministry of National Education is thankfully acknowledged. We gratefully thank BRGM Alsace, INRA Colmar and BEF team from INRA Nancy for special attention to our work, advice and technical support for field experiments.