Weather conditions determine attenuation and speed of sound: Environmental limitations for monitoring and analyzing bat echolocation

Abstract Echolocating bats are regularly studied to investigate auditory‐guided behaviors and as important bioindicators. Bioacoustic monitoring methods based on echolocation calls are increasingly used for risk assessment and to ultimately inform conservation strategies for bats. As echolocation calls transmit through the air at the speed of sound, they undergo changes due to atmospheric and geometric attenuation. Both the speed of sound and atmospheric attenuation, however, are variable and determined by weather conditions, particularly temperature and relative humidity. Changing weather conditions thus cause variation in analyzed call parameters, limiting our ability to detect, and correctly analyze bat calls. Here, I use real‐world weather data to exemplify the effect of varying weather conditions on the acoustic properties of air. I then present atmospheric attenuation and speed of sound for the global range of weather conditions and bat call frequencies to show their relative effects. Atmospheric attenuation is a nonlinear function of call frequency, temperature, relative humidity, and atmospheric pressure. While atmospheric attenuation is strongly positively correlated with call frequency, it is also significantly influenced by temperature and relative humidity in a complex nonlinear fashion. Variable weather conditions thus result in variable and unknown effects on the recorded call, affecting estimates of call frequency and intensity, particularly for high frequencies. Weather‐induced variation in speed of sound reaches up to about ±3%, but is generally much smaller and only relevant for acoustic localization methods of bats. The frequency‐ and weather‐dependent variation in atmospheric attenuation has a threefold effect on bioacoustic monitoring of bats: It limits our capability (1) to monitor bats equally across time, space, and species, (2) to correctly measure frequency parameters of bat echolocation calls, particularly for high frequencies, and (3) to correctly identify bat species in species‐rich assemblies or for sympatric species with similar call designs.


| INTRODUC TI ON
Bioacoustic research is the study of animal sounds, their production, transmission and perception (Bradbury & Vehrencamp, 2011;Fletcher, 2007) and regularly involves the recording and acoustic analysis of animal sounds. The characteristics of a recorded sound are generally determined by (1) the sound source (e.g., the animal), (2) the sound transmission channel (e.g., the animal's environment), and (3) the recording equipment (i.e., microphones). While we are interested in the animal and its sounds, we need to take into account that the transmission channel and the recording equipment can significantly affect the measured sound parameters. On land, the air forms the sound transmission channel through which sound propagates. As air conditions such as temperature and humidity are not constant, but vary over space and time (i.e., weather), the properties of the sound transmission channel also vary (e.g., Marten, Quine, & Marler, 1977;Wiley & Richards, 1978). This paper addresses the influence of the weather, that is, environmental variation in atmospheric conditions, as a ubiquitous source of error on measured sound parameters, particularly for high-frequency sounds such as bat echolocation calls.
Here, I concentrate on two main features of the transmission channel, namely atmospheric attenuation and speed of sound, which are highly relevant when analyzing sounds, both as a bat and as a bioacoustic researcher. Atmospheric attenuation (AA) is the reduction in sound amplitude while the sound travels through the air, caused by absorption of acoustic energy by the air molecules (Attenborough, 2007). AA is determined by four factors: sound frequency, air temperature, relative humidity, and pressure (Attenborough, 2007).
Crucially, these factors interact in a complex, nonlinear fashion, meaning that no simple relationship exists between AA and weather conditions (Attenborough, 2007;Griffin, 1971;Luo, Koselj, Zsebők, Siemers, & Goerlitz, 2013;Stilz & Schnitzler, 2012). The magnitude of AA determines the detection range of sound, which varies with sound frequency and weather conditions. This causes differential detection ranges for different call frequencies and for different weather conditions, which may limit the analysis of call frequency parameters and the detection and identification of bat species.
Likewise, this weather-induced variation in AA is also significant for the bats, as supported by the correlation between geographic and local differences in environmental conditions and bat call frequencies. For example, populations of several horseshoe bat species (Jacobs, Catto, Mutumi, Finger, & Webala, 2017;Maluleke, Jacobs, & Winker, 2017;Mutumi, Jacobs, & Winker, 2016) and Hipposideros ruber (Guillen, Juste, & Ibanez, 2000) exhibit geographic differences in call frequency correlated with average weather conditions, suggesting adaptation to average weather conditions over evolutionary time. Importantly, however, also bats whose echolocation is adapted to average weather conditions experience additional spatial and temporal fluctuations in weather conditions and AA, leading to variation in call and echo detection range. Some bats seem to adapt their calls even to current local weather conditions. Chaverri and Quiros (2017) showed weather-frequency-correlation in the low-frequency call type of two neotropical free-tailed bats, suggesting short-term individual behavioral flexibility in calls optimized for long-range detection.
The speed of sound (c) is the speed by which sounds propagate through the air (often approximated by 340 m/s). It is the fundamental physical sound parameter by which bats compute object range based on echo delay, as well as the fundamental parameter underlying the acoustic localization of echolocating bats and other soundproducing animals (reviewed in Blumstein et al., 2011), a method that is increasingly used to obtain bats' spatial positions based on the differences in arrival time of the same call on multiple microphones (e.g., Fujioka, Aihara, Sumiya, Aihara, & Hiryu, 2016;Goerlitz, ter Hofstede, Zeale, Jones, & Holderied, 2010;Hügel et al., 2017;Lewanzik & Goerlitz, 2018;Seibert, Koblitz, Denzinger, & Schnitzler, 2013;Surlykke, Pedersen, & Jakobsen, 2009).
Although the physical relationships between atmospheric conditions and AA (Bass, Sutherland, Zuckerwar, Blackstock, & Hester, 1995;Bazley, 1976;Evans, Bass, & Sutherland, 1972;Giacomo, 1982) and c (e.g., Cramer, 1993;Wong, 1986) are described, these technical papers are not necessarily read by ecologists and bioacousticians (but see these bat-specific articles: Griffin, 1971;Hartley, 1989;Lawrence & Simmons, 1982;Stilz & Schnitzler, 2012). The objectives of this paper thus are to highlight and summarize the effects of the atmosphere on sound recordings and analysis. Specific objectives are (1) to illustrate the variation in atmospheric attenuation and speed of sound as a function of weather conditions, (2) to show how this variation influences the measurement of acoustic signals, and (3) to discuss how this may cause species-specific limits in call analysis, bat species identification and abundance measures. To achieve these objectives, I aim to provide an accessible overview of the atmospheric effects on AA and c, provide the methods for their calculations in the SI as Matlab, Python, R and Excel code, and discuss their influences on bioacoustic measurements.

| Calculation of atmospheric attenuation and speed of sound
Atmospheric attenuation (AA, in dB/m) was calculated as function of sound frequency (f, in Hz) and the temperature (T, in °C), relative humidity (RH, in %), and pressure (p, in Pa) of the air (ISO standard #9613-1, ISO 1993). Speed of sound (c, in m/s) was calculated as function of temperature, relative humidity and pressure of the air, and the molar fraction of CO 2 in air (Cramer, 1993). All equations are available in the Supporting Information (as text, as Matlab, Python and R code, and as Excel spreadsheets).
Calculations were restricted to sound frequencies and atmospheric conditions most relevant for echolocating bats.
Particularly, I used sound frequencies from 10 to 110 kHz (in steps of 1 kHz), focusing on the dominant call frequencies for many bat species (Safi & Siemers, 2010;Schnitzler, Moss, & Denzinger, 2003). Temperature ranged from 5 to 40°C (step size 1°C), relative humidity from 0% to 100% (step size 1%), and atmospheric pressure from 670 to 1,070 hPa (step size 10 hPa; corresponding to altitudes of approximately 3,300 m, the maximum flight height of Tadarida brasiliensis (Williams, Ireland, & Williams, 1973) to −425 m, the lowest point on Earth at the Dead Sea). The molar fraction of CO 2 was set to approximate current levels of 400 ppm (IPCC, 2013).

| Exemplary weather data
In addition to using the full range of relevant atmospheric parameters, I also calculated AA and c for two sets of exemplary real weather data to show realistic temporal and spatial variation. To show exemplary daily fluctuations in AA and c, I used weather station data (T, RH) from July 2016 in Konstanz, South Germany collected daily at 10 pm (i.e., within the first hour after sunset).
p was set to the local average in July 2016 of 1,020 hPa, and the molar fraction of CO 2 to 400 ppm. A second large-scale set of weather data (T, RH) over three years during bat peak activity was downloaded from Weather Online UK (www.weatheronline.co.uk; cf. Luo et al., 2013) for four areas with different climatic conditions (Germany, Malaysia, Negev desert, South Africa). Here, p was set to 1013.25 hPa and the molar fraction of CO 2 of 400 ppm.

| Estimating localization error
Acoustic localization methods convert time of arrival differences (TOAD) of the same call at multiple microphones into 3D-positions based on speed of sound c, and thus are susceptible to variation in the speed of sound. To estimate the localization error caused by errors in c, I generated the call sequences that a microphone array would receive from a bat at different spatial positions, and then analyzed these sequences with a different c than used during generation. Specifically, I used cross-correlation to calculated TOADs for symmetrical planar star-shaped four-microphone arrays with 60 cm (e.g., Goerlitz, ter Hofstede et al., 2010;Hügel et al., 2017;Lewanzik & Goerlitz, 2018) and 120 cm intermicrophone distance, a c of 338 m/s, and a grid (2 m spacing) of bat positions filling half a hemisphere above the array up to 20 m distance (x = 0-20, y = −20 to 20, z = 2-20; Figure S1). The half-hemisphere left of the array (x = −20 to 0) was omitted as it is identical to the right one (x = 0-20) due to the array's symmetry. Underground positions below the array (negative z-values) were also omitted. Having calculated the TOADs for all positions and both arrays, I then generated call sequences as recorded by the array microphones, using a bat-like chirp (linearly downward-frequency-modulated from 100 to 20 kHz, duration 2 ms) and a sampling rate of 5 MHz. Generated sound files were resampled to 500 kHz and analyzed with the TOADSuite (by Peter Stilz; cf., Lewanzik & Goerlitz, 2018) to obtain 3D-positions for two values of c that were 2 and 5 m/s larger than the correct value used during original TOAD calculation (340 and 343 m/s).

| Atmospheric attenuation
The AA of sound in air is determined by four factors: the sound's frequency f and the air's temperature T, relative humidity RH and pres- (yellow dotted line, Figure 2c), we see that the 20 kHz bat experiences maximum AA around 60% RH, while the 50 kHz bat experiences it at 100% RH. For warmer nights with 20°C (orange dotted line), this peak is shifted by about 30% points to lower humidities of about 30% and 70%, respectively. Note that the calls of many bats are frequency-modulated, and each frequency in such a call will undergo differential atmospheric attenuation (see below and Atmospheric pressure p also slightly influences AA. Generally, increasing p causes a reduction in AA, with temperature and frequency-specific differences ( Figure 2d). However, this effect is much smaller than the effects of T and RH, even for the large total range of p analyzed here (from 670 hPa at >3,000 m altitude of highflying T. brasiliensis to 1,070 hPa at −425 m altitude of the Dead Sea), which most bats will never experience.

| Different parameters cause different amounts of variation in atmospheric attenuation
To quantify the relative contribution of call frequency and the three weather conditions to the total variation in AA, each of the four parameters was systematically varied over its full range (Figure 3a). Note that atmospheric attenuation is mostly determined by sound frequency, but also varies with weather conditions differently for the different frequencies 1°C in T or 1% point in RH. Note, however, that changes in RH affect AA mostly for low RH below about 30%. At higher RH, which is more typical for nocturnal bat habitats, the effect of changing RH becomes smaller, meaning that AA will be mostly influenced by T.
Lastly, to quantify how much variation in AA is caused by each of the four parameters, three parameters were kept constant while the fourth parameter was varied over its full range to obtain the maximum variation in AA caused by variation in this focal param-

| Effect of weather conditions on analyzed call parameters
Any recorded call will have a lower level and a different spectrum than the emitted call due to AA and geometric attenuation (GA).
Geometric attenuation of bat calls usually follows spherical spreading by which the call's total energy is distributed with increasing distance over an increasingly larger spherical surface, reducing call amplitude equally for all call frequencies by 6 dB per each doubling of distance. AA and GA both increase with distance, but differently, and thus their relative contribution to the total attenuation (GA + AA) also changes with distance (Figure 4a). At short distances, total attenuation is mostly determined by GA, while at larger distances, AA becomes relatively more important as it scales per unit of distance, not per doubling of distance, particularly for higher frequencies that experience stronger AA. The exact changes in level and spectrum, however, depend on call frequency, distance, and weather conditions.  Figure S2 presents the same data with equal scaling of the colorcode and y-axes, showing better the differences in AA with frequency instead of with T and RH The frequency-and distance-dependency of AA strongly influences the measured frequency parameters of (ultrasonic) calls, particularly for broadband calls, e.g., the frequency-modulated calls emitted by many species of the worldwide distributed genus Myotis.
To simulate this, we take the call of a trawling Myotis (capaccinii) recorded at about 1 m distance to the bat (Figure 4b, waveform and amplitude spectrum) and apply the frequency-specific AA for larger distances (Figure 4c,d). With increasing distance, higher frequencies are more strongly attenuated than lower frequencies, and this effect differs between typical weather conditions (cf. Figure 1). For example, with increasing distance from 2 to 20 m, the upper −12 dB frequency ("start frequency") is reduced by about 17 kHz (from 74 to 57 kHz) at 10°C and 80% (Figure 4c) and by about 19 kHz (from 74 to 55 kHz) at 20°C and 50% (Figure 4d), that is, by 2 kHz more than for the previous weather condition. Likewise, the frequencyand distance-dependency of AA also reduces the measured peak frequency, in this example from about 44 kHz at close distances (up to 10 m) to about 40 kHz at larger distances (at 20 m), and the measured call duration, here from 3.61 ms at 2 m to 2.92 ms at 20 m (−19%, 10°C/80%) and from 3.58 ms at 2 m to 2.80 ms at 20 m (−22%, 20°C/50%; red lines in Figure 4c,d). Lastly, also note how the level of the received call is affected by weather conditions. After 20 m, the relative level at peak frequency is −24 dB for 10°C/80%, but 4 dB smaller (−28 dB) for 20°C/50%, which affects the signal-tonoise ratio and the call detection probability.

| Speed of sound
Like AA, also the speed of sound (c) is not a constant value, but determined by temperature T, relative humidity RH, atmospheric pressure and the molar fraction of CO 2 . Here, we only consider T and RH, which are fast-changing and have a relevant influence on c ( Figure 5). At first approximation, c linearly increases with increasing T and RH, although the effect of T is much stronger than that of RH (Figure 5a,b). In more detail, c is a nonlinear function of T and RH, resulting in an interaction between both parameters. Thus, the influence of T on c becomes slightly larger at higher RH (Figure 5a), and likewise the influence of RH on c is stronger at higher T (Figure 5b While this variation may seem small, it can be relevant for the increasingly used method of calculating the three-dimensional location of sound sources based on time-of-arrival differences, a method that relies on the speed of sound. Using a wrong value for c and ignoring its variation will result in localization errors that are roughly aligned along the array-bat-axis in most cases. The magnitude of this error depends on the error in c, but also on the array geometry and distance to the array. For a symmetrical planar star-shaped array with 60 cm intermicrophone distance, the median error is 3.6% (Q1-Q3: 1.9-6.0) of the distance to the array if c is assumed to be 2 m/s larger than its correct value, and 5.0% F I G U R E 4 Effect of atmospheric and geometric attenuation on call level and call frequencies. (a) Geometric attenuation (black) and atmospheric attenuation for different frequencies (colored lines) as a function of increasing distance between bat and microphone, for two different weather conditions (left and right). (b) Waveform (left) and amplitude spectrum (right) of a typical frequency-modulated call of a Myotis bat, recorded close to the bat at about 1 m distance. (c,d) Effect of atmospheric attenuation on measured call frequencies: spectrogram (left) and spectra (right) of the recorded call (rec) and after additional atmospheric attenuation over 2, 5, 10, and 20 m distance (colored lines), for two different weather conditions. Note how the peak frequency, the −12 dB call frequencies (red dots) and call duration (red horizontal lines, based on −12 dB threshold) are reduced with increasing distance. Geometric attenuation was disregarded. Slight differences exist in the exact peak frequencies measured in the spectrogram or spectrum, but the pattern is the same F I G U R E 5 Effect of weather conditions on speed of sound in air. Speed of sound increases with temperature (a) and relative humidity (b), with a stronger effect of temperature than humidity. (c) Distribution of temperature (T) and relative humidity during bat foraging times in four countries with different climate, leading to different distributions in speed of sound (c) and relative deviation from median speed of sound (Δc). Boxplots show median, quartiles and whiskers at up to 1.5× the interquartile range beyond the quartiles (2.9-8.3) for 5 m/s error in c. For a larger array of 120 cm intermicrophone distance, these errors become smaller and are 1.6% (1.1-2.7) and 3.8% (2.3-6.2).

| D ISCUSS I ON
The sounds recorded and analyzed by researchers differ from the sounds emitted by the animal due to various physical effects of the sound transmission channel. In the case of bat echolocation calls, the recorded calls have travelled some distance through the air, where it was mostly affected by geometric and atmospheric attenuation (Wahlberg & Larsen, 2017). Only if the distance to the bat and weather data are recorded (which is usually not the case for standard monitoring), can the source sound as emitted toward the direction of the microphone be reconstructed by correcting for geometric and atmospheric attenuation. In addition to these factors that are the focus of this manuscript, other factors cause additional variation in the recorded sound. First of all, variation in the relative orientation of the sonar beam axis and the microphone axis (e.g., due to head movements, beam steering or changes in flight direction) will cause significant variation in recorded call level and spectrum (Ratcliffe & Jakobsen, 2018). Only extended microphone arrays are capable of catching a sufficiently large part of the call to enable identification and reconstruction of the main sonar axis (e.g., Seibert, Koblitz, Denzinger, & Schnitzler, 2015;Surlykke et al., 2009). Further variation can be caused by flight-induced Doppler-shifts of sound frequency, wind and other air turbulences causing variation in sound arrival time and sound level, and temperature-and humidity-gradients causing sound refraction and which cannot be considered by a single local weather measurement.

| Atmospheric attenuation and recorded call level
In most recording situations, the distance between bat and microphone is unknown, resulting in an unknown amount of geometric and atmospheric attenuation (even if weather conditions were known). The total attenuation determines the sound level received at the microphone, and thus the distance over which sounds can be detected. This detection distance will be shorter for faint calls (e.g., those of low-amplitude bat species, or feeding buzzes) than for loud calls (e.g., search calls), resulting in lower detection probabilities for such faint calls, which in turn might be misinterpreted as a lack of low-amplitude bat species and of bat foraging activity. Weatherdependent variation in AA causes additional weather-dependent variation in the received sound level. In turn, this impacts call detection distances and thus call-based estimates of the presence/absence, number, and foraging activity of bats.
From the viewpoint of bats, this daily, seasonal, and spatial variation in atmospheric attenuation appears to be relevant, too, as shown by frequency-adjustments in bats that use echolocation to detect prey over long distances in the open space (Chaverri & Quiros, 2017), and bats emitting high-frequency calls experiencing high atmospheric attenuation (e.g., Jacobs et al., 2017;Maluleke et al., 2017;Mutumi et al., 2016).

| Atmospheric attenuation and call frequencies
The unknown amount of AA causes unknown frequency-specific changes of the recorded call. Measured call frequencies thus vary not only when bats change call parameters (Kalko & Schnitzler, 1993), but also simply when the distance between bat and microphone changes.
This effect is particularly pronounced for high frequencies (i.e., typically the start frequencies of calls) which experience stronger AA than low frequencies. Together with other unknown factors, such as scanning movements of the bat and variation in the relative orientation between call direction and microphone axis, this causes large variation in measured call frequencies between subsequent calls and between different published studies (Thomas, Bell, & Fenton, 1987). This variation is larger for broadband frequency-modulated calls (e.g., Myotis bats, frequency-modulated part of the call of highduty cycle bats such as horseshoe bats) than narrowband calls (e.g., noctule bats, constant frequency part of the call of high-duty cycle bats). Presenting bat call frequencies to an accuracy of less than 1 kHz is for this reason discouraged (in addition to further limitations in frequency resolution of the analysis algorithm, e.g., the FFT size).
Only methods that localize bats in space and compensate for the distance-and frequency-specific AA for each recorded call may allow for higher precision (e.g., Seibert et al., 2015;Surlykke et al., 2009).
This unknown (and thus: noncompensable) variation in frequency parameters, in addition to the naturally existing variability and overlap in call parameters between species, may limit our capability of identifying bat species based on call recordings (Russo & Voigt, 2016;Rydell et al., 2017). This limitation is worse for species-rich areas and for sympatric species with similar call designs (e.g., many Myotis species). In contrast, in areas with less species and/or for species with unique call designs this is less or not problematic. Where limitations exist, these still seem to apply more to automatic species identification than to manual identification by experienced bat researchers, yet both methods are not error-free and require extensive training/ experience and careful validation (Fritsch & Bruckner, 2014).

| Speed of sound
The variation in weather conditions sets a lower environmental limit for the ranging accuracy of echolocation. To convert perceived echo delay into object distance, bats require some internal representation of speed of sound. A mismatch between the internal and real speed of sound will cause errors in the perceived object distance. Varying weather conditions cause variations in the speed of up to 3% leading to distance measurement errors of up to 3% if bats cannot adjust their internal representation. As this is a proportional error, however, the absolute error becomes smaller as the bat approaches an object, from 3 cm at 1 m object distance to only 3 mm at 10 cm object distance. Therefore, I argue that ranging errors caused by unknown variation in speed of sound are negligible for bats, even for the most demanding tasks of pinpointing insects or landing on small twigs.
However, the unknown variation in speed of sound has another consequence on echo delay perception. An average variation in speed of sound of just ±0.5% (Figure 5c) causes an average variation in echo delay of about 30 μs at 1 m object distance. This environmental noise is much larger than the submicrosecond delay accuracy proposed for the bat Eptesicus fuscus (e.g., Moss & Schnitzler, 1989;Simmons, 1979;Simmons, Ferragamo, Moss, Stevenson, & Altes, 1990), yet matches the measured free-flight accuracy of 20-25 μs in the species Glossophaga soricina (Goerlitz, Geberl et al., 2010). Even if bats had submicrosecond delay accuracy, the amount of environmental noise would prohibit a corresponding submillimeter accuracy in absolute target ranging. In contrast, the measurement of relative differences in echo-delay and object-range between two targets, or a single moving target over time, would not be impaired.
Most bioacoustic measurements will be unaffected by variation in speed of sound, except for the acoustic localization of animals in 3D-space based on call time-of-arrival differences (e.g., Fujioka et al., 2016;Goerlitz, ter Hofstede et al., 2010;Hügel et al., 2017;Seibert et al., 2015;Surlykke et al., 2009). Localization errors due to imprecise values for c are mostly oriented along the array-bat-axis (i.e., affecting the estimate of the bat's distance to the array), which is most susceptible to localization errors as comparatively large changes in distance generate only comparatively small and nonresolvable changes in time-of-arrival differences-vice versa, comparatively small changes in time-of-arrival differences cause comparatively large errors in distance. Although this error is rather small (Q3: 8.3%) even for large mismatches in c (5 m/s) and small arrays (60 cm intermicrophone distance), additional error sources such as low signal-tonoise ratio, Doppler shifts or variation in call envelope will impede localization accuracy. Thus, to reduce sound-speed based errors, acoustic tracking should always consider local weather conditions (e.g., Goerlitz, ter Hofstede et al., 2010;Lewanzik & Goerlitz, 2018).

| CON CLUS ION
Weather conditions determine two physical sound parameters that are crucial for bats and researchers: the atmospheric attenuation and the speed of sound in air. Weather-and frequency-dependent variation in atmospheric attenuation causes variation in the received sound level and call spectra, and thus variation in detection distances and call frequencies. In turn, this may limit call-based measurements of the presence/absence and number of bats and bat species identification, depending on the amount of local weather variation and the similarity in call design of the local bat assemblage.

ACK N OWLED G M ENTS
My research is funded through the DFG Emmy Noether Program (grant number GO 2091/2-1). I thank Jens Koblitz, Volker Runkel, Peter Stilz and the members of my research group for discussion and feedback, and Thejasvi Beleyur for help with porting Matlab code to Python and R.

CO N FLI C T O F I NTE R E S T
None declared.

AUTH O R CO NTR I B UTI O N S
HRG conducted all work presented in this article, including research design, data analysis, figure preparation and writing.