Charlotte Roemer

Aurélie Coulon

Thierry Disca

Yves Bas

Keywords: Bat sonar and wing morphology predict species vertical niche predict species vertical niche Wing aspect ratio, echolocation, bat vertical space use, acoustic location

I. INTRODUCTION

Insectivorous bat species have developed through evolution the ability to commute and forage in complete darkness. Although feeding on similar resources (i.e. insects), most sympatric species specialise in their prey selection and therefore in their habitat selection, while some are more plastic [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa, A & C Black[END_REF]. In order to match these particular needs, this diet partitioning is accompanied by morphological and behavioural differences. Illustrating those differences, Myotis nattereri, a small bat (wingspan = 250-300 mm), is able to forage insects resting on leaves under the forest cover while Tadarida teniotis, a large bat (wingspan = 400-450 mm), forages on insect swarms in wide and elevated open spaces [START_REF] Arthur | Les chauves-souris de France, Belgique, Luxembourg et Suisse, Bats of France[END_REF]. In addition, the echolocation system, developed through evolution to sense the environment in the dark, reflects the ability of each species to perceive obstacles and prey [START_REF] Collen | The evolution of echolocation in bats: a comparative approach[END_REF][START_REF] Schnitzler | From spatial orientation to food acquisition in echolocating bats[END_REF][START_REF] Siemers | Echolocation signals reflect niche differentiation in five sympatric congeneric bat species[END_REF]. Indeed, bat echolocation calls are designed in such a way that most species may be differentiated from one another using call peak frequency, duration and bandwidth or call shape, despite some overlap [START_REF] Barataud | Acoustic ecology of European bats: species identification, study of their habitats and foraging behaviour[END_REF][START_REF] Fenton | Recognition of Species of Insectivorous Bats by Their Echolocation Calls[END_REF]. Frequency in echolocation calls varies from 9 kHz, as in calls emitted by Euderma maculatum, Vespertilionidae [START_REF] Fullard | The echolocation calls of the spotted bat Euroderma maculatum are relatively inaudible to moths[END_REF] or Tadarida teniotis, Molossidae [START_REF] Arlettaz | Contribution to the eco-ethology of the European free-tailed bat, Tadarida teniotis (Chiroptera, Molossidae), in the Alps of the Valais (south-western Switzerland)[END_REF], to 212 kHz, emitted by Cloeotis percivali, Hipposideridae [START_REF] Fenton | Recognition of Species of Insectivorous Bats by Their Echolocation Calls[END_REF].

Because atmospheric attenuation increases with call frequency, low frequency signals carry through greater distances than high frequencies, which in turn procure the advantage of a higher structure resolution [START_REF] Pye | Why ultrasound?[END_REF]. On the other hand, low frequencies are associated with long wavelengths, which are unsuitable for the detection of targets such as small insects, and should be the major evolutionary constraint for the use of low frequencies in echolocation [START_REF] Barclay | Prey detection, dietary niche breadth, and body size in bats: why are aerial insectivorous bats so small?[END_REF][START_REF] Waters | Echolocation Call Design and Limits on Prey Size: A Case Study Using the Aerial-Hawking Bat Nyctalus leisleri[END_REF]. Echolocation call length varies from 1 ms as by Myotis brandtii, Vespertilionidae, to more than 80 ms by Rhinolophus ferrumequinum, Rhinolophidae [START_REF] Barataud | Acoustic ecology of European bats: species identification, study of their habitats and foraging behaviour[END_REF]. Long calls allow a better detection of faint and distant echoes through the repeated addition of signal information that evokes the activity of neurons tuned to the frequency of interest, and consequently increase echolocation ranges [START_REF] Neuweiler | Foraging Ecology and Audition in Echolocating Bats[END_REF][START_REF] Schnitzler | From spatial orientation to food acquisition in echolocating bats[END_REF]. Long calls can also provide information on prey fluttering and movement directionality [START_REF] Trappe | Doppler-Shift Compensation in Insect-Catching Horseshoe Bats[END_REF], while the emission of short calls decrease the issue of call-echo overlap [START_REF] Jones | Scaling of echolocation call parameters in bats[END_REF]. Finally, call bandwidth varies from less than 1 kHz, as by Nyctalus noctula, Vespertilionidae [START_REF] Barataud | Acoustic ecology of European bats: species identification, study of their habitats and foraging behaviour[END_REF], to more than 170 kHz in some Kerivoula species (Vespertilionidae) [START_REF] Kingston | Chiroptera: Vespertilionidae) from Malaysia[END_REF]. Large bandwidths enhance range accuracy and resolution (i.e. the differentiation of two targets at close distances) [START_REF] Pye | Why ultrasound?[END_REF][START_REF] Siemers | Echolocation signals reflect niche differentiation in five sympatric congeneric bat species[END_REF] while small bandwidths, combined with long call length, can also be used to detect prey fluttering or increase the detection range. [START_REF] Aldridge | Morphology, Echolocation and Resource Partitioning in Insectivorous Bats[END_REF] studied the links between call shape, wing morphology, manoeuvrability, habitat use and diet in South African insectivorous bats. They found that the differences in acoustic features and wing morphology explained resource partitioning in these species. High wing loading (larger wing area relative to mass) generally correlates with high flight speed while low wing loading favours good manoeuvrability, essential when foraging in clutter [START_REF] Kalko | Flying high-assessing the use of the aerosphere by bats[END_REF][START_REF] Norberg | Ecological morphology and flight in bats (Mammalia; Chiroptera): wing adaptations, flight performance, foraging strategy and echolocation[END_REF]. In addition, high wing aspect ratio (narrow wings) generally correlates with decreases in transport costs thanks to a low wing inertia, and favours good agility at high speeds [START_REF] Kalko | Flying high-assessing the use of the aerosphere by bats[END_REF][START_REF] Norberg | Ecological morphology and flight in bats (Mammalia; Chiroptera): wing adaptations, flight performance, foraging strategy and echolocation[END_REF]. These studies highly contributed to the understanding of the acoustic and morphologic characteristics leading to clutter -or closed -versus open space adaptations in bats [START_REF] Fenton | The foraging behaviour and ecology of animal-eating bats[END_REF]. Several other studies also found strong relationships between body size or mass and acoustic parameters in many bat species all over the world [START_REF] Bogdanowicz | The relationships between echolocation calls, morphology and diet in insectivorous bats[END_REF][START_REF] Jones | Scaling of echolocation call parameters in bats[END_REF][START_REF] Penone | Body size information in large-scale acoustic bat databases[END_REF][START_REF] Thiagavel | Body Size Predicts Echolocation Call Peak Frequency Better than Gape Height in Vespertilionid Bats[END_REF]. These findings highlight the co-evolution of many traits in bats.

In 2001, Schnitzler and Kalko described the concept of bat guilds, which was refined over time [START_REF] Denzinger | Bat guilds, a concept to classify the highly diverse foraging and echolocation behaviors of microchiropteran bats[END_REF][START_REF] Denzinger | The role of echolocation strategies for niche differentiation in bats[END_REF]. Guilds may be used to form consistent species groups for the study of sonar structures, habitat types, diet, foraging modes and other traits. In [START_REF] Denzinger | The role of echolocation strategies for niche differentiation in bats[END_REF], four guilds may be distinguished according to their acoustic strategies: (1) aerial hawkers or trawlers developed a strategy to efficiently locate prey in open and edge space using long quasi-constant frequency (QCF) calls (2) active gleaners mostly use short calls with high frequency compounds and frequency modulated (FM) calls resulting in large bandwidths, useful to detect prey or obstacles in high clutter (3) passive gleaners also use short calls with high frequencies and FM calls, but mostly listen to the rustling sounds of their prey while foraging, and use echolocation for orientation (4) some species also use a strategy implying long constant frequency calls with modulated frequency components (CF-FM) at high frequencies which allow them to evaluate flutter information from the prey returning echoes.

Associations in echolocation, wing morphology and flight behaviour have only been demonstrated for adaptation to clutter [START_REF] Aldridge | Morphology, Echolocation and Resource Partitioning in Insectivorous Bats[END_REF][START_REF] Siemers | Echolocation signals reflect niche differentiation in five sympatric congeneric bat species[END_REF], from studies using material positioned at ground level, with a limited detection range, while bats use a three-dimensional space that can be as elevated as 3000 m for some species [START_REF] Peurach | High-altitude Collision between an Airplane and a Hoary Bat, Lasiurus cinereus[END_REF]Williams et al., 1973). The association between bat sonar or wing morphology and their use of the vertical dimension has never been thoroughly demonstrated. Since the vertical distribution of insects varies according to species [START_REF] Reynolds | Riders on the Wind: The Aeroecology of Insect Migrants[END_REF], and since bats differentiate in their diets [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa, A & C Black[END_REF], the vertical distribution of the different bat guilds is strongly expected to follow that of their prey [START_REF] Norberg | Ecological morphology and flight in bats (Mammalia; Chiroptera): wing adaptations, flight performance, foraging strategy and echolocation[END_REF][START_REF] Roeleke | How Bats Escape the Competitive Exclusion Principle-Seasonal Shift From Intraspecific to Interspecific Competition Drives Space Use in a Bat Ensemble[END_REF]. [START_REF] Roemer | Bat flight height monitored from wind masts predicts mortality risk at wind farms[END_REF] showed that bat guilds according to [START_REF] Denzinger | Bat guilds, a concept to classify the highly diverse foraging and echolocation behaviors of microchiropteran bats[END_REF] could be ordered along the gradient of the rate of time spent at height. It was also shown that the occurrence of certain insect orders in bat diet could be associated with certain bat sonar and morphology features [START_REF] Bogdanowicz | The relationships between echolocation calls, morphology and diet in insectivorous bats[END_REF]. However, the contribution of sonar features and wing morphology to the vertical separation of species was only described from case studies on target species, or from a collection of heterogeneous observations (visual, mistnetting, acoustic) of a bat community [START_REF] Banse | Ableitung des Kollisionsrisikos von Fledermäusen an Windenergieanlagen über biologische Parameter[END_REF][START_REF] Denzinger | The role of echolocation strategies for niche differentiation in bats[END_REF][START_REF] Kalko | Flying high-assessing the use of the aerosphere by bats[END_REF], and remains to be demonstrated with empirical and standardised measurements.

The study of animal use of the vertical space is a challenging task because of the technical difficulties this implies. Stereoscopic cameras are best suited for studies in a restricted volume because field of view is limited [START_REF] Holderied | Flight Dynamics[END_REF]. Tracking of animal movements with radar units only allow poor taxonomic resolution because target echoes provide limited information on animal size and flight behaviour [START_REF] Bruderer | Radar data on wing-beat frequencies and flight speeds of two bat species[END_REF].

Acoustic tracking of animal echolocation calls offers numerous advantages, such as species identification with the acoustic clues of their calls, an omnidirectional detection range, and an easy automation of the process [START_REF] Holderied | Understanding signal design during the pursuit of aerial insects by echolocating bats: tools and applications[END_REF][START_REF] Koblitz | Arrayvolution-Using microphone arrays to study bats in the field[END_REF][START_REF] Roemer | Bat flight height monitored from wind masts predicts mortality risk at wind farms[END_REF]. In addition, the installation of microphone arrays on wind masts allows acoustic location in a space situated at dozens of meters above ground, that is otherwise difficult to access [START_REF] Roemer | Bat flight height monitored from wind masts predicts mortality risk at wind farms[END_REF].

The aim of our study was to investigate the links between the vertical distribution of a community of European insectivorous bats, the acoustic parameters of their sonar (peak frequency, call duration and call bandwidth) and their wing morphology (wing aspect ratios and wing loading). We expected (1) longer call durations to be associated with higher flight heights, (2) higher peak frequencies to be associated with lower flight heights, (3) larger bandwidths to be associated with lower flight heights, (4) narrower wings to be associated with higher flight heights and (5) higher wing loadings to be associated with higher flight heights. To measure bat position in the vertical space, we equipped wind masts with microphone arrays and performed acoustic location of bat echolocation calls.

II. MATERIAL & METHODS

A. Acoustic recordings used to study bat altitudinal behaviour

B. Species identification and flight height classification

Files were decompressed with the WAC2WAV or the Kaleidoscope software (Wildlife Acoustics, Massachusetts, USA). Files were automatically cut in 5 second bouts after each triggered recording to be used as a proxy for a bat pass [START_REF] Barré | Estimating habitat loss due to wind turbine avoidance by bats: Implications for European siting guidance[END_REF][START_REF] Roemer | Bat flight height monitored from wind masts predicts mortality risk at wind farms[END_REF]. SonoChiro (Biotope, France) was used to automatically attribute calls to a species or a species group, and the verification of the result was done by manually checking acoustic sequences.

To identify bat species based on acoustic features, we followed the method developed by [START_REF] Barataud | Acoustic ecology of European bats: species identification, study of their habitats and foraging behaviour[END_REF], which is the most extensive study of European bat calls published today.

Identification criteria are based on the association between acoustic call type, call shapes and measurable parameters (initial frequency, terminal frequency, signal length, maximum energy and its repartition …), their rhythms (interval duration between calls) and the environment (distance to obstacles). With the knowledge accumulated today, this method allows the identification of 29 species out of the 34 extant in France and Belgium under good recording conditions. If a bat was recorded at both microphones at the same time, we checked the sequence which contained the most calls, and that was thus supposed to display the best acoustic quality. Some sequences may only contain faint calls, and yet contain enough clues to attribute the sequence to a species, because the species does not completely overlap the acoustic repertoire of another species (e.g. low frequency calls of Tadarida teniotis or low frequency calls of Hypsugo savii). Call duration and bandwidth are the most affected by atmospheric attenuation, yet other call parameters that are better preserved are sometimes sufficient to make an identification (e.g. peak frequency, inter-call duration, frequency modulation (i.e. shape) of the main part of the call). Yet, some sequences were so affected by atmospheric attenuation that there was no sufficient clue to attribute the sequence to a species. In addition, some species use sonar calls that are sometimes very close, even identical in certain flight circumstances, preventing identification to species level. These acoustic sequences that could not be identified at the species level were either classed in a group of species -when the vertical flight behaviours of all species were equivalent within the same group -or left unidentified and not used for further analysis (8.4 % of all bat passes). Here, Myotis myotis and M. blythii were identified as the "large Myotis" group, all other Myotis as the "small Myotis" group, and all Plecotus calls to the Plecotus spp. group. Species within those two groups present flight heights comparable to the other species of their group (Rodrigues et al., 2015), and similar acoustic features [START_REF] Barataud | Acoustic ecology of European bats: species identification, study of their habitats and foraging behaviour[END_REF]. Great care must be taken in the analysis of the results of the species P. kuhlii and P. nathusii, because acoustic features of these two species are simultaneously very variable and similar to each other. V. murinus is also difficult to distinguish from N. leisleri, but V. murinus is known to be rare in France and Belgium.

To classify flight heights, we used SonoChiro to automatically determine the time at which each call started on each microphone. We then obtained the time differences of arrival (TOAD) for each call detected using the find.matches function of Hmisc package [START_REF] Harrell | Hmisc: Harrell Miscellaneous[END_REF] from R (R Core Team, 2014). With two microphones, flight height cannot be precisely calculated, and TOAD were used to determine to which microphones bats were closer. A height threshold was defined for each site as the median height between the two microphones.

Microphone median height was variable depending on study site (20-50 m) (Figure 2), but this variation did not greatly affect species proportion of flight at height (Figure 3). Using this threshold, bat calls were assigned to two classes following the method described in [START_REF] Roemer | Bat flight height monitored from wind masts predicts mortality risk at wind farms[END_REF]: "at height" if the source of the signal was above the threshold and "at ground level" if it was below the threshold. A ratio of the time spent at height was then calculated for each species. It must be noted that in forest clearings, tree canopy was never higher than the median height between both microphones. Therefore, bats positioned "at height" were flying in an open environment.

A generalised linear mixed model (GLMM) was used to estimate rates of flight at height for each species. Bat pass height was modelled as a binomial variable (at height or at ground level) according to species as a fixed effect. The median height of microphones was introduced as a fixed effect to control for its potential influence. The local environment effect on flight behaviour was taken into account by introducing study sites as a random variable.

The GLMM was built using the glmmTMB function [START_REF] Magnusson | glmmTMB: Generalized Linear Mixed Models using Template Model Builder[END_REF] of R (R Core Team, 2014).

C. Acoustic parameters of species sonars

We chose to study the three main features defining bat call shapes and acoustic properties, namely call duration, peak frequency (i.e. the frequency at the maximum energy), and bandwidth. We referred to the work of [START_REF] Barataud | Update of the 3rd edition (2015) of Acoustic ecology of European bats[END_REF][START_REF] Barataud | Acoustic ecology of European bats: species identification, study of their habitats and foraging behaviour[END_REF] to obtain the mean values of these three acoustic parameters for the species recorded in our study (Table 1). In the group small Myotis, we present results for M. daubentonii, M. nattereri and M. bechsteinii, which were the most common Myotis identified in our recordings. In the same manner, in the group Plecotus spp., we present results for P. auritus and P. austriacus.

D. Wing loading and aspect ratio

We calculated indices of wing morphology based on bone measurements, which are the most practical and consistent indices, following the method of [START_REF] Bader | Mobility explains the response of aerial insectivorous bats to anthropogenic habitat change in the Neotropics[END_REF]. All morphological information was retrieved from [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa, A & C Black[END_REF]. The latter authors provided the minimum and maximum values per species, from which we calculated a mean value that we used for further analyses.

where FA = length of the forearm, d3 = length of the third digit and d5 = length of the fifth digit.

where m = body mass.

E. Correlations between rate of flight at height and species traits

We first checked for normality in the distribution of raw or transformed variables. Most variables did not follow a normal distribution, hence the correlations between each pair of variables were tested with a Kendall correlation test. For data visualisation, we assigned species into exclusive frequency-modulated (FM), constant-frequency with modulated frequency components (CF+FM) and frequency-modulated or quasi-constant frequency (FM/QCF) categories, according to their acoustic strategies [START_REF] Barataud | Acoustic ecology of European bats: species identification, study of their habitats and foraging behaviour[END_REF].

III. RESULTS

In total, 639,734 bat passes were recorded. Table 1 shows bat passes identified at the species or species group level. There was a continuous gradient in the vertical distribution of species from Rhinolophus bats that were never located at height to Vespertilio murinus that was located 86 % of the time at height. Rhinolophus, Barbastella, Plecotus, Myotis, Miniopterus species and Pipistrellus pygmaeus were located less than 5 % of the time at height. Eptesicus serotinus, E. nilsonii, Hypsugo savii, P. kuhlii, P. pipistrellus and P. nathusii were located between 5 and 25 % of the time at height. Nyctalus, Tadarida and Vespertilio species were located more than 30 % of the time at height.

A. Interdependence of traits

Correlation tests for all species showed that all morphological and acoustic features were inter-correlated, except for call peak frequency versus call duration (Table 2).

B. Correlations between proportion of flight at height and traits

Morphological and acoustic features were all correlated to the proportion of flights at height (Table 3, Figure 1). Compared to low-flying species, high-flying species used lower peak frequencies, narrower bandwidths, longer calls, and possessed narrower wings with higher wing loadings (Figure 1). In the correlation between the rate of flight at height and call duration, Rhinolophus species stood as outliers because they use extremely long call duration compared to other species flying near ground level (Figure 1b). Concerning call bandwidth, Myotis species were the outliers because they use extremely large bandwidth compared to other species flying near ground level (Figure 1c).

IV. DISCUSSION

A. Acoustic location from wind masts, a powerful tool for the study of animal flight behaviour We studied to what extent the prevalence of bat species at elevated heights can be predicted by the acoustic features of their sonar and by their wing morphology. In the past, a study by [START_REF] Jensen | Echolocation signals of the bat Eptesicus serotinus recorded using a vertical microphone array: effect of flight altitude on searching signals[END_REF] with a vertical array of three microphones on a 15 meter pole elucidated the links between echolocation features and flight height in E. serotinus, a European bat. A study by [START_REF] Kloepper | Recording animal vocalizations from a UAV: bat echolocation during roost re-entry[END_REF] suggested that the features of echolocation calls in Tadarida brasiliensis, an American bat, vary in function of their flight height. However, our study is the first to assess this relationship in a bat community. The use of wind masts allowed a long-term monitoring of bat flight behaviour and an objective assessment of species vertical flight distribution. The automation of the process allowed us to equip 48 masts over the French and Belgian territories and analyse their results. The combination of long-term monitoring and of the high amount of study sites was an advantage in obtaining enough data for rare species (e.g. E. nilssonii) or species with short detection ranges (e.g. R. hipposideros).

B. Bat traits predict bat vertical niche partitioning

We demonstrate for the first time that the acoustic features of bat sonar predict bat vertical distribution regardless of species acoustic strategies. Call duration was a less reliable predictor than call peak frequency and bandwidth since Rhinolophidae stood as outliers with a very long call duration and an exclusive presence at ground level. This particularity is explained by their echolocation strategy to detect prey flutter by emitting long constant frequencies (CF) calls carrying short frequency modulated (FM) signals with a high duty cycle [START_REF] Schnitzler | Auditory fovea and Doppler shift compensation: adaptations for flutter detection in echolocating bats using CF-FM signals[END_REF]. Rhinolophidae are part of the Yinpterochiroptera suborder, that diverged 60 mya from the Yangochiroptera, [START_REF] Teeling | Hear, hear: the convergent evolution of echolocation in bats?[END_REF], to which the other bat families addressed here belong.

Our study also shows the first correlations based on empirical measures between bat wing morphology and their vertical distribution. It confirmed our hypotheses that narrow wings with high wing loadings are best suited for flying at greater heights.

In the bat community that we sampled, the proportion of time spent at height might be correlated to the availability in the prey on which each species specialises, but the opportunistic high-flying species (e.g. Nyctalus, Tadarida) could also exploit more elevated altitudes to actively avoid spatial competition with other species [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa, A & C Black[END_REF][START_REF] Roeleke | How Bats Escape the Competitive Exclusion Principle-Seasonal Shift From Intraspecific to Interspecific Competition Drives Space Use in a Bat Ensemble[END_REF]. Indeed, the low frequency calls providing long detection ranges to high-flying bats are also less effective in detecting the small prey they feed on than the high frequency calls of species found at lower heights (e.g. Pipistrellus) [START_REF] Waters | Echolocation Call Design and Limits on Prey Size: A Case Study Using the Aerial-Hawking Bat Nyctalus leisleri[END_REF].

C. Constraints of bat flight at great heights

We show that the use of the vertical space in European bats is ordered from Rhinolophus species (always flying near ground level or near background) to Nyctalus and Tadarida species (prevailing at height). In fact, guild categories used to define bat adaptation to clutter (i.e. narrow, edge and open space foragers [START_REF] Denzinger | Bat guilds, a concept to classify the highly diverse foraging and echolocation behaviors of microchiropteran bats[END_REF]) may be ordered along this same gradient from narrow foragers (low-flying species) to open space foragers (high-flying species). Manoeuvrability and the challenging detection of very thin obstacles, or prey at a very small distance from background elements seem to be the main issues limiting species foraging success when flying through cluttered environments [START_REF] Fenton | Bat bioacoustics, Springer handbook of auditory research[END_REF][START_REF] Norberg | Ecological morphology and flight in bats (Mammalia; Chiroptera): wing adaptations, flight performance, foraging strategy and echolocation[END_REF][START_REF] Sleep | An experimental test of clutter tolerance in bats[END_REF]. On the other hand, it is interesting to discuss what limits the ability of bats to reach elevated heights.

In the first instance, we demonstrated that high-flying species possess high aspect ratios and high wing loadings. For foraging purposes, high-flyers cover greater distances than low-flyers [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa, A & C Black[END_REF], possibly because insects are scarcer at height [START_REF] Reynolds | Riders on the Wind: The Aeroecology of Insect Migrants[END_REF].

Economic flights over long distances are facilitated by a low wing inertia, which is associated with a high aspect ratio [START_REF] Norberg | Ecological morphology and flight in bats (Mammalia; Chiroptera): wing adaptations, flight performance, foraging strategy and echolocation[END_REF][START_REF] Pennycuick | Modelling the flying bird[END_REF]. Since high aspect ratios are often associated with short wings, high-flyers tend to also have high wing loadings [START_REF] Norberg | Ecological morphology and flight in bats (Mammalia; Chiroptera): wing adaptations, flight performance, foraging strategy and echolocation[END_REF]. In order to sustain a powered flight, species with higher wing loadings must fly faster, which is precisely an optimal strategy when travelling through long distances between two foraging grounds [START_REF] Grodzinski | Context-dependent flight speed: evidence for energetically optimal flight speed in the bat Pipistrellus kuhlii ?[END_REF][START_REF] Norberg | Ecological morphology and flight in bats (Mammalia; Chiroptera): wing adaptations, flight performance, foraging strategy and echolocation[END_REF], but also for long-distance migration [START_REF] Hedenström | Optimal migration strategies in bats[END_REF]. It was suggested that the swift aspect of Miniopterus schreibersii could be linked to agile flight in high-altitude hawking [START_REF] Norberg | Ecological morphology and flight in bats (Mammalia; Chiroptera): wing adaptations, flight performance, foraging strategy and echolocation[END_REF]. Our results do not support this hypothesis, since this species was very rarely recorded at height. The relatively high aspect ratio of M. schreibersii is probably associated with good agility during fast flights near ground level. This species indeed covers very long distances overnight (up to 40 km) to actively avoid intraspecific competition for food in the vicinity of its very large colonies [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa, A & C Black[END_REF]. As a fast flyer [START_REF] Holderied | Flight Dynamics[END_REF], this species does not have a higher wing loading than the average, because its wings are longer than average due to the unusual length of its third digit, but its wide uropatagium allows for a manoeuvrability not seen in other species with narrow wings [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa, A & C Black[END_REF].

In the second instance, we demonstrated that high-flying bats use shallowerand generally longercalls than low flying species. This call structure carries signals through greater distances than high frequencies because it is more tolerant to atmospheric attenuation [START_REF] Pye | Why ultrasound?[END_REF]. It can be argued that small bats have difficulties producing low frequency echolocation calls since their production requires large body structures, and species are therefore limited by their laryngeal capacity [START_REF] Metzner | Ultrasound production, emission, and reception[END_REF][START_REF] Pye | Why ultrasound?[END_REF]. Several studies indeed found that body size is inversely correlated with echolocation call peak frequencywhen acoustic strategies are taken into account -which corroborates this hypothesis [START_REF] Bogdanowicz | The relationships between echolocation calls, morphology and diet in insectivorous bats[END_REF][START_REF] Jones | Scaling of echolocation call parameters in bats[END_REF][START_REF] Penone | Body size information in large-scale acoustic bat databases[END_REF][START_REF] Thiagavel | Body Size Predicts Echolocation Call Peak Frequency Better than Gape Height in Vespertilionid Bats[END_REF]. Calls used for social communication may be much lower than the echolocation repertoire [START_REF] Chaverri | Social communication in bats[END_REF], but their production is based on the same biomechanical properties of the larynx than the production of echolocation calls [START_REF] Kobayasi | Behavioural and neurobiological implications of linear and non-linear features in larynx phonations of horseshoe bats[END_REF]. Indeed, in isolated larynxes, it was demonstrated that below a certain air flow threshold, the emitted frequencies correspond to the register of echolocation frequencies, but passing this threshold, the emitted frequencies correspond to the register of social communication (much lower frequencies) [START_REF] Kobayasi | Behavioural and neurobiological implications of linear and non-linear features in larynx phonations of horseshoe bats[END_REF]. This jumping from one frequency register to another is similar to yodelling. Nonetheless, we found that species with high-pitched vocalisations (e.g. Myotis sp. or M. schreibersii) could alsoalthough rarelybe found at elevated heights. These individuals either came from the foot of the mast and flew to the top of the mast, a behaviour which was showed in B. barbastellus [START_REF] Budenz | Up and down: B barbastellus explore lattice towers[END_REF], or they were already flying at height when they came across the wind mast. Individuals can lower their call frequency to perceive obstacles from a greater distance [START_REF] Jensen | Echolocation signals of the bat Eptesicus serotinus recorded using a vertical microphone array: effect of flight altitude on searching signals[END_REF][START_REF] Schaub | Echolocation behavior of the bat Vespertilio murinus reveals the border between the habitat types 'edge' and 'open space[END_REF], however we do not expect species such as Myotis sp. to be able to modify their sonar in such a way that they could perceive ground level when flying at more than 20 m, their estimated maximal detection range in open spaces [START_REF] Barataud | Acoustic ecology of European bats: species identification, study of their habitats and foraging behaviour[END_REF]. High-pitched echolocators are more likely to explore wind masts from the bottom, but they could possibly rely only on vision to perceive long-distance obstacles and use their sonar to sense small obstacles such as other flying animals [START_REF] Boonman | It's not black or white-on the range of vision and echolocation in echolocating bats[END_REF].

D. Conclusion and perspectives

Our study contributes to the comprehension of bat use of the vertical dimension, which is often difficult to explore due to technical limitations. We demonstrated that bat vertical niche partitioning is not only constrained by species ability to move and detect prey in cluttered environments, but it is also constrained by their ability to commute and forage at elevated heights with optimal flight energetic costs and with sonar adaptations for long-distance perception of their environment. There are probably many other morphologic traits that were not tested in our study and that may be correlated with species use of the vertical space. For example, long and narrow pinnae (external ears) or tragi (small eminence of the external ear), possibly accounting for the accuracy of vertical localization [START_REF] Fenton | Bat bioacoustics, Springer handbook of auditory research[END_REF], are generally found in low flyers, while short and round pinnae and tragi are found in bats prevailing at height (see [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa, A & C Black[END_REF]. Sonar features do not only vary interspecifically, and individuals can indeed adapt call frequency, duration and bandwidth to commute or forage in different environments [START_REF] Barataud | Acoustic ecology of European bats: species identification, study of their habitats and foraging behaviour[END_REF][START_REF] Moss | Auditory scene analysis by echolocation in bats[END_REF][START_REF] Russo | Bats are still not birds in the digital era: echolocation call variation and why it matters for bat species identification[END_REF]. Studies on E. serotinus and V. murinus (QFC strategy) show that their repertoire is quite variable up to a dozen meters from the background, and then stabilises past that threshold [START_REF] Jensen | Echolocation signals of the bat Eptesicus serotinus recorded using a vertical microphone array: effect of flight altitude on searching signals[END_REF][START_REF] Schaub | Echolocation behavior of the bat Vespertilio murinus reveals the border between the habitat types 'edge' and 'open space[END_REF]. However, it is not known whether this holds true for other echolocating strategies (e.g. FM and CF-FM) and to what extent bat flight height may be predicted intraspecifically from sonar features.

The use of the aerosphere by bats makes them vulnerable to anthropogenic activities such as planes and wind turbines [START_REF] Voigt | Conservation Strategies for Bats Flying at High Altitudes[END_REF]. It was shown that bat species susceptibility to collisions with wind turbines is correlated to their proportion of time spent at height [START_REF] Roemer | Bat flight height monitored from wind masts predicts mortality risk at wind farms[END_REF]. This classification of species susceptibility is of great importance in wind turbine impact assessment studies, which rely on the estimation of bat local abundance to estimate future impacts. However, this classification is only available for European bats and requires important time and human investments to be established for different bat communities. The correlation between species traits and proportion of flight at height presented in the current study should provide a proxy to predict species relative susceptibility to wind turbines in other geographical areas.

categories CF (constant frequencies), FM (frequency modulated), and QFC (quasi-constant frequencies) refer to the acoustic strategy of the different species. The linear regression line is shown. Acoustic parameters are presented on a logarithmic scale. Wing drawings represent the extreme values.

SUPPLEMENTARY FIGURE CAPTIONS

APPENDIX

Table 4 -Mean morphological values used to calculate ARI (aspect ratio index for bat wings) and WLI (wing loading index). These values were retrieved from [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa, A & C Black[END_REF]. Species names are given with the first three letters of genus and species.

  Between 2011 and 2017, recordings were conducted at 48 sites in France and Belgium where bat activity was monitored on 8,435 nights (mean = 175.7 standard deviation = 76.1, min = 19, max = 352 nights per site). Microphones were installed on lattice or monopole wind masts of 50-100 m in height and the wind masts themselves were erected in open or semi-open habitats (i.e. agricultural land, bocage, garrigue, wetlands or forest clearing). Arrays composed of two microphones were achieved with two SMX-US, SMX-U1 (Wildlife Acoustics, USA) or SMX-US (Biotope, France) microphones plugged to an SM2BAT or SM3BAT (all models, Wildlife Acoustics, Massachusetts, USA). Microphones were inserted into tubes, facing downward, to protect them from weather elements. A custom-made aluminium reflector placed below the microphone at a 45° angle minimised the directionality of the setting. Microphones were installed at heights ranging from 4 to 85 m (Figure 2 in suppl. mat.). Recorders were programmed to start each day 30 min before sunset and stop 30 min after sunrise. Whole night recordings were performed on study sites between 2013 and 2017 (38 sites), but from 2011 and 2012 (10 sites) samplings were collected for 10 minutes every 20 minutes. Gain was set at 36 dB, sampling rate at 192 kHz, trigger at 6 dB above background noise and trigger window at 2.5 sec. A 1 kHz high pass filter was used. Files were compressed in WAC4 format and analysed in WAV format or directly recorded in WAV format.

Figure 2 -

 2 Figure 2 -Microphone heights for each study site. Open circles show microphone height and

Figure 3 -

 3 Figure 3 -Influence of microphone median height on the proportion of bat flights at height.

Species Group Forearm length Length of 5 th Length of 3 rd Mass

			(mm)	digit (mm)	digit (mm)	(g)
	Barbar		40.00	50.50	67.00	8.50
	Eptnil		40.65	50.50	65.00	11.00
	Eptser		53.00	64.00	88.00	21.50
	Hypsav		34.65	42.50	57.50	7.00
	Minsch		45.20	52.00	83.50	12.00
	Myobec		43.05	53.50	65.00	8.50
	Myodau Myonat	Small Myotis	37.55 39.20	45.50 53.00	59.00 69.50	8.00 8.50
	Myobly	Large	56.30	72.00	94.00	22.50
	Myomyo	Myotis	60.95	75.50	98.00	23.50
	Nyclas		65.50	71.50	112.00	44.00
	Nyclei		42.55	47.00	74.00	15.50
	Nycnoc		53.10	52.50	91.50	25.50
	Pipkuh		33.85	42.50	57.50	6.50
	Pipnat		34.65	44.50	59.50	8.00
	Pippip		31.25	39.00	53.00	5.00
	Pippyg		30.00	36.50	50.50	5.50
	Pleaur	Plecotus	39.15	50.50	65.00	7.50
	Pleaus	spp.	40.00	51.50	67.50	8.00
	Rhifer		57.70	70.00	86.50	21.00
	Rhihip		37.85	50.00	54.00	5.50
	Tadten		62.30	57.50	108.50	25.00
	Vesmur		45.55	51.00	72.50	12.50

ACKNOWLEDGMENTS

This study was a collaboration between Biotope and the French Muséum national d'Histoire naturelle in the form of a PhD thesis funded by Biotope and the Association Nationale de la Recherche et de la Technologie. We would like to thank Sébastien Devos, Marie-Lilith Patou, Julien Mérot, Alexandre Haquart, Julien Tranchard, Philippe Ferragne, Matthieu Guyot, Antonin Dhellemme, Matthieu Lageard, Paul Gillot, François Huchin, Julien Renglet, Magali Argaud and Estelle Cleach for their important contributions to equipment design and installation, data collection and acoustic analysis. We thank Ugo Schumpp for the infography of bat wings. We are grateful to Yann Gager for his help in finding appropriate references in the literature, and to Jean-François Julien, whose insightful comments improved the manuscript. We thank Marja Roemer for proofreading the manuscript as well as two anonymous reviewers for their comments.

 Williams, T. C., Ireland, L. C., and Williams, J. M. (1973). "High Altitude Flights of the Free-563 Tailed Bat, Tadarida brasiliensis, Observed with Radar," J. Mammal.,54,[807][808][809][810][811][812][813][814][815][816][817][818][819][820][821] doi:10.2307/1379076 565 566 TABLES 567 Table 1 -Summary statistics for mean acoustic parameters (from [START_REF] Barataud | Update of the 3rd edition (2015) of Acoustic ecology of European bats[END_REF][START_REF] Barataud | Acoustic ecology of European bats: species identification, study of their habitats and foraging behaviour[END_REF], 568 mean morphological variables and predicted proportion of flight at height. Species names are 569 given with the first three letters of genus and species. CF: constant frequencies. FM: 570 frequency modulated. QFC: quasi-constant frequencies. N calls = Number of calls measured 571 in [START_REF] Barataud | Update of the 3rd edition (2015) of Acoustic ecology of European bats[END_REF]. N flights = number of acoustic sequences used to calculate the proportion 572 of flights at height. ARI: aspect ratio index for bat wings. WLI: wing loading index. See 573


Charlotte Roemer
email: croemer@biotope.fr

Yves Bas

Thierry Disca

Aurélie Coulon

Influence of landscape and time of year on bat-wind turbines collision risks

Keywords: bat collisions, distance to woodland, topography, per capita collision risks, acoustic location, vertical flight distribution

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Introduction

International projections predict a global increase in solar and wind energy installations for the next decades (AIE, 2017). Despite their benefits for climate, wind turbines (WT) can have strong negative impacts on birds and bats through deaths by collision and barotrauma (Laranjeiro et al., 2018;[START_REF] Loss | Direct Mortality of Birds from Anthropogenic Causes[END_REF][START_REF] Rydell | Bat Mortality at Wind Turbines in Northwestern Europe[END_REF], or because of habitat loss [START_REF] Barré | Estimating habitat loss due to wind turbine avoidance by bats: Implications for European siting guidance[END_REF][START_REF] Millon | Wind turbines impact bat activity, leading to high losses of habitat use in a biodiversity hotspot[END_REF][START_REF] Minderman | Landscape-scale effects of singleand multiple small wind turbines on bat activity[END_REF][START_REF] Minderman | Experimental Evidence for the Effect of Small Wind Turbine Proximity and Operation on Bird and Bat Activity[END_REF]. This has been a rising cause of concern, especially for bats because of their poor conservation status and their low reproductive rate, making them highly vulnerable to additional sources of mortality [START_REF] Barclay | Life histories of bats : life in the slow lane[END_REF]Voigt and Kingston, 2016). Some projections identified WT as a possible cause of extinction for certain bat species [START_REF] Frick | Fatalities at wind turbines may threaten population viability of a migratory bat[END_REF].

Currently, the most efficient way of mitigating bat fatalities is raising the WT cut-in speed (wind speed above which electrical power is produced) at a threshold above which bats avoid flying [START_REF] Arnett | Mitigating wind energy impacts on wildlife: approaches for multiple taxa[END_REF]. Nonetheless, even if mortalities are greatly reduced with this method, they still occur [START_REF] Arnett | Impacts of Wind Energy Development on Bats: A Global Perspective[END_REF]. Some evidence shows that not all bats respond similarly to wind speed, high-flying species being apparently more tolerant to strong winds than low flying species [START_REF] Wellig | Mitigating the negative impacts of tall wind turbines on bats: Vertical activity profiles and relationships to wind speed[END_REF], and WT operational mitigation may selectively affect them [START_REF] Voigt | Wildlife and renewable energy: German politics cross migratory bats[END_REF].

The most efficient strategy to obtain no biodiversity net-loss is the avoidance of the impact [START_REF] Bigard | The inclusion of biodiversity in environmental impact assessment: Policy-related progress limited by gaps and semantic confusion[END_REF]. In this process, landscape planning can be a very efficient tool for species conservation. Indeed, the level of impact of a wind farm may be highly influenced by the type of landscape surrounding it. If wind farm siting is carefully selected to avoid cooccurrence of high-flying species, WT operational mitigation should be more efficient both to avoid bat mortality and to maximise electrical power production. However, even if some initiatives exist at the regional level, we are aware of no national scheme for the strategy of wind energy planning that considers high-risk areas for birds or bats susceptible to WT collisions (Sordello et al., 2019;[START_REF] Voigt | Conservation Strategies for Bats Flying at High Altitudes[END_REF].

Several studies have tried to identify landscape predictors of bat fatalities at wind turbines. [START_REF] Santos | Using species distribution modelling to predict bat fatality risk at wind farms[END_REF] found that mortality probabilities decreased with the distance to eucalyptus forests. Other studies showed that open habitats such as prairies, pastures and croplands triggered fewer collisions than closed habitats such as forests [START_REF] Bolívar-Cimé | Bats in a tropical wind farm: species composition and importance of the spatial attributes of vegetation cover on bat fatalities[END_REF][START_REF] Piorkowski | Spatial Pattern of Summer Bat Mortality from Collisions with Wind Turbines in Mixed-grass Prairie[END_REF][START_REF] Thompson | Factors associated with bat mortality at wind energy facilities in the United States[END_REF]. [START_REF] Piorkowski | Spatial Pattern of Summer Bat Mortality from Collisions with Wind Turbines in Mixed-grass Prairie[END_REF] found more fatalities in ravine topography than in low topography relief and [START_REF] Santos | Using species distribution modelling to predict bat fatality risk at wind farms[END_REF] found that distance to the slope was negatively correlated with mortality risks.

Studies using the count of carcasses to infer the effect of landscape on anthropogenic mortalities have a debatable predictive power at large scale because of small datasets and because different species are often pooled. Indeed, species perceive landscape heterogeneity differently in function of their ecological needs [START_REF] Peixoto | A synthesis of ecological and evolutionary determinants of bat diversity across spatial scales[END_REF] and the influence of the landscape should be studied for each of them. Furthermore, animal carcasses are a response variable that is, in fact, the product of two different components i.e., species local density and species behaviour [START_REF] Zimmermann Teixeira | When roadkill hotspots do not indicate the best sites for road-kill mitigation[END_REF]. Consequently, if a landscape variable has antagonistic effects on animal density and per capita mortality, it will have no effect on the total count of carcasses, and key mechanisms will be missed. Moreover, the use of fatality data is subject to several methodological biases (i.e. carcass persistence time, observer efficiency, land cover, prospection area …) and the scarcity of data often prevents an efficient control of these biases [START_REF] Huso | Estimating wind-turbine-caused bird and bat fatality when zero carcasses are observed[END_REF].

In this study, we used an alternative approach to assess the influence of landscape features on bat collision risks at WT, disentangling their separate effects on bat species local density and on bat vertical distribution. To do so, we used unattended stereo acoustic monitoring, which provides information on species use of sites all-year-round, species density, and species vertical distribution thanks to multiple synchronous microphones [START_REF] Jensen | Echolocation signals of the bat Eptesicus serotinus recorded using a vertical microphone array: effect of flight altitude on searching signals[END_REF].

We assessed the effect of several landscape variables on bat species local density on one hand and on bat vertical distribution on the other hand. We performed those analyses at several spatial scales to identify the most influential on bat mortality risks at WT. We also controlled for the effect of time of the year, which is known to explain the temporal distribution of WT collisions [START_REF] Arnett | Impacts of Wind Energy Development on Bats: A Global Perspective[END_REF].

Material and Methods

Acoustic recordings

48 sites were surveyed in France and Belgium between 2011 and 2018 during a total of 8,435 nights (mean = 175.7, standard deviation = 76.1, min = 19, max = 352 nights per site) (Fig. 1).

Surveys targeted bat annual periods of activity (Fig. A1 in Electronic supplementary material 1). Lattice or monopole wind masts of 50-100 m high were equipped with two ultrasound microphones (SMX-US, SMX-U1 or SMM-U1, Wildlife acoustics, USA, or BMX-US, Biotope, France) plugged to an SM2BAT or SM3BAT recorder (Wildlife Acoustics, USA).

One microphone was installed near ground level and a second at height (Fig. A2 in Electronic supplementary material 1). In forests, wind masts were installed in clearings of 10-30 m radius. Recorders were programmed to start each day 30 min before sunset and stop 30 min after sunrise. Between 2013 and 2016 (38 sites), whole night recordings were performed. Before 2013 (10 sites), samplings were collected for 10 min every 20 min. The gain was set at 36 dB for SMX-US and BMX-US microphones or 0 dB for SMX-U1 and SMM-U1 microphones because they have a pre-integrated gain. Sampling rate was set at 192 kHz, trigger at 6 dB for SM2BAT and 12 dB for SM3BAT (for equivalent sensitivity) and trigger window at 2.5 s. A 1 kHz high pass filter was used.

Species identification and flight height classification

Species identification was performed based on acoustic features as stated in [START_REF] Roemer | Bat flight height monitored from wind masts predicts mortality risk at wind farms[END_REF] using SonoChiro (Biotope/MNHN, France) and a manual check. Bat passes (defined as one or more bat calls within 5 s) that belonged to the genera Pipistrellus, Nyctalus, Eptesicus or Vespertilio and that could not be identified at the species level were marked as unidentified bats. The latter sequences, as well as all other unidentified bat passes, represented 8.4 % of our dataset and were not used for further analyses. Concerning the group of species Pipistrellus kuhlii/nathusii, acoustic knowledge is presently too scarce to differentiate both species with certain confidence. Identifications were achieved using acoustic cues described as "typical" for these species at the time of analysis [START_REF] Barataud | Acoustic ecology of European bats: species identification, study of their habitats and foraging behaviour[END_REF] and with the knowledge that Pipistrellus kuhlii is very rare or absent in Northern France and Belgium [START_REF] Arthur | Les chauves-souris de France[END_REF]. However, readers must be aware of potential biases in the results presented here for P. kuhlii and P. nathusii. Bat passes with no typical feature of either species were not identified (37.5 % of this group).

To obtain species vertical distribution profiles, we calculated the Time of Arrival Difference (TOAD) of each call to both microphones [START_REF] Koblitz | Arrayvolution-Using microphone arrays to study bats in the field[END_REF]. According to the value of TOAD; it was then possible to deduce if the bat was above (i.e. at height) or below (i.e. at ground level) the median height of both microphones (see [START_REF] Roemer | Bat flight height monitored from wind masts predicts mortality risk at wind farms[END_REF] for details about the method).

Landscape variables

To cover the variability of home ranges of European species [START_REF] Arthur | Les chauves-souris de France[END_REF], we described the landscape within buffers of 200 m, 1,000 m and 5,000 m radius around wind masts (Fig. A3 in Electronic supplementary material 1).

We estimated distance to trees, to buildings likely to provide roosts for bats (i.e. with hard roofs and walls), and to water bodies accessible for drinking for bats. Landscape data were retrieved from the BD TOPO 2.2 (Institut National de l'Information Géographique et Forestière, 2017) for French study sites or measured visually on Google satellite pictures for Belgian study sites. To assess the effect of landscape structure, we also calculated for French study sites (46 out of 48) the percentage of woodland and woodland contagion index. The contagion index is an aggregation index implemented in the FRAGSTATS 4.2 software [START_REF] Mcgarigal | FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical and Continuous Maps[END_REF] which provides information about the balance of patch distribution in a defined landscape. It was considered in our study as a basic metric of the presence of landmarks that could be used for species during commuting. A high contagion score means that the landscape was either filled with one patch or empty of the type of patches considered.

A low contagion score means that the different patches were evenly distributed.

Altitudinal variables were retrieved from the ASTER digital elevation model (DEM) version 2 (NASA JPL, 2009). This model represents the elevation of the terrain including buildings or woodland and has a precision of approximately 30 m at the equator. We chose to use this model instead of a classical topographical map (describing bare ground elevation) because we were interested in the influence of all main three-dimensional structures on bat flight height.

We noted the altitude of wind masts at their foot, and for the three different buffers, we calculated their altitudinal amplitude (difference between maximum and minimum elevations within the buffers) and the position of the wind mast on the elevational gradient (difference between mast elevation and minimum elevation multiplied by 100 and divided by the altitudinal amplitude).

The installation of wind masts in forests is preceded by clear-cuts that are generally not considered in the BD TOPO and the DEM. In this case, we manually modified the measured distance to trees using Google satellite pictures or our knowledge of the field. We did not modify the elevation of woodland retrieved from the ASTER digital elevation model to correct for this bias because grid size precision (30 m) exceeds distance to trees in forests.

Statistical analyses

All predictor variables were normalised if necessary and scaled to allow a comparison of effect magnitude. We first tested for any correlation between landscape variables using the corrplot function of the stats package in the R program [START_REF] Core | R: A language and environment for statistical computing[END_REF]. Percentage of the woodland cover was positively correlated with altitude (r = 0.36-0.64 depending on buffer size) and altitudinal amplitude (r = 0.12-0.73 depending on buffer size) and contagion was positively correlated with distance to trees (r = 0.23-0.65 depending on buffer size) (Table A1 in Electronic supplementary material 1). We, therefore, removed percentage of woodland cover and contagion from our analyses to only retain variables that were retrievable with more direct calculations. We removed altitude to keep altitudinal amplitude because it integrated a proxy for slope.

We next separated our analysis in two steps: first the modelling of species density (number of bat passes per night) and second the modelling of species proportion of flight at height (number of bat passes at height divided by the total number of bat passes), both in function of landscape and topography variables. To model species density, the number of bat passes belonging to sites from before 2013 were multiplied by two because samplings were collected for 10 min every 20 min.

The package glmmTMB [START_REF] Brooks | Modeling Zero-Inflated Count Data With glmmTMB[END_REF] of the R program (R Core Team, 2014) was used for both models. Bat density was modelled with a negative binomial distribution (nbinom2) while bat proportion of flight at height was modelled with a binomial distribution.

Each species was modelled separately with the study site as a random effect, and an additional model concerned all species with the study site and species as crossed random effects. To ensure model robustness of species-specific models, we only kept the species for which we had enough bat passes at height in our dataset (> 1000) and that occurred on enough study sites (> 25) (Table A2 in Electronic supplementary material 1). Because some study sites were very close to each other (< 10 km), we avoided spatial autocorrelation of observations by creating a 'Group' variable that gave a common identity to study sites separated by less than 10 km. This variable was used in all models as a random effect. Study sites were nested within groups (i.e. (1|Group/Site)).

Julian day (as a quadratic effect) and microphone median height were introduced as obligatory fixed effects in all models to control for undesired variability in the results.

Latitude and longitude as well as all other landscape and topographical variables were proposed as optional fixed effects and submitted to model selection. Topological and landscape parameters were tested in simple interactions with each other. This was not the case for Julian day, longitude and latitude, that we did not expect to play a role in interaction with other predictors.

A stepwise forward model selection was then performed using Akaike's information criterion (AIC) [START_REF] Bolker | Generalized linear mixed models: a practical guide for ecology and evolution[END_REF][START_REF] Burnham | Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach[END_REF]. At each step of model selection, the VIF (Variance inflation factor), which quantifies the degree of multicollinearity in least squares regression analyses, was calculated. If any of the selected variables had a VIF > 3 [START_REF] Heiberger | Multiple Comparisons, in: Statistical Analysis and Data Display[END_REF][START_REF] Zuur | A protocol for data exploration to avoid common statistical problems[END_REF], the model was not considered as a candidate. At each step of model selection, the model with the smallest AIC was considered.

This model was retained and the selection was allowed to continue as long as its AIC was at least inferior by two points to the AIC of the best model of the previous step [START_REF] Arnold | Uninformative Parameters and Model Selection Using Akaike's Information Criterion[END_REF].

For some species, there were common variables in the two models (bat density and bat vertical distribution). To interpret the effect of these variables on the resulting bat collision risks, we also directly modelled the number of bat passes per night located at height in function of all the variables that were selected in either model. This response was modelled with a negative binomial distribution (nbinom2) using the package glmmTMB [START_REF] Brooks | Modeling Zero-Inflated Count Data With glmmTMB[END_REF] of the R program (R Core Team, 2014). As in the previous models, study sites nested within groups were introduced as a random variable.

Results

Bat activity recorded

In total, 634,000 bat passes were recorded. 17 species were identified with certainty, as well as the groups of Plecotus sp., Myotis blythii/myotis (large Myotis) and the other Myotis (small Myotis) (Table A2 in Electronic supplementary material 1).

Vespertilio, Nyctalus and Tadarida species prevailed at height (20-90 % of the time at height).

They were followed by Hypsugo, Pipistrellus and Eptesicus species (5-35% of the time at height). Myotis, Miniopterus and Barbastella species were rarely recorded at height (< 5 % of the time at height). Rhinolophus species were never recorded at height (Table A2 and Fig. A4 in Electronic supplementary material 1).

From April to November, the mean number of bat passes at height per night and per month overall study sites varied between 3 and 18 (standard deviation varied between 24 and 62).

This high variability was due to one study site that was monitored in October only and that was the only one in wetlands (32 m from a canal, near the Mediterranean coast). It showed an extremely high bat density at height (mean = 256.4 bat passes per night, mostly represented by P.kuhlii/nathusii) compared to all other sites monitored in October (mean = 10.9, standard deviation = 15.8 bat passes per night).

Scale

Larger scales were more effective to explain bat density and flight behaviour than smaller scales (Table 1 andTable 2). Most species responded to buffers of 5,000 m (altitudinal amplitude and position of a mast in elevational gradient), while only P. pipistrellus responded to a scale of 1,000 m (altitudinal amplitude). The scale of 200 m for both response variables was never selected in models.

Control variables

The density of species decreased to the North, except for P. pipistrellus and P. nathusii, and increased to the East, except for P. kuhlii (Table 1). We found a gradual increase in density from spring to summer, followed by a decline in autumn. Patterns were similar for all species; an example is displayed for N. leisleri (Fig. 3a). The proportion of bat passes at height was near minimum at the time when bat density peaked for several species (e.g. N. leisleri (Table 2, Fig. 3b)), however, there was no significant pattern for E. serotinus, P. nathusii and N. noctula (Fig. A6 in Electronic supplementary material 1). Density at height displayed similar patterns as density (ground level and height included), with a peak in summer (Fig. 3c and Fig. A6 in Electronic supplementary material 1). Microphone height influenced measured species density when modelling all species at once but did not influence the measured proportion of flight at height (Table 1 andTable 2). Nonetheless, for P. kuhlii and E. serotinus, higher microphone median heights were associated with a lower density at height (Table A3 in Electronic supplementary material 1).

Landscape

Distance to woodland negatively affected density for species of low or medium flight height (i.e. P. pipistrellus, P. kuhlii and E. serotinus), and more generally on the density of all species (Table 1, Fig. 2a). Distance to water had a negative effect on P. nathusii density.

Altitudinal amplitude negatively affected the density of most species, but this variable was not selected in the model where all species are grouped. Bat density for all grouped species was lower near hill or mountain tops than near to valleys (Fig. 2b). For P. nathusii, in lowlands, density (ground level and height included) decreased when the mast was closer to hilltops, while in mountainous areas, few bats were recorded regardless of the mast position (Fig. A5a in Electronic supplementary material 1). The same pattern was observed for the density of P. nathusii at height (Fig. A5b in Electronic supplementary material 1). For N. leisleri, increasing distance to water increased flight height, and for P. nathusii, the closer to hill or mountain tops, the more elevated the bat passes (Table 2, Fig. A7b in Electronic supplementary material 1). The effects of the relative position of wind masts in the slope on the density (ground level and height included) and on the proportion of flights at height were antagonistic for P. nathusii (Fig. A7a in Electronic supplementary material 1).

There was no significant effect of this variable on density at height (Table A3 andFig

Discussion

To our knowledge, this is the first case where the influence of landscape on bat collision risks with WT is studied while differentiating between bat density and bat proportion of flights at collision risk. Our results show that generally, collision risks are proportional to bat density.

In some cases, the effect of the relative position of wind masts in the slope had antagonistic effects on the collision risks (e.g. P. nathusii). As a result, it was necessary to disentangle the conditioning events of collisions to unravel fine mechanisms leading to bat collisions at WT.

Effect of geographic coordinates

Our models of species density show that bats are less abundant in Northern France and Belgium than in Southern France, except for P. nathusii, more abundant in the North. The density of E. serotinus and N. noctula did not respond to latitude or longitude. This confirms what is known from the literature [START_REF] Arthur | Les chauves-souris de France[END_REF]. [START_REF] Reers | Activity at Nacelle Height Over Forest[END_REF] also found a high influence of longitude and latitude on bat density at WT nacelle height, and [START_REF] Arnett | Impacts of wind energy development on bats: implications for conservation[END_REF] suggest that fatalities might decrease with increasing latitudes on the North American territory. However, these studies did not investigate bat vertical flight distribution.

In the present study, latitude and longitude were never selected in the models for vertical flight distribution, although it is still possible that flight height varies locally, for example in areas where bat migration is concentrated.

Effect of distance to woodland, water and buildings

Distance to trees had a significant effect on the density of species of low or medium flight heights (i.e. P. pipistrellus, P. kuhlii and E. serotinus) but high-flying species (i.e. P. nathusii, N. leisleri and N. noctula) did not respond to this variable, or the effect could be too weak compared to the other variables. [START_REF] Reers | Activity at Nacelle Height Over Forest[END_REF] also found that an increasing percentage of forest in a 500 m buffer enhanced the density of P. pipistrellus at WT nacelle height but not of P. nathusii and the group of Vespertilio/Nyctalus/Eptesicus species. However, these authors did not study bat vertical flight distribution. In our study, distance to trees was never selected to explain vertical flight distribution. This shows that distance to woodland is a factor of WT collision risks with species of low or medium flight heights because it acts on their local density, but not on their flight height. This contradicts a common hypothesis that assumes that bats fly higher over forests than over open landscapes [START_REF] Menzel | Effect of habitat and foraging height on bat activity in the coastal plain of South Carolina[END_REF]. It could still be the case at a very small scale (i.e. a few meters above tree canopy), which would be insufficient to bring low-flying species in the zone at collision risk (> 25 m above ground).

A minimum distance to trees of 200 m is currently a strong recommendation regarding the placement of European WT [START_REF] Rodrigues | Guidelines for consideration of bats in wind farm projects: revision 2014[END_REF]. This recommendation emerged from one bat fatality study [START_REF] Black | Fledermäuse als Opfer von Windkraftanlagen in Deutschland[END_REF], in which the authors state that their sample size per species was relatively small. [START_REF] Heim | The Importance of Landscape Elements for Bat Activity and Species Richness in Agricultural Areas[END_REF], [START_REF] Heist | Assessing bat and bird fatality risk at wind farm sites using acoustic detectors[END_REF] and [START_REF] Kelm | Seasonal Bat Activity in Relation to Distance to Hedgerows in an Agricultural Landscape in Central Europe and Implications for Wind Energy Development[END_REF] provided additional elements that show that bat density at ground level decreases with increasing distance to woodland, but it is not known whether these results obtained at ground level can be generalised at height. Our model for all species predicted a decrease of bat density of 77 %

for masts located at 200 m from trees compared to masts positioned a few meters from trees, but our density models for high flying species (Nyctalus bats), most susceptible to WT collisions, showed no effect of distance to woodland.

Distance to water was only important in explaining P. nathusii density, which is concurring with the literature that shows that this species selects habitats close to water [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa[END_REF]. Besides, N. leisleri was more likely to fly at height when distance to water increased. It is possible that when commuting away from wetlands, N. leisleri flies higherand fastercompared to when it is foraging or drinking at wetlands, as suggested by some pieces of evidences in N. noctula [START_REF] Roeleke | Habitat use of bats in relation to wind turbines revealed by GPS tracking[END_REF].

Effect of topography

Topography had a strong influence on bat density. Indeed, increasing altitudinal amplitude, positively correlated with altitude, significantly decreased the density of all focus species, except for N. leisleri, that did not respond significantly to this variable. This finding supports what is known in the literature [START_REF] Arthur | Les chauves-souris de France[END_REF]. The siting of wind masts near hill or mountain tops also decreased the density in the model for all species. The effect of topography on P. nathusii density was more complex as density was higher in areas with small altitudinal amplitude, and in these areas, density was weaker if masts were installed on hilltops. Besides, our analysis shows that P. nathusii is more likely to fly at height when wind masts were positioned closer to hill or mountain tops than to valleys. This variable thus produced antagonistic effects which resulted in equivalent collision risks at valleys and hilltops for P. nathusii.

The most influential scale for topography description was 5 km, while the 1 km scale was only selected for the P. pipistrellus density model, and the 200 m scale was never selected.

Steep slopes are suspected to generate ascending currents favourable for high altitude flight (Roeleke et al., 2018) and to create thermal conditions favourable for insect aggregations and foraging bats [START_REF] Arnett | Impacts of Wind Energy Development on Bats: A Global Perspective[END_REF]. However, the selected scale for topography description in our models is more likely to be a proxy for the presence of mountainous areas in the 5 km (1 km for P. pipistrellus) buffer, rather than the proxy of the presence of a steep slope near the mast.

Effect of time of the year

The effect of the Julian day on bat vertical flight distribution had never been investigated to our knowledge and was, contrary to our expectations, the most influential factor of bat proportion of flight at height. Its effect on bat density was antagonistic to its effect on bat vertical flight behaviour for several species (Fig. 3, Table A3 in Electronic supplementary material 1). Indeed, bat density peaked in summer/autumn, while the proportion of flights at height peaked in spring and autumn for most bats. Higher bat activity in late summer/autumn is linked to increasing energy demands during migration and in preparation of hibernation, and to the presence of juveniles that temporarily raises population density [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa[END_REF].

Two highly plausible and non-exclusive phenomena could explain higher proportions of flight at height in spring and autumn: (1) they are due to migrating bats that would benefit from exploiting high altitude strong winds during long-distance flights [START_REF] Hedenström | Optimal migration strategies in bats[END_REF] (2) they are due to an increase in prey (i.e. insects) presence at height during favourable conditions for insect migration (high altitude winds blowing to the north in spring, and to the south in autumn) [START_REF] Reynolds | Riders on the Wind: The Aeroecology of Insect Migrants[END_REF]. Bat density located at height was maximal in summer and autumn for all focus species. It is the first time to our knowledge that this phenomenon is clearly demonstrated using acoustic tracking, and it explains WT fatality peaks in late summer and autumn found in numerous studies [START_REF] Arnett | Impacts of Wind Energy Development on Bats: A Global Perspective[END_REF][START_REF] Rydell | Bat Mortality at Wind Turbines in Northwestern Europe[END_REF].

Effect of microphone height

Microphone median height only influenced bat density (ground level and height included) in the model for all species. When microphone median height was more elevated, the lowest microphone was often installed at more than 20 m high (Fig. A2 in Electronic supplementary material 1) and fewer bat passes were recorded. Thus, short-range echolocating species flying near ground level (e.g. Myotis, Plecotus) were probably not recorded. On the contrary, species susceptible to WT collisions such as Nyctalus or Pipistrellus [START_REF] Roemer | Bat flight height monitored from wind masts predicts mortality risk at wind farms[END_REF] are middle-or long-range echolocators, and were never or rarely missed when microphone median height was elevated. Nonetheless, higher microphone median heights were associated with less density at height for P. kuhlii and E. serotinus.

Limits

The predictions of our models are dependent on the features present in our study sites (see Electronic supplementary material 2) and must be interpreted with this knowledge. Indeed, our sampling does not allow predictions for high mountains and we did not test for the influence of the positioning of a wind mast at a marked mountain pass, although it must be noted that [START_REF] Rodrigues | Guidelines for consideration of bats in wind farm projects: revision 2014[END_REF] expect increased collisions in these passes and recommend avoiding them for WT siting. Distance to water was rarely retained in models, possibly because only one study site was closer than 100 m to water. Our study sites do not cover homogeneously the France and Belgium territory. Nonetheless, the locations of our wind masts match with the highest wind energetical density areas selected for the installation of wind farms (ADEME, 2015) and thus adequately cover onshore areas with potential bat-WT conflicts.

At last, our observations were done on wind masts, and not on WT. Several phenomena could lead to differences in bat activity at operating wind turbines compared to lattice masts, and these differences should be tested in future large-scale studies, e.g. ( 1) blade rotationwhich by mixing air layers warms surface temperatures, especially at night [START_REF] Miller | Climatic Impacts of Wind Power[END_REF] could attract insects and in turn attract bats, or (2) the colour of wind turbine poles could attract insects [START_REF] Long | Insect attraction to wind turbines: does colour play a role?[END_REF], and in turn attract bats. Besides, most bats seem to avoid wind turbines at larger scales [START_REF] Barré | Estimating habitat loss due to wind turbine avoidance by bats: Implications for European siting guidance[END_REF][START_REF] Minderman | Landscape-scale effects of singleand multiple small wind turbines on bat activity[END_REF][START_REF] Minderman | Experimental Evidence for the Effect of Small Wind Turbine Proximity and Operation on Bird and Bat Activity[END_REF]. Thus, in the absence of evidence that bat behaviour is not equivalent at both structures, and considering that bat acoustic activity recorded at wind masts was a predictor of the number of bat fatalities at independent wind turbine locations [START_REF] Roemer | Bat flight height monitored from wind masts predicts mortality risk at wind farms[END_REF], we assume that the differences in behaviour are negligible in regard to the questions addressed in our study.

Consideration of guilds in the study of bat landscape ecology

Contrary to the other focus species, the density of Nyctalus species did not respond or responded very little to the landscape variables that we tested. They might respond to more detailed categories of habitat (e.g. for open habitats, differentiation between pastures and arable lands) [START_REF] Mackie | Habitat use varies with reproductive state in noctule bats (Nyctalus noctula): Implications for conservation[END_REF]. However, the perception of landscape heterogeneity varies according to the ecological requirements of each bat species [START_REF] Peixoto | A synthesis of ecological and evolutionary determinants of bat diversity across spatial scales[END_REF].

Thus, high-flyers, which travel greater distances and which perceive background further away than other species thanks to their use of low frequencies [START_REF] Dietz | Bats of Britain, Europe and Northwest Africa[END_REF][START_REF] Roemer | Bat sonar and wing morphology predict species vertical niche[END_REF], might respond more to landscape described at even greater scales than at a radius of 5,000 m. Alternatively, high-flying bats, which forage on high-flying insects, could also select their foraging grounds in a highly opportunistic way depending on nightly wind or lunar conditions that will impact the presence of insects in elevated air layers [START_REF] Reynolds | Riders on the Wind: The Aeroecology of Insect Migrants[END_REF]Roeleke et al., 2018).

Recommendations for wind turbine siting in France and Belgium

WT operational mitigation (i.e. raising of WT cut-in speed) can be efficient to reduce the number of bat collisions while causing reductions in energy production often equivalent to an annual loss of <1% [START_REF] Arnett | Impacts of Wind Energy Development on Bats: A Global Perspective[END_REF][START_REF] Arnett | Altering turbine speed reduces bat mortality at wind-energy facilities[END_REF][START_REF] Martin | Reducing bat fatalities at wind facilities while improving the economic efficiency of operational mitigation[END_REF]. However, it is not a sufficient solution to eliminate collisions, and impacts must be also prevented by avoiding high collision risk areas. Macro-siting can be done based on species occurrence and population densities at the national scale. Our models show that species density decreases to the North of France. If per capita collision probabilities are similar on the whole French territory, prioritising wind energy development in Northern France should lead to a smaller toll on bats, but our models also showed that Northern France is a region with a high P.

nathusii density, and this species is among the most susceptible to WT collisions [START_REF] Roemer | Bat flight height monitored from wind masts predicts mortality risk at wind farms[END_REF]. Prediction maps of bat occurrence and density on smaller (i.e. regional) scales are potentially a very efficient approach to do macro-siting based on landscape and habitat features [START_REF] Newson | Largescale citizen science improves assessment of risk posed by wind farms to bats in southern Scotland[END_REF]. Indeed, contrary to the French national scale where latitude had the greatest influence on bat density, we expect landscape to play a more important role at the regional scale.

After macro-siting based on species distribution, micro-siting is then conceivable using local landscape information such as distance to woodland (including hedgerows). Our model for the density of all species is based on observations of species regardless of their susceptibility to WT collisions. Although, it can be used to mitigate both the impacts of collision and of habitat loss due to WT [START_REF] Barré | Estimating habitat loss due to wind turbine avoidance by bats: Implications for European siting guidance[END_REF][START_REF] Millon | Wind turbines impact bat activity, leading to high losses of habitat use in a biodiversity hotspot[END_REF][START_REF] Minderman | Landscape-scale effects of singleand multiple small wind turbines on bat activity[END_REF][START_REF] Minderman | Experimental Evidence for the Effect of Small Wind Turbine Proximity and Operation on Bird and Bat Activity[END_REF].

Our results support the recommendation that distance to woodland should be maximised to significantly decrease general bat density. However, it is very important to be aware that following this recommendation will not be effective in decreasing the density of high-flying species susceptible to WT collisions. Our results also suggest that placing WT near or at hilltops could be effective in decreasing bat mortalities through a lower local bat density, but it can also enhance the proportion of flights at collision risk for some species. Thus, we strongly recommend that the decision to place WT on hill or mountain tops should be based on bat density found in the zone at collision risk during pre-construction monitoring.

Landscape planning is thus one of the tools that can help species conservation in the context of growing impacts due to anthropogenic activities. We advocate using this tool in a scaledependent process, as described above, especially in developing countries where land is still available for an ambitious wind energy development.

Funding

Fig. 1

 1 Fig. 1 Location of French and Belgian study sites and representation of the elevational gradient.

Fig. 2

 2 Fig. 2 Influence of distance to trees (a) and mast position in elevational gradient (b) on bat density for all species (high values mean a closer mast position from hill or mountain tops). B = Buffer size. 95% confidence intervals are shown. Ticks on the x axis represent the sampled values.

Fig. 3

 3 Fig. 3 Predicted bat density (ground level and height included) (a), proportion of flight at height (b), and bat density at height (c) in function of period of the year for N. leisleri. 95% confidence intervals are shown in light grey.

Table 1

 1 Summarised statistical results of the negative binomial distributed generalised linear mixed effect models (GLMM) for the density of each species.= estimate; SE = standard error; P = significance of P value. Species names are given with the first three letters of the species and genera. Interactions are noted with a colon. B = buffer size. Mic. Med. Height = Microphone median height; Dist. = Distance; Δ Alt. = altitudinal amplitude; Pos. elev. = Position of wind mast in elevational gradient.

		All species	Pipkuh			Pippip		Eptser		Pipnat	Nyclei			Nycnoc
	Variables	SE	P	SE	P	SE	P	SE	P	SE	P	SE	P	SE	P
	Intercept	-0.72 0.63	0.03 0.33		4.21 0.13 *** 0.45 0.24	.	-0.63 0.16 *** 0.63 0.20 ** -2.50 0.40 ***
	Mic. Med. H.	-0.31 0.12 ** -0.34 0.31		-0.19 0.13		-0.26 0.24		-0.05 0.15	0.36 0.19	.	0.43 0.37
	Julian Day	0.09 0.01 *** -0.08 0.04	*	0.05 0.02	*	-0.46 0.05 *** 0.39 0.04 *** 0.27 0.04 *** 0.30 0.06 ***
	Julian Day²	-0.80 0.01 *** -0.87 0.04 *** -0.94 0.02 *** -1.75 0.06 *** -0.46 0.05 *** -0.75 0.04 *** -0.96 0.07 ***
	Latitude	-0.65 0.15 *** -2.40 0.39 *** 0.29 0.13	*			1.05 0.19 *** -0.92 0.20 ***
	Longitude		-1.13 0.37 ** 0.29 0.13	*			0.48 0.17 ** 1.18 0.21 ***
	Dist. water									-0.31 0.18	.

Acknowledgements

We would like to thank Sébastien Devos, Marie-Lilith Patou, Julien Mérot, Alexandre Haquart, Julien Tranchard, Philippe Ferragne, Matthieu Guyot, Antonin Dhellemme, Matthieu Lageard, Paul Gillot, François Huchin, Julien Renglet, Magali Argaud and Estelle Cleach for their important contributions to equipment design and installation, data collection and This study was a collaboration between Biotope and the Muséum national d'Histoire Naturelle in the form of a PhD thesis funded by Biotope and the Association Nationale de la Recherche et de la Technologie.

Table 2 Summarised statistical results of the binomial distributed generalised linear mixed effect models (GLMM) for the proportion of flight at height of each species. = estimate; SE = standard error; P = significance of P value. Species names are given with the first three letters of the species and genera.

Interactions are noted with a colon. B = buffer size. Mic. Med. Height = Microphone median height; Dist. = Distance; Pos. elev. = Position of wind mast in elevational gradient.

Conflict of interest

Biotope is an environmental consultancy involved in wind turbine impact assessment studies.

Two of the authors, Charlotte Roemer and Thierry Disca, were employees at Biotope at the time of submission. Authors thus declare a conflict of interest. However, authors take complete responsibility for the integrity of the data and the accuracy of their analysis.


Samir Chandra

Marc Fivel

Jean-Pierre Franc

Christian Pellone

Cavitation Induced Damage: FEM Inverse Modeling of the Flow Aggressiveness

An inverse method is proposed to identify the pressure fields that could generate individual pits as observed experimentally in eroded samples made of three different materials. Assuming each pit was generated by a single bubble collapse, the pressure load is defined by two parameters, the peak pressure and its radial extent. An inverse method based on finite element modeling is proposed. The method gives access to the load distributions relevant to the aggressiveness of the cavitation test which is found to be consistent with the three materials responses.

Introduction

In order to predict erosion damage, it is essential to know the loading conditions generated by the bubble collapses. However, the determination of the loading conditions due to bubble collapses remains a major issue in cavitating flows. The pressure pulses may be directly measured experimentally inside the cavitation facilities for example by using pressure transducers flush mounted in the region of the bubble collapses [1][2][3]. However this method gives the impact loads in Newtons but the determination of the pressure field in term of stress amplitude (in MPa) is difficult because the loaded surface area is unknown and usually much smaller than the transducer sensitive surface.

Alternatively, CFD simulations could be used but generally these simulations assume that the impacted materials is a rigid surface which is a strong assumption leading to overestimations of the applied pressure.

In order to overcome these measurement difficulties, another option may be used based on an inverse modeling approach. The idea is that each pit is the signature of a single bubble collapse. Then, it can reasonably be expected that the loading conditions be derived from the geometry of the pit and the material properties. In the present work, such a technique is proposed for deriving the loading conditions from pitting tests conducted during the incubation period. It is based on FEM (Finite Element Method) computations of the response of the material to a representative pressure pulse. An inverse procedure is then proposed to derive the distribution of the pressure profiles from the depth and diameter of pits observed experimentally.

Method 2.1 Material characterization

Prior to any simulation, the material behavior needs to be identified. This has been done using spherical nanoindentation tests performed on three tested materials: an Aluminum alloy Al 7075 (Al), a stainless steel A2205 (SS) and a Bronze (NAB). Using Tabor's equation, the tensile equivalent loading curves have been identified as the dashed curves plotted in Fig. 1.

Corresponding author: Marc Fivel E-mail address: Marc.Fivel@simap.grenoble-inp.fr Since a bubble collapse takes place in a very short period of time (typically less than one microsecond), the stress-strain curve has been corrected in order to account for high strain rates. The stress is modified using the Johnson Cook model for which parameter C has been taken from literature (Al: C=0.017 ; SS: C=0.011; NAB: C=0.06). The strain rate effect on the stress-strain curve is shown in Fig. 1. 2.1 Cavitation erosion data Cavitation erosion tests have been performed on the same three materials using the device described in details in [4]. Pits produced at upstream pressure of 10 and 40 bars for exposure times up to 15 minutes have been considered for the current analysis. Sample surfaces after pitting test have been analyzed using a conventional contact profilometer with microprobe of radius 2 µm. For each material, image analysis of the measures gave 200 characterizations of isolated pits as the one shown in Fig. 2b. Each pit is characterized by its diameter and depth.

( )

        + = 0 0 0 ln 1 ε ε σ ε σ & & & C

Finite Element Modeling

For sake of simplicity, the modeling is restricted to a 2D axisymmetric investigation. The applied load consists of a pressure distribution with a Gaussian shape applied on the top surface defined by the hydrodynamic pressure σ H and its extent radius r H .

                - σ = σ 2 H H r r exp
The mesh is locally refined in the vicinity of the maximum loaded zone. Finite Element simulations are conducted using software ABAQUS © and 8100 CAX4R elements surrounded by a layer of CINAX4 infinite elements in the bottom-right sides of the simulation cell. The material behavior is taken as elastic-plastic with the reference curves defined at the strain rate of 1000s -1 (continuous curves in Fig. 1).

Results and Discussion

An inverse method is conducted in a view to find the best set of parameters (σ H ,r H ) that generates a given experimental pit profile. Results are reported in Fig. 4. As expected the higher upstream pressure leads to higher hydrodynamic stresses. In order to quantify the flow aggressiveness, we chose to plot the number of impacts per area and per unit of time. It appears that the points calculated from the three materials do not fall on a given master curve. This indicates that such a plot is not relevant of the flow characteristics. One way to solve this problem is to plot the impact frequency for a given range of r H or σ H . This better addresses the bubble distribution in term of pressures and sizes. This has been done in Fig. 5 where the impact frequency is now plotted as a function of the impact stress σ H , but for a given range of applied pressure radius r H . One can clearly see that the three materials get aligned on a given unique curve.

               -                 σ σ - =

Concluding Remarks

The inverse FEM approach presented here gives an analytical expression of the impact frequency for a given cavitation condition. This expression is material independent and quantifies the flow aggressiveness. Since each material reacts differently to a pressure pulse, they filter the impacts left at the surface so that the material can be viewed as a sensor of the cavitation conditions.

Fig. 1

 1 Fig. 1 Material characterization using nanoindentation data and Johnson-Cook extrapolations to high strain rate.

Fig. 2

 2 Fig. 2 Typical eroded surface of Al sample. (a) 2x3mm scan of the surface with multiple impacts (b) zoom on a 10x10µm zone surrounding a typical pit.

Fig. 3

 3 Fig. 3 Typical FEM mesh used in the simulations (N1=20 N2=30 elements). The figure only shows a magnified view of the loaded zone.

Fig. 4

 4 Fig. 4 Results of the inverse method for the two test conditions (10 and 40 bars).

Fig. 5

 5 Fig. 5 Impact frequency as a function of the pressure stress σ H for a given range of pressure extent r H =d H /2.

Figure 6

 6 Figure6gives the 2D distribution of the impact frequency.

Fig. 6

 6 Fig. 6 2D distribution of impact frequency. Data obtained for the upstream pressure of 40bars. A 3D fit of the surface passing through all the data points give the following analytical expression of the frequency of impacts in function of σ H and d H.



  expression is the signature of the flow aggressiveness.