Gatien N Falconnier

Etienne-Pascal Journet

Laurent Bedoussac

Anthony Vermue

Florent Chlebowski

Nicolas Beaudoin

Eric Justes

Florent Chlébowski

Calibration and evaluation of the STICS soil-crop model for faba bean to explain variability in yield and N2 fixation

Keywords: parameter estimation, yield variability, abiotic stresses, grain legume

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

Introduction

Current cropping systems in Europe are characterized by high productivity but rely on simplification of crop rotations and high level of synthetic inputs which has led to soil, water and air pollution and loss of biodiversity (e.g. [START_REF] Stoate | Ecological impacts of early 21st century agricultural change in Europe -A review[END_REF]). Diversification of current cropping systems with grain legumes can improve agronomic, economic and environmental performance and provide supporting and regulating ecosystem services. In particular, relying on biological N 2 fixation decreases the dependence on synthetic nitrogen fertilizer and reduces the associated direct and indirect greenhouse gases emissions and risks of nitrate leaching [START_REF] Plaza-Bonilla | Innovative cropping systems to reduce N inputs and maintain wheat yields by inserting grain legumes and cover crops in southwestern France[END_REF][START_REF] Reckling | A cropping system assessment framework-Evaluating effects of introducing legumes into crop rotations[END_REF]. However, legumes often suffer from water and temperature stress: i) drought during reproductive phase can cause severe yield reduction [START_REF] Daryanto | Global synthesis of drought effects on cereal, legume, tuber and root crops production: A review[END_REF] and ii) heat can impact negatively seed set and grain filling [START_REF] Prasad | Field crops and the fear of heat stress-Opportunities, challenges and future directions[END_REF]. Even though not always well appreciated, N 2 fixation can also be severely restricted by stresses due to drought, heat, anoxia and soil mineral N content in the root zone [START_REF] Liu | Models of biological nitrogen fixation of legumes. A review[END_REF]. Furthermore, legumes are exposed to damages from pests, diseases and weeds at different time in their growth cycle [START_REF] Rubiales | Achievements and Challenges in Legume Breeding for Pest and Disease Resistance[END_REF]. Strong yield variability and lack of reliable agronomic diagnosis are the main reasons mentioned by farmers for nonadoption of legumes in cropping systems [START_REF] Meynard | Designing coupled innovations for the sustainability transition of agrifood systems[END_REF][START_REF] Watson | Grain Legume Production and Use in European Agricultural Systems[END_REF].

Dynamic process based soil crop models can assist the understanding of current yield variability by simulating patterns of seasonal water and temperature stress [START_REF] Affholder | Diagnosis of the productivity gap using a crop model. Methodology and case study of small-scale maize production in central Brazil[END_REF][START_REF] Hayman | The impact of El Niño Southern Oscillation on seasonal drought in the southern Australian grainbelt[END_REF]. They are useful tools to diagnose agronomic constraints to crop production and to explore the impact of current and future climate variability. Therefore, they can assist the design of more resilient cropping systems by analysing model outputs.

Furthermore, these models allow to estimate indicators that are crucial for the assessment of crop rotations but tedious or expensive to quantify in experimental plots, e.g. biological N 2 fixation [START_REF] Liu | Models of biological nitrogen fixation of legumes. A review[END_REF], water drainage [START_REF] Bruelle | Can conservation agriculture improve crop water availability in an erratic tropical climate producing water stress? A simple model applied to upland rice in Madagascar[END_REF], N 2 O emissions or nitrate leaching [START_REF] Plaza-Bonilla | Cover crops mitigate nitrate leaching in cropping systems including grain legumes: Field evidence and model simulations[END_REF].

The STICS model is a generic dynamic soil-crop model that has been used to assess the agronomic and environmental performances of crop rotations and to support the design of innovative cropping systems in a wide range of agro-pedo-climatic conditions [START_REF] Coucheney | Accuracy, robustness and behavior of the STICS soil-crop model for plant, water and nitrogen outputs: Evaluation over a wide range of agro-environmental conditions in France[END_REF]. For example, [START_REF] Bécel | Assessing nitrate leaching in cropping systems based on integrated weed management using the STICS soil-crop model[END_REF] assessed the impact of various integrated weed management strategies on nitrate leaching. Constantin et al. (2015) determined the optimal date of emergence and destruction of cover crops to reduce nitrate leaching. [START_REF] Jégo | Calibration and performance evaluation of soybean and spring wheat cultivars using the STICS crop model in Eastern Canada[END_REF] analyzed the effect of fertilization, irrigation strategies and climate variability on nitrate leaching in sugar beet/potato cropping systems. So far, spring pea (Pisum Sativum L.) and soybean (Glycine max (L.) Merr.) are the only grain legume calibrated for STICS [START_REF] Corre-Hellou | Adaptation of the STICS intercrop model to simulate crop growth and N accumulation in pea-barley intercrops[END_REF][START_REF] Jégo | Calibration and performance evaluation of soybean and spring wheat cultivars using the STICS crop model in Eastern Canada[END_REF]. STICS can simulate N sharing between companion crops and N carry over effects on following crops, but all the involved crops must be calibrated for STICS. Given the potential of grain legume to improve cropping system sustainability in Europe [START_REF] Watson | Grain Legume Production and Use in European Agricultural Systems[END_REF] and the potential of crop models to help with the design of innovative and resilient cropping systems including legumes, there is a need to broaden the number of grain legume crops calibrated and evaluated with the STICS cropping system model. Faba bean (Vicia Faba L.) is the second most widely grown European grain legumes [START_REF] Watson | Grain Legume Production and Use in European Agricultural Systems[END_REF]. Its proportion of crop N derived from atmospheric N 2 is the greatest among major grain legumes cultivated in Europe (153 kg N ha -1 on average) [START_REF] Jensen | Faba bean in cropping systems[END_REF]. It is a high-biomass crop leaving more residues and giving a greater nitrogen-related yield effect on the subsequent crop compared with low biomass crop like chickpea and lentil for example [START_REF] Watson | Grain Legume Production and Use in European Agricultural Systems[END_REF]. However faba bean, like other legume crops, can suffer from strong yield and N 2 fixation reduction due to abiotic factors [START_REF] Bishop | Susceptibility of Faba Bean (Vicia faba L.) to Heat Stress During Floral Development and Anthesis[END_REF][START_REF] Khan | Faba bean breeding for droughtaffected environments: A physiological and agronomic perspective[END_REF][START_REF] López-Bellido | Chickpea and faba bean nitrogen fixation in a Mediterranean rainfed Vertisol: Effect of the tillage system[END_REF] and pests and diseases [START_REF] Stoddard | Integrated pest management in faba bean[END_REF].

Winter faba bean experiments were conducted in southwestern France over several growing seasons (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) with limited pest, disease and weeds pressure, This dataset provides a rich basis to adapt STICS to faba bean and analyse the capacity of the model to unravel the role of abiotic factors in driving yield and N 2 fixation variability. Our first objective was to calibrate and assess the performance of STICS to simulate N acquisition by soil mineral uptake and biological N 2 fixation, crop development and shoot biomass production, grain yield formation, N content in grain and straw, and soil water and mineral N contents along the whole profile during crop growth and after harvest. By doing so, we explored the hypothesis that the generic model -(i.e. with the same formalism for all crops) can take into account the specificities of faba bean (N 2 fixation) and can be robustly calibrated for this grain legume.

The second objective was to analyze the ability of STICS to generate a robust prediction for an independent dataset and allow a credible agronomic diagnosis of yield and N 2 fixation variability due to abiotic stresses. For this objective, our hypothesis was thatthe spatiotemporal adequacy of soil/crop relationships (e.g. N nutrition based on both mineral-N uptake and N2 fixation) and the realism of the implemented process equations allow for an accurate prediction of abiotic stresses.

Materials and Methods

STICS, a soil-crop model

Overview of the model

The soil-crop model (as well as cropping system model) STICS (Brisson et al., 2008[START_REF] Brisson | STICS: a generic model for simulating crops and their water and nitrogen balances. II. Model validation for wheat and maize[END_REF][START_REF] Brisson | STICS: a generic model for the simulation of crops and their water and nitrogen balances. I. Theory and parameterization applied to wheat and corn[END_REF] was chosen for its agro-environmental purpose, crop genericity (allowing the simulation of crop successions with the same model) and robustness. STICS simulates carbon, water and nitrogen dynamics in the soil-crop system on a daily time step over the crop cycle.

Unlike crop models that combine crop modules with different structures, e.g. DSSAT (Decision Support System for Agrotechnology Transfer, [START_REF] Jones | The DSSAT cropping system model[END_REF] or APSIM ( Agricultural Production Systems sIMulator, [START_REF] Keating | An overview of APSIM, a model designed for farming systems simulation[END_REF], STICS uses a common and generic structure for different crop species. Species-specific sets of parameters define the differences between species. STICS has been adapted and tested for different type of crops (e.g. winter wheat, maize, barley, sunflower, rapeseed, grassland, tomato, grapevines) [START_REF] Coucheney | Accuracy, robustness and behavior of the STICS soil-crop model for plant, water and nitrogen outputs: Evaluation over a wide range of agro-environmental conditions in France[END_REF].

Inputs to the model include daily weather information (minimum and maximum temperature, rainfall, wind and global radiation), soil characteristics (per-layer initial soil water and mineral N content, field capacity and wilting point) and crop/soil management (date and depth of planting, planting density, soil tillage, residues management, organic and mineral fertilisation, irrigation).

Crops are defined by species parameters, ecophysiological options (e.g. effect of photoperiod and/or cold requirements on crop phenology, potential radiation use efficiency) and cultivar specific parameters (e.g. flowering precocity, maximum number of grains per m 2 ). Crop temperature (calculated from weather variables) and photoperiod drive crop phenology. The model dynamically simulates (i) development of the root system that takes up N and water according to root density over the whole soil profile and (ii) the establishment of the canopy that transpires water and intercepts light to produce the crop biomass.

Two processes account for yield formation in the model: (i) setting of grain number per square meter and (ii) accumulation of biomass in grain. The number of grains before the start of grain filling is a function of: (i) the number of days before the beginning of grain filling during which grain number is determined (crop parameter), (ii) the mean canopy growth rate during this phase (calculated by the model), (iii) the sensitivity of grain onset to growth conditions (crop parameter) and (iv) the maximum number of grain (crop parameter). Dry matter accumulation in grains is calculated by applying a dynamic harvest index (grain to shoot biomass ratio) to the dry weight of the plant [START_REF] Amir | A model of the temperature and solar-radiation effects on spring wheat growth and yield[END_REF]. This harvest index increases with time from the beginning of grain filling to physiological maturity, the rate of increase being a crop parameter. A maximum final harvest index (crop parameter) prevent unrealistic remobilization levels. A maximum grain yield corresponding to the simulated number of grains multiplied by the maximum weight of one grain (crop parameter) is computed to avoid unrealistic yield level.

The model also accounts for soil water and N dynamics. Net N mineralization from crop residues and soil organic matter (affected by clay and CaCO 3 content in the topsoil and governed by soil moisture and temperature), nitrification (affected by pH in the topsoil), nitrate leaching and ammonia and nitrous oxide gaseous emissions are daily simulated as well as vertical water drainage when field capacity is exceeded.

STICS also simulates N acquisition by N 2 fixation for legumes. Nodule formation is a function of soil thermal time and sets the potential fixation. Actual N 2 fixation then depends on shoot growth rate (C limitation for N 2 fixation), soil temperature, soil moisture, and a nitrate inhibition effect linked with nitrate-N concentration in the nodulation layer (see section 2.1.2).

The equations governing physical and biological processes occurring in the soil/crop system are based on a unique set of general parameters. Model parameters and equations describing yield formation are of particular interest in this study and are described in details in Table S2.

An exhaustive description of inputs, equations and default parameter values of the STICS model is given in Brisson et al. (2008). [START_REF] Bergez | Evolution of the STICS crop model to tackle new environmental issues: New formalisms and integration in the modelling and simulation platform RECORD[END_REF] give an overview of the latest plant and soil process-based developments of the STICS model, and [START_REF] Coucheney | Accuracy, robustness and behavior of the STICS soil-crop model for plant, water and nitrogen outputs: Evaluation over a wide range of agro-environmental conditions in France[END_REF] detailed the STICS version 8.5 used in this study.

Stress factors

Physical and biological processes are successively addressed in two types of equations: 1) the calculation of the potential flux or rate of the process; 2) the effect of the environmental limiting factors, including the stress factors of the crop (light, C, N and water). Four stress factors can indirectly affect grain yield through plant growth. The first is a water stress factor that affects radiation use efficiency and plant transpiration, and is computed as the ratio of actual evapotranspiration over potential evapotranspiration. Potential transpiration is function of Leaf Area Index (LAI) and daily potential Penman evapotranspiration, as calculated by the model. Actual transpiration is calculated as the minimum between water soil supply and maximal crop demand. The second stress factor is a Nitrogen stress that affects 1) LAI increase, 2) radiation use efficiency and 3) possibly senescence. The N stress index is computed as the ratio of actual Nitrogen concentration over Critical crop N concentration.

Critical crop N concentration is the minimum N concentration that allow to maximise biomass production [START_REF] Lemaire | N Uptake and Distribution in Plant Canopies[END_REF]. Actual N uptake is calculated as the minimum between soil supply and maximal crop demand. The third stress is a heat reduction factor on radiation use efficiency that increases when daily average crop temperature exceeds optimal crop temperature and is maximal when daily average crop temperature exceeds maximal crop temperature. The fourth is a heat stress factor that stops grain yield when daily average crop temperature exceeds maximal temperature for grain filling.

For legumes, STICS also calculates water, heat, anoxia and nitrogen stress factors for N 2 fixation. The water deficit factor for N 2 fixation is the proportion of soil layers in the nodulation area (crop parameter "profnod", set to 30 cm in our study) for which moisture is above wilting point. The heat stress factor for N 2 fixation increases and is maximal when soil temperature in nodulation zone exceeds optimal and maximal temperature thresholds.

Nitrogen stress for N 2 fixation increases and is maximal when the mean amount of mineral nitrogen in the rooting zone (i.e. the upper soil layers where the bacterial symbiosis is the most active) exceeds an optimal or maximal N concentration threshold. Eventually, anoxia stress factor for N 2 fixation increases with the proportion of soil layers in anaerobic conditions.

Stress factors are computed daily and vary between 0 (complete stress) and 1 (no stress).

Model parameters and equations used to compute water stress factor and water deficit factor for N 2 fixation are of particular interest in this study and are described in details in Table S2.

The exhaustive description of the equations and parameters governing the stresses definition can be found in Brisson et al. (2008).

Experimental data

Sites and experimental design

The experimental data was collected in south of France at the experimental sites of INRA in Auzeville (43°31'N 1°28'E), and of CREAB-MP in Auch (43°38'N 0°36'E) during seven growing seasons in each site. In both sites, the climate is oceanic temperate under mediterranean influence and characterized by summer droughts and cool wet winters.

Cumulative global radiation, growing degree-days and rainfall during crop growth (November-July), averaged across growing seasons, were similar in Auch and Auzeville (Table 1). Experimental plots were in the valley on deep (i.e. average maximum rooting depth of 135 cm) clay-loamy soils in Auzeville and on the hillside on shallow (i.e. average maximum rooting depth of 70 cm) clay loamy soils in Auch. As a result, average maximum available water to maximum rooting depth (i.e. soil water content at field capacity minus soil water content at wilting point) was higher in Auzeville (167 mm) than in Auch (64 mm) (Table 1).

Cropping systems strongly differed between experimental sites. In Auzeville, the data originated from two distinct types of experiments. The first type was annual experiments with replicated plots (1.62 m wide x 13m long) of sole faba bean (see [START_REF] Bedoussac | The efficiency of a durum wheat-winter pea intercrop to improve yield and wheat grain protein concentration depends on N availability during early growth[END_REF] and [START_REF] Kammoun | Analyse des interactions génotype x environnement x conduite culturale de peuplement bi-spécifique de cultures associées de blé dur et de légumineuses à graines, à des fins de choix variétal et d'optimisation de leurs itinéraires techniques[END_REF] for a detailed description of experimental design). The second type was a long-term cropping system experiment established in 2003 on 200 x 30 m plots with different three-years rotations varying in the frequency of grain legumes and the use or not of cover crops [START_REF] Plaza-Bonilla | Innovative cropping systems to reduce N inputs and maintain wheat yields by inserting grain legumes and cover crops in southwestern France[END_REF]. Appropriate herbicide and pesticides were applied to control weeds, pests and diseases and no N fertilizer was applied on legumes.In Auch, the data originated from an organic long-term soil fertility monitoring experiment (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013) with 50 x 50 m plots with Faba bean -Oat or wheat -Sunflower rotations [START_REF] Colomb | Des bilans de phosphore majoritairement négatifs pour les systèmes de grandes cultures biologiques sans élevage en Midi-Pyrénées. Quels impacts sur le phosphore biodisponible des sols et l'état de nutrition des cultures?[END_REF].Auch was managed without mineral fertiliser, herbicides and pesticides. As a result, only the plots where the monitoring revealed negligible pests, disease and weed pressure were considered. In both sites, the land was plowed prior to sowing and only in 2007 in Auzeville small amounts of irrigation water (20-50mm) was applied after sowing (Table 2) to ensure satisfactory crop establishment.

The considered faba bean cultivars were Castel and Irena (Table 2). These winter-type cultivars sown between November and January have similar phenology and yield potential [START_REF] Flores | Faba bean adaptation to autumn sowing under European climates[END_REF]. Site, year, and management factors (cultivar, crop density, incorporation of a cover crop before planting and sowing date) defined 35 Site-Year-Management units (Table 2). Site-year-management units covering a broad range of soil types, growing seasons and management situations [START_REF] He | Data requirement for effective calibration of process-based crop models[END_REF] were chosen for the calibration dataset (Table 2).

The remaining units, differing in growing season and/or management (compared with calibration dataset) formed the evaluation dataset (Table 2).

Measurements

Faba bean development stages were recorded in the annual experiments in Auzeville following BBCH scale [START_REF] Meier | Growth stages of mono-and dicotyledonous plants: BBCH Monograph[END_REF], namely (i) BBCH 09: 50% of shoot have emerged through soil surface (ii) BBCH 70: first pods have reached final length (corresponding to "drp" stage in STICS, i.e. the beginning of grain filling). Additionally, interpolation of discontinuous LAI observations allowed for determining the date of the end of juvenile phase (amf stage in STICS, corresponding to maximum growth rate of LAI). The interpolation was carried out with the tool integrated in STICS that uses an functional equation to differentiate LAI growth (logistic equation) and senescence (exponential equation), the difference between the two functions giving the green LAI (see [START_REF] Casa | Forcing a wheat crop model with LAI data to access agronomic variables: Evaluation of the impact of model and LAI uncertainties and comparison with an empirical approach[END_REF], for detailed equations and procedure).

In each experimental field, soil texture and pH were measured over the whole soil profile (0-120 cm). Soil mineral N and water content were measured by layers of 30 cm three times per year: (1) end of autumn prior to sowing, (2) mid-winter and (3) at harvest. Crop variables such as LAI, above-ground biomass, fixed N 2 and total accumulated N, grain yield and grain N content were measured from 1 to 5 times depending on site, year and experiment (Table 2): (1) in mid-March i.e. wheat '1cm ear' stage, (2) in mid-April, i.e. legume flowering, (3) in mid-may i.e. wheat flowering, (4) in early June i.e. wheat ripening, and (5) in early July, i.e. legume maturity. At each measurement, six central rows 0.5 m long (annual experiments in Auzeville), six m 2 (long term cropping system experiment in Auzeville) and nine subplots of two rows 1 m long (in Auch) were harvested by cutting plants at the soil surface. In the annual experiments in Auzeville, a LI-3100 planimeter (LI-COR, Lincoln, NE) was used to determine green leaf area. In all experiments, plant biomass samples were dried at 80°C for 48 h and weighted. At maturity, plants were threshed to determine grain yield and harvest index. Above-ground plant and grain N concentration were determined on finely ground plant material with the Dumas combustion method using a Leco-2000 analyzer (LECO, St. Joseph, MI, US). In Auzeville, N 2 fixation ratio, i.e. the proportion of plant N derived from atmosphere (%Ndfa) was determined using the 15 N natural abundance method [START_REF] Unkovich | Measuring plant-associated nitrogen fixation in agricultural systems[END_REF] with unfertilized wheat and non-legume weeds as reference plants in the annual and long-term experiments respectively. %Ndfa was calculated as follows:

%Ndfa = 100 × (1)
where δ 15 N is the deviation from the international standard of atmospheric N 2 (0.3663% 15 N) for faba bean (δ 15 N faba bean ) and for the reference crop (δ 15 N ref ), and β is the δ 15 N of shoots of faba bean fully dependent upon N 2 fixation, assumed equal to -0.63 ‰ [START_REF] Unkovich | Measuring plant-associated nitrogen fixation in agricultural systems[END_REF].

The amount of N 2 fixed was calculated as the product of %Ndfa and total above-ground plant N.

Moreover, dynamics of maximum rooting depth of faba bean was monitored in 2013 during the annual experiment in Auzeville (Table 2) using a rotary scanner-based minirhizotron system (CI-600, CID Bio-science, Camas, WA, USA) six times during crop growth (16 and 28 March, 12 April, 6 May, 3 June, 17 July).

Calibration procedure

The calibration consisted in choosing the formalisms and corresponding parameters involved in the simulation of crop phenology, leaf area and root system expansion, biomass accumulation, biological nitrogen fixation, nitrogen uptake and grain yield elaboration.

The parameterization procedure included three steps (Figure 1). The first step was a literature review to select the options offered by the model to simulate the different crop processes and determine existing parameter values s. The second step corresponded to the determination of parameters from experimental data by direct measurement or observation (phenology). The last step consisted in a mathematical optimisation based on the approach developed by [START_REF] Guillaume | Methodological comparison of calibration procedures for durum wheat parameters in the STICS model[END_REF], including nine stages representing the different key processes in the simulation of the final outputs of the model (Table 3). For each stage, sensitivity analysis [START_REF] Ruget | Sensitivity analysis of a crop simulation model, STICS, in order to choose the main parameters to be estimated[END_REF] and expert knowledge were used to select the parameters having the strongest impact on model outputs. In total, 29 crop parameters were mathematically optimised (Table 3). Stage-specific target variables were selected: (i) dates of key development stages (emergence, end of juvenile phase, beginning of grain filling and physiological maturity), (ii) dynamic variables (Leaf Area Index, above-ground biomass, fixed N and total plant N, overall soil moisture content and overall soil N content) and (iii) variables at crop maturity (yield components, grain yield and grain N content) (Table 3). The calibration stages were carried out by using the software package OptimiSTICS (Wallach et al., 2011) and the methodology detailed by [START_REF] Buis | The STICS crop model and associated software for analysis, parameterization, and evaluation[END_REF]. Model error was computed as the difference between measured and simulated values for a given target variable at a given date. The goodness of fit Cv was obtained following the formula:

= ∑ ∑ , -" , #$%& ' ( 2
)
Where v is the target variable, s is the site-year-management unit and n s is the number of measurements in s, O s,i is the measured value in site-year-management s on the ith date and P s,i ($) is the corresponding simulated value with the parameter set $.

This average squared error for a given target variable was minimised using a simplex algorithm. For each optimised parameter, , lower and upper limits corresponding to reasonable physiological values were fixed based on literature and expert knowledge (Table 3). The optimised parameter values at a given stage were the default values of the next steps.

The initial plant parameters before optimisation were taken from the spring pea plant file [START_REF] Corre-Hellou | Adaptation of the STICS intercrop model to simulate crop growth and N accumulation in pea-barley intercrops[END_REF]. Given the similarities in crop functioning and yield potential observed in our experiments between the two studied faba bean cultivars (Irena and Castel),

we did not calibrate specific cultivar parameters.

Soil analysis informed the input parameters required for soil in STICS. Moisture at field capacity and wilting point were first obtained using pedo-transfer functions [START_REF] Saxton | Soil water characteristic estimates by texture and organic matter for hydrologic solutions[END_REF] and also based on laboratory measurements on sieved soil for field capacity, and then adjusted by trial and error to minimize the error between simulated and observed soil water content in mid-winter. The recorded crop managements (Table 2) were used to create management files used for each simulation. Initial soil mineral nitrogen (nitrate ammonium) and water content were measured for each experiment and set between 13 and 120 kg N ha -1 and 162 and 342 mm respectively, depending on the different Site-year-management units (Table 2).

Model evaluation

Model performance (with optimised parameter set) was evaluated graphically and quantified by calculating Mean Bias Error (MBE) and its relative value (rMBE), Model Efficiency (EF), Root Mean Square Error (RMSE) and its relative value (rRMSE):

)*+ = ∑ #" - , % (3)
-)*+ = ./0 1 2 × 100 (4) +3 = 1 - ∑ #1 4 5 4 % 6 478 ∑ #1 4 1 2%6 478 (5) 9):+ = ; ∑ # -" , % ' (6) -9):+ = <.=0 1 2 × 100 (7)
where O i and P i are the observed and simulated values for the i th measurement, n is the number of observations and 2 is the mean of the observed values. predictions were judged satisfactory when EF value were greater than 0.5 and rMBE lower than 10%. A summary of the calibration and evaluation procedure can be found in Figure 1.

Stress factors and variability in grain yield and total N 2 fixed

Stress factors calculated by STICS (see section 2.1.2 and Table S2) were averaged over periods ranging from -60 to + 60 days before/after the beginning of grain filling. For each period, the Pearson correlation coefficient (R 2 ) between observed grain yield (total fixed N 2 respectively) and stress factor affecting grain yield (N 2 fixation respectively) over the period was computed. The period corresponding to the maximum R 2 was determined. For this analysis, calibration and evaluation datasets were pooled.

Results

Parameter values obtained from literature, experimental data and optimisation

Eight parameters values were obtained from literature (Table 4). Faba bean shows a long day response to photoperiod [START_REF] Ellis | Effects of Temperature, Photoperiod and Seed Vernalization on Flowering in Faba Bean Vicia faba[END_REF] and needs vernalisation [START_REF] Patrick | Physiology of flowering and grain filling in faba bean[END_REF]) so we activated these physiological options in the faba bean plant file. Faba bean base temperature for crop development (tdmin) was set to 0°C [START_REF] Tribouillois | Determination of Germination Response to Temperature and Water Potential for a Wide Range of Cover Crop Species and Related Functional Groups[END_REF]. Because there was no available data in the literature, base and optimal temperature for photosynthesis (temin and teopt) were approximated from those for emergence rate [START_REF] Tribouillois | Determination of Germination Response to Temperature and Water Potential for a Wide Range of Cover Crop Species and Related Functional Groups[END_REF] (Table 4), based on the assumption that cardinal temperatures for developmental processes are close for a given species (e.g. [START_REF] Parent | Temperature responses of developmental processes have not been affected by breeding in different ecological areas for 17 crop species[END_REF]. Cardinal temperatures for nodulation (tempnod1, tempnod2, tempnod3, tempnod4) were obtained from [START_REF] Boote | Adapting the CROPGRO legume model to simulate growth of faba bean[END_REF] (Table 4).

Four parameters values were obtained using direct in-field measurement (Table 4). Maximum and minimum number of grain per square meter (nbgrmax and nbgrmin), maximum grain weight (pgrainmaxi) and maximum harvest index (irmax) were set to the maximum or minimum measured values in the experiments in Auzeville and Auch with an added or subtracted 10% respectively to reach assumed potential values (Table 4 and Figure 2).

The other 30 parameters values were set according to the result of the sequential optimisation with OptimiSTICS using measured variables (Table 4).

Agreement between simulated and observed values

Crop development and LAI

Calibration led to satisfactory prediction of the dates of emergence, end of juvenile phase, beginning of grain filling and physiological maturity. Relative bias was low (0 -10%) with fair EF values (Figure 3), indicating the relevance of calculating crop development based on vernalisation and photoperiodic and thermal time-course formalisms. Simulated LAI values for the calibration dataset were close to observed values with a low relative bias of 1% and a satisfactory EF of 0.69. Prediction error was however great due to a bias of a few days in the senescence dynamic that had large consequences on the daily agreement between observed and simulated LAI values (rRMSE=56%) (Figure 4a).

Above ground biomass, N 2 fixation and N acquisition

Predicted biomass agreed with observation throughout the growth seasons in both calibration and validation datasets (EF>0.77 and -7% < bias < 0%). Prediction error was high due to senescence defoliation between grain physiological maturity and harvest that was difficult to precisely simulate (rRMSE of 41 and 31% for calibration and evaluation respectively). There was a large variation in faba bean biomass at harvest (1.5 -11.6 t ha -1 and 2.8 -7.2 t ha -1 for calibration and evaluation datasets respectively) depending on site, year and management (Figure 4c,d) and the model was able to reproduce this behaviour.

The calibration of parameters related to N 2 fixation (Table 3 andTable 4) allowed to reach a good agreement of simulated versus observed values throughout crop growth (Figure 4e,f) (EF = 0.77 with negligible bias). EF remained high and bias remained low in the evaluation indicating that the model was able to reproduce the wide range of final N 2 fixed at harvest (62-166 kg N ha -1 , Figure 4f). N acquired (N content in crop aerial parts) was adequately simulated with low bias both in calibration and evaluation (-7 and 2% respectively) and EF values above 0.5 (Figure 4g, h).

Grain yield and grain N content

Observed grain yield greatly varied depending on site-year-management (0.42 -4.7 t ha-1 , Figure 5a). The model performed well in simulating grain yield (EF=0.66 with low relative bias) for calibration dataset. Model performance remained satisfactory during evaluation, with an EF value of 0.65 and a relative bias of -1% (Figure 5b).

Simulated grain N content was slightly underestimated (relative bias of -10%) in the calibration dataset with a satisfactory EF value of 0.60 (Figure 5c). In the evaluation, grain N content was predicted with a low relative bias (3%). The EF was low (0.27) but the range of observed values for evaluation (65-162 kg N ha -1 ) was narrower than for calibration (21-200 kg N ha -1 ).

Soil water and soil mineral N contents

Soil water content over the entire profile was correctly simulated by the model, both during calibration and evaluation (EF>0.70 with small relative bias) (Figure 5e, f). Soil N content was less adequately predicted, with small (0.22) and negative (-1.42) EF values, in calibration and evaluation respectively (Figure 5g,h). Bias was low in the evaluation (-10%), indicating that though the model was not able to reproduce precisely the differences between site, year and management, it predicted soil mineral N content within the range of the rather low observed values.

Impact of temporal dynamics of stress factors

With regard to grain yield, the water stress factor (i.e. water supply/demand ratio, see section 2.1.2 and Table S2) had the strongest explanatory power. Indeed, when averaged over a period of 6 days before the beginning of grain filling (i.e. the end of grain onset), it explained 78% of the observed grain yield variability in the overall dataset (Figure 6a). The model fairly reproduced the temporal dynamic of above ground biomass (Figure 7d, e, f). Water stress during the end of grain onset (Figure 7a,b,c) affected the growth rate of above ground biomass (Figure 7d, e, f), which in turn influenced the final number of grains (Figure 7g, h, i).

In the end, the model was able to simulate contrasting water stresses that occurred in different soil types (valley/hillside) for a range of climatic conditions and their final impact on the number of grain and grain yield (Figure 7). Heat stress effect on radiation use efficiency, conversely, had a limited explanatory power in our conditions. Indeed, when averaged over a period of 26 days after the beginning of grain filling (the period with the best correlation), heat stress explained only 25% of the observed grain yield variability. The model diagnosed no heat stress on grain filling in the majority of the site-year-management units. There were only five days in 2002 in Auch during which crop temperature exceeded the maximal temperature above which grain filling stops (Figure S1).

With regard to N 2 fixation, the water deficit factor had also the strongest explanatory power.

Thus, when averaged over a period of 20 days after the beginning of grain filling, it explained 82% of the observed variability in total fixed N 2 at harvest (Figure 6b). Despite a limited number of within-season measurements in some situations (Figure 8d), the model reproduced reasonably well the temporal dynamic of N 2 fixation (Figure 8c,d). In the end, the model was able to reproduce the wide range of total fixed N 2 at harvest (62-172 kg ha -1 , see Figure 6).

The model diagnosed no stress due to anoxia in any of the cropping situations of this study.

Though the model diagnosed limited heat and nitrogen stresses in some situations (value of 0.67 and 0.58 respectively) the correlation with the amount of N 2 fixed was not significant for any of the periods considered.

Discussion

A method to adapt a generic crop model to a new crop

While the process of calibrating a new cultivar is well described (e.g. [START_REF] Jégo | Calibration and performance evaluation of soybean and spring wheat cultivars using the STICS crop model in Eastern Canada[END_REF], less emphasis has been put on the description of the adaptation of a generic soil-crop model to a new crop. Previous studies mainly described a partial calibration based on a limited set of target variables, e.g. LAI or AGB and Soil water [START_REF] Confalonieri | A preliminary evaluation of the simulation model CropSyst for alfalfa[END_REF][START_REF] Ko | Parameterization of EPIC crop model for simulation of cotton growth in South Texas[END_REF], and did not address the broad range of processes available in the model (e.g. root system expansion, Nitrogen uptake, yield formation). Our study shows that the generic STICS soil-crop model can be successfully adapted to a new crop, and in particular a grain legume having the specificity of N 2 fixation. The adaptation was based on two steps, namely: (i) a parameter estimation based on measurement and literature and (ii) a sound and careful sequential optimisation of crop parameters that were not measured nor estimated using existing literature. Therefore, our work contributes to establish a generic method to calibrate a new annual crop for soil-crop models that (i) have a common structure for different crop species, (ii) are functional deterministic models considering water, C and N cycles, on a daily time step [START_REF] Di Paola | An overview of available crop growth and yield models for studies and assessments in agriculture[END_REF] and (iii) have an available parameter optimisation tool.

Estimating a parameter from direct measurements and literature has the advantage of not being based on the assumption that model formalism and all other parameters are reliable, as it is the case with mathematical optimisation [START_REF] Grant | Modeling transformations of soil organic carbon and nitrogen at different scales of complexity[END_REF]. It should be therefore prioritised and in our approach we had 9 parameters estimated in this way (Table 4). However, this procedure is not always possible for many reasons. Firstly, field measurements of parameters is expensive and time consuming [START_REF] Anothai | A sequential approach for determining the cultivar coefficients of peanut lines using end-ofseason data of crop performance trials[END_REF]. Secondly, the dataset used for model calibration may not be originally intended to cover model calibration issues (as it was the case in our study), so that most of crop model parameters are not directly measured (e.g. radiation use efficiency). Thirdly, the need for similar environmental conditions, varieties and exact correspondence of the measured variable to the process represented by the model limit the number of parameters that can be derived from a literature review. For example, the radiation use efficiency parameters in STICS (efcroijuv, efcroiveg and efcroirepro, see Table 3) correspond to potential conditions with no stress, and the presence or absence of stress is not necessarily mentioned in the literature. Finally, there is a risk of error accumulation when extensively relying on approximate or conflicting literature values [START_REF] Wallach | A package of parameter estimation methods and implementation for the STICS crop-soil model[END_REF]. For all these reasons, recourse to optimisation is advisable. The strength of our approach lies in the rational stepwise optimisation procedure chosen. Rather than an empirical trial and error procedure [START_REF] Flénet | Methodology of adaptation of the STICS model to a new crop: spring linseed (Linum usitatissimum, L.)[END_REF][START_REF] Hartkamp | Adaptation of the CROPGRO growth model to velvet bean (Mucuna pruriens): I. Model development[END_REF], we chose a sequential optimisation procedure that is fully documented and is easily replicable for other crops and cultivars with the STICS model. =Breaking down the optimisation into several stages and using it at the module-scale rather than the scale of the entire model allow to avoid unrealistic simulations where errors in parameter values would offset each other [START_REF] Bechini | Parameterization of a crop growth and development simulation model at sub-model components level. An example for winter wheat (Triticum aestivum L.)[END_REF][START_REF] Grant | Modeling transformations of soil organic carbon and nitrogen at different scales of complexity[END_REF].

Taking into account within-season dynamic measurements to successively calibrate the different model components allows to estimate few parameters simultaneously and therefore to reduce numerical problems [START_REF] Guillaume | Methodological comparison of calibration procedures for durum wheat parameters in the STICS model[END_REF][START_REF] Wallach | A package of parameter estimation methods and implementation for the STICS crop-soil model[END_REF]. The lower and upper boundaries fixed for each parameter during the optimisation ensures that the obtained values correspond to reasonable physiological values thus limiting compensations due to model structure weaknesses. The different optimisation stages and their order following crop development (i.e. phenology, LAI, biomass production and then partitioning) ensure that the parameterisation is relevant according to plant functioning. The order chosen is consistent with previously published calibrations using STICS [START_REF] Corre-Hellou | Adaptation of the STICS intercrop model to simulate crop growth and N accumulation in pea-barley intercrops[END_REF][START_REF] Flénet | Methodology of adaptation of the STICS model to a new crop: spring linseed (Linum usitatissimum, L.)[END_REF] and DSSAT [START_REF] Hartkamp | Adaptation of the CROPGRO growth model to velvet bean (Mucuna pruriens): I. Model development[END_REF]. Finally this method led to a satisfactory match of observed and simulated values, with ranges for statistical indicators (EF, rMBE and rRMSE) consistent with those obtained for the adaption of STICS to wheat and maize [START_REF] Brisson | STICS: a generic model for simulating crops and their water and nitrogen balances. II. Model validation for wheat and maize[END_REF], linseed [START_REF] Flénet | Methodology of adaptation of the STICS model to a new crop: spring linseed (Linum usitatissimum, L.)[END_REF] and spring pea [START_REF] Corre-Hellou | Adaptation of the STICS intercrop model to simulate crop growth and N accumulation in pea-barley intercrops[END_REF]. This approach can be valuable to calibrate new annual crops and other grain legumes (e.g. winter pea, lentil and chick pea) for the STICS model, and probably other generic soil-crop models that have a common structure for all species, e.g. CROPSYST model [START_REF] Stöckle | CropSyst, a cropping systems simulation model[END_REF].

A robust and credible agronomic diagnosis

Agronomic diagnosis is crucial for the identification of constraints affecting crop growth and to help the identification of sound agronomic management. The diagnosis needs to be robust, i.e. reliable under different sets of experimental conditions [START_REF] Sinclair | Criteria for publishing papers on crop modeling[END_REF], and credible, i.e. offering trustworthy causal explanations [START_REF] Cash | Salience, Credibility, Legitimacy and Boundaries: Linking Research, Assessment and Decision Making[END_REF]. Robustness can be ensured by an explicit reference to physical processes in the construction of mathematical relationships so that the model accurately captures the underlying processes driving the system [START_REF] Bellocchi | Validation of biophysical models: issues and methodologies[END_REF]. Lack of robustness can lead to a model being "right for the wrong reasons" [START_REF] Bellocchi | Validation of biophysical models: issues and methodologies[END_REF]. In this section, we want to highlight that we averted these pitfalls, ensuring that our diagnosis was robust and credible.

Our study adds to the body of literature showing that in a temperate climate with rain fed conditions and appropriate control of pest pressure, drought is the prevailing stress and the main driver of yield variability [START_REF] Karrou | Water and land productivities of wheat and food legumes with deficit supplemental irrigation in a Mediterranean environment[END_REF][START_REF] Mafakheri | Effect of drought stress on yield, proline and chlorophyll contents in three chickpea cultivars[END_REF]. The explanations we found to explain yield variability (water stress during grain onset) and N 2 fixation variability (water deficit factor during grain filling) are supported by principles of crop physiology derived from experiments and knowledge on response of legume grain yield and N 2 fixation to water stress. With regard to grain yield, water deficit during grain onset reduces grain legume biomass accumulation (decrease of photosynthesis and reduction of leaf area) and assimilate availability that in turn reduce final seed number [START_REF] Guilioni | High temperature and water deficit may reduce seed number in field pea purely by decreasing plant growth rate[END_REF][START_REF] Jiang | Soybean seed number and crop growth rate during flowering[END_REF][START_REF] Lake | Screening chickpea for adaptation to water stress: Associations between yield and crop growth rate[END_REF]. With regard to N 2 fixation, water stress directly reduce faba bean nodules activity [START_REF] Sprent | The Effects of Water Stress on Nitrogen-Fixing Root Nodules[END_REF] and sensitivity of N 2 fixation to drought is often maximum during grain filling [START_REF] Chalk | Integrated effects of abiotic stresses on inoculant performance, legume growth and symbiotic dependence estimated by 15N dilution[END_REF][START_REF] Mastrodomenico | The response and recovery of nitrogen fixation activity in soybean to water deficit at different reproductive developmental stages[END_REF]. These two stress responses are implemented in STICS. Firstly, final seed number depends on plant growth rate during the grain onset period (see section 2.1.1 and Table S2). . Thus, the magnitude of water stress during grain set and its impact on plant growth rate determines the extent to which the plant can reach the maximum grain number (nbgrmax, see Table and Figure 2). Secondly, in the model, water deficit reduces the potential N 2 fixation, i.e.

nodulation and nitrogen fixation are partially or totally inhibited according to nitrate concentration in the topsoil and when soil moisture in the topsoil drops below permanent wilting point (see section 2.1.2 and Table S2). This careful check of the behaviour of different model functional modules (Figure 7, Figure 8) strongly suggests that the STICS model accurately captured the underlying processes driving grain yield formation, N 2 fixation and water stress. We can therefore be confident in the diagnosis drawn from our site-yearmanagement units with regard to water stress. Thus, the generic STICS processes describing yield formation and water stress, when calibrated for faba bean with the proper options activated, have proven useful in explaining variability in yield for this particular legume crop, without the need to build new processes into the generic model.

The good fit obtained with the evaluation dataset indicates that the current set of parameters could be reliably used in other situations different from the ones in the calibration. This however needs to be confirmed with other studies, e.g. for situations where soil mineral N levels would be higher than in our study (on average 47 kg ha -1 at sowing over the whole profile), which could affect N 2 fixation. We verified by virtual experiment -corresponding to a local sensitivity analysis -that STICS was able to simulate a strong reduction in N 2 fixation when soil nitrate content was higher in the upper layers.

Eventually, by considering both a water deficit factor for N 2 fixation and a water supply/demand ratio (acting on crop biomass), the model allowed unravelling interesting situations where similar faba bean biomass masked differences in the amounts of fixed N 2 .For example, crop biomass and water/supply demand ratio were similarly low in Auzeville in 2011 (3 t ha -1 ) and 2015 (4.1 t ha -1 ) due to similar water stress on biomass (water supplydemand ratio = 0.3). However, the amount of N 2 fixed was doubled (88 kg ha -1 ) in 2015 compared with 2011 (46 kg ha -1 ). The model indicated a stronger water deficit for N 2 fixation in 2011 (water deficit factor = 0.12) compared with 2015 (water deficit factor = 0.32). This understanding of nonlinearities is crucial for the assessment of innovative cropping system.

Pests and diseases can also reduce faba bean grain yield. Coupling STICS with an epidemiological model [START_REF] Donatelli | Modelling the impacts of pests and diseases on agricultural systems[END_REF] would be relevant to refine the diagnosis in situations where damages on leaves (e.g. rust, Uromyces viciae-fabae, or chocolate spot, Botrytis fabae) and nodules (e.g. sitonia beetles, Sitonia lineatus) can occur.

New opportunities to design and assess resilient cropping systems

Though the effects of climate change on cereals in Europe have deserved a great attention (e.g. [START_REF] Bregaglio | Identifying trends and associated uncertainties in potential rice production under climate change in Mediterranean areas[END_REF][START_REF] Dettori | Simulation of climate change impacts on production and phenology of durum wheat in Mediterranean environments using CERES-Wheat model[END_REF], studies on effects of climate change on legume productivity remain scarce. Climate change projections for the temperate and mediterranean regions of Europe point to a decrease in precipitations during spring and summer [START_REF] Gao | Increased aridity in the Mediterranean region under greenhouse gas forcing estimated from high resolution simulations with a regional climate model[END_REF][START_REF] Giannakopoulos | Climatic changes and associated impacts in the Mediterranean resulting from a 2 °C global warming[END_REF]. Water stress will therefore become even more acute with future climate. Our model calibration offers a good opportunity to assess the impact of increased drought-induced stress on faba bean productivity and therefore the potential contribution of legume to sustainable cropping systems in the future.

Dynamic models have often been criticised for putting too much emphasis on single crop assessment on a year-to-year basis [START_REF] Reckling | A cropping system assessment framework-Evaluating effects of introducing legumes into crop rotations[END_REF]. Taking into account pre-crop and rotational effects (e.g. nutrient carry-over and alteration of soil water content) will be crucial to accurately assess the contribution of faba bean and grain legumes in building more diversified and resilient cropping systems. Our robust crop calibration and STICS ability to simulate residues mineralisation [START_REF] Justes | Quantifying and modelling C and N mineralization kinetics of catch crop residues in soil: parameterization of the residue decomposition module of STICS model for mature and non mature residues[END_REF], nitrate leaching and water drainage [START_REF] Plaza-Bonilla | Cover crops mitigate nitrate leaching in cropping systems including grain legumes: Field evidence and model simulations[END_REF], would allow deriving probabilities to achieve a certain level of yield and N provision to the subsequent crop when inserting legumes in cropping systems.

STICS can also simulate intercropping (Brisson et al., 2008). Cereal-legume intercropping (e.g. wheat and faba bean) is a promising integration of legumes in cropping systems in particular in low input cropping systems [START_REF] Bedoussac | Ecological principles underlying the increase of productivity achieved by cereal-grain legume intercrops in organic farming[END_REF]. Many processes (e.g. soil N and water sharing) are simulated similarly in sole crop and intercrops [START_REF] Corre-Hellou | Adaptation of the STICS intercrop model to simulate crop growth and N accumulation in pea-barley intercrops[END_REF], our calibration would therefore allow exploring intercropping performance for a diversity of soils and rainfall patterns. Nevertheless, some formalisms specific to intercrops (e.g. the competition for light) and the corresponding parameters may deserve potential recalibration before the set of parameters proposed here for sole crops can be used. White squares are the observations. Vertical dotted lines delimit the periods during which the correlation between average water supply/demand ratio and grain yield is maximal.

Conclusion

  MBE and rMBE indicate whether the model under/overestimate a given variable, and gives the absolute and relative magnitude and direction of the bias. EF is based on the comparison of the simulation model with a constant model (i.e. the average of measured data) and ranges between -∝ and one. Negative EF values indicate that the constant model performs better than or as well as the simulation model. A value of one indicate a perfect model. EF is a good indicator to compare model simulations with two different sets of parameters (e.g. before/after calibration) against the same dataset. It is however of little value to compare two simulations with the same set of parameters against two different datasets, because it depends on the variance of the observed dataset. RMSE and rRMSE are the model absolute and relative prediction error. The combined analysis of these four indicators give a robust assessment of model accuracy. Similarly to Beaudoin et al. (2008) and Constantin et al. (2015), model

Figure 1 :

 1 Figures:

Figure 2 :

 2 Figure 2: Boxplots of number of grain per square meter (a), weigh of one grain (b) and harvest index (c) in the 35 site-year-management units of the study. The horizontal line in the box indicates the median. The height of the box represents the interquartile range. The whiskers extend to the maximum values. The horizontal dotted line correspond to the maximum measured values with an added 10% to define potential maximum values in the STICS model.

Figure 3 :

 3 Figure 3: Comparison of observed and simulated (STICS model) faba bean phenology.

Figure 4 :

 4 Figure 4: Comparison of observed and STICS simulated LAI, Above ground biomass (AGB), N 2 fixed, and Above ground plant N (AGPN) for calibration and evaluation dataset. rMBE = relative mean bias error, EF= model efficiency, rRMSE = relative Root Mean Square Error. The black line is the 1:1 line. The dotted line represent the regression of simulated against observed values. White symbols correspond to the end of growing season.

Figure 5 :

 5 Figure 5: Comparison of observed and STICS simulated grain yield, grain N, soil water content, and soil mineral N content for calibration and evaluation dataset. rMBE = relative mean bias error, EF= model efficiency, rRMSE = relative Root Mean Square Error. The black line is the 1:1 line. The dotted line represent the regression of simulated against observed values (plotted when significant at 5% risk level). White symbols correspond to the end of growing season.

Figure 6 :

 6 Figure 6: Correlation (a) between grain yield and average water supply/demand ratio during grain onset (over the six days before beginning of grain filling) and (b) total N 2 fixed at harvest and average water deficit factor for N 2 fixation during grain filling (over the first 20 days after beginning of grain filling). Calibration and evaluation datasets were pooled together.

Figure 7 :

 7 Figure 7: Example of contrasted simulated temporal dynamic (black line) of water supply/demand ratio, above ground biomass and number of grain per square meter in Auch in 2007 (a,d,g), Auzeville in 2010 (b,e,h) and Auzeville in 2007 (c,f,i) in the calibration dataset.

Figure 8 :

 8 Figure 8: Example of contrasted simulated temporal dynamic (black line) of water deficit factor for N 2 fixation and N 2 fixed in Auzeville in 2014 (a, c) and 2015 (b, d) in the evaluation dataset. White squares are the observations. Vertical dotted lines delimit the periods during which the correlation between average Water deficit factor and N 2 fixation is maximal.

Table 1 :

 1 Climate and soil characteristics (averaged across growing seasons and experimental fields) in the two experimental sites (standard error

	Tables:
	in brackets)
	Site	Number of growing seasons	November-July Cumulative global Cumulative solar radiation growing degree (MJ m -2 ) days (°C day)	Cumulative rainfall (mm)	Number of experimental fields	Clay content (0-30cm) (%)	pH (0-30cm)	Maximum rooting depth (cm)	Gravimetric moisture at field capacity* (%)	Gravimetric moisture at wilting point* (%)	Maximum available water** (mm to maximum rooting depth)
	Auch	7	3354 (64.8)	3083 (59.1)	542 (47.2)	11	31.8 (1.46)	8.4 (0.03)	70 (4.9)	17.4 (0.45)	12.0 (0.27)	64 (4.8)
	Auzeville	7	3561 (30.4)	3412 (49.1)	528 (42.8)	12	25.9 ( 0.97)	7.4 (0.15)	135 (4.5)	19.4 (0.43)	10.2 (0.23)	167 (8.5)
	*Average across 0-30cm, 30-60cm, 60-90cm and 90-120cm soil layers.

**Soil water content at field capacity minus soil water content at wilting point.

Table 2 :

 2 Description of the Site-Year-Management units in the calibration and evaluation datasets. LAI: Leaf Area Index, AGPN: above-ground plant N, AGB: above-ground biomass, GY: grain yield, GNC: grain N content, SN: Soil N content over the entire profile, SWC: soil water content over the entire profile.

Table 3 :

 3 Description of the nine stages undertaken for parameter optimisation: parameters optimised, minimum and maximum values, and target

	variable. Dd = degree (°C) day
	Parameter

Table 4 :

 4 Values of faba bean parameter as calibrated in the STICS crop model for experiments in Auch and Auzeville, France.

		Parameter
	Process	Acronym	Description

Acknowledgments:

This research was supported by the European Commission (REA) through the LEGATO project (FP7-613551) and the French National Research Agency (ANR) through the LEGITIMES French project (ANR-13-AGRO-0004), the 7 th PIREN-Seine program and the Climate-CAFE European project (selected by the European FACCE-JPI ERA-NET Plus program).

We thank the Centre Régional de Recherche et d'Expérimentation en Agriculture Biologique de Midi-Pyrénées (CREAB-MP) in Auch, France, for making available their faba bean dataset. We are grateful to Loïc Prieur, Didier Rafaillac, Michel Labarrère and several trainees who assisted in data collection and Didier Chesneau and Eric Lecloux who performed the extraction and the analysis of soil mineral N. We thank Patrice Lecharpentier for his help with the Optimistics software.

Management

Number


Nathalie Lamoureux

Laurent Gasnot

Pascale Desgroux

Quantitative NH measurements by using laser-based diagnostics in low-pressure flames

Keywords: NH, CRDS, LIF, low-pressure flame, prompt-NO

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

Introduction

The NH radicals, which are important intermediate species in the NO formation process, have been measured in the past using laser-based diagnostics in flames. Relative NH species profiles were obtained in premixed flames by using Laser Induced Fluorescence (LIF) since the 80-90's [1][2][3][4][5][6].

Measurements were exclusively performed in mixtures seeded with N-containing species (NO, NO 2 , N 2 O, NH 3 ) that allow increasing the NH quantity. The LIF measurements were performed either in the A 3 Π-X 3 Σ -(0-0) vibrational band of NH around 336 nm or in the (1-0) vibrational band around 303 nm.

Relative LIF measurements were calibrated using absorption methods [1,3,4]. The detection limit was found to be around 1 ppm. Brackmann et al. [6] measured NH profiles in atmospheric NH 3 /air flames by using saturated LIF. The NH-LIF signal was calibrated in mole fraction by using a bidirectional LIF method applied to OH with an overall uncertainty estimated to be 40% and a detection limit of 2×10 13 molecule cm -3 . Derzy et al. [7] measured mole fraction profiles of NH using Cavity Ring-Down Spectroscopy (CRDS) in low-pressure CH 4 /air flames seeded with 1.7% of N 2 O. They estimated the detection limit for measuring NH to be 4×10 10 molecule cm -3 probing the R 1 (6) transition at 333.9 nm. To the best of our knowledge, native NH has been measured only once in atmospheric CH 4 /air flames by using saturated LIF [8]. The LIF signal was calibrated into mole fraction by Rayleigh scattering with a value as low as 0.3 ppm (i.e. 10 12 molecule cm -3 ) and an overall uncertainty estimated at about 40%.

In our laboratory, we have previously shown the strong complementarities of LIF and CRDS to quantify trace species in premixed flames provided that they fluoresce. The LIF/CRDS coupling already allowed measuring species with mole fractions as low as a few ppb in the case of NCO [9].

In the continuation of our previous works carried out for the prompt-NO formation in premixed low-pressure flames [10], the present paper reports quantitative measurements of native NH by using LIF and CRDS techniques for the first time. LIF profiles of NH were measured in five lowpressure flames by probing the R 1 (6) transition at 333.9 nm. The absorption oscillator line strength was calculated with the PGOPHER program [11]. LIF profiles of NH were converted into mole fraction profiles by using the integrated spectral absorptivity obtained by CRDS in a flame seeded with 2.2% of N 2 O. The LIF detection limit is significantly improved in the present work by optimizing the collection volume and the LIF signal processing. The experimental NH profiles were compared to those simulated using the NOMecha2.0 submechanism which has been recently validated for the prompt-NO formation [10]. NOMecha2.0 is associated either to a methane mechanism [12] or to a acetylene mechanism [13].

2 Experimental setup the height above the burner (HAB). Details about the burner and the gas supply were given in [14,15].

Additionally, a N 2 O-doped flame (named CH4-N2O) was stabilized in order to calibrate relative concentration of NH species in mole fraction by CRDS. Flame compositions and volumetric gas flow rates are reported in Table 1. These flame conditions, identical to those previously studied in the laboratory, were used to validate NOMecha2.0 [10]. The temperature profiles were previously obtained by LIF thermometry according to a procedure described in [14]. They are reported in [10],

except for flame CH4-N2O in which the temperature was measured equal to 1790 K at HAB=5.75 mm [9]. and recorded on a digital oscilloscope (Lecroy HDO4000, 12-bit vertical resolution, 1GHz bandwidth, 1.25 GS/s). During spectrum acquisition, the laser wavelength was scanned at a rate equal to 0.25 pm s -1 and the signal was averaged over 10 laser shots. For species profiles measurements, the signal was averaged over 300 laser pulses. Signals from the oscilloscope and the dye laser wavelength were transferred in real time on a PC, and treated with Labview programs.

LIF

The laser beam was introduced unfocused parallel to the burner surface and shaped using a horizontal slit of 300 µm height and 2 mm width in front of the burner. The LIF signal was collected at f/4 by a two-lenses system and focused on the entrance slit of a 0.275 m monochromator. The entrance slit (200 µm width, 10 mm height) was parallel to the laser axis. The collection volume is estimated to be equal to 4 mm 3 . The output slit was adjusted to obtain the desired collection bandwidth. For measurements performed in the C 2 H 2 /O 2 /N 2 flames, the PMT saturation due to the strong flame emission at 338 nm was avoided by the use of a fast electronic shutter (Oriel fast shutter 76994/76995) placed in front of the monochromator. The shutter opening (with a gate of 13 ms) was synchronized with the laser Q-switch signal and delayed appropriately in order to collect the fluorescence signal.

The prompt-LIF signal is measured at the peak value of the temporal LIF signal, limiting the effect of possible quenching variations. It allows measuring the relative population of the species in the rotational level J", N J" .

CRDS

CRDS measurements for NH were performed by using an experimental set-up and data processing similar to the one described for CH measurements in [14,15]. The 420 mm length cavity is ended by two highly reflective mirrors (LaserOptik, 25 mm diameter, 250 mm radius of curvature, reflectivity>0.997). The laser beam was shaped with a system consisting of a 100 µm pinhole aperture and two lenses (100 and 175 mm focal lengths) in order to match approximately the TEM 00 transverse mode of the optical cavity. The CRD signal was collected by the PMT in front of which was placed a UG11 filter. Cavity decaytimes were determined from an exponential fitting over 1.6 µs. The ringdown decaytime in the burned gases (in absence of NH absorption) was typically equal to 475 ns. The concentration of the absorbing species is determined from the measurement of the decaytime on-and off-resonance with the transition as detailed in [16,[START_REF] Mercier | Cavity Ring-Spectrosc. Tech. Appl[END_REF]. The off-resonance wavelength was selected by detuning the laser by 30 pm from the on-resonance one.

NH spectroscopy

The PGOPHER program (version 9.1.100) [11] allows calculating the absorption spectrum in absolute intensity, and also extracting the rotational terms of energy (E J" ), the rotational Einstein A coefficients (A J'J" ), or the rotational oscillator strength (f J"J' ). The revised spectroscopic constant values of NH in the A 3 Π-X 3 Σ -system proposed by Ram and Bernath [START_REF] Ram | [END_REF] were introduced in PGOPHER. The vibrational and rotational partition functions in the ground state X 3 Σ -were calculated by using the equilibrium molecular constants reported by Brooke et al. [19]. The Boltzmann factors were determined as function of the temperature by using E J" calculated by PGOPHER.

In order to calculate the values of A J'J" and f J"J' , the electronic transition moment ( ′ "

) that is required, was calculated (in D) from the vibronic Einstein A coefficient (A v'v" in unit s -1 ) according to Eq. ( 1) derived from Larsson [20]:

" = 3.1895 × 10 , , " " Eq. ( 1
)
where ν is the center wavenumber of the (v'v") transition in cm -1 . For a Π Σ transition, the ratio (2-

! ",Λ ′)/(2-! ",Λ ′ #Λ "
) (where δ is the Kronecker delta) is equal to one [20].

According to the Einstein A coefficient values newly determined by Fernando et al. [21],

(A 00 = 2.54×10 6 s -1 and A 11 =2.18×10 6 s -1 ), the values of the electronic transition moment calculated from Eq. ( 1) are equal to 0.554 D and 0.516 D respectively for the (0-0) and (1-1) bands. For the R 1 (6) transition at 29948.45 cm -1 (333.9 nm), PGOPHER calculations return A J'J" = 1.375×10 6 s -1 and f J"J' = 2.653×10 -3 . The absorption line strength is equal to 3.992, in good agreement with the value of 3.988 reported by Derzy et al. [7].

LIF and CRDS measurements of NH in flames 4.1 Excitation LIF and CRDS absorption spectra

Experimental spectra were measured in flame CH4-N2O at the NH peak location (HAB=5.5mm),

where the temperature was previously determined to be equal to 1790 K [9]. The absorption spectrum of the NH radical was recorded by using CRDS. The excitation LIF spectrum was also recorded in the linear regime (8µJ/cm 2 /pulse) with a collection spectral bandwidth of 9.0 nm. Figure 1 presents the experimental spectra measured by CRDS and by LIF, compared to the absorption spectrum simulated with PGOPHER at 1790K by applying a Voigt lineshape function with a Gaussian linewidth of 0.25 cm -1 and a Lorentzian linewidth of 0.15 cm -1 . All spectra have been scaled with respect to the experimental absorption spectrum reported in losses per pass along the flame diameter. Spectra show three intense transitions which correspond to R transitions in the 3 sub-bands (R 1 , R 2 , R 3 ) of the lower state N"=5 in the (0-0) band. Two small transitions (R 2 (9), R 1 (10)) in the (1-1) band are also observed.

A fairly good agreement between the experimental intensities and the simulated intensities is found.

However, the intensity of the two satellite transitions (Q 32 (5), Q 21 (6)) in the (0,0) band measured by LIF is higher than the simulated intensity while the absorption experimental spectrum is perfectly simulated. The simulated spectrum being an absorption spectrum, it does not correct for the fluorescence quantum yield. Therefore the disagreement observed for the two satellite lines indicates that their fluorescence quantum yield differs from the one of the main transitions.

More details concerning the dispersed fluorescence spectrum and the temporal fluorescence decays of NH in flames are given in the Supplementary Materials.

Experimental NH mole fraction profiles

The NH mole fraction profiles were measured by using LIF and CRDS. The rotational population (N J" ) was probed at the well-resolved R 1 (6) transition at 333.9 nm by LIF. The rotational distribution shows that the level J"=6 is one of the most populated levels in the temperature range (1000-1800 K), with a limited temperature sensitivity of the Boltzmann factor (2×10 -5 K -1 ). The axial NH relative concentration profiles as function of HAB were obtained by LIF that allows spatially resolved measurements. The relative concentration species profile in each flame was scaled at its peak value with respect to the one obtained in flame CH4-N2O (calibration flame). This latter one was calibrated into absolute population by using CRDS. The integrated spectral absorptivity A($̅ ) (in cm -1 ) was determined according to Eq. ( 2) [START_REF] Mercier | Cavity Ring-Spectrosc. Tech. Appl[END_REF]:

&$̅ ) = ' (&$̅ ))$̅ = &*+ , - ⁄ )/ 0"0′ 1 0" 2 3 Eq. ( 2
)
where , -*+ ⁄ is equal to 1.13×10 12 cm -1 , l s is the absorption length (in cm). L($̅ ) represents the net losses per pass due to the absorption of the species (N J" ) as a function of the wavenumber $̅ .

Conversion into absolute concentration N tot was completed by dividing the rotational population by the Boltzmann factor f B (J",T), calculated by using the experimental temperature profiles previously obtained in [10,14].

Relative NH profiles by LIF

In order to maximize the signal and prevent any perturbation from the excitation laser radiation, the fluorescence signal was collected along the Q-and P-branches, with a spectral bandwidth of 9 nm centered at 339 nm. The fluorescence lifetime was found nearly identical in all flames and almost constant (80 ns) along the flames axis indicating that the NH quenching rates are similar. Thanks to this observation, the steadiness of the quenching rate allows to assume that the degree of saturation of the LIF signal is similar in each flame. Therefore, we have chosen to work in a partially saturated LIF regime (13-14 µJ/cm 2 /pulse) in order to improve the signal-to-noise ratio. The off-resonance signal was found negligible.

The relative peak values of N J" measured in all flames are reported Table 2. The relative standard deviation of the ratios between the flames is lower than 5%. The temperature values previously measured in [9,10,14] are also reported at the NH peak location.

Mole fraction profiles of NH by CRDS

The NH net losses L($̅ ) were measured in flame CH4-N2O. The net losses profile is in agreement with the scaled LIF profile as shown in Fig. 2. The enlargement of the line-of-sight CRDS profile at high reported by [21]. Finally, the accuracy of the NH mole fraction determination was estimated to be ±20%, neglecting the possible spatial inhomogeneity of the NH distribution.

Modeling and discussions

Modeling was performed using either the GDFkin ® 3.0 model [12] for CH 4 oxidation or the Lindstedt and Skevis model [13] for C 2 H 2 oxidation (named LS hereafter). These models were completed with the NOMecha2.0 submechanism [10]. NOMecha2.0 was fully validated in low-pressure flames for the prompt-NO formation against a large experimental database gathering species such as NCN, NCO, HCN, CN, CH and NO. NH was one of the missing intermediate species involved in the prompt-NO scheme. Calculations were done with the Chemkin/Premix-II package, using the experimental temperature profiles previously reported in [10,14]. The NH profiles were simulated in all flames. The acetylene oxidation mechanism proposed by Lindstedt and Skevis [13] was previously adopted to simulate prompt-NO and intermediate species in the acetylene flames as reported in [10,14]. This model allowed good predictions of the CH and NCN mole fraction profiles obtained in flames C2H2(100) and C2H2(125). However as shown in Fig. 4, the experimental NO mole fraction profiles were underestimated by the model by a factor of 1.2 and 1.6 in the rich and stoichiometric flames, respectively. No change of the mechanism was performed in [10] to improve the agreement between the experimental and the simulated profiles of NO. The NH mole fraction profiles simulated with the LS model underpredicted the experimental profiles with a factor of 5.2 and 3.7 in flames C2H2(100) and C2H2(125), respectively. are mostly formed from the reaction HNCO+H=NH 2 +CO and consumed according to the reaction NH 2 +H=NH+H 2 through the newly additional pathway HCN/HNC/HNCO/NH 2 /NH as discussed in [10]. This sequence was mostly updated from [23] and [24]. The experimental HCN peak mole fraction values were satisfyingly predicted for all flames [10]. HNCO is formed from the reaction HNC+OH=HNCO+H in both flames, but in the acetylene flames it is also formed through the reaction of isomerisation HCNO+H=HNCO+H. According to [25], HCNO is produced from the reactions HCCO+NO=HCNO+CO and CH 2 +NO=HCNO+H. In the methane flames, these two reactions are involved yielding a simulated peak mole fraction of HCCO around a few tens of ppm in the rich conditions. On the contrary, the first reaction is the only one involved in the HCCO formation with a simulated peak mole fraction around 10 times higher in the rich acetylene flame. As previously described in [14], HCCO is the first intermediate species of the acetylene oxidation, whereas CH 3 is the first intermediate species of the methane oxidation. Indeed, in the acetylene flames, HCCO plays an important role due to the reaction C 2 H 2 +O=HCCO+OH [26]. The reactions C 2 H 2 +O and HCCO+O 2 are well-known to be very sensitive for modeling the acetylene/air laminar flame velocities as previously mentioned by Lindstedt and Skevis [13], and recently by Shen et al. [26].

In order to improve the agreement between the experimental and the simulated mole fraction profiles of NH in the acetylene flames, the rate constant values of the reactions C 2 H 2 +O and HCCO+O 2 have been modified in the LS model as listed in Table 3. These modifications increase the simulated peak mole fraction of HCCO by a factor of 2, and the one of 1 CH 2 by a factor 1.5 in flame C2H2(125). The modifications also yield an increase of the simulated CH peak mole fraction by a factor of 1.6. Indeed as shown in [14], CH radicals are formed through the sequence HCCO/ 1 CH 2 / 3 CH 2 /CH in the acetylene flame. In order to restrain the simulated CH mole fraction profiles (in agreement with the experimental profiles), the rate constant value of the reaction CH+H 2 = 3 CH 2 +H was modified according to [27]. The predictions of the species profiles previously considered to validate the original LS mechanism by [13] were not altered. Figure 4 shows the experimental and the simulated mole fraction profiles of NH, CH and NO in the acetylene flames. For clarity, the species profiles simulated before and after the aforementioned kinetic modifications are presented here. Additionally, the species profiles of NCN and HCN are presented in the Supplementary Materials. These modifications allowed matching the simulated CH peak location with the experimental ones, especially in the flame C2H2(100). They also led to increase the simulated NH mole fraction profiles, but they still underestimate the experimental profiles by a factor of 2.7 and 1.6, respectively for flames C2H2(100) and C2H2(125). The predicted NO mole fractions in the burned gases were found in better agreement with the experimental values (within the experimental uncertainties) than previously shown in [10]. Globally, the simulated peak mole fractions of CH, NO, NCN, HCN and NH have been increased (shown in the Supplementary Materials), yielding a better agreement with the experimental ones. However, the simulated HCN profiles are much larger than the experimental ones in the acetylene flames. This observation deserves further investigations.

Conclusions

The mole fraction profiles of NH have been measured in flames of CH 4 /O 2 /N 2 or C 2 H 2 /N 2 /O 2 stabilized at low pressure (5.3 kPa). Measurements have been possible thanks to the combination of two laser-based spectroscopic techniques: LIF and CRDS. The LIF technique offers an excellent sensitivity and spatial resolution for measuring the relative species profiles in flames. We have estimated the limit of detection of NH of around 4.5×10 8 molecules cm -3 , i.e. 2 ppb at 1600 K, while this limit was estimated to 0.4 ppm in [8]. The high improvement of the detection limit is mainly due to the larger volume of collection. As the laser is not focused, the volume is enlarged in a plane parallel to the burner surface. The CRDS technique allows quantifying in absolute concentration but

List of figure captions

Fig. 1 .

 1 Fig. 1. NH absorption spectrum (symbols) and excitation LIF spectrum (dashed line) collected at 336 nm with a spectral bandwidth of 9 nm, at 5.5 mm in flame CH4-N2O. Comparison with the simulated spectrum obtained with PGOPHER (solid line) at T=1790 K by using a Voigt lineshape function. Transitions in the (0-0) and (1-1) bands are indicated on the top.

Figure 3

 3 Figure3shows the comparison between the experimental and the simulated profiles in the methane

Fig. 3 .

 3 Fig. 3. Experimental NH mole fraction profiles in flames CH 4 at φ=1.25 and φ=1.0. Comparison with simulated profiles obtained with NOMecha2.0 [10] associated to GDFkin ® 3.0 [12].

Fig. 4 .

 4 Fig. 4. NH mole fraction profiles in flames C 2 H 2 (a) φ=1.25 and (b) φ=1.0. Comparison with the simulated profiles obtained with NOMecha2.0 model [10] associated to the revised LS model (solid lines) and the unmodified LS model [13] (dashed lines).

Fig. 1 .

 1 Fig. 1. NH absorption spectrum (symbols) and excitation LIF spectrum (dashed line) collected at 336

Fig. 2 .

 2 Fig.2. N J" profiles (net losses/pass, L(ν )) measured by using LIF and CRDS in flame CH4-N2O.

Fig. 3 .

 3 Fig. 3. Experimental NH mole fraction profiles in flames CH 4 at φ=1.25 and φ=1.0. Comparison with simulated profiles obtained with NOMecha2.0 [10] associated to GDFkin ® 3.0 [12].

Fig. 4 .

 4 Fig. 4. NH mole fraction profiles in flames C 2 H 2 (a) φ=1.25 and (b) φ=1.0. Comparison with the

2.1 Low-pressure burner and gas supply

	Experiments were undertaken in laminar CH 4 /O 2 /N 2 or C 2 H 2 /O 2 /N 2 premixed flames stabilized at
	5.33±0.01 kPa (40 Torr) on a 6-cm diameter bronze water-cooled McKenna burner. Regulation of the
	pressure is achieved within ±0.3% by using an automatic valve (Oerlikon CMOVE/MOVE1250). The
	burner is mobile in translation in the vertical axis allowing measuring species profiles as function of

Table 1

 1

	. Flame compositions. Gas flow rates are reported in slpm (standard refers to 0°C and atmospheric pressure). φ is the equivalence ratio.

.2 Laser set-up

	The pulsed laser system consists of a frequency-doubled Nd:YAG laser (Powerlite DLS8000,
	Continuum) pumping a dye laser (ND6000, Continuum). Wavelengths around 335 nm with a spectral
	bandwidth of 0.3 cm -1 were provided by doubling the fundamental dye radiation of a mixture
	(LDS698+DCM) diluted in methanol.
	LIF and CRDS signals were collected by a photomultiplier tube (PMT) (XP2020Q, Photonis)

Table 2 .

 2 Relative rotational population (N J" ), absolute concentration (N tot ), mole fraction (χ NH ) of NH measured at the peak location in all flames. Temperature at the peak was previously determined in[9,10,14].

	flame	N J" rel LIF	N J" CRDS (molecule/cm 3 )	NH peak (mm)	T (K) at NH peak	N tot (molecule/cm 3 )	χ NH (ppb)
	CH4-N2O	100	4.70×10 10	5.50	1790	1.33×10 12	6172
	C2H2(125)	3.66	1.72×10 9	2.75	1640	4.54×10 10	193
	C2H2(100)	1.43		2.75	1565	1.72×10 10	70
	CH4(125)	0.94		9.00	1750	1.23×10 10	56
	CH4(100)	0.29		6.75	1770	3.90×10 9	18

Table 3 .

 3 Modified reaction rate constant values in the LS model[13]. k=AT n exp(-E/RT), units in cal, mole, cm -3 and K.

	reaction	A	n	E	references
	4.7×10 7 1.4 2204 Shen et al. /5 [26] 9.36×10 8 1.4 2204 Shen et al. [26] 1.91×10 11 0 1023 Shen et al. [26] Shen et al. [26] HCCO+O 2 =CO 2 +CO+H 4.78×10 12 -0 1150 C 2 H 2 +O= 3 CH 2 +CO C 2 H 2 +O=HCCO+H HCCO+O 2 =2CO+OH CH+H 2 = 3 CH 2 +H 1.75×10 14 0 3320 Baulch et al. [27]

Proceedings of the Combustion Institute, 37 (2), pp.1313-1320. 10.1016/j.proci.2018.09.007. hal-

Acknowledgments

This work is a contribution to the CPER research project CLIMIBIO. The authors thank the French Ministère de l'Enseignement Supérieur et de la Recherche, the Hauts-de-France Region and the European Funds for Regional Economical Development for their financial support to this project. SMM.pdf file containing additional information concerning dispersed fluorescence spectra, temporal fluorescence decays, and species profiles (experimental and simulated obtained in the acetylene flames).

HAB can be due to a possible flame curvature as shown previously [22] although the flame was visually flat. Possible inhomogeneities at the flame edge are known to affect the axial mole fraction. In this work, the radial NH mole fraction profiles have not been measured. Therefore the NH mole fraction profiles are not corrected for the effective absorption pathlength which is assumed to be the flame diameter (2 3 = 6 cm) in Eq. (2). The NH mole fraction was measured by probing the R 1 (6) transition at the NH peak location in flames CH4-N2O and C2H2(125). The signal to noise ratio was around 3-4 only in the latter flame.

From the integrated spectral absorptivity, N J" was determined to be equal to 4.70×10 10 molecule cm -3 in flame CH4-N2O with a relative standard deviation of 2.5%. The ratio of the rotational populations between this flame and flame C2H2(125) using CRDS was found in perfect agreement with the ratio of N J" measured by LIF (Table 2). Then, considering the temperature equal to 1790 K at the NH peak location in flame CH4-N2O, the NH peak mole fraction was calculated to be equal to 6.17 ppm.

After the calibration performed in flame CH4-N2O, the profiles of the relative rotational population were converted into mole fraction by considering the Boltzmann factor and the temperature profiles. Thanks to the combination of LIF and CRDS techniques, the NH profile in the stoichiometric flame could be measured with a peak mole fraction value as low as 18 ppb. The accuracy of the rotational absorption line strength was estimated to be ±10%, in agreement with the estimated error with a detection limit around 2×10 10 molecules cm -3 , similarly to [7] . In the present work as in [7], the NH spatial distribution was assumed homogeneous along the absorption pathlength.

Modeling calculations were performed using the NOMecha2.0 submechanism recently developed for the prompt-NO formation [10]. Simulated NH profiles in the methane flames were found 30% lower than the experimental profiles. Modeling of the acetylene flames showed larger discrepancy with the experimental results. Acetylene oxidation yields intermediate species such as ketenyl radicals that play an important role in the prompt-NO formation through the formation of HNCO species. As previously indicated, the HNCO isomers are important for predicting NH species in the acetylene flames. The modification of five reaction rate constant values in the LS model [13] allowed retrieving a better agreement between the simulated and experimental species profiles (CH, HCN, NCN, NH and NO). The refinement is clear for the NO simulated profiles which now agree well with the experimental profiles (within the experimental uncertainty). This was made possible thanks to the quantitative measurements of the trace radical NH in flames fueled either with methane or with acetylene. This confirms the robustness of the NO submechanism NOMecha2.0 [10] that has been completely reassessed in our laboratory thanks to the large experimental database of intermediate species involved in the prompt-NO formation.