Frederic Yves Bois
email: frederic.bois@ineris.fr

Statistical Analysis of Clewell et al. PBPK Model of Trichloroethylene Kinetics

Keywords: Bayesian, human, Markov chain Monte Carlo, mouse, PBPK model, rat, TCE, toxicokinetics, tricholoroethylene, uncertainty analysis

A physiologically based pharmacokinetic model for trichloroethylene (TCE) in rodents and humans was calibrated with published toxicokinetic data sets. A Bayesian Statistical framework was used to combine previous information about the model Parameters with the data likelihood, to yield posterior parameter distributions. The use of the hierarchical Statistical model yielded estimates of both variability between experimental groups and uncertainty in TCE toxicokinetics. After adjustment of the model by Markov chain Monte Carlo sampling, estimates of variability for the animal or human metabolic Parameters ranged from a factor of 1.5-2 (geometric Standard deviation [GSD]). Uncertainty was of the same order äs variability for animals and higher than variability for humans. The model was used to make posterior predictions for several measures of cancer risk. These predictions were affected by both uncertainties and variability and exhibited GSDs ranging from 2 to 6 in mice and rats and from 2 to 10 for humans.

The recent development of a comprehensive physiologically bascd pharmacokinedc (PBPK) model of trichloroethylene (TCE) disposition and metabolism in mice, rats, and humans (/) offers us the opportunity to examine issues of variability and uncertainty for diät solvent. In particular, uncertainties in predicrion of various cancer dose merrics deserve to be computed, since they could be directiy used äs input for improved risk assessments.

PBPK modeling provides a strong mechanistic basis for predicrion of disposition and metabolism of toxicanis. Yer much uneasiness remains with the use of these modeis in toxicology [START_REF] Kohn | Achieving credibility in risk assessment modeis[END_REF]. Similarly, äs discussed in a recent review and an accompanying commentary, PBPK modeling has not seen the development it promised for therapeuric compounds [START_REF] Charnick | Physiologicaliy based phannacokinetic modeling äs a tool for drug development[END_REF][START_REF] Ludden | Commentary on "Physiologicaliy based pharmacokinetic modeling äs a tool for drug development[END_REF]. The reason for this essenrially lies in the lack of Statistical merhods for calibraring these modeis. Because ofindividual variability and uncertainty, many parameters are difficult to measure accurately even for inbred animal strains. Using input parameters or presenting results in the form ofa single value can therefore be very misleading [START_REF] Louis | Assessing, aecommodating. and interpreting the influences of heterogeneity[END_REF]. In the absence of rigorous Statistical treatment, inference presenred by PBPK modeling is largely empirical, hypotheses are left unvalidaced, and predictions lack realisric measures of uncerrainry. This srate ofaffairs is unformnate, when considering the consequences (for public health and national weifare) of the decisions made using these modeis.

Obviously, correct Statistical treatment of PBPK modeis is difficult, since these are large nonlinear modeis with relatively small data sets and a high degree of uncertainty and biological variability [START_REF] Woodruff | Optimization issues in physiological toxicokinetic modeling -a case study with benzene[END_REF]. It is also essential to respect the fundamental specificity of PBPK modeis, i.e., their high prior information conrent, which they provide through the opportunity ro use physiological information on parameter values. Yet, although several parameters have physiological meaning and a narrow ränge ofpossible values, others-often specific of the compound studied-lack such definition and need to be identified by the fitting of the model to concentration-time profiles. Finally, most of the time, prior physiological information is simply about population averages and is not directiy applicable to any particular individual for which data were obtained. Fortunately, all these problems can be solved in a unified way though a Bayesian population toxicokinetic approach, which is worth implemenring even in the case of small numbers of study subjects [START_REF] Vozeh | The use of population pharmacokinetics in drug development[END_REF][START_REF] Bois | Population toxicokinetics of tetrachloroethylene[END_REF][START_REF] Bois | Population toxicokinetics of benzene[END_REF][START_REF] Gelman | Physiological pharmacokinetic analysis using population modeling and informative prior distributions[END_REF]. Bayesian staristics provides a natural way of merging a priori knowledge gained by implemenring a physiological model, with the in vivo experimental data. A Bayesian numerical treatment can also deal efficiently with the multilevel error strucrure of pharmacokinetic data (11). This is achieved through the use of an explicit srarisrical model, describing the links between the various sources ofvariance (e.g., measurement errors, popularion variability) present in the data, in which the physiological model is imbedded äs a determinisric component. These techniques are demonscrated here in the case ofTCE PBPK modeling.

Methods

Data

Mice. Similar to the study of Clewell et al. (l), data from six published repons were used. From the reported experiments, a total of 33 groups of animals were defined. Fisher and Allen [START_REF] Fisher | Evaluating the risk of liver cancer in humans exposed to trichloroethylene using physiological modeis[END_REF] exposed groups of3or4 male and fcmale B6C3F] mice each (body weight [bw] 30 g), by gavage to TCE at concentradons of 487, 973, and 1,947 mg/kg (males, groups 1-3; females, groups 4-6, respectively). Trichloroacetic acid (TCA) concentrarions in venous blood were measured at various rimes in all groups, äs well äs the venous blood concentrarions ofTCE for dosing group 2.

Fisher et al, [START_REF] Fisher | Physiologicaliy based pharmacokinetic modeling with trichloroethylene and its metabolite. trichloroacetic acid, in the rat and mouse[END_REF] exposed groups of 14 female B6C3Fi mice each (bw 26.5 g) by Inhalation to TCE in a closed chamber of 9.1 L, at concentrarions of300, 700, 1,100, 3,700, and 7,000 ppm (groups 7-11) and groups of 15 male mice (bw 31g) each to 1,020, 1,800, 3,800, 5,600, and 10,000 ppm (groups [START_REF] Fisher | Evaluating the risk of liver cancer in humans exposed to trichloroethylene using physiological modeis[END_REF][START_REF] Fisher | Physiologicaliy based pharmacokinetic modeling with trichloroethylene and its metabolite. trichloroacetic acid, in the rat and mouse[END_REF][START_REF] Larson | Metabolism and lipoperoxidative activity of trichloroacetate and dichloroacetate irrrats and mice[END_REF][START_REF] Templin | Relative formation of dichloroacetate and trichloroacetate from trichloroethylene in male B6C3F1 mice (correction/addition)[END_REF][START_REF] Larson | Species differences in the metabolism of trichloroethylene to the carcinogenic metabolites trichloroacetate and dichloroacetate[END_REF]. The concentrarion ofTCE in the air chamber was measured. The same study also exposed four groups of 3 or 4 male B6C3Pi mice each to TCE (bw 31 g) for 4 hr at concentrarions of 110, 297, 368, and 748 ppm (groups [START_REF] Prout | Species differences in response to trichloroBthylene. l: Pharmacokinetics in rats and mice[END_REF][START_REF] Templin | Relative formation of dichloroacetate and trichloroacetate from triehloroethytene in male B6C3F1 mice[END_REF][START_REF] Templin | Factors affecting Species differences in the kinetics of metabolites of trichloroethylene[END_REF][START_REF] Monster | Kinetics of trichloroethylene in volunteers: influence of work load and exposure concentration[END_REF]; four groups of3 or 4 female mice each ro TCE for 4 hr at concentrarions of42,236,368,and 889 ppm (groups [START_REF] Monster | Kinetics of trichloroethylene in repeated exposure of volunteers[END_REF][START_REF] Müller | Metabolism of trichloroethylene in man. il: Pharmacokinetics of metabolites[END_REF][START_REF] Müller | Metabolism of trichloroethylene in man. III: Interaction of trichloroethylene and ethanol[END_REF][START_REF] Stewart | Experimental human exposure to trichloroethylene[END_REF]. The venous blood concentrarions of TCE and TCA were measured at various rimes.

Larson and Bull [START_REF] Larson | Metabolism and lipoperoxidative activity of trichloroacetate and dichloroacetate irrrats and mice[END_REF] exposed groups of4 male B6C3F] mice each (average bw 27 g) by gavage to TCA at concentrarions of 20 and 100 mg/kg (groups 25 and 26). The venous blood concentrations of TCA and dichloroaceric acid (DCA) were measured. Given the analytical technique used, it is suspecred that the DCA concentrarions may be artifaccually high [START_REF] Templin | Relative formation of dichloroacetate and trichloroacetate from trichloroethylene in male B6C3F1 mice (correction/addition)[END_REF].

Larson and Bull (16) exposed groups of 5-6 male B6C3F] mice each (bw 26.4 g) by gavage to TCE at concentrations of 15 mmol/kg (1972 mg/kg), 4.5 mmol/kg (592 mg/kg), and 1.5 mmol/kg (197 mg/kg) (groups [START_REF] Oavidian | Nonlinear Models for Repeated Measurement Data[END_REF][START_REF] Gelman | Bayesian Data Analysis[END_REF][START_REF] Gelfand | Sampling-based approaches to caiculating marginal densities[END_REF]. The venous blood concentrations of TCE, free trichloroethanol (TCOH), and TCA were measured at various rimes. The venous blood concentrarions of DCA were also measured in mice for group 27. Here also the DCA concentrarions may be arrifactually high. Prout et al. (17) exposed male mice of unspecified strain, most likely B6C3F; (bw 29.5 g) by gavage to 1,000 mg/kg TCE (group 30). The venous blood concentrarions ofTCE. free TCOH, and TCA, äs well äs Ae cumulated amount of TCE exhaled, were measured ar various times.

Templin et al. [START_REF] Templin | Relative formation of dichloroacetate and trichloroacetate from triehloroethytene in male B6C3F1 mice[END_REF] exposed groups comprising 4 male B6C3F[ mice each (bw 27 g) to TCE at concentrations of 3.8 mmol/kg (500 mg/kg), 0.76 mmol/kg (100 mg/kg), and 15 mmol/kg (1,972.5 mg/kg) (groups [START_REF] Gelfand | Bayesian analysis of con-Strained Parameter and truncated data Problems using Gibbs sampling[END_REF][START_REF] Gelman | Iterative and non-iterative Simulation algorithms[END_REF][START_REF] Tanner | Tools for Statistical Inference -Observed Oata and Data Augmentation Methods[END_REF]. The venous blood concentrations of DCA were measured in all groups. The venous blood concentrations of TCE, free TCOH, and TCA were also measured at various times for group 31. The DCA concentrations may be artifactually high.

Rats. Ten experimental groups of rats were identified in a subset of the abovedescribed reports. Fisher et al. [START_REF] Fisher | Physiologicaliy based pharmacokinetic modeling with trichloroethylene and its metabolite. trichloroacetic acid, in the rat and mouse[END_REF] exposed groups comprising 6 female F344 rats each (bw 186 g) by inhalarion to 600 ppm TCE for 4 hr (group l). The venous blood concentrations of TCE and TCA were measured at various times. Under similar conditions, groups comprising 6 male F344 rats each (bw 236 g) were exposed to 529 and 505 ppm TCE (groups 2 and 3). The venous blood concentrations ofTCE were measured in group 2; the venous blood concentrations of TCA were measured in group 3.

Larson and Bull [START_REF] Larson | Metabolism and lipoperoxidative activity of trichloroacetate and dichloroacetate irrrats and mice[END_REF] exposed groups comprising 4 male F344 rats each (bw 331 g) by gavage to TCA at concentrations of 20 and 100 mg/kg (groups 4 and 5). The venous blood concentrations of TCA and DCA were measured. For die same reasons äs above, the DCA concentrations may be artifactually high.

Larson and Bull (16) exposed groups comprising 5 or 6 male Sprague-Dawley rats each (bw 404 g) by gavage to TCE at concentrations of 1.5 mmol/kg (197 mg/kg), 4.5 mmol/kg (592 mg/kg), and 23 mmol/kg (3,024 mg/kg) (groups 6-8). The venous blood concentrations of TCE, free TCOH, and TCA were measured at various times.

Prout et al. [START_REF] Prout | Species differences in response to trichloroBthylene. l: Pharmacokinetics in rats and mice[END_REF] exposed male rats of unspecified sirain (bw 190 g) by gavage to 1,000 mg/kg TCE (group 9). The same variables äs in mice were measured.

Templin et al. [START_REF] Templin | Factors affecting Species differences in the kinetics of metabolites of trichloroethylene[END_REF] exposed groups comprising 4 male F344 rats each (bw 275 g) with 0.76 mmol/kg (100 mg/kg) TCE (group 10). The venous blood concentrations of TCE, free TCOH, and TCA were measured.

Humans. A set of published human volunteer experimenis was also analyzed. were repeatedly exposed to 70 ppm TCE for 4 hr/day for 5 days. In addition to the variables measured in group l, the cumulated quantky of trichloroethanol glucuronide (TCOG) excreted in urine was recorded at various times.

Müller et al. [START_REF] Müller | Metabolism of trichloroethylene in man. il: Pharmacokinetics of metabolites[END_REF] exposed a group of humans (group 3) to 100 ppm TCE for 6 hr. The same variables äs for group 2 were followed. Müller et al. [START_REF] Müller | Metabolism of trichloroethylene in man. III: Interaction of trichloroethylene and ethanol[END_REF] exposed a group of volunteers (group 4) ro 50 ppm TCE for 6 hr/day for 5 days. The venous blood concentrations of free TCOH and TCA, and the cumulated quantities of TCA and TCOG excreted in urine were recorded. In the same articie, Müller et al. report exposure of two groups (5 and 6) of volunteers to 100 ppm TCE for 6 hr. For group 5, the exhaled air concentrations and venous blood concentrations of TCE, and the venous blood concentrations of free TCOH and TCA were measured. For group 6, only the venous blood concentrations of free TCOH and TCOG are reponed.

Finally, group 7 comprises volunteers that Stewart et al. [START_REF] Stewart | Experimental human exposure to trichloroethylene[END_REF]. exposed ro 198.3 ppm TCE, 7 hr/day (with a 30 min break in the middle) for 5 days. In this experiment, the exhaled air concentrarion and venous blood concentrations of TCE, and the cumulated quantities of TCA and TCOG excreted in urine were recorded.

Toxicokinetic and Stadsdcal Model

The description of the physiological model used can be found in Clewell et al. [START_REF] Vozeh | The use of population pharmacokinetics in drug development[END_REF]. The model equations were transcribed to a format suitable for MCSim [START_REF] Bois | MCSim: a Simulation program[END_REF]. Three modifications were made to the model: a) One compartment was added to describe closedchamber exposures of mice by Fisher et al. [START_REF] Fisher | Physiologicaliy based pharmacokinetic modeling with trichloroethylene and its metabolite. trichloroacetic acid, in the rat and mouse[END_REF]. V) The volume of the poorly perfused companment and c) the blood flow to the richly perfused comparunent were computed by difference at each Iteration so that the sum of the organ volumes equaled 82% of the body weight and the sum of organ flows equaled cardiac outpur. Given this reparameterization, the model has a total of 55 independent parameters. Only 45 of diese were adjusted for mice and rats and 40 for humans because there is no information in the above described data about the remaining 10 or 15 parameters. Neither do diese 10 or 15 parameters influence the fit to the data.

The statistical model describing uncertainries and variabiliries was constructed using a hierarchical population approach [START_REF] Gelman | Physiological pharmacokinetic analysis using population modeling and informative prior distributions[END_REF][START_REF] Wakefield | The Bayesian analysis of population pharmacokinetic modeis[END_REF], äs illustratecl in Figure l. It has two major components: the group level and the species or population level. At the group level, various concentrations or quantities (y) were measured. The expected values of these measuremenrs are a funcrion (f) of exposure level (E), time (t), a set of physiological parameters of unknown values [START_REF] Bois | Population toxicokinetics of benzene[END_REF], and a set of measured, covariate parameters ((p) such äs body weight. E, t, 6, and (p are experiment specific. All animal or human subjecis in an experiment were supposed to have behaved similarly from a toxicokinetic point of view. The funcrion / is the pharmacokinetic model described above. The concentrations or quantities actually observed are also affecied by measurement error and interindividual variability within the group. Since the data are aggregated at the group level, it is not possible to reliably disentangle the two sources ofvariability. The corresponding errors were assumed to be independent and log-normally distributed, with mean zero and variance O 2 (on the log scale). This corresponds to a proportional error model commonly used in pharmacokinetic modeling [START_REF] Gelman | Physiological pharmacokinetic analysis using population modeling and informative prior distributions[END_REF][START_REF] Wakefield | The Bayesian analysis of population pharmacokinetic modeis[END_REF][START_REF] Oavidian | Nonlinear Models for Repeated Measurement Data[END_REF]. The variance vecror O 2 had nine components for mice (since nine dirferent variables were measured) and eight components for rats and humans.

At the species level each component of the 9 parameter set was assumed to be distributed log-normally, with species averages p and variances 2? (in log scale). Some a priori knowledge of p and S 2 is available in the form of "Standard" values for sonne parameters. Uncertainry in these averages and variances

Prior Parameter Distriburions

A major advantage of physiological modeling is to provide a priori information on several of the mean parameter values for a species, äs well äs some idea of the variability of the parameters across individuais. Values for the hyperparameters M were set on the basis of the parameter values used by Clewell et al. [START_REF] Vozeh | The use of population pharmacokinetics in drug development[END_REF]. For VMTC and KMT (the Michaelis-Menten parameters for the formation of DCA from TCA) Clewell et al. assumed null values for mice and humans. A low value, with large uncertainty, was assumed here. To speciry S, the vector of a priori uncertainty (Standard deviarions [SDs]) on the average parameter values, a disrincrion can be made between the physiological parameters or partition coefficients (which are quite well known) and the other merabolic or pharmacokineric parameters (which are model specific and little known a priori). For the first group of parameters, values of S corresponding to coefficients of Variation (CVs) of 20-50% were assigned [START_REF] Bois | Population toxicokinetics of tetrachloroethylene[END_REF][START_REF] Bois | Population toxicokinetics of benzene[END_REF][START_REF] Gelman | Physiological pharmacokinetic analysis using population modeling and informative prior distributions[END_REF]. An exception is the volume of the tracheobronchial compartment, quite uncerrain and for which S was set to correspond to 200% CV. For the second group of parameters, a "vague" distribution was assumed and S was set to correspond to 200% CV (quite uncertain) or 500% CV (very uncertain). For those parameters "the data were left to speak," All priors on p were truncared (o ±2 X S or ±1.5 X S to avoid reaching unrealistic values. The prior SD, 2o, on group variability, was'set to 0.47 (corresponding to a CV of 50%) for all parameters. The square of that value was used äs parameter ß in the inverse-gamma distribution, a default choice for variance components in normal modeis [START_REF] Gelman | Bayesian Data Analysis[END_REF], togecher with a, a of l, giving a vague shape to chis prior. Table l gives the values of exp(M)-i.e. the geometnc mcanthe natural scale.

-and exp(S), which lie on

The Standard no-informative prior distrib-

n/ _ 1 -")\ _ _') -.')
or 2 x...x G" • was urion /'(Gi 2 ,...,^2) .

used for O 2 . To avoid the risk of overparameterizarion (a perfect fit could be obcained for some data sets, leading to implausible null escimates of variance), diese variance components were constrained to be larger than 0.29. That value corresponds to a CV of approximarely 30%, a reasonable, minimal value for die compounded measurement uncertainty and interindividual variability.

Starisrical Computation ofPosterior Parameter Distribudons

Information about the distribution ofa group's 0 parameter values (which in this case are ehe parameters of interest) is given by ehe experimental data and by the species parameters. The species parameters are determined by the 0 variables and their priors, which were set. The variances CT 2 are also estimated but are of lesser importance to us (however, high posterior variances may indicate a poor fit). From Bayes' theorem, the joint posterior distribution of the parameters to esrimate, W, a 2 , p, ^ly, (p, E, t. M, Z, Eo), is proportional to the likelihood of the data multiplied by the parameters' priors:

W^p^ly^E.t.M.S,! 2 ) -J\y\Q, a 2 , (p, E, t)']\6\ii, J?)'F(a 2 ) • ^pIM.S) • fl;2?12 2 ) [l]
The likelihood term is given by the normal measurement model: log(J) -Mlog/(9, (p, E, t)G 2 ), [START_REF] Kohn | Achieving credibility in risk assessment modeis[END_REF] As mentioned above, the prior distribution for O 2 is; P(aI 2 ,...,0" 2 ) -Gi~2 X ... xo"- 2 .

The prior distribution of each component of9 is an independent normal distribution: [START_REF] Charnick | Physiologicaliy based phannacokinetic modeling äs a tool for drug development[END_REF] with truncarion constraints.

Finally each component of p, or Z 2 is assigned an independent hyperprior distribution, \i -N(M,S 2 ) and £ 2 -inversegamma(2,£ 2 ), äs described above.

Current practice in Bayesian statisrics is to summarize a complicated high-dimensional poscerior distribution by random draws ofthe vecror of parameters. This is currently the most effecrive way ro perform high-dimensional numerical Integration. Further simulations can then be performed to compute, under specified conditions, posterior distributions of quantities of interest, such äs various measures more closelv related ro cancer risk than exposure to TCE. Because there are many parameters to esrimate, a combination ofGibbs sampling and Metropolis-Hasring sampling was used to perform a random walk through the posterior distribution. These iterative sampling procedures are parricularly convenient in the case of hierarchical modeis. They belong ro a class of Markov chain Monte Carlo (MCMC) techniques that has recently received much interest {10, [START_REF] Gelfand | Sampling-based approaches to caiculating marginal densities[END_REF][START_REF] Gelfand | Illustration of Bayesian inference in normal data modeis using Gibbs sampling[END_REF][START_REF] Gelfand | Bayesian analysis of con-Strained Parameter and truncated data Problems using Gibbs sampling[END_REF][START_REF] Gelman | Iterative and non-iterative Simulation algorithms[END_REF][START_REF] Tanner | Tools for Statistical Inference -Observed Oata and Data Augmentation Methods[END_REF][START_REF] Wakefield | Bayesian analysis of linear and non-iinear population modeis using the Gibbs sampler[END_REF]. Three independent Markov chain Monte Carlo runs were performed for each species. Convergence was monitored using the method ofGelman and Rubin [START_REF] Gelman | Inference from iterative Simulation using multiple sequences (with discussion)[END_REF].

Posterior Distribution ofPredicrions

The model was used to compute, a posteriori, several Surrogate exposure metrics. For lung tumors, the dose metrics proposed are the lifetime average daily area under the chloral concentrarion-time curve (LAD-AUC, in mg-hr-L" 1 ) in the tracheobronchial region, and the maximal chloral concentration achieved in the tracheobronchial region (Oma' ln n^g'L" 1 ); for kidney tumors, metrics computed are the lifetime average daily amount of cytotoxic metabolites (originaring from dichlorovinylcysteine) generated by gram of kidney (LAD-A, in mg-g~1); for liver tumors, the LAD-A UC and C"ax ofTCA and DCA are the proposed metrics.

To obtain the distribution of Surrogate dose measures, several exposure scenarios were simulated for each species (either .continuous exposure through Inhalation or drinking water, Inhalation exposure 8 hr per day, 5 days per week, inhalation exposure 7 hr per day, 5 days per week, or gavage once per day, every day). A population of 1,000 individuais was simulated by sampling for each one a random parameter vector from N(p.,£), for a random set of the final estimates of p and £. This sampling accounts for covariance becween values of the population parameters, since the l ,000 parameter sets are random draws from their joint (mulrivariate) distributions, not just from the marginal distributions. These simularions required sampling several parameters that could not be estimated wich the dara at hand. The sampling distributions of these parameters (summarized in Table 2) were defined on the basis ofClewell et al. estimares (l). In the absence of relevant information, no covariance was specified between those parameters.

Results

After a few thousand iterarions, the trajectory of each parameter oscillates randomly around a mean value, and these oscillations have stabilized to a starionary regime. Remember that the simularions converge ro a distribution, not to a point. For mice and humans, 7,000 iterarions wert necessary to reach convergence; for rats 12,000 had ro be performed. One of every 5 of ehe last 5,000 simularions of three independent Markov chains were recorded, yielding 3,000 sets of parameter values from which the inferences and predicrions presented in the following were made.

Quality of Data Adjustment

Figure 2 presents die data values predicted for each species versus their observed counterparts Table 2. Sampling distributions of the unadjusted parameters. All numbers are on the natural scale. (all data values are concentrations). Predicrions were made with ehe parameter set ofhighesc posterior density. For a perfect fit, all points would fall on the diagonal (equalky of predicred and observed values). Such an adjustment is not expected given the analyrical measurement errors in the data, but the deviadons are small and the fit seems overall reasonable. The graph is presented on log-log scale, since the errors are assumed to be lognormally disu-ibuted and span a wide ränge. The residuais are evenly spread along the diagonal, in particular for mice. For ratä, there seems to be one ouclying point in the venous blood concentrations offree TCOH, the model fitting well all other data points in the same experiment. The fit to human data leaves four groups of points with high residuais. There seems ro be one oudier in the TCA blood concentration data of Monster et al. [START_REF] Monster | Kinetics of trichloroethylene in repeated exposure of volunteers[END_REF], and the last points are very variable. More troublesome is the systemaric underestimarion, by a factor of5, ofTCE concentration in exhaled air during exposure for the experiments of Muller et al. [START_REF] Müller | Metabolism of trichloroethylene in man. il: Pharmacokinetics of metabolites[END_REF][START_REF] Müller | Metabolism of trichloroethylene in man. III: Interaction of trichloroethylene and ethanol[END_REF].

The posterior means of the intragroup SDs 0 (representing measurement error and intersubject variability) are mostly between 0.3 and 0.5 (corresponding to coefficients of Variation ofabout 30-50%). Larger values are found in mice for the venous blood concentration ofTCE (ü = 0.55), caused by the "noisy" data ofFisher and Allen (12) and of Prout et al. [START_REF] Prout | Species differences in response to trichloroBthylene. l: Pharmacokinetics in rats and mice[END_REF], for the blood concentration of DCA (ü = 0.60) due to the noise and underprediction ofthe data (14,16,18}, and for the blood concentration of free TCOH (ü = 0.65) in the data of Prout et al. in which various animals were observed at various times. For rats, the blood concentration of DCA (G = 1.14) seems to be systematically underpredicted. For human;,, äs menrioned above, the concentration of TCE in exhaled air in the experiments of Müller et al. [START_REF] Müller | Metabolism of trichloroethylene in man. il: Pharmacokinetics of metabolites[END_REF][START_REF] Müller | Metabolism of trichloroethylene in man. III: Interaction of trichloroethylene and ethanol[END_REF] is systematically overesiimated and some noise exists in the Siewart et al. [START_REF] Stewart | Experimental human exposure to trichloroethylene[END_REF] data. This leads to high residual errors (G = 0.79).

Figure 3 presents the fit to the mouse data of Fisher et al. [START_REF] Fisher | Physiologicaliy based pharmacokinetic modeling with trichloroethylene and its metabolite. trichloroacetic acid, in the rat and mouse[END_REF]. The residual error is small, albeit with some degree of autocorrelation. But, by their nature, these data are prone to exhibiting such dependency of errors and are quite difficult to model.

Fits to human data are crucial to risk assessment and human toxicology of TCE. Figures 4567show that very nice fits can be obtained with the model to a ränge of data. the TCE blood concentration data in the decay portion. The two "misfits" are cenainly related. However, me venous blood TCA and TCOH concentrations fi-om the same experiments are well fitted (data not shown). A similar Situation is observed in mice and rats, for example, for the DCA data.

Posterior Parameter Distributions

The joint discriburion ofall parameters is obtained in Output of the Markov chain Monte Carlo simularions. This allows considerarion ofmarginal distriburions (distriburions of the parameters considered individually) but also ofcorrelarions ofany Order. Table 3 summarizes the distriburions of the species-level parameter values obtained in the last 1,000 iterations of the three runs performed (results of the three runs are pooled, and the distriburions are established with 3,000 values). The geometric means can be interpreted äs representing the values for an "average" mouse, rat, or human. Note that the columns of geometric Standard deviarions (GSDs) represent group variability among the species. Means could be given for each animal or human group defined in the data secrion above, buc the tables are too large ro be presented here.

The following summarizes the informarion the simulations give on the various strains or individuais studied. Overall, the parameters retain physiologically plausible values.

Mice. For mice the posterior mean values for flows, volumes, and partition coefficients and most metabolic paramerers are not very different from their prior mean. However, KM (oxidative affinity for TCE) is rwice äs high äs a priori estimated. Noticeable differences are also found for KEHBC (biliary excretion rate ofTCOG), which decreases by a factor of 7, KEHRC (enteroheparic recirculation rate ofTCOH), VMTC and KMT (Michaelis-Menten parameters for the reducrion ofreduction ofTCA to DCA), KUTC (urinary excretion ofTCA), the last four parameters being higher by a factor of2, KFC (production ofDCVC from TCE), twice less important than a priori assumed, VMTBC (V^ for TCE in Clara cells) is also lower, but with a large uncertainty, and finally KTSD (transport rate from stomach to duodenum) posterior mean is somewhat higher than its prior escimate. Uncenainties (SDs) about all these geometric means ränge from a few percencs (for physiological parameters) up to a facror of2 for son-ie metabolic parameters. These uncertainties are usually much lower than the prior uncertainties, showing that subscantial informarion on about all parameters has been gained from the experimental data.

Variabilities, äs estimated by the intergroup GSD (Table 3), ränge from 1.23, which corresponds to a CV of about 20% for some organ volumes, to 2.7 for KAD (intesrinai absorption rate, from duodenum ro liver). Metabolic parameters have intergroup variabilities of at least 1.34 (about 30% CV). Differences between groups do not seem to be caused by differing sexes or exposure levels, äs no such pattern emerges from examination of group means. Strain cannot be a factor, since only B6C3F; mice were studied. Differences should therefore be ascribed to interindividual variability or to differences between laboratories (which could have unreported experimental differences, such äs animal providers). Note that, a posteriori, there does not seem to be a parricular problem with the DCA measurements in Larson and Bull [START_REF] Larson | Metabolism and lipoperoxidative activity of trichloroacetate and dichloroacetate irrrats and mice[END_REF][START_REF] Larson | Species differences in the metabolism of trichloroethylene to the carcinogenic metabolites trichloroacetate and dichloroacetate[END_REF] data (groups 25-29) or Templin et al. ( 18) data (groups [START_REF] Gelfand | Bayesian analysis of con-Strained Parameter and truncated data Problems using Gibbs sampling[END_REF][START_REF] Gelman | Iterative and non-iterative Simulation algorithms[END_REF][START_REF] Tanner | Tools for Statistical Inference -Observed Oata and Data Augmentation Methods[END_REF]. The metabolic parameters directiy related to DCA are not systemarically different for these groups, and the fits to the data are äs good äs for other experiments. Only two DCA concentrarion-time poinrs (at 0.25 hr) in experiments 25 and 26 (14) may be too high (the model underpredicts them by a factor of 2 or 2.5), but this may be simply due to noise in the data.

Rats. For rats the posterior mean values for most parameters are dose to their prior mean. The largest differences are found for the scaling coefficients of the volume of distribution ofTCOH (VDBWC, increased by a factor of 1.4), and of DCA (VCDCAC, decreased by a factor of 1.4), the fracrional split ofTCE to TCA (PO) doubled, and the enteroheparic recircularion of parameter of TCOH (KHERC) tripled. SDs for these geometric means reach a factor of 3 and tend to be higher than those for mice (this can be explained by the smaller rat data set).

Variabilities, äs estimated by the intergroup GSD, also tend to be higher for rats: they ränge from l .32 to 3.6 for KAD (duodenum to liver absorption rate). Differences between groups, most apparent for KAD, the urinary excretion ofTCA (KUTC), and the volume of distriburion ofTCA (VCTCAC), cannot be ascribed to sex, strain, exposure level, or laboratory, äs no parricular pattern emerges from examinarion of group means. Differences are therefore due to interindividual variability. Here also there does not seem to be a parricular problem with DCA measurements in groups 4 and 5 {14). Metabolie parameters direcdy related to DCA are not systematically different for these groups, and die slight underpredicrions ofdie model for early time points (at most 70%) could be due to rneasurement uncertainiy.

Humans. The ratios of posrerior to prior mean values for metabolic parameters in humans ränge from a factor of 0.2 for VMTC (the maximal rare of DCA formadon from TCA) to a factor of6 for KEHBC (the biliary excretion ofTCOG). The difference for VMTC is actually a nice result; without imposing a priori a null value to this parameter, the resuking posterior is very low, indicating that according to the human data very little DCA is produced, even if this observation is indirect (i.e., this result is imposed by the implicit mass balance of the other metabolkes in humans). SDs for these geometric means are also quite higher than for animals, and reach a factor of3.2. This, äs for rats, can be explained by the small human data set.

Interestingly, variabilities for physiological parameters are systematically higher than for animals but about the same for metabolic parameters. DifFerences between groups cannot be ascribed to sex, since only males were studied. They may be due to interindividual variability. The subjects studied by Müller et al. [START_REF] Müller | Metabolism of trichloroethylene in man. il: Pharmacokinetics of metabolites[END_REF][START_REF] Müller | Metabolism of trichloroethylene in man. III: Interaction of trichloroethylene and ethanol[END_REF] have much higher blood over air partition coefficients than subjects in other studies. This is linked to the poor fit of the model for the same subjects. The model cannot accommodate the (apparently) differing blood-air partition coefficient observed during exposure and after exposure. This could be linked to an experimental peculiarity in exhaled air concentrarion measurements for those studies.

Table 4 shows the highest covariances between pairs of parameters for human group 4).

2 [START_REF] Oavidian | Nonlinear Models for Repeated Measurement Data[END_REF]. Similarly, high correlations are obtained for every animal or human group. These covariances can be up to 0.81 (between VMOC and KMO, Figure 8) or even 0.94 (between the parameters VMRC and KMR). Any Simulation neglecting to estimate these covariances will produce incorrect predictions, since these parameters cannot be sampled independendy without producing highiy improbable combinations and hence highiy improbable predicrions.

Piedicdons of Cancer Dose Metrics

Additional subjects were simulated by sampling parameier values from the esrimated population distributions summarized in Table 3 and from the additional distributions given in Table 2. Sampling took inro account paramecer covariance for the parameters listed in Table 3, since it was made from l ,000 random samples of the MCMC runs, at equilibrium. Remember that these parameter sets are randomly drawn from their joint (mulrivariate) distriburion not jim from marginal distributions. Tables 5 to 8 summarize the posterior distributions of LDA-AUC and C"" for TCA and DCA in liver for several exposure scenarios. The results for lung, kidney were also computed (data not shown). The 95% posterior confidence intervals presented are defined äs the inrerval between rhe 2.5th percentile and the 97.5th percentile. Figures 9 and10 present histograms of the posterior distributions of TCA LDA-AUCand C"", in the liver for humans exposed continuously to l ppm TCE. The impact of uncenainty and variability is large but not unrealisric; in these extrapolations geometric SDs correspond to facrors from l .8 to 9 (for chloral concencration in human lung when exposed through drinking water). Except for one case, the values found by Clewell et al. ( 7) are all contained within the 95% posterior confidence intervais. The only area of disagreement is in the mouse response to low-dose drinking

Sensitivity ofDose Metrics to Modd

Parameters Results of a stepwise multiple regression of TCA LDA-AUC-with respect ro ehe model parameters in the case ofhumans-continuously exposed to l ppm TCE indicates that many parameters condition the results (data not shown). Among them figure key merabolic constants but also physiological parameters or partition coefficienis. The number of parameters conditioning TCA LDA-AUC explain the relatively large SDs for the risk estimates presented in Table 5. The same variables, in about the same order, influence TCA C"^ (data not shown).

Discussion

Data

The grouping by studies is somewhat arbitrary but was imposed on us by the aggregate reporring of the data. It can still be jusrified, since heterogeneity in batches of animals and differences in laboratory procedures are expected. As a consequence, all individuais were supposed to behave similarly in a given experiment. This is likely to lead to a moderate underestimation of variability. Note also that omer data sources could have been considered, in particular for humans {36-43}, These additional data seis might be usefui for external validarion ofthe model.

Method

. The proposed methodology is gaining interest and is establishing itself for the calibrarion and validarion ofPBPK modeis [START_REF] Bois | Population toxicokinetics of tetrachloroethylene[END_REF][START_REF] Bois | Population toxicokinetics of benzene[END_REF][START_REF] Gelman | Physiological pharmacokinetic analysis using population modeling and informative prior distributions[END_REF][START_REF] Fanning | Population toxicokinetics of benzene and its metabolites[END_REF][START_REF] Johanson | Development of new technique for risk assessment using physiologically based toxicokinetic modeis[END_REF]. A Bayesian analysis allows us to combine rwo fonns of informarion: a) prior knowledge from the scientific licerature, and b) data from Monster's experiments, in the context of the physiological compartmental model. Neither source of informarion is complete. If prior knowledge were suffident, experiments would not need to be performed, but data alone are insufficient to pin down all parameters ro reasonable values. Our goal was to fit the data using scientifically plausible parameier values. The posterior (i.e., after fitting) uncertainty for such parameters is underesrimated if all physiological parameters are considered perfectiy known and sei to predefined values, a practice too often adopted to alleviate computational bürden. Prior uncenainry about physiological parameter values needs to be taken into account, unless it can be proven negligible by sensitivity analysis of the posterior parameter distriburions (not by sensitivity of the final predicrions to be made). However, such a sensitivity analysis of the fitting process itself, in the case of PBPK modeis, is more difficult to perform than simply considering all parameters uncertain. To obiain samples from the joinr posterior distribution of all parameters, MCMC sampling was used. Figure 11 is an illustrarion of MCMC sampling compared to simple Monte Carlo sampling. In the former, the values drawn for each parameter start from the prior distribution and converge, äs iterations progress, to a data-adjusted, or updated, posterior distribution. The posterior density corresponds to the product ofthe prior density by the data likelihood. In the case of simple Monte Carlo sampling, all values are drawn from the same distribution (equivalent to a nonupdared prior). Beyond improving the fit, the method used here also provides distributions of esrimates directiy usable äs inputs for uncertainty analysis of cancer dose-response relarionships. In addition, the posterior distributions of Table 3 can be taken äs new priors in ftiture smdies. Finally, it can be checked a posteriori that strong correlarions exist between parameters (Table 4). A calibration neglecring to estimaie and account for these covariances would have produced incorrect estimates of uncertainty, since these parameters cannot be sampled independently without producing highiy improbable combinarions of values and hence highiy improbable predicrions. Another sensitivity issue stems from the fact that when good prior information is missing the definition of some priors is vague and somewhai arbkrary. Sensitivity analyses with respect to those priors ideally should be performed. However, in the context of a complex PBPK model, such sensidvity analyses would involve very heavy computarions.

Results

Interindividual human variability of TCE metabolism, äs estimated here, is not very large-GSDs of merabolic parameters ränge from a facior of 1. Natural Logarlthm öl TCA AUC-LAD in Human Liver Figure 9. Posterior distribution histogram (n = 1,000) of the natural logarithm of TCA LAD-AUC in human liver, for a continuous 1-ppm inhalation exposure Isee Table 5). The spread of these model-predicted values is conditioned by uncertainty and variability. The smooth line represents the corresponding normal approximation [geometric mean: log(88l = 4.48; GSD: log(2.5) = 0.92). were not discarded from the data set. The model is not much affected by the misfit, and metabolite levels are well predicted. The posterior predictions for risk measures are affected by expectedly large uncertainries and some degree of variability. Uncertaindes depend on species (condirioned by the amount of data available for that species), end points (still conditioned by the data), or exposure levels and patterns (since different parameters or combinations thereof condition outcome in different siruations). Variabllities seem to be of about the same magnitude in small groups of humans and animals. For the modeling of animal cancer bioassay internal exposures or human population exposures, the variability found here [START_REF] Louis | Assessing, aecommodating. and interpreting the influences of heterogeneity[END_REF]. The spread of these model predicted values is conditioned by uncertainty and variability. The smooth line represents the corresponding normal approximation (geometric mean: log(3.9) = 1.36; GSD: log(2.6) = 0.96).

would be damped by averaging effects. Uncertainty would therefore dominate, and variability could be neglected, in a first approximation. This would require condidoning internal exposure esumates at various dose levels on the same parameter vectors; exposure groups would not be simulated independently.

Finally, one of the challenges to modeling in toxicology is the füll exploitarion of the numerous data sets collected during epidemiological or occupadonal hygiene studies, and generally in settings where exposure levels are unknown. Most of the rimes very simplisric analyses of such data are performed because oflack of experience in more powerfui methodologies. There is no difficulty, in the above statistical framework, in considering exposure äs a paramcter or function to esrimate. A major problem, however, resides in accounting fully for the uncertainties scemming from unknown time-varying exposures. The impact of pamcular functional forms for the time evolution of exposure has not yet been thoroughiy studied and validated. As progress is made on such questions, toxicokineric modeling will become a more powerfui and widespread tool for drug development and toxicity assessment. A publidy accessible database of individual animal and human data on kinetics and metabolism ofmajor solvents should be gathered and offered to public access. This would allow a standardizarion ofanalyses and their improvement.

Figure

  Figure 1. Graph of the statistical model describing the

  Abbreviations: BW, body weight; duod., [luodenum; Ke, Elimination rate; K/, formation rate; K,,, Michaelis-Menten coefficient: ox. oxidative metabolism; TB, tracheobronchiai; V^g^ maximal rate. ^caled parameter = scaling formula x scaling coefficient. Units: weights in kg. flows in L/hr. volumes in L, kinetic parameters in mg/hr, mg/1. or hr' (;). For all parameters the scaling coefficients were assumed to be log-normally distributed with truncations at 12 SDs except where indicated. 'Measured values given in the data section were used when available. 'Truncation at -2 x SDs and +1.5 x SDs to respect summation constraints.

'Figure 2 .

 2 Figure 2. Predicted versus observed data values (all concentrations or quantities) for the Monte Carlo iterations of highest posterior probability. The outlying points for humans are 2 points in Monster et al. [20,21} experiments (see Figure5) and misfitted points in Müller et al.[START_REF] Müller | Metabolism of trichloroethylene in man. il: Pharmacokinetics of metabolites[END_REF][START_REF] Müller | Metabolism of trichloroethylene in man. III: Interaction of trichloroethylene and ethanol[END_REF] experiments.

Figure 4 .

 4 Figure 4. Maximum posterior probability fit of Monster et al. {20,21} human data on TCE concentration in exhaled air during and arter inhalation exposures. Dark circles: repeated exposures to 70 ppm TCE; open circles: 4-hr exposures to 70 ppm TCE; crosses: 4-hr exposures to 140 ppm TCE.

Figure 5 .

 5 Figure 5. Maximum posterior probability fit of Monster et al. [20.21) human data on TCA concentration in venous blood during and after TCE inhalation exposures. Dark circles: repeated exposures to 70 ppm TCE: open circles: 4-hr exposures to 70 ppm TCE; crosses: 4-hr exposures to 140 ppm TCE. Note the dispersion of points at later times.

Figure 6 .

 6 Figure 6. Maximum posterior probability fit of Monster et al. [20,21) human data on cumulated TCA quantity excreted in urine during and after TCE inhalation exposures. Dark circles: repeated exposures to 70 ppm TCE; open circles: 4-hr exposures to 70 ppm TCE.

Fignre 7 .

 7 Fignre 7. Maximum posterior probabitity fit of Monster et al. (20,21) human data on total TCOH concentration in venous blood during and after TCE inhalation exposures. Dark circles: repeated exposures to 70 ppm TCE: open circles: 4-hr exposures to 70 ppm TCE; crosses: 4-hr exposures to 140 ppm TCE.

Figure 3 .

 3 Figure 3. Evolution of TCE concentration in the exposure chamber of groups of mice (13) äs a function of time. The continuous lines show maximum posterior probability fits.

aVMOCFigure 8 .

 8 Figure 8. Correlation between the natural logarithms of VMOC (l<n" for oxidation of TCOH to TCA) and KMO [corresponding («n,] tor human group 2 (21}}. The correlation coefficient is 0.81 (see also Table4).

"

  Inhalation exposures in ppm; oil gavage and drinking water exposure in mg/kg/day. 'Cl means confidence interval. 'Continuous exposure. 'txposure 8 hr per day. 5 days per week. "Exposure 7 hr per day. 5 days per week. 'Gavage once per day, even/ day.

Figure 10 .

 10 Figure10. Posterior distribution histogram (n= 1,000) of the natural logarithm of TCA C^ax in human liver. for a continuous 1-ppm inhalation exposure (see alsoTable 5). The spread of these model predicted values is conditioned by uncertainty and variability. The smooth line represents the corresponding normal approximation (geometric mean: log(3.9) = 1.36; GSD: log(2.6) = 0.96).

Figure 11 .

 11 Figure 11. Illustration of Markov chain Monte Carlo (MCMC) sampling, compared to simple Monte Carlo sampling. In MCMC sampling, the values drawn for a Parameter 6 (circles) Start from the prior distribution and converge, äs iterations progress, to a data-adjusted, or updated, posterior distribution. The posterior density corresponds to the product of the prior density by the data likelihood. In the case of simple Monte Carlo sampling (crosses), all values are drawn from the same distribution (equivalent to a nonupdated prior).

  Monster et al. (20) exposed volunteers (group l-average weight, 69.8 kg; alveolar Ventilation rate, 16.7 L/hr; fraction of weight äs fat, 15%) to 70 and 140 ppm TCE for 4 hr. The exhaled air concentrations and venous blood concentrations of TCE, venous blood concentrations of free TCOH and TCA, and the cumulated quanrity of TCA excreted in urine were recorded. In 1979, Monster et al. (21) reponed another set of experimenrs in which a group of volunteers (group 2-average weight, 80.2 kg; alveolar Ventilation rate, 16.7 L/hr; fraction of weight äs fat, 15%)

y, experimental data; o 2 , variance of the experimental measurements.

	1. Graph of the statistical model describing the dependence relationships between several groups of variables. Symbols are P, prior distributions; |i, mean parameters for a species; 2?, variances of the species-level parameters; E, exposure; t. experimental sampling times; 9, unknown "average" physiological parameters for the individuais of a group; 9, measured physiological parameters; /, toxicokinetic model; • was acknowledged under ehe form of a priori log-normal distriburions for ehe population means p (with hyperparameters M and S) and a Standard inverse gamma distribution, with Parameters a =1 and ß = £ 2 for the popu-lation variances Z 2 (see section below on a priori parameter values). Three types ofnodes are featured in Figure l: • Square nodes represent variables for which the values were observed, such äs y or <p; were fixed by the experimenters, such äs E and t; or were fixed by our-selves, such äs the prior on p and Z 2 . • Circle nodes represent unknown variables, such äs O 2 , 9, p, or Z 2 . • The triangle represents the deierministic physiological model /. An arrow between two nodes indicates a direct statistical dependence between the variables ofthose nodes.

Table 1 .

 1 Prior population geometric means, exp(M), and associated geometric Standard deviations, exp(S), for the PBPK model scaling coefficients. All numbers are on the natural scale. The GSDs measure uncertainty about the mean.

		Scaling	Scaling	Prior popi
	Parameter 3	coefficient	formula	Mice
	Body weight Cardiac Output Alveolar Ventilation rate	BW QCC QPC	BW 0 -75 BW 075	ti 16(1.34) 24(1.34)
	Blood flows Fat Gastrointestinal tract	QFC QGC	QCC • BW-75 QCC • BW°7 5	0.05(1.47) 0.14(1.34)
	Liver Muscie and skin Tracheobronchial	QLC QSC QTBC	QCC • BW 075 QCC • BW"-75 QCC • BW 075	0.02(1.34) 0.25(1.34) 0.005 (2.0)
	Volumes
	Fat	VFC	BW	0.07(1.47)
	Gastrointestinal tract	VGG	BW	0.04(1.22)
	Liver	VLC	BW	0.05(1.22)
	Other visceras	VRC	BW	0.05(1.22)
	Tracheobronchial	vTBC	BW	0.0007(1.22)
	l^TCOH	VOBWC	BW	0.65 (2.0)
	^TCA	VDTCAC	BW	0.24(2.0)
	1<,DCA	VDDCAC	BW	0.2(2.0)
	Partition coefficients
	Blood/air	PB		14(1.6)
	Fat/blood	PF		36(1.6)
	Gut/blood	PG		1.8(1.6)
	Liver/blood	PL		1.8(1.6)
	Richly perfused/blood	PR		1.8(1.6)
	Slowly perfused/blood	PS		0.75(1.6)
	Tracheobronchial/blood	PTB		1.8(1.6)
	Metabolie parameters
	l^aJCE-> ox.	VMC	BW 075
	^TCE->ox.	KM
	TCE/TCA ratio ^JCOH-»TCA	PO VMOC	BW 075
	^TCOH-^TCA IroJCOH-DCA	KMO VMRC	BW°7 5
	i<",TCOH->DCA	KMR
	1<",JCOH-^ TCOG	VMGC	BW 075
	<nTCOH-»TCOG	KMG
	TCOG biliary K,	KEHBC	BW-025
	TCOH recirculation TCOG urine Ke	KEHRC KUGC	BW-0 -25 BW-°' 25
	l ' ' ™, TCA-> DCA	VMTC	BW 075
	K^ TCA -> DCA TCA urine Kg	KMT KUTC	BW-025
	<fTCE->DCVC	KFC	BW-0 ' 25
	TBI/nigJCE-ox.	VMTBC	BW 075
	TB<",TCE->ox.	KMTB
	Kduod. -> liver	KAD
	Kstomach -> duod.	KTSD
	14"DCA->...	VMDC	BW 075
	Kn,OCf\->... DCA urine Ke	KMD KUDC	BW-025

  The model has been formally fitted and the adjustments are systematically better than those, already reasonable, obtained by Clewell et al. (l). However, äs menrioned above, some data remain poorly fitted. The model overesrimates exhaled air concentrations measured by Müller et al., while underesrimaring part of

Table 3 .

 3 Summary statistics of the species level (i.e., population) posterior parameter distributions for trichloroethylene. The GSDs measure variability ."All numbers are on the natural scale. Geometrie mean and GSD are in parentheses and are given for each estimated population parameter. The GSD, in that case, measures uncertainty in location or spread.

	Scaling	Mouse populatio	n posterior	Rat populatior	i posterior	Human populati ion posterior
	coefficient	Geo. mean	GSD	Geo. mean	GSD	Geo. mean	GSD
	BW	-	-	-	-	72 (8.25)	1.36(1.10)
	QCC	20.1(1.08)	1.25(1.04)	16.8(1.16)	1.38(1.09)	15.2(1.16)	1.41(1.12)
	QPC	21.8(1.08)	1.32(1.05)	23.1(1.15)	1.37(1.09)	16.1(1.16)	1.39(1.10)
	QFC	0.054(1.14)	1.34(1.06)	0.08(1.16)	1.39(1.10)	0.05(1.16)	1.47(1.12)
	QGC	0.18(1.08)	1.25(1.04)	0.14(1.15)	1.36(1.09)	0.18(1.17)	1.43(1.12)
	QLC	0.021(1.11)	1.29(1.05)	0.028(1.15)	1.36(1.09)	0.050(1.19)	1.42(1.11)
	QSC	0.247(1.11)	1.29(1.05)	0.32(1.15)	1.36(1.09)	0.21(1.16)	1.41 (1.11)
	QTBC	0.005(1.36)	1.48(1.11)	0.018(1.44)	1.52(1.15)	0.025(1.19)	1.43(1.12)
	VFG	0.063(1.12)	1.36(1.06)	0.13(1.21)	1.42(1.11)	0.20(1.13)	1.37(1.10)
	VGC	0.040(1.07)	1.23(1.03)	0.030(1.11)	1.32(1.07)	0.017(1.13)	1.37(1.10)
	VLC	0.050(1.07)	1.23(1.03)	0.034(1.11)	1.33(1.08)	0.026(1.13)	1.37(1.10)
	VRC	0.050(1.06)	1.23(1.03)	0.042(1.11)	1.32(1.07)	0.048(1.13)	1.37(1.10)
	VTBC	0.0007(1.07)	1.23(1.03)	0.001(1.11)	1.32(1.07)	0.0007(1.13)	1.37(1.10)
	VD8WC	0.55(1.33)	1.46(1.11)	0.9(1.50)	1.61(1.20)	0.97(1.24)	1.51(1.15)
	VDTCAC	0.26(1.19)	1.41(1.08)	0.3(1.27)	1.55(1.16)	0.11(1.26)	1.50(1.16)
	VDDCAC	0.19(1.31)	1.54(1.13)	0.14(1.44)	1.58(1.19)	-	-
	PB	16.4(1.13)	1.44(1.09)	20.1(1.22)	1.41(1.12)	13.7(1.19)	1.52(1.14)
	PF	30.6(1.15)	1.41(1.08)	32.1 (1.24)	1.45(1.12)	53.0(1.22)	1.50(1.15)
	PG	1.71(1.21)	1.37(1.08)	1.29(1.29)	1.49(1.13)	6.23(1.33)	1.51(1.15)
	PL	1.73(1.20)	1.38(1.08)	1.32(1.30)	1.48(1.13)	6.69(1.32)	1.52(1.16)
	PR	1.75(1.21)	1.38(1.07)	1.31(1.30)	1.47(1.13)	5.05(1.28)	1.51 (1.16)
	PS	0.76(1.21)	1.38(1.07)	0.55(1.29)	1.49(1.13)	2.70(1.23)	1.49(1.15)
	PTB	1.82(1.21)	1.38(1.08)	1.30(1.29)	1.48(1.13)	6.75(1.32)	1.52(1.17)
	VMC	38(1.15)	1.74(1.15)	13.2(1.30)	1.45(1.13)	43.8(1.97)	1.70(1.28)
	KM	0.47(1.57)	2.34(1.28)	0.21 (2.40)	1.82(1.35)	0.54(2.35)	1.76(1.35)
	PO	0.044(1.27)	1.46(1.11)	0.04(1.29)	1.43(1.13)	0.10(1.36)	2.03(1.28)
	VMOC	1.41(1.49)	1.49(1.16)	0.08 (2.28)	1.75(1.32)	16.9(2.11)	1.64(1.25)
	KMO	0.23(1.91)	2.52(1.40)	0.33 (2.66)	1.78(1.36)	321(2.15)	1.66(1.27)
	VMRC	0.91(1.61)	1.96(1.31)	0.11(2.75)	1.77(1.35)	6.82(1.67)	1.49(1.16)
	KMR	8.50 (2.06)	1.69(1.24)	10.6(2.94)	1.80(1.36)	19.9(1.78)	1.53(1.20)
	VMGC	83.1(1.37)	1.55(1.18)	138(1.96)	1.57(1.19)	7.46(1.76)	1.56(1.20)
	KM6 •	21.1 (1.70)	2.14(1.36)	16.9(2.14)	1.61(1.23)	11.5(1.87)	1.58(1.21)
	KEHBC	0.15(1.35)	1.50(1.12)	0.97 (2.37)	1.90(1.38)	5.99(1.64)	1.61 (1.23)
	KEHRC	0.024(1.81)	2.04(1.38)	0.030 (2.50)	2.36(1:59)	0.59(1.52)	1.57(1.21)
	KUGC	0.75(1.26)	1.43(1.11)	0.54(1.51)	1.58(1.18)	1.25(1.45)	1.54(1.17)
	VMTC	0.10(1.56)	1.63(1.22)	0.18(1.85)	1.73(1.29)	0.009 (2.00)	1.69(1.30)
	KMT	2.22 (2.09)	1.74(1.26)	13.3(2.46)	1.72(1.29)	6.36(2.11)	1.79(1.39)
	KUTC	0.074(1.13)	1.34(1.06)	0.052(1.27)	1.60(1.17)	0.023(1.23)	1.45(1.14)
	KFC	0.75(1.55)	1.57(1.18)	2.27 (2.48)	1.79(1.33)	2.23 (2.77)	1.83(1.41)
	VMTBC	1.99(1.81)	1.62(1.23)	0.30(2.92)	1.82(1.37)	0.0042(3.16)	1.81 (1.36)
	KMTB	0.25 (2.24)	1.69(1.25)	0.26 (2.80)	1.76(1.34)	1.54(2.94)	1.85(1.41)
	KAD	1.14(1.36)	2.70(1.23)	0.54(1.60)	3.60(1.44)	-	-
	KTSD	17.3(1.24)	1.41(1.10)	11.6(1.42)	1.61(1.20)	-	-
	VMDC	118(1.93)	1.59(1.21)	41.3(2.33)	1.84(1.35)	-	-
	KMD	1,200(1.93)	1.57(1.20)	1,212(2.60)	1.76(1.32)	-	-
	KUDC	0.044(2.27)	1.70(1.25)	0.05(2.86)	1.83(1.37)	-	-
	Geo, geometric. "

Table 4 .

 4 Correlation coefficients among estimated model parameters for human group 2[START_REF] Monster | Kinetics of trichloroethylene in repeated exposure of volunteers[END_REF]. Parameter pairs for which correlation coefficients were higher than 0.5 are in bold face.

		QCC	QFC	QGC VDTCAC	PF	PO	VMOC	KMO VMRC KMR VMGC KMG
	QCC	1.00
	QFC	-0.25	1.00
	QGC	-0.54	0.50	1.00
	VDTCAC	0.07	-0.04	-0.06	1.00
	PF	0.55	0.55	0.02	0.00	1.00
	PO	0.03	0.00	-0.04	0.65	0.01	1.00
	VMOC	-0.10	-0.05	0.01	-0.01	-0.13	-0.13	1.00
	KMO	-0.11	-0.01	0.01	0.02	-0.11	0.22	0.81	1.00
	VMRC	0.02	-0.01	0.05	0.04	0.03	0.02	0.15	0.11	1.00
	KMR	-0.02	-0.04	0.04	0.10	-0.04	0.07	0.14	0.12	0.94	1.00
	VMGC	-0.10	0.01	0.02	0.11	-0.07	0.13	0.21	0.22	0.08	0.04	1.00
	KMG	-0.16	0.01	0.00	0.22	-0.13	0.26	0.06	0.22	-0.00	0.14	0.60 1.00

Table 5 .

 5 Posterior disfribution summaries for the liver tumor dose metric LAD-AUC of TCA concentration in liver." All numbers are on the natural scale.

		Mouse	LAD-AUC	Rat L, W-AUC	Hurr
	Exposure conditions 3	Geo. mean (GSD)	95% posterior CI"	Geo.mean (GSD)	35% posterior CI"	Geo. mean (GSD)
	Inhalation
	Ŵ	-	-	-	-	88(2.5)
		-	-	-	-	1,200(2.5)
	50"	-	-	-	-	1,500(2.
	W	500(2.1)	120-1,900	110(2.4)	18-700
	100"	-	-	-	-
	510-16,000 300 6	970(2.0)	270-3,600	230 (2.4)	39-1,300
	450°6	1,200(2.0)	330-4,400	280 (2.4)	44-1,600
	00°O	1,300(2.0)	370-5,000	310(2.5)	48-1,800
	ilgavage3
	57	-	-	290 (2.5)	48-1,700
	538	990(2.1)	230-3,900	350 (2.5)	58-2,200
	714	1,100(2.1)	250-4,400	400 (2.5)	66-2,500
	1,076	1,300(2.1)	290-5,200	460 (2.6)	77-3,000
	1.448	1,400(2.1)	320-5,900	510(2.6)	83-3,200
	Drinking water 0.0286 C • 7.6 C	-43(2.7)	-4.3-200	-17(2.5)	-2.8-110

Table 6 .

 6 Posterior distribution summaries for the liver tumor dose metric Cmax of TCA concentration in liver.3 All numbers are on the natural scale. Inhalation exposurss in ppm; oil gavage and drinking water exposure in mg/kg/day. ^l means confidence interval. °Continuous exposure. 'txposure 8 hr per day, 5 days par week. "Exposure 7 hr per day, 5 days per week. tavage once per day, every day.

		Mou: SO ^fngx	Ral • r • ^max	Hun ian C"a,
	Exposure conditions 3	Geo. mean (6SD)	95% posterior CI"	Geo. mean IGSD)	95% posterior CI"	Geo. mean (GSD)	95% posterior CI"
	Inhalation
	Ŵ	-	-	-	-	3.9 (2.6)	0.54-23
		-	-	-	-	53 (2.5)	6.9-270
	50"	-	-	-	-	77 (2.4)	12-390
	W	62(1.9)	17-200	10(2.2)	2.1-51	-.	-
	W	-	-	-	-	170(2.4)	28-830
	300°4 50 e	100(1.8) 120(1.8)	33-300 38-370	20 (2.3) 22(2.3)	4.2-97 4.6-120	--	--
	600°O	130(1.8)	4M10	24 (2.3)	4.8-130	-	-
	il gavage3
	57	-	-	18(2.3)	4.0-100	-	-
	538	81 (1.8)	26-260	21 (2.4)	4.4-120	-	-
	714	89(1.8)	29-290	23 (2.4)	4.6-130	-	-
	1,076	100(1.8)	32-340	26 (2.5)	4.9-150	-	-
	1,448	110(1.8)	33-370	28 (2.5)	5.0-170	-	-
	Drinking water
	0.0286 1: 7.6' :	-1.8(2.7)	-0.19-8.9	-0.80 (2.5)	-0.13-5.9	0.18(2.4) -	0.030-0.80 -
	'

Table 7 .

 7 Posterior distribution summaries for the liver tumor dose metric L4D--4ÜCof DCA concentration in liver.3 All numbers are on the natural scale. Inhalation exposures in ppm; oil gavage and drinking water exposure in mg/kg/day. 'Cl means confidence interval. 'Continuous exposure. ''Exposure 8 hr per day, 5 days per week. "Exposure 7 hr per day, 5 days per week. tavage once per day, every day.

	Exposure conditions"	Mouse Geo. mean (GSD)	LAD-AUC 95% posterior CI"	RatL' \D-AUC 95% posterior Geo. mean (GSD) C1"	Humi an iAD-AUC Geo.mean 95% posterior (GSD) CI 6
	Inhalation 1''	-	-	-	-	0.45 (2.2)	0.080-1.7
	W W	--	--	--	--	4.1(2.2) 4.9(2.2)	0.68-16 0.83-19
	W mi 300»	19(2.6) -32 (2.7)	3.2-120 -5.2-250	17(4.2) -29(4.1)	0.76-230 -1.5-390	-9.6 (2.2) -	-1.7-38 -
	450°6 00°O	37(2.7) 40 (2.8)	6.0-300 6.4-340	32(4.1) 34(4.11	1.7-430 1.9-450	--	--
	ilgavage3
	57	-	-	32 (4.0)	1.9-380	-	-
	538	33 (2.7)	5.1-270	37 (4.0)	2.1-420	-	-
	714	36(2.7)	5.6-310	39 (4.0)	2.3^(50	-	-
	1,076	41 (2.8)	6.3-350	43 (3.9)	2.6-480	-	-
	1,448	44(2.8)	6.8-400	45 (3.9	2.7-510	-	-
	Drinking water
	0.0286 C 7.6 C	-6.4 (2.6)	-0.94-39	-3.5(4.3)	-0.16-54	0.027 (2.0) -	0.0060-0.094 -
	'water administration of TCE, for which a
	lower amount of TCA and a higher amounr
	of DCA are predicted here, compared to
	Clewell er al. esrimates.

Table 8 .

 8 Posterior distribution summaries for the liver tumor dose metric Cmas of DCA concentration in liver.3 All numbers are on the natural scale. ppm; oii gavage and drinking water exposure in mg/kg/day. ^l means confidence interval. "Continuous exposure. ' ' Exposure 8 hr per day. 5 days per week. "Exposure 7 hr per day, 5 days per week. 'öavage once per day, every day.

		Moi use Cma,	RE itC^,	Hui manCnKK
	Exposure conditions 3	Geo. mean (GSD)	95% posterior CI"	Geo. mean (GSD)	95% posterior CI"	Geo. mean (GSD)	95% posterior CI"
	Inhalation 1' W 50" 100°1 00"	---2.0(2.9) -	---0.31-18 -	---1.3(3.7) -	---0.074-14 -	0.019(2.2) 0.17(2.2) 0.45 (2.3) -0.84(2.2)	0.0033-0.073 0.028-0.69 0.073-1.8 -0.14-3.4
	W 450°6 00°O	3.6(3.0) 4.1 (3.0) 4.4(3.0)	0.51-32 0.58-36 0.585-42	1.9(3.8) 2.0(3.8) 2.1 (3.8)	0.12-20 0.12-22 0.12-23	---	---
	llgavage3 57	-	-	1.8(3.8)	0.11-20	-	-
	538 714 1,076 1,448	4.0(2.9) 4.2 (2.9) 4.3(2.9) 4.4 (2.9)	0.54-32 0.56-35 0.57-39 0.58-40	2.0(3.9) 2.1 (3.9) 2.2(3.9) 2.25 (3.9)	0.12-22 0.12-23 0.13-25 0.14-26	----	----
	Drinking water o.02Q6 c 7.6 C	-0.27 (2.6)	-0.040-1.6	-0.17(4.4)	-0.0073-2.7	0.0011(2.0) -	0.00025-0.0039

-

Inhalation exposures in

This work has been supported by the D.S. Environmental Protection Agency.


1+ A Thomasson

S Geffroy

E Frejafon

D Weidauer

R Fabian

Y Godet

M Nominé

T Ménard

P Rairoux

D Moeller

J P Wolf
email: wolf@lasim.univ-lyonl.fr

LIDAR MAPPING OF OZONE EPISODE DYNAMICS IN PARIS AND INTERCOMPARISON WITH SPOT ANALYZERS

Keywords:

Continuous mapping of an ozone episode in Paris in June 1999 has been performed using a Lidar-DIAL System. The 2D ozone concentration vertical maps recorded over 33 hours at the Champ de Mars are compiled in a video clip that gives access to local photochemical dynamics with unprecedented precision. The Lidar data are compared over the whole period with point monitors located at 0, 50, and 300 m altitudes on the Eiffel Tower. Very good agreement is found when spatial resolution, acquisition time, and required concentration accuracy are optimized. Sensitivity on these parameters for successful intercomparison in urban areas is discussed.

Introduction

Differential Absorption Lidar (DIAL) has, in the recent years, been widely used to characterize urban and industrial pollution. Its unique feature of providing 2D-and 3D-maps of pollutant concentrations at high sensitivity (in the parts per billion range) and over large distances (several km) has appeared as extremely valuable to quantify the impact of spot emitters, monitor urban pollution [START_REF] Wolf | Encyclopedia of Analytical Chemistry[END_REF], or evaluate predictive numerical models [1].

A key issue, however, to further use the Lidar technique for enforcement purposes in environmental protection agencies is the evaluation of Lidar systems within the framework of the present standards. This evaluation process can be achieved with two different types of experiments: (1) Evaluation using reference gases within procedures in agreement with national standards [START_REF]VDI-DIN 4210[END_REF][START_REF] Ménard | [END_REF][START_REF] Eickel | Quality Assurance and Standardisation of Remote Sensing Methods[END_REF] and [START_REF]Elight Laser Systems GmbH, Elight Laser Systems[END_REF] Intercomparison with calibrated gas analyzers. In this latter case, the main difficulty is to find a site where the DIAL measurement (representing an average over some tens or hundreds of meters) can successfully be compared to values provided by spot monitors. This requires specific conditions where concentration gradients are small compared to the detection limits of the devices. In case of ozone, former intercomparison campaigns have therefore been performed in the countryside where no local nitrogen oxide s sources were present [START_REF] Goers | [END_REF]. Recently a campaign has been performed in Berlin (OLAK) in order to intercompare Lidar systems and airborne ozone analyzers in urban conditions [START_REF]GKSS Report 2000/24[END_REF]. Comparison with airborne measurements is difficult because the measured air volumes by the Lidars and the balloon-or aircraft-borne analyzers are never exactly the same.

We present here a continuous mapping of ozone in a large urban area, synchronously compared to spot measurements at different altitudes, over a 33 hour ozone episode. This continuous mapping, which has been displayed as a video clip [ref electronic journal version], depicts the whole ozone episode dynamics. Compared to former studies, in Athens [START_REF] Fiorani | [END_REF][START_REF] Weidauer | Advances in Atmospheric Remote Sensing with Lidar[END_REF][START_REF] Weidauer | [END_REF] or Seville [START_REF] Frejafon | [END_REF]8], the obtained succession of ozone 2D-maps (vertical profiles) provide significantly more information about local gradients and mass transfers.

Continuous intercomparison at three altitudes (up to 300 meters) moreover allowed to verify whether this evaluation procedure is suitable in urban areas and to find the origin of potential discrepancies between DIAL measurements and spot analyzers.

Experiment

In 1999, INERIS (1) , which is in charge in France of calibrating and evaluating optical systems such as DOAS and Lidar, organized a large Lidar ozone measurement campaign in Paris from July 12 to 20. This campaign was performed under the French Ministry of Environment's coordination (2) , in collaboration with AIRPARIF (Air Quality Network of Paris and the Region Ile de France). The main purpose was the evaluation of a&-ozone Lidar working in actual urban conditions.

A key feature to successfully achieve this study was to use a reliable, easy to operate DIAL system. The chosen system is a 'Lidar 510 M' model, manufactured by Elight Laser Systems. This mobile (van-integrated) all-solid-state DIAL system has been extensively described elsewhere [START_REF]Elight Laser Systems GmbH, Elight Laser Systems[END_REF]. Briefly, it is based on a flashlamp-pumped Ti:Sapphire laser, with a dual wavelength oscillator (for both reference A, o ff and probe A, O n wavelengths), which provides after frequency doubling and tripling some mJ between 250 nm and 290 nm. Both wavelengths position and linewidths are controlled using an optogalvanic reference cell INERIS: Institut National de l'Environnement Industriel et des Risques MATE: Ministère de l'Aménagement du Territoire et de l'Environnement (Galvatron). The laser beam is 10X expanded to emit radiation well below limits of eye safety requirements (according to VDI-DIN 0837).

The laser beam is sent into the atmosphere with a dual scanning periscope that also directs This DIAL provides concentration maps of O3, SO2, NO2, Benzene and Toluene. For ozone, the standard wavelength couple is X o ff = 286.3 nm and X O n = 282.4 nm. The manufacturer specifies a detection limit of 2 ug/m 3 (for 1 km integration length, 15 min. integration time)

and a maximum measurement distance of 2500 m, according to the VDI-DIN 3210 standard [START_REF]VDI-DIN 4210[END_REF]. Evaluation at INERIS using reference gases [START_REF] Godet | rapport INERIS (Institut National de l'Environnement Industriel et des Risques) -Loi sur l'Air -Convention 13/98[END_REF] yielded slightly higher detection limits (4-6 ug/m ) but longer maximum distance (3500 m).

The DIAL system was located at the Champ de Mars facing the Eiffel Tower. This site provided free optical path over 1.4 km, without major traffic roads, limiting local nitrogen oxides gradients. Reference ozone analyzers from AIRPARIF were located at three different levels at the Eiffel Tower (ground, 50 m. and 300 m.). Intercomparison between Lidar and spot monitors data could be obtained at these three altitudes over 33 continuous hours, during an ozone smog episode. The reference spot monitors form AIRPARIF (from "Thermo Electron" and "Environment S.A.") are specified with a detection limit below 5 u.g/m 3 . They are calibrated every 3 months using a NIST standard transfer, and maintenance is carried out twice a month. Sampling uses PFA-Teflon pipes of a few meter length. This equipment is completed by NOx and SO2 analyzers, temperature sensors, and, at 300m high, wind direction/velocity measurements (sonic anemometers).

Results

2D-maps of ozone concentrations have been recorded by accumulating 1000 shots in each measurement direction (500 on X on and 500 on A. ot f representing 1 minute) over 33 hours (Sat. For Rayleigh scattering (1013 mbar, 298 K) [10], this yields to a correction of-4 jag/m 3 . For Mie scattering, a first order empirical correction has been used, based on the meteorological visibility range VM [10]. In our case the visibility range of 13 km (clear atmosphere) yields a systematic correction of -10 j-ig/m 3 . The errors induced by these constant corrections are discussed below.

The snapshots selected from the video clip, in figure 2 ) is confined in a layer of 120-280 m thick close to the ground. At higher altitudes (from 280 m ->1500 m), a much higher concentration (80-150 |ig/m3) layer seems unperturbed by the NO emitted at ground level. This suggests that most of the traffic related NO has been consumed in the reaction converting O3 into NO2 within a vertical diffusion length of typ. 300 m (which corresponds to the urban layer). While depletion at low altitude exhibits a strong diurnal cycle, the ozone concentration above 300 m remains high regardless the daily hour. This behavior has been observed in other cities, and is referred to as the "tropospheric ozone storage layer" [START_REF] Wolf | Encyclopedia of Analytical Chemistry[END_REF][START_REF] Weidauer | [END_REF]. Notice also that small scale fluctuations appear within the storage layer and on the border of the storage layer and the mixing layer. This vertical double layers structure remains over the night until 7 a.m. (local time). From 7 a.m. to 12 p.m. a very interesting vertical mixing occurs, as shown in figures 2(c)-(g). The process occurs first locally (see localized ozone bubbles at about 600 m. from the Lidar system) and then on larger scale over the whole mixing layer. A major reason for this is convection and turbulence induced by solar heating of the ground and lower atmospheric air layers. Diurnal solar radiation also photodissociates the NO2 present at that time, the concentration of which has been enriched by the nighttime reactions between O3 and NO. The NO? photolysis creates NO + O* and thus regenerates ozone in the whole afternoon until 9 p.m. This well known photocycle leading to the Leighton relationship [9], although very simple, can reasonably explain the observed behavior, since ozone generation in this case is NOx-limited [11]. For a quantitative evaluation of the processes, numerical photochemical codes including volatile organic compounds (VOCs) reactions have to be used. Comparison of such models with the maps presented here, but this is beyond the scope of the present paper.

The concentration distribution in the afternoon of July 18 n is very homogenous and of very high absolute value (170-220 (.ig/m 3 ), characteristic of an ozone episode. Notice the limited Lidar measurement range, due to the very high ozone absorption. At this point, a change of the selected (A. o ff, A, O n) wavelength couple towards less absorbed wavelengths (300 nm) would have been judicious. However, we decided to keep all parameters identical during the whole episode.

In the evening of July 18 (figure 2(g)-(h)) the lower atmospheric layer clears up again due to the lack of solar radiation and the presence of traffic related NO emission. The following night dynamics (figure 2(i)-(j)) is similar to the situation of the night from July 18-19.

From the successive 2D-maps, ozone vertical profiles can be computed for any horizontal location. Figure 3

Intercomparison

As mentioned above, three of the measurement directions were chosen in order to analyze air volumes at the Eiffel Tower location as close as possible to the reference point sensors installed by AIRPARIF. depending on the measurement configuration (temporal and spatial integration). As it can be seen from these temporal profiles, the overall behavior as well as the absolute values are excellent agreement at every altitudes and over the whole period. More precisely, figure 5 presents the histogram of differences between the ozone concentrations measured by the sensors and the ones measured by Lidar: AC = Csensor -Cudar-The mean value of AC (offset) is of the order of 1 ug/m 3 , while the standard deviation on the difference (statistical errors) o( AC) is only a few ug/m 3 as well. This is particularly satisfactory since the measured values spans a very broad concentration range from 20 to 180 ug/m 3 . It is also interesting to observe that in stable and reasonably clear weather conditions, first order constant Rayleigh-Mie corrections are sufficient to obtain very satisfactory results. In atmospheric conditions exhibiting strong aerosol gradients this would obviously not be the case anymore. Further intercomparison statistics have been performed for different Lidar spatial resolutions (AR=200 m. and AR=1000 m ) and different "integration times" (15 minutes and 1 hour). On this latter point, it is important to notice that in a 15 minutes measurement cycle, the actual Lidar acquisition time for one reference point is only 1 minute (1000 shots averaged on each direction of the scan, see section 3). For the hourly values, four successive Lidar measurements at 15 minutes interval are averaged. The results are summarized in table 1. Best agreement is found for AR=200 m. Averaging over 4 measurements (hourly comparison) does not improve the statistical result, indicating that significant ozone concentration fluctuations occur on shorter timescales. An interesting feature is that spatial averaging on longer distances along the beam degrades the results as well. The reason is spatial fluctuations of the ozone concentration. Averages over longer distances are less comparable to the air volume measured by the spot monitor. This is very well illustrated by the observed negative offset increasing with altitude on the 1 km averaged results (table 1). As shown in figure 2, ozone is destroyed at low altitude at night. Since the beams are sent at finite angles (figure 1

Conclusion

Very satisfactory Lidar-sensor intercomparison can be achieved in actual urban measurement conditions results if the atmospheric spatial and temporal fluctuations are matched with the respective resolutions of the devices. In particular, a compromise has to be found between two

Figure Captions

  photomultiplier, through a motorised monochromator, in order to automatically select the

07/ 17 -

 17 figure 1, three of which corresponding to altitudes at the Eiffel Tower (900 m from the

  (a)-(j), very well depict the formation dynamics of the ozone episode in Paris. On figures 2(a)-(d) (Saturday July 17, 21:00 -Sunday July 18, 08:30, local time), the maps show with unprecedented realism the destruction of ozone at lower altitudes mainly by the traffic emitted NO at night. This lower ozone concentration (around 50 u-g/m 3

  shows the ozone vertical profiles at the level of the Eiffel Tower over the 33 hours. This figure very well summarizes the observations depicted above: ozone destruction at low altitude during the night, quasi homogenous storage layer above 300 m., overall ozone concentration increase due to solar radiation at daytime, mixing of both layers around 10 a.m. (local time, TU+2h) leading to homogenous high concentrations in the afternoon. However, this representation does not show the local dynamics and exchanges observed in the series of 2D-maps.

Figure 4 (

 4 a)-(c) shows the intercomparison between Lidar and spot analyzers at the 3 different altitudes (ground level, 50 m, and 300 m) with a range resolution AR on the Lidar profile of 200 m at the Eiffel Tower location. The experimental accuracy on the point sensors data are typically 15%, according to the users experience, while a statistical height 20m 50m 300m

  Ci/. '• treatment of the Lidar data yields experimental standard deviation between 15 to 20 ug/m3

  ), averaging over 1 km necessarily integrates lower ozone concentration values from low altitude leading to a negative offset compared to the concentration at the Eiffel Tower level. Spatial fluctuations of typical characteristic lengths of 50 m are also clearly observed on the video clip or the snapshots of figure 2.

opposite requirements: ( 1 )

 1 spatial averaging improves the signal to noise ratio (SNR) of the Lidar data and thus the accuracy of the concentration measurements, and (2) averaging over longer paths provides mean values that are less comparable to spot measurements because of local concentration gradients. In our conditions, the optimum parameters were AR=200 m associated with an accuracy of 15 ug/m J . However, these values are connected with the 1 minute time averaging. If only one measurement direction had been chosen, and intercomparison with only one spot monitor, the Lidar data could have been continuously averaged over 15 minutes, significantly improving the SNR. The accuracy and/or spatial resolution could thus have been further improved accordingly. This strategy, however, would have prevented 2D-mapping of the ozone concentration, which was the other main goal of the campaign.

Fig I :

 : Fig I : Measurement site and principal Lidar measurement directions. The 3 lowest angles are selected in order to match the location of reference ozone sensors on the Eiffel Tower.

Fig 2 :

 2 Fig 2 : Continuous Lidar 2D-mapping of the ozone episode (snapshots form the video clip, which can be integrally seen on the electronic version of the paper).

Fig 3 :Fig 4 :

 34 Fig 3 : Evolution of the ozone vertical profiles, measured by Lidar, at the Eiffel Tower, location

Fig 5 :

 5 Fig 5 : Histogram of the concentration differences AC between spot analyzers and Lidar.

  18/07 18/07 18/07 18/07 18/07 18/07 18/07 18/07 18/07 18/07 18/07 18/07 19/07 19/07 19/07 19/07 19/07

Acknowledgements

The authors acknowledge Jerome Kasparian for fruitful discussions and suggestions. J.P.W. acknowledges the Institut Universitaire de France for support.

6.

References