Maharavo Marie

Julie Ramanantenasoa Radomahaleo

Sophie Génermont
email: sophie.genermont@inra.fr

Jean-Marc Gilliot

Carole Bedos

David Makowski

Julie Ramanantenasoa

Meta-modeling methods for estimating ammonia volatilization from nitrogen fertilizer and manure applications

Keywords: Meta-modeling, Volt'Air, ammonia emission, fertilization, process-based model

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In France, 98% of ammonia (NH3) is emitted by the agricultural sector of which 35% is due to the application of nitrogen (N) fertilization and 65% to manure management including manure spreading (CITEPA, 2017a). A better estimation of the quantities of NH3 emitted is necessary to define effective strategies for reducing emissions at national and regional levels, and mitigating the potential negative impact of NH3 on human health [START_REF] Moldanová | Chapter 18. Nitrogen as a threat to European air quality[END_REF] and ecosystems [START_REF] Bobbink | The effects of air-borne nitrogen pollutants on species diversity in natural and semi-natural European vegetation[END_REF]IPCC, 2006). Accurate NH3 volatilization estimations are also required for improved fertilization management and better adjustment of N fertilization to soil and climate characteristics [START_REF] Dupas | Integrating local knowledge and biophysical modeling to assess nitrate losses from cropping systems in drinking water protection areas[END_REF][START_REF] Parnaudeau | A tool to assess N losses towards environment at the cropping system scale: the software Syst'N[END_REF].

Currently, the French national inventories of NH3 emissions use the default Tier 2 emission factors (EF) proposed by the EMEP Guidebook [START_REF] Citepa | Inventaire des émissions de polluants atmosphériques et de gaz à effet de serre en France -Séries sectorielles et analyses étendues -Format SECTEN[END_REF]EMEP/EEA, 2016a, b). Tier 2 EF do not take into account national specificities such as agricultural practices that may differ between countries. EF values were estimated from an international literature review of experimental measurements of volatilization collected in different conditions (EMEP/EEA, 2016a, b) and with various measurement methods [START_REF] Sintermann | Are ammonia emissions from field-applied slurry substantially over-estimated in European emission inventories?[END_REF]. Process-based models represent an interesting alternative by describing the effect of different factors on NH3 volatilization. They can be used to calculate EF for different regions with different pedo-climatic conditions and various types of fertilizer, as shown by [START_REF] Ramanantenasoa | A new framework to estimate spatio-temporal ammonia emissions due to nitrogen fertilization in France[END_REF]. In France, Volt'Air was developed to predict NH3 volatilization after N fertilizer and manure applications. This model incorporates the effect of the main agronomic, soil and meteorological factors influencing NH3 volatilization in agricultural fields (EMEP/EEA, 2016a, b;[START_REF] Garcia | Accounting for Surface Cattle Slurry in Ammonia Volatilization Models: The Case of Volt'Air[END_REF][START_REF] Génermont | A mechanistic model for estimating ammonia volatilization from slurry applied to bare soil[END_REF][START_REF] Huijsmans | Simulating emission of ammonia after liquid manure application on arable land; Preliminary performance assessment of the Volt'Air model for manure application conditions in the Netherlands[END_REF][START_REF] Le Cadre | Modélisation de la volatilisation d'ammoniac en interaction avec les processus chimiques et biologiques du sol: le modèle Volt'Air[END_REF][START_REF] Smith | Simulated management effects on ammonia emissions from field applied manure[END_REF][START_REF] Sommer | Processes controlling ammonia emission from livestock slurry in the field[END_REF]. However, Volt'Air includes a rather large number of input variables and its implementation on a large scale requires long computation times that may restrict its use by public environmental agencies.

In this study, we emulate the Volt'Air process-based model using simple statistical metamodels. A meta-model is a model of a model. It may be seen as a simplified version of the original model. A meta-model may be run as a substitute for the original complex model when that model cannot be conveniently used, such as when the number of inputs in the original model is high, when these inputs cannot be easily measured, or when the computation time of the original model is too high for some applications. Meta-models are currently used in various research areas, for example, in hydrology [START_REF] Razavi | Review of surrogate modeling in water resources[END_REF], ecology [START_REF] Conti | Bayesian emulation of complex multi-output and dynamic computer models[END_REF] and agronomy [START_REF] Makowski | A statistical analysis of ensembles of crop model responses to climate change factors[END_REF][START_REF] Britz | Development of marginal emission factors for N losses from agricultural soils with the DNDC-CAPRI meta-model[END_REF]. However, not many publications describe meta-models for estimating emissions of gas produced by agricultural practices, such as nitrous oxide (N2O) emissions [START_REF] Giltrap | Upscaling NZ-DNDC using a regression based meta-model to estimate direct N2O emissions from New Zealand grazed pastures[END_REF][START_REF] Villa-Vialaneix | A comparison of eight metamodeling techniques for the simulation of N2O fluxes and N leaching from corn crops[END_REF] and CH4 emissions [START_REF] Katayanagi | Development of a method for estimating total CH4 emission from rice paddies in Japan using the DNDC-Rice model[END_REF]. Regarding NH3 emissions, this study is the first attempt to develop meta-models emulating an NH3 volatilization process-based model as complex as Volt'Air.

Here we present an approach to producing meta-models used as surrogates of the Volt'Air process-based model for estimating N emission rates after mineral fertilizer and manure applications in France. We develop and compare a large number of meta-models based on different statistical methods and on different sets of input variables for three types of fertilizer (N solution, pig slurry and cattle farmyard manure (FYM)) with average agronomic properties, at regional and national scales. All developed meta-models are fitted to a set of NH3 emissions simulated by the Volt'Air process-based model. The meta-models are evaluated by cross-validation for their ability to approximate the emissions simulated by Volt'Air, and the results are used to select parsimonious meta-models providing a good approximation of Volt'Air.

MATERIALS AND METHODS

The Volt'Air model

Volt'Air is a process-based model predicting NH3 emissions after N fertilization and manure applications on bare soils. It explicitly describes the physical and chemical equilibria between the various types of ammoniacal N (N as NH4 + and NH3) using Henry's law for air/water equilibrium, the acid-base equilibrium for ionic dissociation and the Freundlich adsorption equation for soil minerals and organic matter. This model takes into account the effect of agricultural, soil and meteorological factors on NH3 volatilization [START_REF] Garcia | Assessing the ability of mechanistic volatilization models to simulate soil surface conditions: a study with the Volt'Air model[END_REF][START_REF] Garcia | Accounting for Surface Cattle Slurry in Ammonia Volatilization Models: The Case of Volt'Air[END_REF][START_REF] Génermont | A mechanistic model for estimating ammonia volatilization from slurry applied to bare soil[END_REF][START_REF] Voylokov | Accounting for fym and composts in ammonia volatilization models: The case of volt'air[END_REF][START_REF] Le Cadre | Modélisation de la volatilisation d'ammoniac en interaction avec les processus chimiques et biologiques du sol: le modèle Volt'Air[END_REF]. It simulates NH3 emissions following applications of organic manures, such as typical slurries and farmyard manure, and mineral fertilizers, such as ammonium nitrate and urea in granular form as well as N solutions. Volt'Air runs at an hourly time step and at field scale for a period of several weeks, i.e., covering the duration of the volatilization event after fertilizer application. A more detailed description of the model may be found in [START_REF] Génermont | A mechanistic model for estimating ammonia volatilization from slurry applied to bare soil[END_REF] and [START_REF] Garcia | Accounting for Surface Cattle Slurry in Ammonia Volatilization Models: The Case of Volt'Air[END_REF].

Here we consider a single model output: the N emission rate over 30 days after fertilizer application, i.e., the cumulative N emission over 30 days after fertilizer application divided by N fertilizer dose. In most cases, volatilization simulated using Volt'Air is complete 30 days after the date of fertilizer application, even for mineral fertilizers showing longer volatilization periods compared to organic manure [START_REF] Theobald | An ammonia emission model for fertiliser applications suitable for use in climate change scenarios[END_REF]. Volt'Air can be run for real or virtual fields, with an average computation time of 32 s per simulation using a Dell precision T7910 workstation with two Intel Xeon 2.4 GHz processors (20 cores) and 128 GB RAM.

Simulated datasets used to develop the meta-models

The dataset used to develop the meta-models includes 106,092 NH3 emission simulations performed within the CADASTRE_NH3 framework using the Volt'Air model (Ramanantenasoa et al., 2018). These simulations encompass three types of fertilizer, five geographical areas, and weather conditions corresponding to three contrasted crop years.

Simulation units of CADASTRE_NH3 are the Small Agricultural Areas (SAR): a SAR is considered to be geographical entity with homogeneous characteristics of agricultural activities, weather and soil conditions (http://agreste.agriculture.gouv.fr). SAR sizes range from 1,096 to 440,650 ha, and the number of SAR per region varies from 6 to 74. Within our dataset, each SAR is characterized each year by the area of the cultivated crop species, the weather conditions, and soil types. Fertilization management is characterized at the regional scale.

Areas of cultivated crop species were derived from the European Land Parcel Identification System for France [START_REF] Martin | Cost of best management practices to combat agricultural runoff and comparison with the local populations' willingness to pay: Case of the Austreberthe watershed (Normandy, France)[END_REF]. Data on weather conditions were provided by the French national meteorological service "Météo-France". Data on the spatial distribution of soils were derived from the European Soil DataBase (ESDB) [START_REF] Panagos | European Soil Data Centre: Response to European policy support and public data requirements[END_REF] and the soil properties were derived from the Harmonized World Soil Database (FAO et al., 2012). Data on cultural practices were derived from the survey conducted in 2005-06 by the Service de la Statistique et de la Prospective of the French Ministry of Agriculture, for 10 main arable crops (soft wheat, durum wheat, barley, grain maize, forage maize, oilseed rape, sunflower, peas, sugar beet and potato) and two types of grasslands (grass leys and intensive permanent grasslands) in 21 French regions (Corse region was excluded) (AGRESTE, 2006), following the methodology of [START_REF] Mignolet | Spatial dynamics of farming practices in the Seine basin: methods for agronomic approaches on a regional scale[END_REF].

Fertilization was defined as a succession of fertilizations on a given crop species. Each fertilizer application was characterized by the date of application, type of fertilizer (3 mineral fertilizers: ammonium nitrate, N solution, urea; 5 organic manure: cattle farm yard manure (FYM), cattle slurry, sheep FYM, pig slurry, and vinasse), and dose applied. For the simulations with Volt'Air, fertilizers were assumed to be applied on the surface without abatement techniques, at a single time, 8:00 am UTC.

Each simulation covered the cumulative NH3 emissions over 30 days after a specific fertilizer application on a specific SAR*crop*fertilization*year combination. A more detailed description of the dataset and of the simulation procedure may be found in [START_REF] Ramanantenasoa | A new framework to estimate spatio-temporal ammonia emissions due to nitrogen fertilization in France[END_REF]. Part of the dataset including the simulations of Volt'Air was made freely available in the related data paper [START_REF] Génermont | Data on spatio-temporal representation of mineral N fertilization and manure N application as well as ammonia volatilization in French regions for the crop year 2005/06[END_REF].

Meta-models were developed separately for each type of fertilizer. The three selected fertilizers (N solution, cattle FYM, and pig slurry) were among the most applied fertilizers in France in 2005-06; N solution accounted for 38% of N applications from simple mineral N fertilizers (UNIFA, 2015); cattle FYM and pig slurry accounted for 82% and 7% of N applications from organic fertilizers, respectively (AGRESTE, 2006(AGRESTE, , 2010)).

Meta-models were developed separately for the national and the regional scales. Four French regions characterized by contrasting agricultural, climatic and soil conditions were selected; the North-Western Bretagne region is characterized by a high use of organic manure due to the dominance of livestock farming, an oceanic temperate climate, and acidic soils; the North-Eastern Champagne-Ardenne region is a major arable crop farming area, encountering a semi-continental temperate climate, with a dominance of alkaline soils; Ile-de-France, located in the North Center of France, is an arable crop farming area, with soil and weather conditions in-between these two former regions; the South-Eastern Rhône-Alpes region is a more agriculturally diverse region, with southern semi-continental climatic conditions. In order to capture the possible effect of weather variables between years, weather conditions of two contrasting crop years were added: 2007-08 and 2010-11. Crop year 2005-06 was characterized by a dry spring and a hot summer (AGRESTE, 2010); 2007-08 enjoyed favorable conditions for crop growth, i.e., a humid spring with temperatures close to the seasonal average and a hot summer with rainfall close to the seasonal average (JRC, 2008); 2010-11 was characterized by a very dry, hot spring and a rainy summer (AGRESTE, 2014). The same sites and cultural practices were analyzed for the three years; only the weather conditions were changed.

The sizes of national and regional datasets per fertilizer type and per geographical area and the numbers of SAR per geographical area are given in Table 1. Note that no simulation was available for pig slurry in Champagne-Ardenne, Ile-de-France and Rhône-Alpes. This type of fertilizer is barely used in these three regions.

Inputs of the meta-models

A total of 16 original input variables were chosen from all the Volt'Air input variables for meta-modeling (Table 2) because they were expected to have an impact on NH3 volatilization and showed a wide range of variation in the data sources. Some of these 16 inputs were not taken into account in a few fertilizer * region combinations considered. Thus, Dose of application was not used for cattle FYM and pig slurry because its range of variation for these two types of fertilizer was too narrow. Bulk density was not used for Bretagne, for the same reason. Note that variables describing fertilizer and manure properties were not considered here because specific meta-models were developed for each fertilizer separately.

The variables describing geographical location, soil and cultural practices were not timedependent. In contrast, all variables describing weather conditions were defined for 23 different time-periods:

-10 different daily periods; 1 st (i.e., the day of fertilizer application), 2 nd , 3 rd , 4 th , 5 th , 6 th , 7 th , 8 th , 9 th and 10 th days following fertilizer application.

-10 different cumulative periods; 2, 3, 4, 5, 6, 7, 8, 9, 20 and 30 days following fertilizer application.

-three ten-day periods; 1 st , 2 nd and 3 rd , from the 1 st to the 10 th day, from the 11 th to the 20 th day, from the 21 th to the 30 th day respectively following fertilizer application,.

For each period, the values for Mean air temperature, Relative air humidity, Incident solar radiation, and Wind speed were averaged over the period considered. The values for Minimum air temperature and Maximum air temperature were set at the minimum and maximum air temperature over the period. The values for Cumulative rainfall were set at the sum of rainfall over the timeperiods considered. A separate meta-model was constructed for each time-period.

Two additional non-weather related variables were considered to account for regional effects on volatilization; the categorical variable Region and the continuous variable Longitude. Note that the continuous variablen Latitude is a Volt'Air variable. With these three variables, we were able to produce a unique meta-model per fertilizer type at the France scale while accounting for regional specificities. -kg.m -3 -g.kg -1 of dry soil -g.kg -1 of dry soil -g.kg -1 of dry soil -g.kg -1 of dry soil Weather conditions -Minimum air temperature -Mean air temperature -Maximum air temperature -Specific air humidity -Incident solar radiation -Wind speed -Cumulative rainfall (a) The Region variable was added for the development of meta-models at the national scale only.

-K -K -K -kg.kg -1 -W.m -2 -m.s -1 -mm.s -1 / 3600
(b) Dose of application was not used for cattle FYM and pig slurry meta-models.

(c) Bulk density was not used for Bretagne.

Boxplots of the 17 quantitative explanatory variables chosen are presented in Figure S2 in the supplementary material.

Additional input variables were defined from the original variables listed in Table 2 for potential inclusion in the meta-models; the quadratic terms of several variables (see Tables S1 andS2 in the supplementary material) and interaction terms between pairs of variables (i.e., multiplication between two variables). Interactions were chosen with respect to formalisms chosen to describe the processes of Volt'Air. Interaction between Cumulative rainfall and Air temperatures (minimum, mean, maximum) (i.e., three pairs), interaction between Cumulative rainfall and Wind speed, and interaction between Cumulative rainfall and Soil texture (Silt, Clay) were chosen because infiltration depends on both the quantity of water and the state of the soil surface, which in turn depends on evaporation potential, driven by both temperature and wind-speed, and on soil texture [START_REF] Garcia | Accounting for Surface Cattle Slurry in Ammonia Volatilization Models: The Case of Volt'Air[END_REF]. The interaction between Cumulative rainfall and Air temperatures reflects the effect of these factors on physicochemical equilibria, through dilution by rainfall and the high dependence of the equilibrium constants on temperature. For N solution and pig slurry, interactions between Soil pH and Air temperatures (minimum, mean, maximum) were also considered. As those products are incorporated to the first soil layer, soil pH together with N solution pH or pig slurry pH directly drive physicochemical equilibria, which are also highly dependent on temperature.

Types of meta-model

For a given type of fertilizer, meta-models were fitted to each regional dataset of simulated NH3 emissions and then to the whole dataset at the national scale. Five different types of metamodel were developed with each dataset. The first three types of model (ordinary linear regression, Least Absolute Shrinkage and Selection Operator, and Partial Least Squares Regression) assumed a linear relationship between N emission rate over 30 days (or its transformed-value) and input variables. The last two types of model (Generalized additive model, Random Forest) dealt with nonlinear relationships between volatilization rates and input variables. The inputs of generalized additive model and random forest were selected using a regression method (ordinary linear regression, Least Absolute Shrinkage and Selection Operator, or Partial Least Squares Regression, see section 2.5 for details on the selection procedure). Below, we briefly present the main characteristics of each type of model. Details on the meta-model selection procedure are given in Section 0. The equations of the meta-models are described in Table 3 together with the R functions used for their implementation. The R functions mentioned in Table 3 are freely available from https://cran.r-project.org. They can be easily used to develop meta-models from the dataset described in 2.2. The present study was performed with the 3.2.3 version of R.

Ordinary linear regression (LM, Linear Model) was used to relate emission rates (noted y in Table 3) to quantitative and categorical input variables (noted X1, …, Xp in Table 3) through a linear equation. Here the flexibility of linear models was increased through the inclusion of quadratic terms and interactions between inputs. Several variants of ordinary linear regression models were developed. In some variants, model inputs were selected using a stepwise or a forward selection procedure based on the Akaike Information Criterion (AIC) (Figure 1). All linear models were fitted using Ordinary Least Squares (OLS) with the R function lm().

Least Absolute Shrinkage and Selection Operator (LASSO) is a well-known regularization technique that can be applied to reduce variance of the parameter estimators in linear regression models [START_REF] Tibshirani | Regression shrinkage and selection via the lasso[END_REF]. LASSO is based on the same model equation as LM, i.e., a linear equation relating the emissions rates to the input variables. However, instead of using OLS for obtaining the parameter estimates, LASSO is subjected to constraints on parameters defined through a penalty term based on the absolute values of the parameters. With this approach, some parameters become equal to zero by tuning the penalty term for minimizing prediction errors, leading to the selection of a reduced subset of input variables. LASSO was implemented here using the R function cv.glmnet() of the package glmnet.

Partial Least Squares Regression (PLSR) can improve the accuracy of linear regression models when the input variables are strongly correlated [START_REF] Abdi | Partial least squares regression and projection on latent structure regression (PLS regression)[END_REF]. PLSR may be seen as an improved version of principal component regression (PCR). In PCR, principal components are expressed as linear combinations of original variables, such that the variability in the data may be described by a small number of these new variables. In PLSR, the original input variables are also replaced by linear combinations of inputs, but these combinations are selected to describe most of the input data variability while showing a strong correlation to the response (Table 3). PLSR was implemented here using the R function plsr() of the pls package.

Generalized Additive Models (GAM) assume that the response variable Y (emission rate) can be expressed as a linear combination of several unknown smooth functions of the inputs [START_REF] Wood | Generalized Additive Models: An Introduction with R, Second Edition[END_REF]. The equation used by GAM is more general than the linear equations used by LM, LASSO, and PLSR and is expressed as μ + s(X1) + ⋯ + s(XP), where s(.) are several smoothing functions (splines) of the inputs. Here, the volatilization rate is expressed as a linear combination of the smoothing functions. We used smoothing splines as smoothing functions because these types of function are very flexible. This model does not assume that the volatilization rates are linearly related to the inputs and can describe complex response curves. As the model is expressed as a sum of independent functions, the effect of each input on the output can be easily interpreted. GAMs were fitted here using the R function gam() of the mgcv package.

Random Forest (RF) is a machine learning technique that builds an ensemble of classification (or regression) trees (Breiman and Cutler, 2003). RF creates a set of binary decision rules based on the input variables. The first step of the method is the random selection, with replacement, of a sample of data (called the "in-bag") of equal size to the total number of data. The remaining part of the data is referred to as "out-of-bag" (OOB) data. The second step involves the random selection of explanatory variables. The third step involves the building of a tree based on the in-bag data and a subset of variables selected. The tree is built by recursively partitioning the initial data into smaller groups, called nodes, through binary splits based on a single input variable.

Examples of regression trees are given in Figure S3 in the supplementary material. The whole process is repeated several thousand times, to generate many trees. At each iteration, the OOB data are used to evaluate the accuracy of the fitted trees. The output of RF is calculated by averaging the outputs of the individual trees (Table 3). Here RF models were fitted with the R function randomForest() of the randomForest package and the R function ranger() of the ranger package.

Ranger is a fast implementation of random forests [START_REF] Breiman | Random forests[END_REF] and was used here to fit the RF meta-model for N solution in France to reduce computation time.

Table 3 : Description of the statistical and machine learning methods used to develop the meta-models of Volt'Air. The methods are based on different types of models whose parameters are estimated using an optimization algorithm implemented with R functions of specific R packages. Each meta-model computes NH3 volatilization rates y (or log/box-cox transformed volatilization rates) from a series of inputs X1, X2…, Xp.

Selection of meta-models

For each type of fertilizer and each geographical area, 602 meta-models were developed and assessed according to the four-step selection procedure presented in Figure 1 and detailed below.

Each model was defined by a specific statistical method (among LM, LASSO, PLSR, RF, GAM), the type of response variable (untransformed or log/box-cox-transformed emission rate), the timeperiod used to define the weather inputs, the inclusion or not of quadratic terms and interactions, and the input selection method (none, stepwise, forward). The box-cox transformation has the form wi = yi λ, if λ ≠ 0 and wi = log (yi), if λ = 0 with wi the transformed variable, yi the initial response variable, and λ the parameter for the transformation (estimated from the data).

In Step 1, three types of linear model were fitted and compared by cross-validation: ordinary linear models (LM), LASSO, and PLSR. Two sets of inputs were considered successively: the inputs listed in Table 2, and an expanded set of inputs including quadratic terms and interactions.

With LM, input variables were selected using either a stepwise or a forward selection procedure based on the AIC criterion [START_REF] Juillet ; Akaike | Enquête Pratiques culturales 2011: Principaux résultats[END_REF]. The total number of models tested in Step 1 was 598.

In Step 2, the two best linear meta-models were selected using cross-validation. Crossvalidation is a standard method for evaluating the accuracy of the model predictions [START_REF] Efron | Estimating the error rate of a prediction rule: improvement on cross-validation[END_REF].

It allows one to estimate how the model is expected to perform when used to make predictions on data independent from those used for estimating the model parameters. The general principle is to split the dataset into K groups. The first group is removed from the dataset. The remaining part of the dataset is used to fit the model. The fitted model is then used to predict the discarded group of data. The whole procedure is repeated over all groups, and the accuracy of the prediction is evaluated by computing the root mean square error of prediction (RMSEP) over the K groups. Here, two procedures were used successively to define the groups of data, leading to two different types of cross validation. The first type of cross-validation was implemented SAR by SAR in order to estimate the root mean square error of prediction of each meta-model (RMSEP_SBS). RMSEP_SBS measures the ability of each meta-model to approximate the emission rates simulated by Volt'Air in a new SAR, i.e., a SAR not originally included in the dataset used to develop the meta-model considered. The second type of cross-validation consisted of dividing the dataset by years. This is also referred to as year-by-year cross-validation and the associated RMSEP is denoted RMSEP_YBY. This value of RMSEP measures the ability of each meta-model to approximate the emission rates simulated by Volt'Air for a new year, not originally included in the dataset used to develop the meta-model.

In

Step 3, two RF and two GAM meta-models were developed. They included the input variables of the two best linear models selected in Step 2, i.e., the linear models characterized by the lowest values of RMSEP_SBS and RMSEP_YBY (Linear MM_SAR and MM_YEAR). These models were thus developed from the input variables selected in Step 2. The output and input variables were used in their original form, i.e., without transformation or interaction.

In Step 4, cross-validations (SAR-by-SAR and year-by-year) were carried out again to select the two best meta-models from the two best linear models, RF, and GAM. The two meta-models selected at this step were denoted Final MM_SAR and MM_YEAR.

The whole procedure was applied for each fertilizer type, for each region and for France.

When two or more meta-models had similar RMSEPs (to two decimal places), we favored the metamodel including the smallest number of inputs (inputs related to the geographical location of the site, i.e., latitude, longitude and region, were not counted because they are always available at zero cost). When two meta-models had similar RMSEPs and the same number of inputs, we chose the meta-model with weather condition variables calculated over the longest time-period because these variables were smoother than variables calculated over shorter time-periods, and were thus less sensitive to extreme, short-term meteorological events.

SELECTION OF THE FINAL TWO BEST METAMODELS AMONG THE TWO BEST LINEAR MODELS, THE TWO GAMs, AND THE TWO RFs

Final MM_SAR with the lowest RMSEP_SBS Final MM_YEAR with the lowest RMSEP_YBY (1) For each type of linear model, 23 variants were developed; each variant corresponds to a specific time-period.

Figure 1: Meta-modeling selection procedure. This four-step approach is applied for each type of fertilizer for each region and at the national scale. The selected models are those minimizing the root mean square error of prediction (RMSEP) computed by cross-validation. Two types of cross-validation are implemented, i.e., by removing each small agricultural region (SAR) in turn, or each year in turn. The two cross-validations lead to two different RMSEPs (RMSEP_SBS and RMSEP_YBY, respectively). Two sets of inputs were considered: Set 1with the original variables, and Set 2 including in addition quadratic terms and interactions. LM1-LM2: ordinary linear models (with/without quadratic and interaction terms). LASSO1-LASSO2: LASSO regression models (with/without quadratic and interaction terms). PLSR1-PLSR2: PLSR regression models (with/without quadratic and interaction terms). RF: random forest. GAM: generalized additive models.

Comparison of meta-models at the regional scale

After the selection described in Figure 1, two types of meta-model were available for estimating emission rates in a given region: the regional meta-models derived from the set of simulated NH3 emissions obtained for that region specifically, and the France meta-models derived from the whole set of simulated emissions at the national level (i.e., over the 21 French regions).

The meta-models selected at the national level can be used to estimate emission rates in a specific region because they include the categorical input Region and/or the quantitative inputs Latitude and Longitude accounting for a possible regional effect. So we compared regional and France metamodels for their ability to estimate emission rates for each selected type of fertilizer and each region. To do this, the best France meta-models were run on site*crop*fertilization*year of the regional datasets, and the resulting RMSEP values were compared with those calculated with the best regional metamodels. For each selected region and fertilizer type, the RMSEP of the regional and France meta-models were compared and the model producing the lowest value was finally selected.

RESULTS

Comparison of Volt'Air and meta-model outputs

Over all meta-models (before selection), values of RMSEP range from 0.002 to 0.729 kg N.kg -1 N and values of RRMSEP range from 3% to 755% of the mean emission rates. For N solution, values of RMSEP range from 0.033 to 0.729 kg N.kg -1 N and values of RRMSEP range from 24 to 755 % of the mean emission rates. For cattle FYM and pig slurry, values of RMSEP range from 0.002 to 0.074 kg N.kg -1 N and 0.045 to 0.598 kg N.kg -1 N, respectively, and values of RRMSEP range from 3 to 105 % and 17 to 260 % of the mean emission rates, respectively.

For a given fertilizer type, the RMSEP of the best meta-models fitted at the regional and national scales are close, and the regional meta-models do not systematically outperform the national metamodels (Figure 2). For N solution, the France meta-model produces a smaller RMSEP, thus providing a more accurate approximation of Volt'Air than regional meta-models in all considered regions except in Bretagne for the meta-model selected using a year-by-year cross-validation. For pig slurry in Bretagne, the France meta-model performs better than the regional meta-model. For cattle FYM, regional and France meta-models show very similar performances.

In the following, only the meta-models showing the lowest RMSEP are considered. Regional emission rates are thus further estimated using either France or regional meta-models, depending on their RMSEP values. Similar results are observed for SAR-by-SAR and year-by-year cross-validation methods. The performances of the meta-models did not differ much among regions. No single region showed systematically lower RMSEP or RRMSEP. The RMSEP tended to be higher when calculated year by year than SAR by SAR (Figure 3ab). This result was expected, because a larger number of data were removed at each iteration of the cross-validation when implemented year by year. The differences were large for N solution, small for pig slurry, and non-detectable for cattle FYM.

The distributions of the emission rates obtained with the selected meta-models were very similar to those obtained with Volt'Air, both at regional and national scales. This is illustrated in Figure 5 for the meta-models selected by year-by-year cross-validation; results were similar with the meta-models selected by SAR-by-SAR cross-validation and are therefore not shown. In Figure 5, each box-plot presents the minima, 1st quartiles, medians, 3rd quartiles, and maxima calculated over the entire considered site*crop*fertilization*year, using the selected meta-models and Volt'Air. Differences between the meta-models and Volt'Air were very small, especially for the minima, 1st quartiles, medians, and 3rd quartiles. These results indicate that the emission rate distributions produced by the meta-models and by the process-based model shared similar characteristics. content was selected in one meta-model only, as was the Region variable, which was an input candidate for three meta-models. The Dose of fertilizer application was never selected but it was an input candidate for one meta-model only (Table S1). All other variables were selected in at least half of the meta-models. The number of selected inputs ranged from 6 to 15 (if we exclude the quadratic and interaction terms), depending on the meta-model considered. These numbers should be compared to the total number of candidate inputs, comprised between 15 and 18 (Table 2). Metamodels 1 and 3 were the most parsimonious; they included 10 selected inputs from the 18 input candidates and 6 selected inputs from the 17 input candidates, respectively, i.e., about half or one third of the number of candidate inputs (Table S1). Conversely, the meta-models 2 and 4 included a large share of the input candidates (12/15 and 15/18, respectively). The time-period used to calculate the weather inputs ranged from six to seven successive days for N solution and from one to three successive days for cattle FYM; for pig slurry, it was five successive days (Tables S1 andS2).

The seven meta-models selected by year-by-year cross-validation shared certain similarities with the four meta-models selected by SAR-by-SAR cross-validation. The inputs of these metamodels (Table S2) were often the same as those reported in Table S1. Initial soil water content, Mean air temperature, Incident solar radiation, Wind speed and Cumulative rainfall were frequently selected, while the Dose of fertilizer application, Soil organic carbon content, Region, Latitude, Longitude and Relative air humidity, were less frequently selected. Soil properties (Bulk density, Silt content, Clay content and Organic carbon content) were less frequently selected in N solution metamodels. The total number of selected inputs also ranged from 6 to 15 (if we exclude the quadratic and interaction terms), depending on the meta-model considered. These meta-models exhibited several differences compared to those selected by SAR-by-SAR cross-validation. In particular, most of the meta-models selected by year-by-year cross-validation were ordinary linear regression models (Table S2); RF was used by only two meta-models. All the five selected ordinary linear regression models included quadratic and interaction terms (Table S2); two out of them included a box-cox

The relatively poor performances of the N solution meta-models may be due to the small number of soil variables selected (see below). Other variables may have a strong influence on volatilization, at least for some of the considered years. Our meta-models may not fully account for the soil characteristics influencing soil transfer of heat, water and ammoniacal-N species. The better performance obtained for N solution by year-by-year cross validation may be due to a higher interannual variability of volatilization for this type of fertilizer, or to the fact that more data are needed to develop an accurate meta-model for this fertilizer. Almost all the selected meta-models incorporate some nonlinear effects. The regression models include quadratic terms and interactions, and Random Forest models deal with nonlinear responses through their splitting rules. The presence of nonlinear terms in the selected meta-models emphasizes the need to take nonlinear responses and interactions into account. The results of our selection are consistent with those reported in previous meta-modeling studies. Regression metamodels including linear, interaction, and quadratic terms and transformation of the output were indeed commonly used for meta-modeling [START_REF] Britz | Development of marginal emission factors for N losses from agricultural soils with the DNDC-CAPRI meta-model[END_REF][START_REF] Giltrap | Upscaling NZ-DNDC using a regression based meta-model to estimate direct N2O emissions from New Zealand grazed pastures[END_REF]. RF meta-models were also already used by [START_REF] Villa-Vialaneix | A comparison of eight metamodeling techniques for the simulation of N2O fluxes and N leaching from corn crops[END_REF] and were found to be an accurate meta-modeling method for emulating models of nitrous oxide (N2O) emission and N leaching.

Four weather variables (Wind speed, Air temperature, Cumulative rainfall, Incident solar radiation) were always selected in the meta-models regardless of the type of fertilizer and geographical area. This is consistent with the Volt'Air sensitivity analyses performed by [START_REF] Theobald | An assessment of how process modelling can be used to estimate agricultural ammonia emissions and the efficacy of abatement techniques[END_REF][START_REF] Theobald | An ammonia emission model for fertiliser applications suitable for use in climate change scenarios[END_REF] which showed that air temperature and wind speed are the most influential climatic factors in the Volt'Air model. This result is due to the fact that Henry's Law and the acid-base equilibrium constants are both expressed as exponential functions of temperature, increasing temperatures leading to increased volatilization [START_REF] Sommer | Processes controlling ammonia emission from livestock slurry in the field[END_REF]. Furthermore, wind speed promotes the dispersion of NH3 in the gas phase and thus volatilization. Volt'Air is also sensitive to rainfall [START_REF] Génermont | A mechanistic model for estimating ammonia volatilization from slurry applied to bare soil[END_REF]; rainfall events after fertilizer application decrease NH3 emissions by promoting the infiltration of slurry and soil solution containing ammoniacal N [START_REF] Sanz-Cobena | Effect of water addition and the urease inhibitor NBPT on the abatement of ammonia emission from surface applied urea[END_REF][START_REF] Sanz-Cobena | An inhibitor of urease activity effectively reduces ammonia emissions from soil treated with urea under Mediterranean conditions[END_REF]van der Weerden and Jarvis, 1997).

The time-periods selected to calculate the effect of the weather variables correspond to the period of high volatilization for each type of fertilizer. The time-period selected for cattle FYM is the shortest (less than three successive days versus five days or more for other fertilizers); there are two reasons for this. First, cattle FYM has high dry matter content and is known not to infiltrate into the soil: this was conceptualized in Volt'Air by adding a cattle FYM layer on the soil surface [START_REF] Garcia | Accounting for Surface Cattle Slurry in Ammonia Volatilization Models: The Case of Volt'Air[END_REF][START_REF] Voylokov | Accounting for fym and composts in ammonia volatilization models: The case of volt'air[END_REF] whereas pig slurry and N solution are directly added to the first soil layer. Second, cattle FYM has a higher pH (8.00) than pig slurry (7.50) and N solution (5.77), and Volt'Air is highly sensitive to pH; the higher the pH, the higher the volatilization [START_REF] Génermont | A mechanistic model for estimating ammonia volatilization from slurry applied to bare soil[END_REF][START_REF] Le Cadre | Modélisation de la volatilisation d'ammoniac en interaction avec les processus chimiques et biologiques du sol: le modèle Volt'Air[END_REF][START_REF] Theobald | An assessment of how process modelling can be used to estimate agricultural ammonia emissions and the efficacy of abatement techniques[END_REF]. This information on the time-period during which weather factors drive NH3 volatilization is useful for further recommendations to adapt the experimental design to capture the dynamics of NH3 volatilization, as the time window for applying abatement techniques depends on fertilizer type.

Soil properties were less frequently selected than weather variables in all meta-models, especially for N solution (Tables S1 andS2). These variables had smaller variation ranges than the meteorological variables, which probably led to their elimination during automatic variable selection.

Moreover, several soil properties are strongly correlated with Soil pH and Initial soil water content (see Figure S1 in the supplementary material1), which were always selected in our meta-models (except for cattle FYM, as explained below). As stated above, Volt'Air is highly sensitive to Soil pH.

Similarly, Initial soil water content is among the most influential parameters in the Volt'Air model [START_REF] Theobald | An assessment of how process modelling can be used to estimate agricultural ammonia emissions and the efficacy of abatement techniques[END_REF]. It influences the availability of volatile N on the soil surface by conditioning the infiltration of the fertilizer's liquid fraction. The fact that cattle FYM stays on the soil surface and does not infiltrate also explains why soil properties (especially Soil pH) are less frequently selected for FYM meta-models.

The variable Region at the France level was selected only for N solution meta-models. For cattle FYM and pig slurry, this variable was not selected in the France meta-models regardless of cross-validation type but regional meta-models performed better than France meta-model. For these two types of fertilizer, the meta-models account for regional characteristics through their soil and weather inputs, Latitude and Longitude, and the Dates of fertilizer application.

The first advantage of using meta-models instead of Volt'Air is their extremely short computation time. For example, the meta-model for N solution in France required less than 1s to make 70,299 simulations whereas Volt'Air required approximatively 1.5 days for the same number of simulations with a parallel implementation on a Dell precision T7910 workstation with two Intel Xeon 2.4 GHz processors (20 cores) and 128 GB RAM. Meta-models can thus easily be implemented at large scales or in other applications requiring large amounts of data. The time required to build the meta-models and to select the best meta-models according to the selection method in Figure 1 was approximately three days with the R software on a desktop computer (Processor 2.7 GHz, 8Go RAM). SAR-by-SAR cross-validation was the most computationally expensive step, especially for calculations at the France scale where the number of SARs was 706 while it ranged from 25 to 76 for the four selected regions. RF and GAM required more computation time than the other techniques, especially when the dataset was large, as with N solution in France.

Ordinary linear regression had the lowest computational cost.

The second advantage of using the meta-models is that they need fewer inputs than the total number required for running Volt'Air. In our case study, Volt'Air required 16 types of input variable, and five of them (i.e., the weather variables) needed to be provided at an hourly time-step for one month (Section 2.1) leading to at most a total of 3,611 input variables. The use of Volt'Air is thus relatively costly in terms of data acquisition. The total number of selected inputs in the meta-models ranged from 6 to 15 (if we exclude the quadratic and interaction terms). In the meta-models, weather inputs need to be supplied over at most seven days.

The meta-models produced here combine qualities of both the process-based model Volt'Air and the empirical models developed and used for calculating NH3 volatilization in the field [START_REF] Génermont | Ammonia volatilisation after application of fertilisers and organic products: Potential for updating emission factors[END_REF]. Our meta-models include a small number of input variables and have a very short computation time. But they do not suffer from the same drawbacks as purely empirical models based on a limited number of experimental datasets. The domain of validity of our meta-models is related to the domain of validity of Volt'Air and the extent of the dataset used to build the metamodels. Thus we can expect a larger domain of validity than for the empirical models which generally focus on specific conditions, for example, that of Menzi [START_REF] Menzi | A simple empirical model based on regression analysis to estimate ammonia emissions after manure application[END_REF], which was constructed for cattle slurry applied to grassland with a splash plate, a total ammoniacal nitrogen (TAN) content of 0.7 5 g. kg -1 , a mean temperature ranging from 0 to 25°C, mean relative humidity of air ranging from 0.5 to 0.9 % and no rain. The model constructed by [START_REF] Misselbrook | A simple process-based model for estimating ammonia emissions from agricultural land after fertilizer applications[END_REF] and adjusted by [START_REF] Chadwick | Emissions of ammonia, nitrous oxide and methane from cattle manure heaps: effect of compaction and covering[END_REF] does not account for the effect of wind speed on NH3 volatilization from mineral fertilizers.

Our meta-models offer a good alternative to the default emission factors proposed by the EMEP guidebook for the official French NH3 emission inventories (CITEPA, 2017; EMEP/EEA, 2016), because of their relative simplicity compared to process-based models. The meta-models could also be connected to crop models (e.g., CERES-EGC, [START_REF] Gabrielle | Process-based modeling of nitrous oxide emissions from wheat-cropped soils at the subregional scale[END_REF]STICS, Brisson et al., 2003;SYST'N, Dupas et al., 2015;[START_REF] Parnaudeau | A tool to assess N losses towards environment at the cropping system scale: the software Syst'N[END_REF] to improve decision support tools used for fertilization management.

The meta-modelling approach presented here is generic. It can be implemented again with new sets of simulations provided by an upgraded version of Volt'Air, in new geographical areas, for

Figure 2 :

 2 Figure 2: Comparison of RMSEP by (a) SAR-by-SAR cross-validation and (b) year-by-year crossvalidation, obtained for each region and each type of fertilizer with meta-models fitted at the regional and France scales.

  (a) SAR-by-SAR cross-validation (b) Year-by-Year cross-validation

Figure 4 :

 4 Figure4: Scatter plot of meta-models selected by year-by-year cross-validation versus Volt'Air simulated emission rates (in kg N.kg -1 N). The letters R and F stand for regional and France metamodel, respectively, for each fertilizer type.

Figure 5 :

 5 Figure 5: Distributions of the nitrogen emission rate calculated with the meta-models selected by year-by-year cross-validation (MM_YEAR) and with the process-based model Volt'Air (in kg.kg -1 N). Each box-plot describes the minimum, 1 st quartile, median, 3 rd quartile and maximum values of the emission rates over the considered site*crop*fertilization*year.

Table 1 :

 1 Numbers of simulations of the Volt'Air model in the national and regional datasets and numbers of SARs per geographical area

	Type of fertilizer		France	Bretagne	Champagne-Ardenne	Ile-de-France	Rhône-Alpes
	N solution	Number of simulations	70,299	2,388	3,852	5,286	6,951
		Share of total (%)	100	3	5	8	10
	Cattle FYM	Number of simulations	13,725	147	804	558	1,452
		Share of total (%)	100	1	6	4	11
	Pig slurry	Number of simulations	405	225	0	0	0
		Share of total (%)	100	56	0	0	0
	Total number of simulations	84,429	2,760	4,656	5,844	8,403
	Total number of SARs	706	25	34	36	76

Table 2 :

 2 List of input variables of the meta-models

	Category	Variable	Unit
		-Latitude	°
	Location of site	-Longitude -Region (a)	° Categorical variable
	N fertilization management	-Date of N application -Dose of application (b)	-Number of days from origin 01/01/2005 -kg N.ha -1

(RRMSEP) as %). For cattle FYM, the RMSEP values were very low (<0.005 kg N.kg -1 N) and the RRMSEP did not exceed 8% of the mean emission rates. Values of RMSEP were higher for pig slurry and the corresponding RRSMEP ranged from 17 to 19% for this type of fertilizer. For N solution, the RMSEP values were of the same order of magnitude as those obtained for pig slurry; they never exceeded 0.06 kg N.kg -1 . But as the mean emission rates were low for N solution, the corresponding RRMSEP values were systematically higher than 21% (Figure 3). These results show that the metamodels provided a better approximation of Volt'Air for cattle FYM than for pig slurry and N solution.

This result is confirmed in Figure 4, where the relationships between the meta-model and the Volt'Air outputs are stronger for cattle FYM (RRMSEP<8%) than for the other two types of fertilizer (RRMSEP>17%).

Characteristics of selected meta-models

Over the five considered geographical areas (four regions plus France) and the three types of fertilizer, four different meta-models were selected by SAR-by-SAR cross-validation, versus seven by year-by-year cross-validation (Table S1 in the supplementary material). This difference is due to the number of meta-models selected for N solution and cattle FYM. For N solution, a single metamodel (the France meta-model) was indeed selected using SAR-by-SAR cross-validation for four different regions (Table S1) while the same meta-model was selected using year-by-year crossvalidation for three different regions (Table S2). For cattle FYM, a single meta-model (the France meta-model) was selected using SAR-by-SAR cross-validation for three different regions (Table S1) while the same meta-model was only selected using year-by-year cross-validation for one region, Ilede-France (Table S2).

Half of the meta-models selected by SAR-by-SAR cross-validation were Random Forest models; while the other half were ordinary linear regression models (Table S1). The two linear regression models selected by SAR-by-SAR cross-validation included quadratic and interaction terms and one of them (Meta-model 4) was fitted using a box-cox transformation of the output. The interaction Wind speed * Cumulative rainfall and the quadratic terms Latitude 2 , Longitude 2 , Date of N application 2 , Mean air temperature 2 and Cumulative rainfall 2 were frequently selected (see Tables S1 andS2 in the supplementary material2). The quadratic terms of "Dose of fertilizer application", "Soil organic carbon content" and "Maximum air temperature" were never selected, nor was the interaction "Mean air temperature * Cumulative rainfall". Among the considered statistical methods, GAM, PLSR, and LASSO were never selected whatever the type of cross-validation used.

In the four meta-models selected by SAR-by-SAR cross-validation, a number of weather input variables (e.g., Mean air temperature, Wind speed, Cumulative rainfall and Incident solar radiation) and Initial soil water content were systematically selected. The Soil organic carbon transformation of the output while the other three linear meta-models included untransformed output.

In the five selected linear regression meta-models, the interactions Minimum air temperature * Cumulative rainfall, Maximum air temperature * Cumulative rainfall, and the quadratic terms Wind speed 2 , Soil bulk density 2 , Mean air temperature 2 , Incident solar radiation 2 and Cumulative rainfall 2 were frequently selected (see Tables S1 andS2 in the supplementary material2).

The R objects of the meta-models based on linear regression and Random Forest are available on request from the authors.

DISCUSSION

Our meta-model assessments show contrasting results. For cattle FYM and pig slurry, on the one hand, meta-models provide a good approximation of Volt'Air, with an RRMSEP always lower than 8% and 19% of the mean emission rates, respectively. For N solution, meta-models provide a good approximation of Volt'Air for Champagne-Ardenne, Ile-de-France and France when they were assessed by the SAR-by-SAR cross-validation: RRMSEP ranged from 21% to 24% of the mean emission rates. The meta-models are less accurate for N solution in other situations, specifically in Bretagne and Rhône-Alpes with SAR-by-SAR cross-validation, and in all the geographical areas with year-by-year cross-validation; RRMSEP ranged from 31% to 40% of the mean emission rates in these situations. Despite these contrasting results, our meta-models provide a good approximation of the distributions of emission rates at the regional scales for all fertilizer types, including N solution (Figure 5). They give realistic ranges of emission rates and could thus be used for regional NH3 emission inventories. new management techniques (i.e., abatement techniques), or for new types of fertilizer. Our approach can thus be used to produce a variety of meta-models suitable for a diversity of situations and applications.

Zaman, M., Saggar, S., and Stafford, A. D. (2013). Mitigation of ammonia losses from urea applied to a pastoral system: The effect of nBTPT and timing and amount of irrigation. Proceedings of the New Zealand Grassland Association 75, 209-214.

Web references

http://agreste.agriculture.gouv.fr/definitions/zonages/. Last accessed 19 th April 2018.


Jean-François Lachaux

O Mornex

J Guillaud

P Restier

Joly

Dr Olivier Guillaud
email: olivier.guillaud@chu-lyon.fr

Jérôme Dumortier
email: jerome.dumortier@chu-lyon.fr

Julie Traclet
email: julie.traclet@chu-lyon.fr

Lioara Restier
email: lioara.restier@chu-lyon.fr

Philippe Joly
email: philippe.joly@chu-lyon.fr

Colette Chapuis Cellier

Alain Lachaux
email: alain.lachaux@chu-lyon.fr

Jean François Mornex
email: jean-francois.mornex@chu-lyon.fr

Institutionnal Adresses

Assessment of liver fibrosis by transient elastography (Fibroscan((R))) in patients with A1AT deficiency

Keywords: Alpha-1-antitrypsin deficiency, liver disease, fibrosis, cirrhosis, transient elastography, Fibroscan ABBREVIATIONS Alpha-1 antitrypsin deficiency (A1ATD), liver function tests

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Alpha-1 antitrypsin deficiency (A1ATD) is a common autosomal codominant genetic disorder which can cause severe pulmonary and/or liver diseases [START_REF] Silverman | Clinical practice. Alpha1-antitrypsin deficiency[END_REF]. The molecular defect is a specific mutation of the SERPINA1 gene leading to the synthesis of an abnormal protein (mostly A1AT Z) that cannot be secreted and polymerizes in the endoplasmic reticulum of hepatocytes [START_REF] Stoller | Alpha1-antitrypsin deficiency[END_REF][START_REF] Teckman | Alpha-1 antitrypsin and liver disease: mechanisms of injury and novel interventions[END_REF]. The inter-individual variability in the responses to intracellular stress induced by the accumulation of abnormal polymers, and in the mechanism allowing their degradation, is responsible for the different clinical manifestations of the liver disease which can vary from abnormal liver function tests (LFT), neonatal cholestasis to chronic hepatitis, cirrhosis and sometimes hepatocellular carcinoma [START_REF] Lachaux | Hepatic involvement in hereditary alpha-1-antitrypsin deficiency[END_REF][START_REF] Muensch | Liver disease and alpha 1-antitrypsin deficiency[END_REF][START_REF] Antoury | Alpha-1 antitrypsin deficiency and the risk of hepatocellular carcinoma in end-stage liver disease[END_REF][START_REF] Propst | Prevalence of hepatocellular carcinoma in alpha-1-antitrypsin deficiency[END_REF][START_REF] Sveger | Liver disease in alpha1-antitrypsin deficiency detected by screening of 200,000 infants[END_REF][START_REF] Sveger | The natural history of liver disease in alpha 1-antitrypsin deficient children[END_REF]. It is estimated that 10-15% of homozygous individuals for the Z allele (PiZZ) may develop liver fibrosis. So far, there is no approved specific treatment for the liver disease associated with A1ATD which accounts for 1-2% of annual liver transplantation in western countries [START_REF] Carey | Outcomes for recipients of liver transplantation for alpha-1-antitrypsin deficiency-related cirrhosis[END_REF]. Several complementary approaches dealing with increasing the autophagy process, silencing the expression of A1AT or preventing polymerization are currently in development and sometimes already in early clinical trials [START_REF] Lomas | Update on alpha-1 antitrypsin deficiency: New therapies[END_REF][START_REF] Puls | Autophagyenhancing drug carbamazepine diminishes hepatocellular death in fibrinogen storage disease[END_REF].

Liver involvement may be recognized late in the absence of systematic and complete liver evaluation. Furthermore, regular tests such as LFT and ultrasound (US) may be not sensitive enough to identify patients with early and reversible impairment. Liver biopsy, which was the gold standard in the diagnosis of most of liver diseases, has a morbidity in 0.5% patients (bleeding or pneumothorax) and a mortality of 0.02%, and can therefore not be recommended routinely in all patients [START_REF] Atwell | The timing and presentation of major hemorrhage after 18,947 image-guided percutaneous biopsies[END_REF]. For these reasons, noninvasive tests, either physical, such as measurement of liver stiffness by impulsive elastometry, or biological, with development of different scores (Fibrotest, Fibromètre, APRI, FIB-4, ELF, …) have been developed to evaluate liver fibrosis and tend to replace the biopsy in many diseases either during the initial work-up or during the follow-up [START_REF] Imbert-Bismut | Biochemical markers of liver fibrosis in patients with hepatitis C virus infection: a prospective study[END_REF][START_REF] Calès | A novel panel of blood markers to assess the degree of liver fibrosis[END_REF][START_REF] Sandrin | Transient elastography: a new noninvasive method for assessment of hepatic fibrosis[END_REF][START_REF] Castera | Noninvasive Assessment of Liver Fibrosis[END_REF][START_REF] Patel | Diagnosis of liver fibrosis: present and future[END_REF][START_REF] Boursier | Determination of reliability criteria for liver stiffness evaluation by transient elastography[END_REF][START_REF] Corpechot | Baseline values and changes in liver stiffness measured by transient elastography are associated with severity of fibrosis and outcomes of patients with primary sclerosing cholangitis[END_REF].

The aim of the present prospective study was to perform a systematic noninvasive evaluation of the liver fibrosis by elastometry using Fibroscan® in a cohort of A1-AT deficient patients with emphysema.

PATIENTS AND METHODS

Adults patients with an A1AT deficiency (A1ATD) and followed in our respiratory unit were enrolled prospectively in this study. Patients with an acute respiratory decompensation were excluded from the study. Twenty-eight patients PiZZ were included in this study. Four patients (2 with PiSZ and 2 with PiZ null) were screened but excluded because the risk of liver involvement is unclear in this setting.

Informed consent was obtained for all patients. This study was approved by the Ethical Review Board of South East IV (CPP Sud-Est IV) on 7 th April 2011, ID RCB Number 2011-A00264-37 and was registered as NCT01455298 on https://clinicaltrials.gov.

On the same day, all patients underwent a physical examination (with determination of Body Mass Index (BMI) and daily alcohol consumption), a biochemical profiling (which AST, ALT, GGT, ALP, INR, platelet count), an ultrasound (with determination of hepatomegaly, steatosis, dysmorphy and splenomegaly) and a transient elastography (Fibroscan®). Normal ranges were respectively 9-45 IU/L for AST, 9-65 IU/L for ALT, 12-64 IU/L for GGT, 35-130 IU/L for ALP.

Measurement of liver stiffness by transient elastography was performed using a Fibroscan® with a M probe as previously described [START_REF] Sandrin | Transient elastography: a new noninvasive method for assessment of hepatic fibrosis[END_REF][START_REF] Ziol | Noninvasive assessment of liver fibrosis by measurement of stiffness in patients with chronic hepatitis C[END_REF]. The results were expressed in kilopascals (kPa). Measures were considered reliable when they fulfilled all the following criteria: ≥10 valid measurements, ≥60% success rate and interquartile range / median ratio (IQR/M) ≤30.

Fibrosis was considered significant in case of liver stiffness > 7.2 kPa. Cirrhosis was defined by liver stiffness >14 kPa and/or US signs of cirrhosis (hepatic dysmorphy with splenomegaly) [START_REF] Castera | Noninvasive Assessment of Liver Fibrosis[END_REF].

APRI and FIB-4 scores were calculated for all patients and patients with APRI > 1 and/or FIB-4>3.25 were considered to have severe fibrosis [START_REF] Wai | A simple noninvasive index can predict both significant fibrosis and cirrhosis in patients with chronic hepatitis C[END_REF][START_REF] Sterling | Development of a simple noninvasive index to predict significant fibrosis in patients with HIV/HCV coinfection[END_REF].

Statistical analysis was performed using SPSS software, version 23.0 (IBM, Armonk, NY). Categorical variables were expressed as percentages and compared with the Chi-square or Fischer's exact tests. Continuous variables were expressed as median (ranges) and compared using the Mann-Whitney's test. A p value less than 0.05 was considered statistically significant.

RESULTS

The clinical characteristics of patients are shown in Table 1. Twenty-nine patients, 19 males and 10 females, were enrolled in this study. Median age was 50.4 yrs (21.5-67.2). Median serum A1AT level was 0.20 g/L (0.15-0.33). Diagnosis of respiratory emphysema was performed 65 months prior to this evaluation. Twenty-three patients were on augmentation therapy. The abnormalities revealed by abdominal US were hepatomegaly in 6 patients, steatosis in 2 patients, hepatic dysmorphy in 1 patient and splenomegaly in 1 patient. In one patient with dysmorphic hepatomegaly, steatosis and splenomegaly, the radiological evaluation was in favor of cirrhosis.

Impulsive elastometry was possible in 28/29 (97%) patients. The patient who failed Fibroscan® evaluation had complete normal LFT, US and FIB-4 and APRI values. Median liver stiffness was 4,5 kPa (2.8-32.8) (Table 1), and was >7,2 kPa in 5/28 (18%) and >14 kPa in 2/28 patients (7%).

FIB-4 and APRI scores were respectively >3.25 and >1 only in the two patients with Fibroscan® value >14 kPa.

When possible, Fibroscan® was increased in 2/2 (100%) patients with abnormal LFT and US, in 1/4 (25%) with normal LFT and abnormal US and in 2/22 (10%) patients with normal LFT and US (figure 1). Median Age, gender, median BMI and alcohol consumption was not different between the group of patients with significant fibrosis ≥F2 estimated by Fibroscan® and the group without fibrosis (p>0.05). Median AST, ALT, GGT were significantly higher in patients with significant fibrosis but remain in the normal range (Table 2). Median ALP, total bilirubin and platelet count were not different between the 2 groups.

DISCUSSION

The best strategy to identify PiZZ A1ATD individuals with liver impairment remains unclear. It has been shown that an increase in ALT has a low sensitivity to identify A1ATD adults with liver disease [START_REF] Clark | Liver test results do not identify liver disease in adults with alpha(1)-antitrypsin deficiency[END_REF], however the mean levels of liver enzymes were more elevated in patients with portal hypertension but frequently within normal range [START_REF] Teckman | Baseline Analysis of a young α-1-antitrypsin deficiency liver disease cohort reveals frequent portal hypertension[END_REF]. We found the same result in our study with a median value of transaminases in the normal range but 2-fold higher in the group of patient with significant fibrosis identified by Fibroscan®. In another study, ALT and GGT levels were similar to patient without liver disease and lower than patients with Non Alcoholic Fatty Liver Disease (NAFLD) [START_REF] Kim | Magnetic resonance elastography identifies fibrosis in adults with alpha-1 antitrypsin deficiency liver disease: a prospective study[END_REF].

Our results show that, in a cohort of PiZZ adult patients, Fibroscan® can identify in a non invasive way, complementary to LFT and US, 17% of patients with suspected significant fibrosis (≥F2) and 7% of patient with cirrhosis (≥F4). These results are consistent with those of a recent study where a systematic liver evaluation with liver biopsy was performed in 23 patient candidates for lung transplantation [START_REF] Morer | Liver involvement in patients with PiZZ-emphysema, candidates for lung transplantation[END_REF]. Morer et al. have shown that 13% of patients had moderate fibrosis (F2) and 8% severe fibrosis (F3 or F4). In another study, the prevalence of severe fibrosis or cirrhosis was 17,5% in PiZZ A1ATD patients who presented with either abnormal transaminases or abnormal platelet count or abnormal US [START_REF] Dawwas | Prevalence and risk factors for liver involvement in individuals with PiZZ-related lung disease[END_REF].

Recently, a pilot study has shown that liver stiffness evaluated by Magnetic Resonance Elastography (MRE) was significantly higher in eleven A1ATD patients compared to controls (2.6 vs 2.2 kPa) and was similar to patients with NAFLD (2.6 vs 2.7 kPa) [START_REF] Kim | Magnetic resonance elastography identifies fibrosis in adults with alpha-1 antitrypsin deficiency liver disease: a prospective study[END_REF]. As expected, MRE value was higher in patients according to the degree of fibrosis on histological evaluation. An MRE threshold of ≥3.0 kPa provided 88.9% accuracy with 80% sensitivity and 100% specificity to detect the presence of any fibrosis. MRE seems to be a promising technique to evaluate fibrosis in many diseases [START_REF] Kim | Comparison of gradient-recalled echo and spin-echo echoplanar imaging MR elastography in staging liver fibrosis: a meta-analysis[END_REF] however the availability, the duration and the cost of the procedure could be a brake on expansion of this modality, at least in a short period of time. On the contrary, Fibroscan® is an easy, rapid and somewhat costless procedure which has shown its interest in the most frequent liver diseases (chronic viral hepatitis, alcoholic liver disease, NAFLD, autoimmune hepatitis) [START_REF] Wilder | The clinical utility of FibroScan(®) as a noninvasive diagnostic test for liver disease[END_REF]. Even if the threshold to identify significant fibrosis or cirrhosis may vary according to the etiology, the different values are overall in the same range. To date, there is no data regarding the performance of Fibroscan® on A1ATD patients, probably because of its rarity. We were worried about the possible difficulties to perform Fibroscan® in patients with severe emphysema and thoracic distension but in our cohort the failure rate was only 3% ie in the normal range [START_REF] De Lédinghen | Transient elastography (FibroScan)[END_REF].

The absence of liver biopsy is the major limitation of our study. However because of the absence of specific treatment in case of liver involvement in one hand and on the other hand the risk of complications and the possible sampling error we decided to avoid this procedure which will not have changed the clinical management. In the future, soon hopefully, in case of specific treatment of the liver impairment, these patients would benefit from a biopsy to confirm or not the liver impairment as a pretherapeutic work-up. Currently, patients with either abnormal LFT or US but also with abnormal Fibroscan® are included in a program with a close monitoring in the liver clinic.

In conclusion, Fibroscan® is a well-known easy and repeatable tool and our results suggest that it can also be used in PiZZ patients to screen for the presence of significant liver fibrosis and to identify patients at higher risk to develop liver complications in the future and who may benefit from a closer surveillance. (LFT were considered elevated if one of the different parameters (AST, ALT, GGT or ALP) was upper the limit of the normal range. US was considered abnormal in case of the presence of one of the following items (hepatomegaly, steatosis, hepatic dysmorphy or splenomegaly). Fibroscan was considered abnormal when the stiffness was > 7.2 kPa).

TABLES

  Median BMI was 22.6 (18.0-31.2). Five patients were overweight (BMI 25-30) and one was obese (BMI >30). One patient had excessive daily alcohol consumption (>21 units per weeks), 16 patients were occasionnal drinkers. The biological and ultrasonography findings are shown in table 1. LFT were abnormal in 3 (10%) patients. Median ASAT, ALT, GGT, ALP and total bilirubin were respectively 28 IU/L (19-91), 23 IU/L (17-62), 33 IU/L (12-237), 72 IU/L (43-148), 11 µmol/L (11-52).

Table 1 :

 1 Clinical, biological, ultrasonography and elastometry characteristic of the patients (biological and elastometry values are expressed with median)

	Characteristic	Value	Range
	Clinical
	Number of patients	29
	Male, n (%)	19 (66)
	Age at evaluation (median)	50.4	21.5-67.2
	Serum A1AT level (g/L) (median)	0.20	0.15-0.76
	Emphysema, n (%)	28 (97)
	Augmentation therapy, n (%)	23 (79)
	Excessive alcohol consumption, n
	(%)	1 (3)
	BMI (median)	22.6	18.0-31.2
	BMI >25, n (%)	6 (21)
	Biological
	AST, IU/L	28	19-91
	ALAT, IU/L	23	14-62
	GGT, IU/L	33	12-237
	ALP, IU/L	72	43-148
	Total bilirubin, µmol/L	11	7-52
	Hb, g/L	151	130-173
	Platelets, G/L	255	125-394
	Ultrasonography
	Hepatomegaly, n (%)	6 (21)
	Steatosis, n (%)	2 (7)
	Dysmorphy, n (%)	1 (3.5)
	Splenomegaly, n (%)	1 (3.5)
	Elastometry
	Liver stiffness, kPa	4.6	2.8-32.8
	Success rate, %	80	60-100
	IQR/med, %	22	7-29

Table 2 :

 2 Biological results according to the value of Fibroscan® (all biological data are expressed with median (range)) Flow chart describing the results of liver function tests and liver imagery in the 28 patients with interpretable Fibroscan®.

		Fibroscan® > 7.2 kPa Fibroscan® ≤ 7.2 kPa
	n	5	23
	AST, IU/L	41 (22-91)	25 (19-40)	p=0.027
	ALT, IU/L	45 (23-56)	21 (14-45)	p=0.002
	GGT, IU/L	55 (34-194)	29 (12-62)	p=0.004
	ALP, IU/L	96 (45-148)	72 (43-104)	p=0.239
	total bilirubin, µmol/L	11 (9-52)	11 (7-20)	p=0.264
	platelet median, G/L	212 (125-394)	268 (140-374)	p=0.215

ACKNOWLEDGEMENTS

The authors would like to thank LFB Biomedicaments (France) for their financial support which allowed the collection of data.