Nathalie Quiniou
email: nathalie.quiniou@ifip.asso.fr

Alice Cadero

Michel Marcon

Ludovic Brossard
email: ludovic.brossard@inrae.fr

MODELLING AMBIENT CONDITIONS IN THE FATTENING ROOM AND CORRESPONDING PERFORMANCE OF PIGS WITH THERMIPIG MODEL

Keywords: Pig, modelling, fattening room, climatic conditions, insulation, ventilation, performance, energy consumption

A mechanistic, dynamic and determinist model, called ThermiPig, has been developed by combining a growth model and a bioclimatic model. It allows for the prediction of the within-room thermal balance at the room level and its consequences on the daily and individual performance of group-housed pigs. As this research is part of the Pigsys ERA-Net project, co-funded under EU Horizon 2020 RI program (SuSan, www.erasusan.eu, Grant Agreement n°696231) by the French ANR (grant n°ANR-16-SUSN-0003-02), a survey was performed in different European countries by the partners of the project in order to describe different types of fattening rooms, feeding strategies and climatic conditions. Afterwards, the objective of the study was to use the results of the survey and to combine different characteristics of the fattening room (insulation, cooling and/or installed heater capacity when available, regulation rules of the climate control box) to simulate the corresponding impacts on (i) the thermal balance at room scale, (ii) growth performance, (iii) direct and indirect energy use, and (iv) nitrogen output in pigs. Simulations were performed over the whole fattening duration with each combination using 30 virtual batches of pigs, generated from an average animal growth profile. Based on outputs of the model, it is possible to evaluate the influence of insulation of walls or heater capacity under different climates or to optimize regulation rules of the climate box control of the ventilation system in terms of feed efficiency, margin on feed cost and nitrogen output.

INTRODUCTION Due to a poor insulation of the skin and limited sweating capacities, the pig is very sensitive to ambient temperature (Le [START_REF] Dividich | Thermoregulation[END_REF]. Like in other homeothermic animals, different mechanisms are involved in the thermoregulation and successively activated when the pig is exposed to ambient conditions outside its thermoneutral zone. Exposure to cold conditions is associated with an extra requirement in energy, which is met by an increase in feed intake (FI) when pigs are fed ad libitum, or a decrease in energy available for growth under restricted feeding conditions. In both situations, the feed conversion ratio increases as well as the indirect energy consumption (due to FI) and the feed cost. On the opposite, hot exposure induces a decrease in FI and growth rate (through average daily gain, ADG). In an all-in all-out system, it can compromise the final body weight (BW) at delivery to the slaughterhouse and consequently the income of the farmer.

When building new facilities, insulation, type of equipment and management rules are supposed to be adapted to the local climatic conditions. However, many pig farms have been designed many years ago. In a context of global warming, more frequent extremely episodes are observed, such as hot waves during late spring and summer or extremely cold episodes in winter. In EU and North America, the available equipment may become limiting, especially when pigs are heavy and produce a lot of heat. Independently of investment in new equipment, alternative management strategies in terms of feeding level, dietary formulation, regulation rules of the climate box control, could be interesting not only to mitigate the impact of outdoor climate on indoor conditions and the associated technical and economic performance at the farm level, but also to reduce the global impact of pig production, through a lower use of direct energy or improved efficiency of resources.

A dynamic model called ThermiPig has been developed that simulates the thermal balance at the fattening room scale based on the difference between the heat produced by the group of pigs and the heat lost due to fattening conditions [START_REF] Brossard | Combining a bioclimatic and a growth model to assess the effect of management practices and building ambiance on growing pig performances at the batch level[END_REF]. It can be used to evaluate in silico the impacts of the factors mentioned above on the thermal balance of the fattening room and on the associated growth performance of pigs. The aim of the present study was to investigate, using ThermiPig, the return on performance, environmental impact, economy and overall energy consumption that can be expected from new equipment or changes in farmer's practice, depending on the climatic conditions.

MATERIAL AND METHODS Simulations are performed with the ThermiPig model. This model is written in Python language and organised in three modules, corresponding to a growth model (InraPorc, van Milgen et al., 2008;[START_REF] Cadero | Modelling interactions between farmer practices and fattening pig performances with an individual-based model[END_REF], a bioclimatic model (ThermiSim, [START_REF] Marcon | MEDIBATE, a dynamic model of direct and indirect energy exchanges in pig barns for field decision support[END_REF] and a coupling module developed in the PigSys Susan-Eranet project. Indoor temperature (Tin) is predicted with the model with an accuracy of 0.5°C [START_REF] Brossard | Combining a bioclimatic and a growth model to assess the effect of management practices and building ambiance on growing pig performances at the batch level[END_REF][START_REF] Quiniou | Simulating with the ThermiPig model the impact of fattening room characteristics under different climates on the performance of pigs[END_REF]. Both static basic inputs and dynamic inputs are required to represent the room, the animals, the management rules, and the outdoor climatic conditions (Figure 1). In the present study, a single type of pigs and a single room are considered. But different level of insulation of the wall, rules of the climate box control of ventilation, feeding strategies and use of additional equipment are investigated under different climatic conditions. Insulation The room is supposed to be in a row of rooms. Therefore, we assume that heat losses are due to the only one wall facing the outside and the ceiling. Thermal exchanges at the bottom of the slurry pit are considered negligible. The ground under the concrete slab of the building is supposed to be already warmed by the previous batch of pigs. The total heat transfer coefficient (HTC, W.m -2 .°C -1 ) of walls depends on the thickness and thermal conductivity of the different materials used. The reference (WallRef) corresponds to a 0.20 m thick monolithic terracotta brick paneling which overall HTC is 0.55 W.m -2 .°C -1 . It was compared to three options: a three-layer paneling (WallOp 1; overall thickness: 0.35 m; HTC: 0.27 W.m -2 .°C -1 ), a 1-layer concrete paneling (WallOpt 2; overall thickness: 0.15 m; 11.33 W.m -2 .°C -1 ) or a thicker monolithic terracotta brick panelling (WallOp 3; overall thickness: 0.30 m; HTC: 0.35 W.m -2 .°C -1 ). The ceiling is insulated with 10 cm of glass wool (HTC = 0.32 W.m -².°C -1 ).

Characteristics of the fattening room

Ventilation The room is equipped with two fans of 400 mm in diameter which are managed in a normal way by a climate box control. The minimum and maximum ventilation rates are fixed to 10 and 100%, respectively. The other regulation rules are detailed in Table 1 for the reference (VentilRef) or the tested options (VentilOpt n).

Other equipment Heaters and pad cooling are not set up in the reference room but considered in simulations. The regulation of the heating system is based on a minimum and maximum heating rate of 0 and 100%, and three heating powers: 18.8, 37.6 or 50.0 W/pig. The initial and final setpoint temperatures of the heating system were fixed to 25 and 22°C, respectively, with an interval of 15 days to switch from initial to final T setpoint linearly. The temperature setpoint of the pad cooling system is fixed at 25°C outside, meaning that cooling starts only when outside temperature reaches 25°C. Characteristics of the pigs Data collected in a previous study performed on crossbred (Large White × Landrace) × (Large White × Piétrain) pigs, in the reference room, were used to parameterize an average growth profile. Growth curve was described according to a Gompertz function with relevant information for the initial BW (30.2 kg at 70 days of age), the average protein deposition rate (138.4 g/d), the Gompertz coefficient of precocity (0.0162/d), and the age at 110 kg (158 d). A feed curve was also modelled with a gamma function of net energy (NE, MJ/d) intake with BW, with the criterion "a" adjusted to 4.805 and "b" to 0.0214/kg. The model is deterministic but can account for variability amongst individual pigs within the batch and amongst batches when each pig in the group is described by a specific growth profile. A generator of virtual pigs is used to create 30 populations of 96 individual animals, based on a generic covariance pattern amongst parameters of the average growth profile [START_REF] Vautier | Accounting for variability among individual pigs in deterministic growth models[END_REF]. Thereafter, simulations were performed 30 times with ThermiPig, i.e. with 30 different groups of pigs. The limits of the thermoneutral zone were calculated on an individual and daily basis. Based on the reviews published by [START_REF] Verstegen | The effects of temperature and type of floor on metabolic rate and effective critical temperature in groups and growing pigs[END_REF] and [START_REF] Holmes | The influence of climatic variables on energy metabolism and associated aspects of productivity in the pig[END_REF], the lower critical temperature for group-housed pigs on fully slatted floor was supposed to decrease linearly with BW (kg): LCT (°C) = 22.5 -0.031 BW. The upper critical temperature was defined according to [START_REF] Renaudeau | A meta-analysis of the effects of high ambient temperature on growth performance of growing-finishing pigs[END_REF]: UCT (°C) = 40.9-4.4 × ln(1+BW).

Feeding strategy

The feeding strategy depends on the feeding level (ad libitum or restricted feeding) and the feeding sequence, i.e. the number of diets and their characteristics. Simulations are performed in ad libitum (AL) feeding conditions with a 2phase feeding strategy. A grower diet is supposed to be delivered up to 60 kg average BW at the group level, then a finisher diet. Both diets are formulated for 9.60 MJ of NE per kg and for 0.9 and 0.8 g of standardized ileal digestible lysine per MJ NE, respectively. The heat increment due to the ingestion, digestion and metabolic use of metabolizable energy (ME) contributes to the total heat produced by the pig [START_REF] Noblet | Prediction of net energy value of feeds for growing pigs[END_REF]. The thermic effect of feed (TEF) can be described by the NE/ME ratio. Two sequences were investigated in ad libitum conditions with NE/ME ratio of 74.4 and 74.8%, respectively for the grower and finisher diets in the conventional (TEF+) sequence, and 75.8 and 76.3% for the TEF-sequence, respectively. The cumulated energy demand (1.8 nonrenewable fossil + nuclear) at plant was 4157.594, 3782.039, 6330.812 and 5732.601 MJ/ton, respectively for the four diets. It was calculated with the methodology of life cycle assessment from cradle to field gate, to storage agency, to mill gate or to French port depending on the ingredient [START_REF] Wilfart | ECOALIM: a dataset of environmental impacts of feed ingredients used in French animal production[END_REF] and used to assess the indirect energy consumption. In the context of feedstuff prices of December 2019 in Brittany (France), the feed prices were 246.00, 238.00, 229.42 and 220.28 €/ton, respectively.

Other inputs In addition to the maximum occupation time of the room, other inputs are considered in the model to run simulations at the batch level, such as the loss of pigs before the end of the fattening period or the strategy of delivery of pigs to the slaughterhouse. In the present study, the maximum duration of the fattening period is fixed to 119 days, with two deliveries to the slaughterhouse organized with a 7-day interval and an expected average body weight at delivery of 115 kg. Based on the overall mortality rate observed in the room during an in vivo study, this input is fixed to 5.2%, each death occurring randomly all along the whole fattening period.

Combination with local climatic conditions

The aim of our study was to evaluate how the French room, supposed to be representative of a typical French pig room, would perform and, eventually, be inadequate under much colder winter conditions or warmer summer than presently observed in France. Data of hourly outdoor temperature (Tout) were collected at different locations and seasons over the year in Western France (FR) and upper Northern Sweden (SW) (Figure 2). The arrival of the batch of pigs was assumed to occur at different time, either on January 1 st (month 1) or June 1 st (month 6) corresponding to fattening at different seasons, i.e. winter and summer, respectively. The a b impact of cold was investigated, using datasets of hourly climatic data over 119 days labelled FR01 or SW01 when fattening started in month 1 in France or Sweden, respectively. The impact of warm weather was studied when fattening started on June 1 st (month 6) under FR climate, labelled FR06. Hourly Tout is presented in Figure 2 over 331 days. Under the FR01 climate, the average daily Tout ranges between -3 and 19°C (-7 and 27°C for hourly Tout) in winter (Figure 2a). Average daily Tout ranges between -33 and 6°C under the SW01 climate in winter (Figure 2b). Corresponding hourly Tout ranges were -35 to 12°C. In summer, the hourly Tout ranges between 4 and 34°C in FR06 conditions, corresponding to average daily values ranging between 12 and 25°C (Figure 2a). The corresponding ranges in SW06 were between 0 and 28°C on an hourly basis, and between 6 and 18°C, on a daily basis (Figure 2b).

Calculations and statistical analyses Depending on outdoor thermal conditions and condition of simulation, the model simulates the thermal balance at the room scale and the consequence of resulting Tin on performance of individual pigs. Thereafter it is possible to calculate the average or cumulated daily characteristics of pigs at the group scale (n = 30) and the overall performance from the beginning of the fattening period to the first delivery to the slaughterhouse or to the end of the fattening period.

Calculations Each day the model generates outputs either at room scale (Tin, energy consumed by the equipment…) or at pig scale (feed intake, BW, N retention…).

Growth performance Results obtained daily on each pig delivered to the slaughterhouse are used to calculate the individual average growth performance, i.e. daily feed intake (DFI), ADG, feed conversion ratio (FCR), nitrogen (N) balance and carcass leanness.

Environmental impact

The amount of individual N intake is calculated from the individual intake of each diet, and the corresponding crude protein content, divided by 6.25. The N retention is assessed according to the simplified balance method proposed by [START_REF] Dourmad | Évaluation des rejets d'azote, phosphore, potassium, cuivre et zinc des porcs Influence de l'alimentation, du mode de logement et de la gestion des effluents[END_REF], i.e. as the difference between the final and the initial body protein content divided by 6.25. The efficiency of N retention is calculated as the ratio between N retention and N intake. The amount of N output per pig is obtained by difference between N intake and N retention. The daily intake of the different diets and the amount of N output per pig (even when they die before the end) are cumulated at the batch scale over the fattening period. The total energy consumption per batch expressed in international standard energy unit is obtained from the demand of energy due to total feed intake (in MJ, obtained from cumulated amount of feed intake and their cumulated energy demand per ton), and the electricity (direct energy) consumed by equipment (kWh) multiplied by 13.3 MJ/kWh (corresponding to the electricity French energy mix produced from nuclear and fossil energies, assessed with the SimaPro® LCA software). The results are divided by 96, i.e. the number of pigs at the beginning of the fattening period.

Economic performance

The margin on feed cost is calculated per pig as the difference between the carcass value and the cost of feed intake. At slaughter, the economic value of the carcass is calculated for each pig, based on the French payment grid that takes into account the hot carcass weight and the carcass leanness (http://www.uniporc-ouest.com/, 30 March 2015). The price observed on average in December 2019 in Brittany (France, (http://www.marche-porc-breton.com/pdf/ntm/ntm1219.pdf) is used as the reference (1.496 €/kg). The cost of feed intake is calculated from the amount of each diet and its price based on the price of feedstuffs (available at Rennes, France) in December 2019, including 20 €/ton of delivery costs at the farm gate. The price of electricity used by equipment is fixed to 0.09 €/kWh (French average cost).

Statistical analyses Results obtained on average for each batch and each simulation are submitted to an analysis of variance (proc GLM, SAS, v9.4, Inst. Inc. Cary, NC) with the factors studied as the main effects and the batch as a random effect.

RESULTS AND DISCUSSION

Impact of room insulation Variation in Tin all along the fattening period was first simulated with different wall conductivities under the FR01 or SW01 climate, with similar regulation rule (VentilRef) and feeding sequence (TEF-).

Under mild winter There are only small differences between simulated Tin for the highest insulations tested (i.e., WallRef, WallOpt 1 and WallOpt 3), and Tin remains within the expected range of values parameterized in the climate box control of ventilation from the beginning of fattening to the first delivery to slaughterhouse (Figure 3a). With WallOpt 2, insulation is not high enough to prevent Tin from dropping below the minimal T setpoint especially at the beginning of the fattening period, when pigs are light, or just after the first delivery.

The increase in Tin during the last hours of the fattening period is related to an increase in Tout that occurs when pigs are heavy and produce a lot of heat.

Differences observed or not between the different types of wall insulation are due to their respective HTC. As the HTC of a homogeneous material depends directly on the thickness of the material (e, m) and the thermal conductivity (ʎ, in W.m -1 .°C -1 ) according to an asymptotic function (HTC = ʎ / e), any extra centimeter of insulation is more effective when thickness is small. Insulation is expected to improve significantly when an insulation layer is added to a concrete wall (WallRef or WallOp 1 vs. WallOp 2) whereas 5 additional cm have a limited impact when the wall is already insulated (WallOp 3 vs. WallRef).

As the surface of the wall that exchanges heat with outside is 27 m² and the HTC of WallRef is 0.55 W.m -².°C -1 , the heat loss through the wall is around 0.15 W/°C per pig (96 pigs in the room). If heat loss through the ceiling is also considered (0.40 W/C° per pig), 0.55 W/C° per pig is lost across the structure of the room with this type of insulation. This value is very low compared to heat loss due to air renewal, which can be estimated to 2.72 W/°C per pig when the minimum air flow rate is 8 m 3 /h (recommended value for a 30-kg pig), with a 0.34 W.m -3 .°C -1 volumetric heat capacity of moist air at 20°C and standard air pressure. The limited contribution of insulation to total heat loss already reported by The Pigsite (2010) and [START_REF] Harmon | Farm energy: sizing minimum ventilation to save heating energy in swine housing[END_REF][START_REF] Harmon | Farm energy: managing swine ventilation controller settings to save energy[END_REF] explains why differences in Tin are so small amongst WallRef, WallOpt 1 and WallOpt 3 that they can be considered as comparable.

Under very cold winter When the coldest Tout are observed at the beginning of the fattening period, the highest insulations (i.e. low HTC) help to regulate Tin (Figure 3b). However, not enough heat is produced by the animal to balance the heat lost through the wall and due to air renewal even when ventilation rate is minimal (Figure 3B). Hence, with a T setpoint that decreases from 24 to 22°C over the first 15 days (i.e., over the first 360 hourly data) in the VentilRef rules, Figure 3b illustrates that expectations are not met without any other source of heat when Tout is extremely cold. Subsequently, Tin decreases at the beginning of the fattening period when pigs are light and do not produce a lot of heat. After the first delivery to the slaughterhouse when the number of pigs in the room decrease in Tin is limited compared to what is observed at the beginning of the period due to the higher amount of heat produced at this stage by each pig. Then Tin remains close to or above LCT, which is assumed to be close to 19°C around 100 kg BW when pigs are housed on fully slatted floor [START_REF] Quiniou | Simulating with the ThermiPig model the impact of fattening room characteristics under different climates on the performance of pigs[END_REF]. Comparison of multicriteria performance As Tin regulation was similar with WallOp 1 and WallOp 3 under both climates, only results obtained with WallOp 3 (monolithic brick) and WallOp 2 (concrete paneling) are compared statistically in Table 2. Even when exposure to cold conditions occurs during a limited number of days at the beginning of the fattening period under the SW01 climate, it influences significantly all components of the performance, depending on the insulation level. The significant interaction observed between the climate and the wall insulation agrees with the differences in Tin observed between both options in Figure 3ab. With the highest insulation (WallOp 3), lower DFI and FCR, feed cost and indirect energy utilization are obtained under both climates than with WallOp 2 (P < 0.001). The difference is more important under SW01 than under FR01, with DFI reduced by 11 vs. 7 g/d, FCR reduced by 33 vs. 5 g/kg of BW gain, feed cost reduced by 49 vs. 10 c€/pig, and indirect energy reduced by 14 vs. 3 MJ/pig.

When wall insulation is improved, the margin on feed cost is improved by 70 and 23 c€/pig under the SW01 and FR01 climates, respectively. This result is explained mainly by the decrease in feed cost and to a lesser extend by differences in carcass value. Differences in carcass leanness between WallOp 2 and WallOp 3 are significant but depend on the climate (interaction: P < 0.001). Under the FR01 climate, the improved carcass leanness may be related to the higher amount of energy available for growth, especially for muscle deposition, at the beginning of the fattening period with WallOp 3. Under the SW01 climate, a similar effect would be expected but the intensity of cold exposure questions the way carcass leanness is calculated presently in the model. A linear relationship based on the concentrations in protein and lipid in the empty body weight at slaughter is used (InraPorc®, v1.7.1.0). But this equation does not account for the effect of the change in the partition of lipid gain between peripheric and internal fat tissues when Tin is out of the thermoneutral zone. According to Rinaldo and Le [START_REF] Dividich | Influence of environmental temperature on growth performance in pigs[END_REF] and Čobanović et al. (2020), more fat is deposited in backfat than in belly under cold stress. Then, for a given lipid deposition rate, a reduced exposure to cold would result in a thinner backfat. When this criterion is used to assess the carcass leanness at slaughter and when the carcass payment grid is strongly driven by carcass leanness (like in France), the carcass value would be also higher with an increased wall insulation. In practice, the impacts of wall insulation under extremely cold Tout are also probably underestimated as health problem induced by cold exposure and consequence of cold air flow and poor air quality associated with minimal ventilation rates are not considered presently in the ThermiPig model.

The last dimension of pig performance concerns the environmental impact of pig production, assessed locally by the amount of N output per pig and globally through the energy consumption. Nitrogen retention is similar with both options of wall insulation, whilst N intake is reduced with WallOp 3 compared to WallOp 2. Subsequently, N output is reduced when wall insulation is improved (P < 0.001). The higher decrease in DFI under SW01 climate induces a more important decrease in N output, but also a more important decrease in total energy consumption. In practice, in order to compare the different options, a grade-color scale could ease the comparison (for example for a given criteria, from the worse result in red to the best one in green) and identify at a glance the option that gives the most interesting combination of criteria. (HTC = 0.27 W.m -2 .°C -1 ) vs. Op 3: monolithic brick (HTC = 0.35 W.m -2 .°C -1 ), with similar ventilation rules (VentilRef) and feeding strategy (TEF-), and no heating power. 2 Analysis of variance with the climate (C), wall insulation (W) and interaction CxW as main effects (see P-values in the table: *** P < 0.01, ** P < 0.01, * P < 0.05) and the batch (n = 30) as a random effect, RSD: residual standard deviation. Different superscripts on the same row indicate that means differ with a probability of 5%. The cell of the most interesting result is colored in intense green color, the less interesting one in intense green, and the intermediate values are colored in pastel. 3 Performance of pigs alive at the end of the fattening period, feed conversion ratio is expressed in grams of feed intake per kg of body weigh gain. 4 Cumulated at the batch scale and divided by 96.

Impact of the heater capacity. Previous simulations performed with VentilRef regulation rules illustrate that wall insulation and heat produced by animals are not high enough to allow for balancing Tin under extremely cold outdoor conditions. Other characteristics of the room or management can be questioned in these conditions. The management of the air renewal is crucial to limit the loss of heat and the decrease in Tin [START_REF] Harmon | Farm energy: managing swine ventilation controller settings to save energy[END_REF], indeed heat loss can be halved by a minimum ventilation rate regulated with a high accuracy (IFIP, 2013). Supply of extra heat is another effective solution to limit the drop in Tin, at least at the beginning of the fattening period or when the number of pigs decreases after the first delivery. Simulations are performed without or with three heating power capacities as illustrated in Figure 4 and Table 3 under the SW01 climate. Figure 4a illustrates that differences in Tin are not observed amongst options of heating power all the time, but only when ventilation is at the minimal rate (Figure 4b) as this is the condition required by the system to provide extra heat.

Obviously, the higher the power capacity is, the smaller the drop in Tin observed at the beginning of the fattening period (Figure 4a). Although Tin is improved only during a limited period, FCR is improved by increased heating power. Up to 37.6 W/pig, it is associated with a significant decrease in DFI and an increase in ADG, corresponding to a reduced energy demand for thermoregulation at the expense of growth. Subsequently, the indirect energy use from the feed, feed cost and N output decrease also (Table 3). Increasing the power capacity above 37.6 W/pig only improves marginally these components of the performance. Without consideration of the impact of cold exposure on health and welfare of the pigs and the farmer, improved growth performance, economic return and environmental impact do not compensate for the extra cost of electricity presently. But, as mentioned before, the carcass value is probably underestimated when cold exposure is reduced, due to the way carcass leanness is assessed. Combined with a reduced feed cost, the margin of feed cost is expected to be higher than estimated presently and it may compensate or not for the extra cost of electricity, depending on the market price of meat and electricity.

Impact of the ventilation rules Effects of the regulation rules are investigated in a room insulated with monolithic brick (Wallop3), without any additional equipment but ventilation under FR01 and FR06 climates and with different heater capacities under SW01 climate.

When simulations are performed under the FR06 climate (result not presented), the DFI is increased (+20 to 80 g/d) when the final T setpoint is reduced from 22 to 15 or 17°C. Pigs are also heavier on average at delivery (+0.3 to +0.9 kg on average), but without an increase in final BW variability. Simultaneously a slight increase in FCR is observed as well as a limited decrease in carcass leanness. Both results contribute to decrease the margin on feed cost compared to the result obtained with VentilRef. However, it remains better (around + 2 €/pig) than in winter. The impacts of hot exposure on physical activity (activity, postural changes…) and behavior of pigs beside appetite are not considered presently in the model. The farmer may decide to overcome the limited differences mentioned above based on his knowledge and expertise and to promote one of these options. 1. 4 Analysis of variance with the ventilation rule (V, see P-value in the table) as main effect and the batch (n = 30) as a random effect.

Impact of pad cooling The pad cooling system is activated when Tout increases above 25°C, that occurs frequently under the FR06 climate (Figure 6a). When pad cooling is activated, Tin remains almost all the time below 28°C, whereas higher values are observed otherwise (Figure 6b). With the TEF+ strategy When conventional diets are used, the reduced exposure to acute heat stress associated to pad cooling activation allows for an improvement of DFI by 140 g/d and of ADG by 37 g/d that results in a heavier final BW (+1.9 kg, Table 5). Beside FCR is increased by 54 g/kg and N output by 224 g/pig, margin on feed cost per pig is 0.5 € lower, and the decrease in direct energy (-2 MJ/pig) does not compensate for the indirect energy consumption (+38 MJ/pig). Based on the present results, the first conclusion would be that pad cooling is not worth it, even when extra consumption of water is not considered. But it may be reconsidered in the future. Le [START_REF] Bellego | Effect of high ambient temperature on protein and lipid deposition and energy utilization in growing pigs[END_REF] and [START_REF] Serviento | Chronic prenatal heat stress alters growth, carcass composition, and physiological response of growing pigs subjected to postnatal heat stress[END_REF] observed significant effects of hot temperature on the metabolism, especially on protein synthesis, that would mean that carcass leanness (then carcass value and margin on feed cost) is overestimated when no pad cooling is used.

With the TEF-strategy Under hot conditions, a slight but significant increase in DFI of TEFdiets is observed as expected. As less heat is produced during the metabolic use of these diets, a given cumulated amount of heat produced by the group of pigs can be obtained from a higher amount of feed intake with a limited impact on the thermal balance at the room scale. Increased DFI is associated to an increased ADG, and FCR is also improved without pad cooling (Table 5). The most important effect is observed on N intake, as low TEF diets present usually a lower crude protein content than conventional (TEF+) diets for the same concentration in essential amino acids. Subsequently, the lower N intake, associated with a significant decrease in FCR or not, contributes to an important decrease in N output (-403 and -422 g/pig, without and with pad cooling, respectively).

CONCLUSION Nowadays, dealing with climate change and the efficient use of resources when designing or renewing pig barns is necessary, but it is difficult with regards to the numerous characteristics that must be considered, either solely or in combination. The modelling approach gives cheap and unlimited possibilities to compare in a very reactive way different options with regard to their specific impacts on the multicriteria performance of the pigs. Based on in silico results (not on absolute values), it is possible to compare different options and to consider the positive and negative variation before making a decision, depending on the weight given to each component of the performance (feed efficiency, economic result, environmental impact, energy consumption…) by the farmer or the technical designer. The investigation carried out with the ThermiPig model in the present paper demonstrate its ability to describe the multicriteria performance of pigs associated with different characteristics of the room or management. The outputs of the bioclimatic growth model are expected to be further improved in the future. Ongoing developments focus on the thermodynamic representation of slurry and its contribution to the thermal balance and air quality at room scale. Additionally, the impact of housing conditions on metabolism and composition of body weight gain but also on animal welfare, health and resilience will be considered. With this kind of promising tool, it becomes easy to test different systems of pig production and to select the most optimal one depending on the climate.

  A fattening room representative of the IFIP experimental facilities (Romillé, France) is used. Its dimensions, i.e. width, length, and height are 10.41 m x 11.61 m x 2.60 m, respectively. It has been designed for 96 fattening pigs housed in 16 pens with 0.7 m²/pig on fully slatted-floor, extra corridors required for demonstration activities, and a suspended ceiling. The characteristics of this real room correspond to the reference values, and alternative ones are tested.

Figure 1 .

 1 Figure 1. Inputs considered in the ThermiPig model to simulate the thermal balance at the room scale.

Figure 2 .

 2 Figure 2. Hourly outdoor temperature in Western France (a) or Northern Sweden (b) for 330 successive days from November 1 st and indication about seasonal conditions used in simulation.

Figure 3 .

 3 Figure 3. Effect of the heat transfer coefficient (HTC) of walls 1 on the hourly indoor temperature (a, b) and the ventilation rate (A, B) all along the fattening period either under the FR01 2 (a, A) or the SW01 3 (b, B) climate.

Figure 4 .

 4 Figure 4. Effect 1 of the heating power capacity (W/pig) on the hourly indoor temperature (a) and ventilation rate (b) all along the fattening period under the SW01 climate 2 1 Ventilation rules: Ventil Ref , heating regulation rules: Heater Op 1 , wall insulation: Wall Op 3 , feeding strategy: TEF+. 2 See Figure 2.

Figure 5 .

 5 Figure 5. Hourly outdoor temperature under FR06 climate (a) and effect 1 of pad cooling on the hourly indoor temperature (b).1Wall insulation: WallRef, ventilation rule: VentilRef, feeding sequence: TEF+.

Table 1 .

 1 Description of the setpoint temperature curves considered in different regulation rules of ventilation.

	Regulation rules	Reference			Option
	Rules	VentilRef	1	2	3	4	5	6
	Temperature (T) curve
	Initial T setpoint (°C)	24	24	24	20	20	18	18
	Final T setpoint (°C)	22	17	17	17	17	15	15
	Setpoint interval (d) 1	15	77	77	77	77	77	77
	Bandwidth (°C) 2	6	6	10	6	10	6	10
	1 Number of days required to switch linearly from initial to final T. 2 Number of degrees between the T setpoint
	and the T at which ventilation rate reaches its maximal value.

  Simulations performed with the same ventilation rules (VentilRef) and feeding strategy (TEF-), without heating power, and with different HTC for WallRef, WallOp 1, WallOp 2, and WallOp 3: 0.55,0.27, 11.33 and 0.35 W.m -2 .°C -1 , respectively. 2 Lines obtained with WallRef, WallOp 1 and WallOp 3 under FR01 climate and with WallOp 1 and WallOp 3 under SW01 climate are confounded.3 WallRef was not simulated under the SW01 climate.

	1
	First delivery	First delivery

Table 2 .

 2 Comparison of performance obtained with different heat transfer coefficients (HTC) of walls under SW01 or FR01 climate 1 .

	Climate	FR01	SW01			Statistics 2
	HTC	Op 2	Op 3	Op 2	Op 3	RSD 2	C	W	CxW
	Growth performance 3
	Final body weight (kg)	118.4	118.3	117.9	118.0	0.3	***		t
	Feed intake (g/d)	2387 a	2380 b	2418 c	2407 d	5	***	***	*
	Average daily gain (g)	860 a	859 a	846 b	852 c	2	***	***	***
	Feed conversion ratio	2796 a	2791 b	2880 c	2847 d	7	***	***	***
	Carcass leanness	59.86 a	59.94 b	59.96 b	59.90 c	0.07	*		***
	N balance (g) 4
	Intake	5577 a	5564 b	5719 c	5659 d	24	***	***	***
	Retained	2168 a	2168 a	2158 b	2159 b	10	***
	Output	3409 a	3396 b	3561 c	3500 d	18	***	***	***
	Economic result (€) 4
	Feed cost	53.60 a	53.50 a	54.94 b	54.43 c	0.37	***	***	**
	Margin on feed cost	92.63 a	92.86 b	90.82 c	91.52 d	0.31	***	***	***
	Electricity	0.966 a	0.969 b	0.956 c	0.958 c	0.004	***	***	***
	Energy (MJ) 4
	Indirect (from feed)	1425 a	1422 b	1462 b	1448 c	10	***	***	**
	Direct (electricity)	142.8 a	143.2 b	141.5 c	141.6 c	0.3	***	***	***
	Total consumption	1567 a	1565 a	1603 b	1589 c	10	***	***	**
	1 Op 2: concrete paneling

Table 3 .

 3 Comparison of performance 1 obtained with different heater power capacities under the SW01 climate 2 . See Table2.2 Wall insulation: WallOp 3, ventilation rule: VentilRef, feeding sequence: TEF+.3 Analysis of variance with the heating power (HP, see P-value in the table) as main effect and the batch (n = 30) as a random effect.

	Heater power, W/pig	0	18.8	37.6	50.0	RSD 1	HP 2
	Growth performance
	Final body weight (kg)	118.0 a	118.1 ab	118.2 b	118.4 c	0.3	***
	Feed intake (g/d)	2405 a	2400 b	2398 b	2400 b	4	***
	Average daily gain (g)	852 a	855 b	857 c	859 d	2	***
	Feed conversion ratio	2844 a	2827 b	2818 c	2815 c	7	***
	Carcass leanness	60.01 a	59.94 b	59.88 c	59.83 d	0.07	***
	N balance (g)
	Intake	6102 a	6073 bd	6057 c	6063 d	21	***
	Retained	2163	2164	2165	2168	6	t
	Output	3938 a	3909 b	3892 c	3895 c	18	***
	Economic result (€)
	Feed cost	58.64 a	58.32 b	58.16 b	58.15 b	0.35	***
	Margin on feed cost	87.42 a	87.74 b	87.84 bc	87.91 c	0.31	***
	Electricity	0.958 a	2.129 b	2.882 c	3.200 d	0.068	***
	Energy consumed (MJ)
	Indirect (from feed)	953 a	948 b	945 bc	945 c	6	***
	Direct (electricity)	142 a	315 b	426 c	473 d	10	***

Table 4 .

 4 Comparison of performance 1 obtained with different ventilation rules under the FR01 climate 2 . See Table 2. 2 Wall insulation: Wall Ref , heating power: null, feeding sequence: TEF-. 3 See Table

	Ventilation rule 3	Ref	Op 1	Op 2	Op 3	Op 4	Op 5	Op 6	RSD 1	V 4
	Growth performance
	Final body weight (kg)	118.3 a 118.9 b 118.8 bc 118.7 c 118.7 c 118.6 c 118.7 c	0.3	***
	Feed intake (g/d)	2380 a 2441 b	2430 c	2461 d 2443 e 2529 f 2493 g	5	***
	Average daily gain (g)	859 a	869 b	867 c	866 d	866 d	861 e	863 f	2	***
	Feed conversion ratio	2791 a 2831 b	2822 c	2865 d 2841 e 2960 f 2912 g	7	***
	Carcass leanness	59.94 a 59.38 b 59.41 bc 59.43 c 59.43 c 59.68 d 59.55 e 0.07 ***
	N balance (g)
	Intake	5563 a 5678 b	5650 c	5737 d 5688 b 5917 e 5825 f	23	***
	Retained	2168	2167	2164	2165	2164	2169	2166	9	ns
	Output	3400 a 3511 b	3487 c	3572 d 3522 e 3748 f 3659 g	18	***
	Economic result (€)
	Feed cost	53.51 a 54.53 b 54.26 c 55.14 d 54.64 b 56.95 e 55.94 f 0.35 ***
	Margin on feed cost	92.86 a 91.17 b 91.39 c 90.45 d 90.97 e 88.92 f 89.69 g 0.34 ***
	Electricity	0.969 a 0.999 b 0.988 c 1.001 d 0.995 e 1.047 f 1.021 g 0.002 ***
	Energy consumed (MJ)
	Indirect (from feed)	1422 a 1449 b	1442 c	1465 d 1452 b 1513 e 1486 f	9	***
	Direct (electricity)	143.2 a 147.7 b 145.9 c 149.2 d 147.0 e 154.8 f 151.0 g	0.3	***

Table 5 .

 5 Comparison of performance 1 obtained with two feeding sequences with or without pad cooling under summer climate FR06 2 . Wall insulation: WallRef, ventilation rule: VentilRef.3 Analysis of variance with the pad cooling (Pc), thermic effect (TE) of feed and their interaction (PcxTE) as main effects (see P-values in the table) and the batch (n = 30) as a random effect.

	Thermic effect of feed	TEF+	TEF+	TEF-	TEF-	RSD 1		Statitics 3
	Pad cooling	No	Yes	No	Yes		Pc	TE	PcxTE
	Growth performance
	Final body weight (kg)	114.8 a	116.7 b	115.0 c	116.7 b	0.3	***
	Feed intake (g/d)	2120 a	2260 b	2122 a	2264 c	5	***	***
	Average daily gain (g)	794 a	831 b	797 c	834 d	2	***	***
	Feed conversion ratio	2683 a	2737 b	2679 c	2735 b	7	***	*
	Carcass leanness	62.59 a	61.29 b	62.47 c	61.13 d	0.07	***	***
	N balance (g)
	Intake	5553 a	5790 b	5153 c	5363 d	3	***	***	**
	Retained	2157 a	2169 b	2159 a	2165 b	9	***		*
	Output	3396 a	3620 b	2993 c	3198 d	2	***	***	**
	Economic result (€)
	Feed cost	53.14 a	55.53 b	53.20 a	55.48 b	0.43	***
	Margin on feed cost	91.40 a	90.91 b	91.50 a	90.83 b	0.30	***
	Electricity	1.127 a	1.115 b	1.126 c	1.114 d	0.002	***	***
	Energy consumed (MJ)
	Indirect (from feed)	865 a	903 b	866 a	902 b	7	***
	Direct (electricity)	166.6 a	164.8 b	166.4 c	164.6 d	0.2	***	***

1 See Table

2

.

2

Acknowledgements. The authors acknowledge Finn Udesen and Katarina Nielsen Dominiak (from SEGES, Denmark), Anne-Charlotte Olsson and Knut-Håkan Jeppsson (from SLU, Sweden), and David Renaudeau, Jean-Yves Dourmad and Florence Garcia-Launay (from INRAE -Institut-Agro, France) for sharing their data or expertise. Preliminary results were presented at the 70 th EAAP meeting, in Ghent, Belgium.


"Facilitating access to results encourages the re-use of research outputs and supports Open Science. This is essential for Europe's ability to enhance its economic performance and improve the capacity to compete through knowledge. […] Results of publicly-funded research can therefore be disseminated more broadly and faster, to the benefit of researchers, innovative industry and citizens.

Examples of federations

Three "use cases" of federations

  Europe has been continuously reinforcing its policy for facilitating open access to data Data management plans are evaluated in EU projects proposals ELIXIRCyril Pommier (FR), Astrid Junker (DE),Kristina Gruden (SL) Data is scattered in an "ecosystem" of information systems Insertion of data repositories in federations of information systems 2010: set of interoperable databases 2002of (stable/sustainable) nodes -A central portal offering services (e.g. search data) Backbone of good practices enabling such infrastructures Wilkinson et al (2016) SCIENTIFIC DATA, 3:160018, DOI: 10.1038/sdata.2016.18

-Collaboration

  The Wheat Initiative (G20 Initiative) and its Wheat Information System Expert Working group (www.wheatis.org). Also supported by the Research Data Alliance.-The European Infrastructure for Multi-scale Plant Phenomics and Simulation (EMPHASIS) and its information system (https://emphasis.plantphenotyping.eu/e-Infrastructure). In the frame of a strong collaboration with ELIXIR -The data federation of the ELIXIR Plant Science community (https://elixir-europe.org/communities/plantsciences ) Semantic • Description of the data • Controlled vocabularies: term name and definitions • Ontologies: semantic links between terms • Biologist driven Structure • Formatting and Organizing the data • Data Models • Standards : VCF, GFF, MIAPPE (www.miappe.org) , etc… • Biologist & Computer scientist driven Technical • Data integration and sharing • Interoperability : tools and systems • GA4GH • Breeding API www.brapi.org • Computer scientist driven Example of needed resources for a federation of phenotyping data From C. Miguel and C. Pommier • Development of a standard API : • Calls for plant material aligned with MCPD • Calls for phenotyping experiments aligned with MIAPPE and of a supporting data model • Next steps: develop the same type work on the calls for genotyping data (coordination with GA4GH) Breeding API initiative Selby et al. Bioinformatics (2019), doi.org/10.1093/bioinformatics/btz190 and Open Data requires a multidisciplinary cooperation : • Biologists • Bioinformaticians • specialists of ontologies/semantics

Acknowledgements URGI team H. Quesneville C. Pommier M. Alaux M. Buy D. Charruaud G. Cornut J. Destin S. Diagne S. Durand B. El-Houdaigui R. Flores C. Guerche E. Kimmel T. Letelllier C. Michotey N. Mohellibi

This policy is implemented via the European Open Science Cloud (EOSC) • The European infrastructures in Life Science should contribute to EOSC • E.g. European Infrastructure of Bioinformatics for Life-sciences: ELIXIR (23 countries)

Publishing FAIR data in GnpIS


"Facilitating access to results encourages the re-use of research outputs and supports Open Science. This is essential for Europe's ability to enhance its economic performance and improve the capacity to compete through knowledge.

[…] Results of publicly-funded research can therefore be disseminated more broadly and faster, to the benefit of researchers, innovative industry and citizens.

Europe has also been continuously reinforcing its policy for facilitating open access and interoperability

Recently funded projects were asked to add a WP supporting a FAIR compliant Data Management Plan

• Generic search tool used for the WheatIS: light tool that allows community building -> Monitoring of the interest of end users to be done in more detail

• BrAPI : same good properties + the possibility to diversify services

• One big challenge still ahead: get the data and get it FAIR during all its life cycle.

Conclusions and perspectives

From Rowan University, NJ, USA

There is still a challenge in providing operational environments facilitating data management all along its life cycle

Researcher's view

Infrastructures Data's view (EUDAT)

There is still a challenge in providing operational environments facilitating data management all along its life cycle

  of (stable/sustainable) nodes -A central portal offering services (e.g. search data)

Global plant phenology data portal: www.plantphenology.org Pan European PEP725 Plant phenology database: http://www.pep725.eu/

	Example: modelling the impact of climate
	change using plant phenology
	Date associated to: -Geo-reference -species -event (e.g. 50% of opened flowers) Interoperability	Date associated to: • Geo-reference • Measures (e.g T°C, …) • Events (e.g. hail, …)
	Phenology data : different sources, different accuracy in terms of
	identification of the species, scoring methods, record formats
	• Modelers of the impact of climate change
	• Geneticists, Breeders
	• Genbank managers
	• Experimental station managers
	4 • Civil (economic) society: e.g. vintage dates, cherry blooming date…

Phenology data Climatic data GeneBank & EMBL archives GLIS/DOI BioSample Gramene ORCAE VitisCyc VVIC VitisDB GRIN GnpIS Crop Ontology Infrastructures for genomic data production Grapevine Germplasm Repositories Infrastructures for plant phenotyping Individual data producers Communitity standards Data + metadata

	International	Grapevine	Data production
	repositories	community's
		repositories
	Standardized
	data, identifiers
	Curated data
	Agroportal Biosharing	Identifiers, reference data
	Data integration,
	knowledge development

KnetMiner InterPRO… From Adam-Blondon et al (2016) HortRes, 3:16056

	Development of an INRA information
	system for crops, forest trees and
	pathogens
	Data is scattered in an
	"ecosystem" of information
	systems

Acknowledgements URGI team Financial supports H. Quesneville C. Pommier M. Alaux M. Buy D. Charruaud G. Cornut J. Destin S. Diagne S. Durand B. El-Houdaigui R. Flores C. Guerche E. Kimmel T. Letelllier C. Michotey N. Mohellibi

This policy is implemented via the European Open Science Cloud (EOSC) • The European infrastructures in Life Science should contribute to EOSC • E.g. European Infrastructure of Bioinformatics for Life-sciences: ELIXIR (23 countries)

There is still a challenge in providing operational environments facilitating data management all along its life cycle Infrastructures Identity and access view

National and International infrastructures/initiatives

National and international Wheat projects

Thank you!


"Facilitating access to results encourages the re-use of research outputs and supports Open Science. This is essential for Europe's ability to enhance its economic performance and improve the capacity to compete through knowledge. […] Results of publicly-funded research can therefore be disseminated more broadly and faster, to the benefit of researchers, innovative industry and citizens.

Europe has been continuously reinforcing its policy open access to FAIR research data

First part aimed at making an overview:

Institute policies in terms of open data and of access to computing resources

  10 institutes/countries involved in ELIXIR infrastructure, 2 in Life Watch +/-GBIF, 1 in DISSCO, 1 in PRACE, 1 in EMBL

	• National policies about open data in research • Access to compute infrastructures • Involvement in international infrastructure on bioinformatics or open data • Use of database for the storage of data produced by the research units • Needs in terms of training in bioinformatics • Needs in terms of infrastructures 2 4 6 8 10 12 14 Country/0 16
	Do not know	yes (Institute)	In progress	no (country)
	Answers from 21 institutes of 16 countries (country)
		open data	compute

Recently funded projects were asked to add a WP supporting a FAIR compliant Data Management Plan

What would be the priority in terms of training?

• Genomic data analysis is the first need and to a lesser extent data standardization • The target is mostly students but some mentioned also the management • Online material, resources to allows students to attend courses are problematic for some respondents

What would be the priority in terms of access to a bioinformatic infrastructure?

• Access to stable/reliable tools for omics data analysisis the most frequently cited need • Storage capacity • Help for the development of a policy and legislation compliant infrastructures • National and transnational access (without the need to develop ad hoc collaborations) to powerful computing infrastructures

Short Survey sent to all the MC members

The second part aimed at digging a bit more into the data you produce and the way you manage it:

• What types/volumes of genomics-related data are you currently producing?

• How do you expect this to change over the next 5 years?

• How do you currently publish the data? Do you publish them at all?

• What are the obstacles to publishing the data?

• Are there data types you cannot publish?

• When you seek to use relevant published data, is it FAIR (Findable, Accessible, Interoperable, Re-usable)? If not, why? • Are there existing norms in the area of data publishing that you adhere to? • Are there candidate norms that you would like the community to adopt? • Are there new norms that the community could usefully develop? • Does the grape research community need its own dedicated Grape Information System, and if so, what would you like to be able to use or to contribute?

Answers from 10 institutes


••

  Enhancing the characterization of genetic resources as a lever for their better use • Developing FAIR compliant data management practices as a lever for enhancing access to data and knowledge on genetic resources An instrument developed by ECPGR: the facilitation of public-private European Evaluation (EVA) Networks of genetic resources https://www.ecpgr.cgiar.org/european-evaluationnetwork-eva • Networking with many stakeholders at the international level : facilitators such as international infrastructures (GBIF, ELIXIR), consortia (DivSeek), governed networks (ECPGR, ERFP, EUFGIS) • Networking with many stakeholders at the national level: facilitators National Focal Points/Inventories, national infrastructures/institutes Skills: data stewards • Guidelines, recommendations for FAIR compliant data management: general and domain related specifications; associated to catalogs • Operational implementations of these guidelines by: • Partners from the ELIXIR plant Science community • Genbank managers • Wheat and barley european public-private evaluation network

• Are necessary to understand and agree on details (this is where the devil lies usually)

• To agree on who is responsible of what when decision and actions are necessary (the devil is here also)

Examples:

Who is responsible for issuing DOI to accessions (Laboratories, Genbanks, national focal points or EURISCO)? Who is responsible for issuing unique Sample identifiers and do we use also project internal ID in addition of BioSample IDs?

• Sharing experience on guidelines implementations

• Contributing to raise awareness • In the scientific community about guidelines and best practices • To our institutes and funders: on the importance of skills and means for data stewardship.

• See for instance OECD (2020), "Building digital workforce capacity and skills for data-intensive science", OECD Science, Technology and Industry Policy Papers, n°90, Éditions OCDE, Paris, https://doi.org/10.1787/e08aa3bb-en.

Still a long way to go but we can help each others

GenRes Bridge partners (WP4)

• M. Bozzano (EFI, coord), M. Westergren (Gozdis) Thank you!


Malo Cadoret

Estefania De Mirandes

Pierre Cladé

Saïda Guellati-Khélifa

Catherine Schwob

François Nez

Lucile Julien

François Biraben

Combination of Bloch oscillations with a Ramsey-Bordé interferometer : new determination of the fine structure constant

Keywords: numbers: 37.25.+k, 37.10.Jk, 06.20.Jr, 37.10.De

We report a new experimental scheme which combines atom interferometry with Bloch oscillations to provide a new measurement of the ratio h/m Rb . By using Bloch oscillations, we impart to the atoms up to 1600 recoil momenta and thus we improve the accuracy on the recoil velocity measurement. The deduced value of h/m Rb leads to a new determination of the fine structure constant α -1 = 137.035 999 45 (62) with a relative uncertainty of 4.6 × 10 -9 . The comparison of this result with the value deduced from the measurement of the electron anomaly provides the most stringent test of QED.

The fine structure constant α characterizes the strength of the electromagnetic interaction. It is a corner stone of the adjustment of the fundamental constants [1] and its determination is made in different domains of physics. The most precise values of α are deduced from the measurements of the electron anomaly a e made in the eighties by H.G. Dehmelt at the University of Washington [2], and, recently, by G. Gabrielse at Harvard University [3]. This last measurement and an impressive improvement of quantum electrodynamics (QED) calculations [4] gives a value of α with a relative uncertainty of 3.7 × 10 -10 which surpasses the Dehmelt's result by one order of magnitude. Nevertheless this recent determination of α relies on very difficult QED calculations. To test them, other determinations of α, independent of QED, are required. The most precise are deduced from the measurement of the ratio h/m between the Planck constant and the mass of an atom thanks to the relation deduced from the ionization energy of hydrogen:

α 2 = 2R ∞ c m m e h m , (1)
where m e is the electron mass. The limiting factor is the ratio h/m: the uncertainty of the Rydberg constant R ∞ is 7 × 10 -12 [5,6] and that of the mass ratio m/m e 4.8 × 10 -10 [1,7]. This principle has been used on Cs atom by S. Chu and colleagues with an atom interferometer to measure the recoil velocity v r = k/m of the atom when it absorbs a photon of momentum k and to deduce α with a relative uncertainty of 7.4 × 10 -9 [8]. In 2005, our group used the Bloch oscillations (BO) of Rb atoms in an optical lattice to transfer a large number of photon momenta to the atoms: we achieved a precise measurement of atomic recoil velocity and a determination of α with a relative uncertainty of 6.7 × 10 -9 [9,10].

In this letter, we present a combination of the two methods: we use BO to transfer a large number of photon momenta and a Ramsey-Bordé interferometer to precisely measure the induced atomic velocity variation. This leads to a value of α with a relative accuracy of 4.6 × 10 -9 . The comparison of this result, which is very slightly dependant on QED, with the value of α deduced from the electron anomaly is the most stringent test of the QED calculations.

Bloch oscillations have been first observed in atomic physics by the groups of C. Salomon and M.G. Raizen [11,12]. The atoms are placed in an optical lattice by shining on them two counter-propagating laser beams whose frequency difference is swept linearly. The atoms undergo a succession of Raman transitions which correspond to the absorption of one photon from a beam and a stimulated emission of a photon to the other beam. The internal state is unchanged while the atomic velocity increases by 2v r per oscillation. The Doppler shift due to this velocity variation is periodically compensated by the frequency sweep and the atoms are accelerated. This method is very efficient to transfer to the atoms a very large number of photon momenta [13]. Another point of view is to consider that the atoms are placed in a standing wave which is accelerated when the frequency difference between the two laser beams is swept. In the atomic frame, the atoms undergo an inertial force. This system is analog to the BO of an electron in a solid submitted to an electric field [11]. There is a similar context when an atom is placed in a vertical standing wave in the gravitational field. This situation has been already investigated for measuring the local acceleration of gravity [14,15,16]. It has also been suggested to use BO to probe forces near surfaces at a microscopic scale [17,18].

In our experiment BO are combined with a Ramsey-Bordé interferometer [19] following the scheme of Fig. 1. BO are inserted between two pairs of π/2 laser pulses. Each pulse drives a Doppler-sensitive Raman transition between the two hyperfine ground states labeled |g and |e (F = 2 and F = 1 in the case of 87 Rb). The first pair of π/2 pulses creates the two coherent atomic wavepack- ets in internal state |e . We then blow away the atoms remaining in the initial state |g by using a laser beam tuned to a single photon transition. Both wavepackets are accelerated by N BO. The second π/2 pair recombines the two atomic wavepackets and readouts the phase difference between the two paths. The interferometer can also be understood in momentum space. After the first pair of π/2 pulses, the shape of the velocity distribution of the atoms in the level |e is a Ramsey fringe pattern. The fringe spacing varies as 1/T R (T R is the delay between the two π/2 pulses). These atoms are adiabatically loaded into the first Brillouin zone of the optical lattice. Following the Bloch formalism, if the atom has a well defined momentum q 0 with |q 0 | < k, the atomic wave function is modified when the optical potential is increased adiabatically (without acceleration) and becomes in the first energy band [10]:

|Ψ 0,q0 = l φ 0 (q 0 + 2lk)|q 0 + 2lk (2)
with l ∈ Z. Here |q 0 designs the wave function associated to a plane wave of momentum q 0 and the amplitudes φ 0 correspond to the Wannier function [20] in momentum space of the first band. When the potential depth is close to zero, the limit of the Wannier function φ 0 is 1 over the first Brillouin zone and zero outside. On the contrary, if the potential depth is large, the Wannier function selects several components in the velocity space. When the optical lattice is accelerated adiabatically, the Wannier function is continuously shifted in the momentum space following the relation: The experimental set-up has been described previously [9,10]. A cold atomic sample of 3 × 10 7 atoms ( 87 Rb) is produced in a σ + -σ -optical molasses loaded from a magneto-optical trap (MOT). The atoms are then optically pumped to the F = 2, m F = 0 sub-level. The optical lattice is derived from the interference of two counterpropagating vertical beams generated by a Ti-Sapphire laser. Its frequency is blue detuned by ∼ 40 GHz from the D2 line. The lattice is adiabatically raised during 500 µs, then accelerated during 3 ms and adiabatically lowered (500 µs). The lattice depth is about 100 E r (E r = 2 k 2 /2m is the recoil energy). The π/2 laser pulses are derived from two external cavity phase-locked diodes lasers. The power of these Raman beams is 13 mW (per beam), their radius at 1/e 2 is 2 mm. Their frequencies are blue shifted by 310 GHz from the D2 line in order to reduce photon scattering and light shifts. Their beat frequency is precisely controlled: a frequency sweep is used during each pair of π/2 pulses in order to balance the acceleration of gravity and a frequency jump allows to compensate the Doppler shift due to any velocity variation ∆v between the two pairs of π/2 pulses. We use a symmetric Ramsey-Bordé interferometer i.e. the laser beams directions are the same for the four pulses. In this case, we are only sensitive to the velocity variation induced by the BO and the acceleration of gravity.

|Ψ(t) = l φ 0 (q 0 + 2lk -mv(t)/ )|q 0 + 2lk (3)
When we increase the number of BO up to 50, the atoms collide with the window of the vacuum chamber. To overcome this problem, we load the atom interferometer with atoms initially accelerated using also BO. In such a way, the atomic velocity at the end of the interferometric trajectory is close to zero [9,10].

The ratio of h/m Rb is deduced from four spectra obtained by using a first experimental protocol P1. It consists in : (i) accelerating the atoms either upwards or downwards keeping the same spacing time T between the two π/2 pulses pairs (the numbers of BO are respectively labeled N up and N down ). In both cases the velocity variation due to the gravity acceleration g is g×T , and can be canceled by making the difference between the two measurements. (ii) For each initial acceleration, we record two spectra by exchanging the directions of the Raman beams. In this case the contribution of some systematics arising from parasitic level shifts (ac stark or second order Zeeman effect) changes sign and is then substantially Here N1 and N2 are respectively the number of atoms in F=1 and F=2 after the second pair of π/2 laser pulses.

reduced by averaging these two measurements. Two typical interference fringes patterns are shown in Fig. 2. The effective number of BO is N up + N down = 1000, corresponding to 2000 recoil velocities between the upper and lower trajectories. The spacing time T R is 2.6 ms and the duration of each π/2 pulse is 400 µs. The central fringe is determined with an uncertainty lower than 1.4 Hz (∼ v r /10000). Each spectrum is plotted with 200 points and is obtained in 6 min. We achieve an excellent fringes visibility of about 30% for 600 BO.

The number of BO and the spacing time between the two π/2 laser pulses can be potentially increased. They are still limited respectively by the displacement of the atoms in the vacuum chamber and vibrations. To overcome the first limit, we have built an "atomic elevator". The idea consists in displacing the atoms to the bottom or the top of the cell after the molasses phase. For that we take advantages of the high efficiency and the precise acceleration control of BO (through the control of the frequency difference between the two laser beams). We then start the measurement protocol at this position instead of the center of the cell. Fig. 3 illustrates the new experimental sequence (protocol P2) and the corresponding atomic trajectories: after the cooling process all the atoms are accelerated for instance in the upward direction by using N elv BO, thereafter when they come near the upper window they are stopped by using -N elv BO. We then perform a measurement following the protocol P1 on a longer interaction distance. In such a way, we transfer 1600 photon momenta and obtain a fringes pattern with a typical visibility of 30% (see Fig. 3). Moreover the uncertainty on the fringes center is reduced to less than 0.7 Hz by increasing the delay T R to 5.4 ms and by implementing a vibration isolation platform.

We have used both protocols P1 and P2 to obtain 221 determinations of α. For these measurements, the effective number of BO N up + N down varies between 200 and 1600. The dispersion of the values is χ 2 /(n -1)=1.85 and the resulting statistical uncertainty on α is 3 × 10 -9 .

The systematics effects are already detailed in [9,10]. For instance, in the case of the P2 protocol, they are listed in Table I. These corrections and uncertainties are Although the uncertainty of this value is more than 10 times smaller than our result, the comparison of these two results provides the most stringent test of the QED. To improve it, we are investigating deeply the limits of our experiment. We are building a larger vacuum chamber to increase the number of BO. A relative uncertainty lower than 10 -9 can be reasonably expected with a better control of the magnetic field and of the geometric parameters of the laser beams. This performance would provide the possibility to reach an unprecedented test of the QED theory, or, if we consider the QED theory exact, a test of a possible substructure of the electron [21,22].

In conclusion, we have demonstrated the possibility to combine the BO with an atom interferometer. Compared with our previous work, this combination allows to increase the resolution without decreasing the signal to noise ratio. We have obtained a new determination of the fine structure constant in agreement with our last determination based on a non interferometric method. The comparison of this result with the value of α deduced from the measurement of the electron anomaly is the best test of QED. This paper also opens a new way for the design of atom interferometers based on BO. The combination of atom interferometry with BO can be used for the measurement of the gravity constant g as proposed in [16]. It could significantly improve the sensitivity of measurements of g done with a very large number of BO [23,24]. Thanks to a larger vacuum chamber, we plan to increase the number of BO in order to reduce the uncertainty of our measurement to 1 ppb. In this letter, we have studied a simple scheme where the BO are inserted between the two pairs of π/2 pulses. Another way to improve the precision of atom interferometers consists in using n-photons momentum beam splitter [25]. As described in [26], BO can be used to realize a large mo-mentum beam splitter. The idea consists to initially create two coherent wave-packets by using a π/2 Raman pulse and then load those wave-packets in the first and third band of an accelerated optical lattice. By choosing suitable lattice parameters, only atoms in the first band will be accelerated, increasing the relative momentum between the two interfering paths. A preliminary calculation of the phase shifts due to the BO shows the possibility of increase the sensitivity by a factor n of the order of ten.

FIG. 2 :

 2 FIG. 2: Typical set of two spectra used for a determination of α corresponding to the up (a) and down (b) trajectories.Here N1 and N2 are respectively the number of atoms in F=1 and F=2 after the second pair of π/2 laser pulses.

FIG. 3 :

 3 FIG.3: Trajectories of the atom using the "atomic elevator" technique and the corresponding pulses sequence. The spectra (a) and (b) correspond to an up and a down trajectory.

  Consequently, if the initial atomic velocity distribution fits the first Brillouin zone, it is exactly shifted by 2N v r without deformation. The second pair of π/2 laser pulses is used to readout the accelerated velocity distribution. By scanning the frequency of the second pair of π/2 pulses, we realize the convolution of this distribution by a second Ramsey fringe pattern. The shift of the resonance is 2N kv r . The resolution of the recoil measurement is inversely proportional to the spacing between Ramsey fringes and proportional to the number 2N of transferred recoils.

	where v(t) is the velocity of the optical lattice. The
	enveloping Wannier function φ 0 is shifted by mv(t) in
	momentum space. After the acceleration, the potential
	depth is decreased adiabatically and, in equation 3, the
	Wannier function selects only one component of the ve-
	locity distribution. At the end, the wave function is
	|Ψ = |q

0 + 2N k . If ∆v is the velocity variation due to the acceleration, the number of Bloch oscillations N is such as | q 0 + m∆v -2N k| < k.

TABLE I :

 I Error budget on the determination of 1/α (systematic effect and relative uncertainty in ppb).

	h/m(Cs) h/m(Cs)
					h/m Rb (LKB 05) h/m Rb (LKB 05)
			a e (U-Wash 87) a e (U-Harvard 06) a e (U-Wash 87) a e (U-Harvard 06)
				a e (U-Harvard 08) a e (U-Harvard 08)
						h/m Rb (LKB 08) h/m Rb (LKB 08)
	599,8 599,8	599,85 599,85	599,9 599,9	599,95 599,95	600 600	600,05 600,05	600,1 600,1
			(a -1 -137.03) × 10 5 (a -1 -137.03) × 10 5
	FIG. 4: (Color online) The most accurate determinations of
	the fine structure constant, in green the recent determination
	deduced from the g -2 measurement (U-Harvard 08) and in
	red this work (LKB 08).
	which summarizes the most relevant determinations of
	the fine structure constant [1, 2, 3, 4, 8, 9, 10]. This new
	determination is in agreement with our previous value
	(dot labeled LKB 05) and with the last result deduced
	from the electron anomaly [3]:
	α -1 (a e ) = 137.035 999 084 (51) [0.37 × 10 -9 ] (5)
							Source	Correction	Relative uncertainty
							Laser frequencies	0.4
							Beams alignment	-2	2
							Wavefront curvature and Gouy phase	-11.9	2.5
							2nd order Zeeman effect	4.9	1
							Quadratic magnetic force	-0.59	0.2
							Gravity gradient	-0.07	0.02
							light shift (one photon transition)	0.1
							light shift (two photon transition)	0.01
							light shift (Bloch oscillation)	0.48	0.2
							Index of refraction atomic cloud	0.3
							Index of refraction background vapor	-0.36	0.3
							Rydberg constant and mass ratio [1]	0.23
							Global systematic effects	-9.54	3.4
							very similar to those of the 2005 measurement. We have
							reduced the uncertainties of the two main corrections,
							due to the second-order Zeemann effect and to the ge-
							ometry of the laser beam, thanks to a careful mapping
							of the magnetic field and a precise measurement of the
							wavefront curvature. Finally the global correction on α -1
							is (-9.54 ± 3.4) × 10 -9 . Taking into account the statisti-
							cal uncertainty (3 × 10 -9 ), the total relative uncertainty
							on α is then 4.6 × 10 -9 . We obtain for h/m Rb the value
							4.591 359 246 (42) × 10 -9 m 2 • s -1 and for α:
							α -1 (LKB 08) = 137.035 999 45 (62) [4.6 × 10 -9 ] (4)
							This value is reported on the Fig. 4 (dot labeled LKB 08)

This experiment is supported in part by the Laboratoire National de Métrologie et d'Essais (Contrat 033006), by IFRAF (Institut Francilien de Recherches sur les Atomes Froids) and by the Agence Nationale pour la Recherche, FISCOM Project-(ANR-06-BLAN-0192).