Atmospheric conditions conducive to long-range transmission of low-frequency sound as used by elephants are found to exist in the Etosha National Park in Namibia during the late dry season. Meteorological measurements show that strong temperature inversions form at the surface before sunset and decay with sunrise, often accompanied by calm wind conditions during the early evening. These observations are used in an acoustic model to determine the sensitivity of infrasound to the effects of (a) the strength, thickness and elevation of temperature inversions, and (b) the growth and decay of an inversion typical of dry, elevated African savannas. The results suggest that the range over which elephants communicate more than doubles at night. Optimum conditions occur 1–2 h after sunset on clear, relatively cold, calm nights. At these times, ranges of over 10 km are likely, with the greatest amplification occurring at the lowest frequency tested. This strong diurnal cycle in communication range may be reflected in longer-lasting changes in weather and may exert a significant influence on elephant behaviour on time scales from days to many years.

The systematic study of the use of sound by animals accelerated greatly as a result of advances made in underwater acoustics during the Second World War. Watkins and Wartzok (1985) review marine mammal sensory and communications systems and provide a list of some 67 species of marine animals whose sounds have been recorded. Spiesberger and Fristrup (1990), in a paper dealing with bird calls, review the transmission of sound in the atmosphere and the ocean and describe processes in each fluid that influence the transmission of sound. They draw upon the analogy between light and sound and treat high-frequency sound transmission in the atmosphere in terms of rays.

Payne et al. (1986) were the first to document the use of low-frequency sound or infrasound by elephants. Initial studies of elephants begun in zoos (Payne et al. 1986; Langbauer et al. 1989) were extended to the wild (Poole et al. 1988; Langbauer et al. 1991). These studies show that elephants use infrasound with fundamental frequencies from 14 to 35 Hz for long-distance communication at ranges up to 4 km. The apparent selection of low-over high-frequency sound by these animals may have been because the transmission of sound of higher frequency is limited in range by atmospheric attenuation. Evolutionary selection for long-range low-frequency communication would be further enhanced by the existence of a low-frequency sound channel. The sound channel would have to be relatively stable and contain relatively still air (low wind speeds), otherwise wind noise would prevent communication.

In this paper, evidence is presented that a high savanna environment that is typical for Loxodonta africana has atmospheric conditions conducive to low-frequency sound transmission. The physical and mathematical conditions that must be met in order to describe low-frequency sound transmission are shown to be compatible with atmospheric conditions typical of the African savannas. Temperature profiles measured above such a savanna show that strong nocturnal inversions replace daytime lapse conditions. Nighttime cooling stratifies the air near the ground, often resulting in calm conditions and reduced wind noise at the surface. An acoustic model predicts that, under these conditions, low-frequency sound propagation is enhanced and ranges of communication are maximized soon after sunset. The findings contribute to the interpretation of elephant behaviour and provide clear-cut hypotheses which can be tested in the field.

Low-frequency sound transmission in the atmosphere

Theoretical considerations

Sound propagation in a stratified atmosphere is approximated by the Helmholtz form of the acoustic wave equation:
formula
and by the effective speed of sound, ceff:
formula
where c = γRT = the speed of sound = ω/k, ω is angular frequency, k = 2’πf/ceff = wave number, f is the frequency, w is the horizontal component of wind in the direction of propagation, γ = Cp/Cv = 1.4, which is the ratio of specific heats at constant pressure, P, and constant volume, V, R is the gas constant for air (287 J kg−1 K−1), T is atmospheric temperature (K), p is the pressure amplitude of the sound wave, ∇ is a del operator, see equation 3 below, 3 is a unit impulse function, and x, y and z are spatial variables in a Cartesian coordinate framework.

The wave equation provides a description of the transmission of sound in a fluid medium such as the atmosphere or the ocean (Rayleigh, 1878; Pierce, 1981). A complete solution of the wave equation in the atmosphere is both mathematically and computationally impractical because the speed of sound and the fluid velocity vary unpredictably in space and time.

Solutions for sound of audible or higher frequencies may be obtained by the ray approximation, in which the acoustic-wave equation is simplified to treat sound in terms of rays in the form of the Eikonal equation (Pierce, 1981). In this form, sound travels along ray paths that are determined by solving Snell’s Law governing refraction through the medium. The intensity of the sound at the receiver is then the sum of the intensities of all the rays reaching the receiver by all possible paths (Fig. 1). The ray equation is also referred to as the high-frequency solution because it is valid when the acoustic wavelength is small, compared with the length scale over which significant change occurs in the atmospheric refractivity.

Fig. 1.

Ray approximation in which rays (A) are bent through a stratified atmosphere, (B) received directly from the source and (C) reflected off the ground.

Fig. 1.

Ray approximation in which rays (A) are bent through a stratified atmosphere, (B) received directly from the source and (C) reflected off the ground.

The ray approximation does not hold at low frequencies in the atmosphere. At low frequencies, a large portion of the wavefront, rather than the few locations assumed in the ray approximation, contributes to the received signal. Analogy to slit diffraction illustrates these concepts (Fig. 2). As parallel waves approach a wall at normal incidence, their behaviour on the other side of a slit in the wall depends on their frequency. High-frequency waves (Fig. 2A) look like rays, but low-frequency waves (Fig. 2B) are strongly diffracted and spread much more widely. Only the ray can be said to have directionality.

Fig. 2.

(A) High-frequency transmission through a slit approximated by a ray on the other side of the wall. (B) Low-frequency transmission through a slit spreading by diffraction on the other side of the wall. z, altitude.

Fig. 2.

(A) High-frequency transmission through a slit approximated by a ray on the other side of the wall. (B) Low-frequency transmission through a slit spreading by diffraction on the other side of the wall. z, altitude.

For low-frequency (15–30 Hz) atmospheric sound transmission, which is the focus of this paper, a more complete solution of the wave equation must be used. The atmosphere is assumed to consist of n homogeneous layers (Fig. 3) with layer n next to the ground and layer 1 the highest layer that has any significant effect on the sound levels at the height of interest. For each layer, the Helmholtz equation (equation 1) operates for a harmonic point source of angular frequency, ω, and wave number, k, and is solved in cylindrical coordinates where:

Fig. 3.

Layered atmosphere bounded by the ground and a top layer, in which the top layer is the highest layer of interest at the ground.

Fig. 3.

Layered atmosphere bounded by the ground and a top layer, in which the top layer is the highest layer of interest at the ground.

formula
where r is the horizontal distance from the source and < is the azimuth angle. If cross-wind effects are negligible, azimuthal symmetry may be assumed and equation 3 reduces to:
formula
This is the two-dimensional cylindrical form of the Helmholtz equation, which can now be reduced to a one-dimensional equation by a Hankel transform:
formula
where is the pressure transform, r is the horizontal radial distance from the source, z is altitude, J0 is the 0th-order Bessel function of the first kind, and K is the transform variable corresponding to r.
This yields a form of Bessel’s equation in the transformed domain:
formula
where zS is the source height.
Discrete samples of the wave number space can now be obtained, and equation 5 can be approximated by a Fast Fourier Transform. The pressure variable p(r,z) at a range of points is yielded by a single transform. This method, because of its computational speed, is called the Fast Field Program or FFP (Lee et al. 1986). Equation 6 is then solved with an impedance boundary condition at the ground and a radiation boundary condition at the top of the atmosphere. Equation 6 is a one-dimensional Helmholtz equation in a layered medium and can be solved by a variety of techniques. In the particular FFP used for calculation in this paper, the equation is solved using a transmission line analogy for wave propagation in layered media giving p(K,z). The inverse Hankel transform:
formula
is then computed, yielding p(r,z), the acoustic pressure field.
In the sections that follow, pressure fields will be discussed in terms of the sound pressure level (SPL). The SPL, given in decibels (dB), is defined by:
formula
where P2 and Pr2 are, respectively, the mean squared pressure at the point in question and at a reference distance (Pierce, 1981; p. 61). In this paper, the SPL is taken relative to the sound pressure at 1 m from the source. The FFP computations in this study were performed on an RS6000 computer at the University of Virginia, USA.

Physical factors

Practical application of the above theory still requires that a number of assumptions be made as well as consideration of other physical effects, not dealt with above, which may influence low-frequency sound propagation in any given situation.

Simplifications include the assumption that the emitting source is stationary; that the sound emitted is a simple sine wave of angular frequency, ω, radiating equally in all directions; that the acoustic response is linear, i.e. twice the source pressure will result in twice the pressure at the receiver; and that there is no seismic contribution, i.e. there is negligible transmission in the earth’s surface.

Physical effects that may influence low-frequency sound propagation in the atmosphere include ground attenuation, the effects of topography, scattering by vegetation, atmospheric absorption, attenuation by turbulence and wind shear, and the effects of temperature gradients.

Over a perfectly hard, flat surface, sound levels will be doubled as a result of reflection. Real surfaces have a complex impedance, which Attenborough (1985) has modelled as a function of flow resistivity, porosity and pore and grain shape factors. The Attenborough four-parameter model is incorporated into the FFP. Vegetation can reduce impedance by loosening the soil. Reduced impedance causes a loss of strength and a phase change in the reflected signal. The phase change causes a shadow effect, which reduces sound levels at long distances. Impedance is frequency-dependent: surfaces are more reflective of lower frequencies, and low-frequency sound produces ground and surface waves which penetrate the shadow zone. Only very porous or nonresistive soils, soft sand and thick forest humus (Price et al. 1988) have a sufficiently low impedance to attenuate sound of a frequency of 30 Hz or less by more than 6 dB over 10 km. At 15 Hz, all but the softest surfaces are almost perfect acoustic reflectors; for example, even snow has little effect below 100 Hz (Nicolas et al. 1985). Topography with slopes of less than 1° can noticeably reduce shadow zones (Piercy et al. 1977). Canard-Carauna et al. (1990) provide corroboration that a mild upward slope can increase enhancement. Robertson et al. (1989) performed a numerical study of the effects of a triangular ridge 100 m high on low-frequency sound propagation. Peak topographic enhancement occurs at or in front of the ridgetop on the slope facing the source, and peak attenuation occurs at the base of the ridge on the far side. The shadow zone is extended when the ridge is closer to the source. At 10 Hz, this can cause a 5 dB enhancement at the ridgetop and a 5 dB attenuation at the base of the ridge on the far side. The enhancement and attenuation increase to 10 dB at 20 Hz. If the ridge is downwind from the source, a strong acoustic shadow can develop behind the ridge. For upwind propagation, sound levels behind a ridge are enhanced relative to those measured over flat ground. Similar effects to those noted above have been modelled for higher-frequency sound using ray-tracing (Lamancusa and Doroux, 1993).

Vegetation, depending on geometry, can increase or decrease sound levels. Canard-Carauna et al. (1990) found that the narrowing of a forest gap in the direction of propagation enhanced 63 Hz sound levels by 3 dB. Scattering from vegetation, particularly large tree trunks, can significantly attenuate sound. However, theory suggests that scattering is only significant when the size of the scatterer is of the same magnitude or larger than the wavelength of the sound. The largest trees have diameters of perhaps 3 m, while 30 Hz sound has a wavelength of more than 10 m and 15 Hz sound has a wavelength of more than 20 m in the atmosphere. Thus, infrasonic communication should not be strongly affected by scattering from vegetation. In an experimental study of sound propagation in a forest, Price et al. (1988) found that from a peak at about 250 Hz attenuation fell sharply as the frequency decreased to 100 Hz, the lowest frequency tested.

Atmospheric absorption of sound is significant at audible frequencies, exceeding 40 dB per 100 m at the upper range of human hearing. In the infrasonic range, absorption is essentially nonexistent under normal conditions, never exceeding 1 dB per 10 km for frequencies below 30 Hz and relative humidity above 20% (Bass et al. 1990; Zuckerwar and Meredith, 1984). Under extremely dry conditions (relative humidity well under 5%), absorption may have some importance, since an attenuation of up to 1 dB per 1000 m is possible for completely dry air.

Wind is highly detrimental to low-frequency sound communication. Wind noise from intrinsic turbulence is proportional to ρUu′, where ρ is the air density, U is the wind speed (typically the average speed over a 5–15 min period) and u′ is the average instantaneous fluctuation speed. Wind noise grows rapidly with wind speed and fluctuation speed, increasing, for example, by approximately 20 dB as wind speed increases from 3 to 10 m s−1. Hot-wire anemometer studies (Morgan and Raspet, 1992) show that wind noise at 20 Hz is approximately 10 dB greater than that at 200 Hz. This is because the majority of the turbulent kinetic energy in the atmosphere lies below 40 Hz. These turbulent pressure fluctuations, although not sound by its strict definition as a propagating pressure wave, are nonetheless indistinguishable from sound when measured by instruments or by the ear and form an important source of random noise. Induced turbulence, which is highly dependent on receiver geometry, also adds to wind noise and makes the effects of wind noise difficult to quantify (Schomer et al. 1990). However, it is generally true that communication range will be greatly degraded under windy conditions.

The effect of turbulent scattering on low-frequency sound transmission is small (Daigle, 1979). This is because the scattering strength of atmospheric turbulence for infrasound is proportional to the product of the square of the average index of refraction (μ2) and to the square of the the wave number (k2), both of which are small for the atmospheric propagation of infrasound.

Changes in atmospheric temperature with height above the surface have a marked effect on sound transmission. In general, lapse conditions, in which the atmospheric temperature decreases with height, are upward-refracting and tend to decrease sound levels near the surface. Shadow zones may be formed, beyond which, according to ray theory, sound propagation is forbidden. Inversions, in which temperature increases with height, are downward-refracting and will increase sound levels. Canard-Carauna et al. (1990) observed an enhanced acoustic signal around sunset and sunrise compared with the middle of the day. These correspond to the times of formation and decay of temperature inversions. Similarly, wind shear tends to enhance propagation downwind and to attenuate it upwind. This makes propagation directional and effectively degrades two-way communication. A downward-refracting atmosphere increases acoustic energy levels near the surface, but at the same time causes multiple ground reflections. Since acoustic energy is lost with each bounce, ground attenuation can be greater with distance under extreme temperature gradients or wind shear than under moderate gradients or shear (Raspet et al. 1992).

The impact of each of the above factors upon the transmission of low-frequency sound as estimated by the FFP depends upon the surface and atmospheric conditions encountered in the field. These are addressed in the section below.

Surface and atmospheric conditions in the field

Okaukuejo (latitude 19°S, longitude 16°E), in the south-central part of the Etosha National Park of Namibia, was chosen as the field site. Field measurements were taken from 1 September to 15 October 1992 at the end of the dry season. The location, at 1100 m, is typical of the elevated dry African savannas. The topography is largely flat. The savanna vegetation in Etosha often thins to open grassland and the surface is stony, with extensive areas of calcrete.

Continuous measurements of temperature, humidity, pressure and wind velocity were made at Okaukuejo at two levels (5 and 10 m) above ground. Global radiation (solar direct + solar diffuse) and rainfall were also measured. Specialized low-level soundings measuring temperature, humidity, pressure and wind speed and direction were made from the surface to about 1.5 km using a tethered balloon system. The tethered balloon measurements of air temperature shown in Fig. 4 provide high vertical (<10 m) and time (every hour) resolution of the temperature structure in the lowest 1300 m of the atmosphere. Soundings by the tethered balloon were concentrated around sunset and sunrise, which are times of rapid change in the thermal structure of the atmosphere near the surface. Measurements during the rest of the day and night, when little change was taking place, were made less frequently. Routine upper air soundings, which penetrate to much greater eights in the atmosphere than the tethered balloon measurements, were made twice a day at 12:00 h and 24:00 h Universal Time (UT). These soundings are not capable of providing either the vertical space resolution or the necessary time resolution to capture the thermal structure delineated by the tethered balloon measurements. Measurements of soil and air temperatures from 10 cm below the surface to 2 m above the surface were also made.

Fig. 4.

Tethered balloon soundings of temperature at Okaukuejo at 17:00 h LST (solid line), 18:00 h sunset (long-dashed line), 19:00 h (short-dashed line) and 20:00 h (dotted line) on a clear, calm evening (18 September 1992).

Fig. 4.

Tethered balloon soundings of temperature at Okaukuejo at 17:00 h LST (solid line), 18:00 h sunset (long-dashed line), 19:00 h (short-dashed line) and 20:00 h (dotted line) on a clear, calm evening (18 September 1992).

The period of measurement, at the end of the dry season prior to the onset of the summer rains, was characterized by dry, cloudless conditions. The larger-scale weather pattern was typically dominated by the south Atlantic subtropical anticyclone, with high-pressure ridging extending over the subcontinent (Garstang et al. 1994). It rained on two of the 45 days in the field, giving a total of 4 mm of recorded precipitation. Twenty-three of the field experiment days were essentially cloud-free. Cloud cover on 5 days reduced the measured solar insolation to less than 50% of the integrated clear day value.

Under these conditions, outgoing long-wave radiation from the surface exceeds incoming solar radiation as early as 16:00 h Local Solar Time (LST). Local Solar Time (UT+1 h) is used because of the importance of the radiative balance (solar minus terrestrial radiation) on surface temperatures. Sunrise and sunset are at approximately 06:00 h and 18:00 h LST. From this point until after sunrise the next day, the surface cools in response to long-wave radiational losses. The most rapid cooling takes place during the late afternoon and soon after sunset, creating a strong low-level inversion, as illustrated in Fig. 4. With the formation of this nocturnal inversion, stability increases and the surface layers of the atmosphere are thermally decoupled from the deeper atmosphere. The inversion may weaken later during the night in response to mixing (wind), but will remain in place until after sunrise.

The above conditions are typically accompanied by a strong diurnal cycle in wind speed and direction (Fig. 5). Daytime wind speeds may be either strong or weak depending on synoptic weather conditions. However, because of the decoupling of the surface layer mentioned above, nocturnal speeds are usually weak, dropping to calm or low speeds after sunset, as shown in Fig. 5. Roughly one-third of all days in the field had an early evening wind minimum similar to that shown in Fig. 5. Topographically induced slope winds are observed at Etosha after 20:00 h LST (Fig. 5) (Preston-Whyte et al. 1994). The topographic winds weaken the nocturnal inversion through mixing. Thus, although the low-level inversion may persist through the night, it frequently reaches its maximum in the early evening. In contrast to the nighttime conditions, daytime surface heating under clear skies is intense. Super-adiabatic conditions, in which temperature drops rapidly with height above the hot surface, can prevail from mid-morning to mid-afternoon. Days with significant surface winds (greater than 7 m s−1) result in moderate turbulent mixing and adiabatic lapse rates.

Fig. 5.

Wind direction (A) and wind speed (B) at 10 m above the ground at Okaukuejo over 24 h (18 September 1992). Time is in Local Solar Time (LST) with sunrise near 06:00 h and sunset near 18:00 h.

Fig. 5.

Wind direction (A) and wind speed (B) at 10 m above the ground at Okaukuejo over 24 h (18 September 1992). Time is in Local Solar Time (LST) with sunrise near 06:00 h and sunset near 18:00 h.

The surface and atmospheric conditions as encountered in the field, together with the known effects on low-frequency sounds, eliminate a number of effects from consideration while identifying others as crucial to the propagation of low-frequency sound. Effects which are essentially eliminated from consideration are scattering by vegetation and turbulence, upslope enhancement, downslope degradation and wind shear. In each case, the above effects are less pronounced for low than for high frequencies, but all are at a minimum or negligible in the Etosha location. This is due to the intrinsic nature of the site: hard, flat ground, with sparse vegetation and small slopes. It may also be due to the physical nature of the system, where wind speeds at certain times may drop to low or calm values. Effects encountered in the field that remain crucial to frequencies used in elephant communication (14–35 Hz) are limited to the role of vertical gradients of temperature, wind and wind noise. Wind noise grows rapidly both with average wind speed and with the speed of turbulent fluctuations. Both these wind noise effects, however, are at a minimum at certain times of day. Thus, low-level vertical gradients of air temperature emerge as the single most important physical factor controlling the transmission of low-frequency sound under the conditions described in this paper.

Inversion sensitivity studies

In this section, the FFP model is used to determine the sensitivity of low-frequency sound propagation to the vertical gradients of air temperature immediately above the surface. Three characteristics of temperature inversions are examined: inversion strength, inversion thickness and the height of the inversion above the ground. These three characteristics are then combined in a simulation of inversion growth and decay. The vertical lapse of temperature is considered between the surface and 200 m above the surface. Atmospheric effects on the propagation of low-frequency sound generated at the surface are not considered above a height of 200 m. The propagation of two sound frequencies, 15 and 30 Hz, is considered in this 200 m thick surface layer. The two frequencies chosen represent the highest and lowest frequencies used by elephants for long-range communication (Payne et al. 1986; Langbauer et al. 1989). The source of the sound at these frequencies is considered to be a point source at 2.5 m and the receptor to be at 3 m above the surface. The sensitivity of the calculations to source and receptor heights was tested and found to be insignificant for heights between 1 and 10 m. The heights chosen in the range 1–10 m are thus not critical, but are close to the heights of the possible sound generators and receptors of an adult elephant.

Fig. 6A provides a reference adiabatic lapse rate. Fig. 6B shows a typical super-adiabatic lapse rate near the surface changing to an adiabatic lapse rate above 50 m, which is usual on a hot, clear day in Etosha National Park. The composite daytime sounding of temperature (Fig. 6B) consists of three sections. In the first 10 m above the ground, the temperature decreases logarithmically from 40 to 30°C. Between 10 m and 50 m, the temperature decreases linearly by 1°C over 40 m. Above 50 m, the temperature decreases at the dry adiabatic rate of 0.98°C per 100 m.

Fig. 6.

Reference and case study temperature lapse rates based upon Okaukuejo soundings between the surface (0 m) and 200 m. (A) Reference (theoretical) sounding: dry adiabatic lapse rate. (B) Reference sounding: super-adiabatic lapse rate immediately (0–50 m) above the surface typical of hot surface daytime conditions. (C) Case study sounding: strength of the inversion ranging through six strength levels between the surface and 50 m above the surface, 0, 1, 2, 3, 5 and 10°C. (D) Case study sounding: a 5°C inversion, 10, 20, 30, 40, 50, 100, 150 and 200 m thick. (E) Case study sounding: elevation of the inversion where a 5°C inversion 10 m thick is elevated from 0 to 150 m above the surface. (F) Case study sounding: growth of the inversion from 1°C strength and 10 m height to 5°C strength and 50 m height. (G) Case study sounding: decay of the inversion where a 5°C, 50 m inversion decays in stages 1–5 from 50 m thick to an elevated 10 m thick inversion.

Fig. 6.

Reference and case study temperature lapse rates based upon Okaukuejo soundings between the surface (0 m) and 200 m. (A) Reference (theoretical) sounding: dry adiabatic lapse rate. (B) Reference sounding: super-adiabatic lapse rate immediately (0–50 m) above the surface typical of hot surface daytime conditions. (C) Case study sounding: strength of the inversion ranging through six strength levels between the surface and 50 m above the surface, 0, 1, 2, 3, 5 and 10°C. (D) Case study sounding: a 5°C inversion, 10, 20, 30, 40, 50, 100, 150 and 200 m thick. (E) Case study sounding: elevation of the inversion where a 5°C inversion 10 m thick is elevated from 0 to 150 m above the surface. (F) Case study sounding: growth of the inversion from 1°C strength and 10 m height to 5°C strength and 50 m height. (G) Case study sounding: decay of the inversion where a 5°C, 50 m inversion decays in stages 1–5 from 50 m thick to an elevated 10 m thick inversion.

Fig. 6C–E isolates three factors that may influence low-frequency sound transmission: (1) the strength of the inversion; (2) the thickness of the inversion; and (3) the elevation of the inversion. Fig. 6F,G combines these factors to show the growth and decay of an inversion considered typical of African savannas. In each instance, we have constrained the limits of change to be within or close to values observed in the field and detailed by Garstang et al. (1994). For example, the most extreme inversion modelled (Fig. 6C) is a lapse of 10°C per 50 m. The most extreme ground-level inversion observed at Etosha National Park during the experiment was 9°C over 50 m.

The calculations for each of the above three inversion cases must assume surface (ground) characteristics. Hard ground (flow resistivity = 500×103 kg m−2 s−1), including the real and imaginary parts of the impedance, has been taken as representative of surface conditions in the Etosha National Park. Such an assumption produces an enhancement of low-frequency sound transmission under non-refracting conditions of about 6 dB near the source, decreasing to 3 dB at 10 km from the source. This surface effect is included in all the cases that follow. Temporal changes, however, are the subject of this paper, and the ground impedance will not change significantly in the dry season from day to day or over the whole season.

In a homogeneous atmosphere and far from the ground, sound travels in a spherical wave and the sound pressure level (SPL) drops by 6 dB for each doubling of distance from the source (see, for example, Pierce, 1981, p. 43). The acoustic enhancement, defined by removing the spherical wave component from the calculated SPL, is the increase in SPL due to ground effects and atmospheric inhomogeneities. The acoustic enhancement is the negative of the more commonly used excess attenuation, when the latter is used correctly. This has been a source of confusion throughout the literature. The graphs that follow depict the acoustic enhancement, rather than the SPL, in order to emphasize the effects of inhomogeneities in temperature with height.

Inversion strength

Fig. 7A, for a frequency of 15 Hz, and Fig. 7B, for a frequency of 30 Hz, show the effects of inversion strength on sound propagation. The temperature fields used in the FFP model are those of Fig. 6C, with an increase in temperature between the surface (0 m) and 50 m above the surface, and adiabatic conditions prevailing above 50 m. Effects under adiabatic and super-adiabatic lapse conditions (Fig. 6A,B) are shown for comparison, as are results for isothermal conditions between the surface and 50 m (Fig. 6C).

Fig. 7.

Effects of inversion strength (in°C) on sound transmissions at frequencies of (A) 15 Hz and (B) 30 Hz for conditions depicted in Fig. 6C.

Fig. 7.

Effects of inversion strength (in°C) on sound transmissions at frequencies of (A) 15 Hz and (B) 30 Hz for conditions depicted in Fig. 6C.

Enhancement increases with inversion strength for both frequencies. For 15 Hz (Fig. 7A), a 5°C inversion gives an enhancement of 12–15 dB for all ranges exceeding 0.8 km. This may be thought of as a duct in which sound pressures in all directions are at least four times greater than those of a reference adiabatic atmosphere at all distances from 1.6 km up to 10 km.

The ducting effect is not as strong for 30 Hz (Fig. 7B); the enhancement diminishes more with distance but, compared with propagation in the adiabatic atmosphere, the pressure is tripled beyond 2.5 km. The inversion profiles for both frequencies contrast even more strongly with the super-adiabatic case, in which the enhancement lessens greatly with distance, becoming negative beyond 1–2 km.

The oscillations in the 10°C case are due to mode interference, an effect beyond the scope of this paper (for details, see Raspet et al. 1992). Sound levels received at long ranges depend on the energy trapped in the surface duct and on ground attenuation. In Fig. 7B, the 10°C gradient gives less enhancement than the weaker inversions. Although it traps more energy, the extreme gradient results in multiple ground reflections and enhanced losses with distance. This is more pronounced at 30 Hz, because the ground impedance effects are greater for this frequency than for 15 Hz. This same effect would be observed in Fig. 7A if the predictions were extended to even longer ranges.

Inversion thickness

Fig. 8A,B shows the effects of inversion thickness on acoustic enhancement for inversions of strength 5°C and 0 m elevation (Fig. 6D). For 15 Hz, the increase in enhancement is large for thicknesses between 10 and 30 m. Additional thickness, greater than 30 m, has little further effect on enhancement. For 30 Hz, there is little change in enhancement once thicknesses equal or exceed 20 m.

Fig. 8.

Effects of inversion thickness (in m) on sound transmissions at frequencies of (A) 15 Hz and (B) 30 Hz for conditions depicted in Fig. 6D.

Fig. 8.

Effects of inversion thickness (in m) on sound transmissions at frequencies of (A) 15 Hz and (B) 30 Hz for conditions depicted in Fig. 6D.

The salient point is that even a shallow inversion (20–30 m) may strongly enhance sound propagation. Since inversions tend to grow rapidly in thickness as sunset approaches and radiative cooling sets in, a sharp increase in low-frequency sound propagation can be expected before and immediately after sunset. This suggests that the enhancement of low-frequency sound propagation approaches a maximum within 1–2 h after sunset.

Mode interference effects (oscillations) are quite pronounced for inversion thicknesses greater than 100 m. Oscillations are a function of stability, so signal fluctuations are likely as inversion thickness increases. A steady signal is therefore more likely during the early evening, when the inversion is still shallow.

Elevation of the inversion

Fig. 9A,B shows the effects of changing the height above the surface of a 5°C inversion with a thickness of 10 m. As shown in the section above, changing the thickness of the inversion to more than 20 m has little further effect on the thickness, the increase in enhancement is much less. Actual inversions (Fig. 4) show a rapid and simultaneous growth in both strength and thickness, exceeding 5°C and 50 m within 2 h of sunset. The changes in low-frequency transmissions due to inversion growth and decay are examined in this section.

Fig. 9.

Effects of inversion elevation (in m) on sound transmissions at frequencies of (A) 15 Hz and (B) 30 Hz for conditions depicted in Fig. 6E.

Fig. 9.

Effects of inversion elevation (in m) on sound transmissions at frequencies of (A) 15 Hz and (B) 30 Hz for conditions depicted in Fig. 6E.

In the model of evening inversion formation (Fig. 6F), the strength and thickness intensify from 1°C and 10 m to 5°C and 50 m. The model of morning inversion decay (Fig. 6G) shows how surface heating simultaneously decreases the strength of the inversion, elevates it and decreases its thickness, giving rise to an adiabatic layer from ground level to the base of the inversion. Figs 10 and 11 show the effects of evening growth and morning decay of the inversion on sound propagation. The temporal progression of acoustic enhancement follows the numbered sequence of growth and decay used in Fig. 6F,G.

Fig. 10.

Effects of the growth of an evening inversion on sound transmissions at frequencies of (A) 15 Hz and (B) 30 Hz for conditions depicted in Fig. 6F. Numbers 1–5 refer to stages of growth, see text.

Fig. 10.

Effects of the growth of an evening inversion on sound transmissions at frequencies of (A) 15 Hz and (B) 30 Hz for conditions depicted in Fig. 6F. Numbers 1–5 refer to stages of growth, see text.

Fig. 11.

Effects of the decay of a morning inversion on sound transmissions at frequencies of (A) 15 Hz and (B) 30 Hz for conditions depicted in Fig. 6G. Numbers 1–5 refer to stages of decay, see text.

Fig. 11.

Effects of the decay of a morning inversion on sound transmissions at frequencies of (A) 15 Hz and (B) 30 Hz for conditions depicted in Fig. 6G. Numbers 1–5 refer to stages of decay, see text.

Fig. 10A shows that the change in sound amplification is Surface greatest between stages 1 and 3. By stage 4, the enhancement for 15 Hz has reached 14.3 dB at 4750 m from the source. The sense of change at 30 Hz (Fig. 10B) is the same as that at 15 Hz, but with a maximum enhancement of 13 dB observed much closer to the source (1450 m).

Morning decay of the inversion (Figs 6G, 11A,B) shows transmission levels similar to the maximum values reached in the evening, but the decay is much more rapid (large changes between stages 3 and 5). The effects of decreasing strength are initially offset by increasing elevation.

The effects of evening development and morning decay of the inversion on the propagation of sound suggest that acoustic transmission of 15 or 30 Hz sound. This observation guided our choice of the thickness (10 m) of the inversion to be tested for changes in elevation.

A large increase in enhancement of more than 10 dB at 10 km occurs when the height of the base of the inversion changes from 0 m elevation to a height of 10 m. Changes in elevation between 10 m and 50 m above the surface have little further effect at 15 Hz. At 100 and 150 m above the surface for 15 Hz, and at 50 m and above for 30 Hz, mode interference (oscillation) occurs. This may be the result of transferring a strong inversion (5°C over 10 m) to elevations as high as 50–150 m above the surface. The large increase in transmission between the surface and 10m demonstrates the effect of ground attenuation on long-range sound propagation in an inversion. Ground interaction is reduced as the inversion lifts off the surface.

Inversion growth and decay

The studies isolating the strength and thickness effects discussed above both show that enhancement in sound propagation occurs early in the development of the inversion, rapidly reaching a maximum. Beyond 3°C strength or 20–30 m enhancement should reach a maximum early in the nocturnal cooling cycle and decay rapidly with daytime heating. During the night, development of local circulation fields responding to surface cooling will weaken the inversion and hence reduce the enhancement of low-frequency sound transmission.

Standardized evening inversion

A standard evening inversion (SEI) representative of the optimum evening conditions at Etosha National Park can be used to illustrate the combined effect of all the inversion characteristics considered upon low-frequency sound transmission. An SEI with a strength of 5°C, a thickness of 50 m and with the base of the inversion at the surface (profile 5, Fig. 6F) is assumed. Fig. 12 contrasts the acoustic enhancement in an SEI with the enhancement during adiabatic and super-adiabatic conditions. Fig. 12A, for 15 Hz, shows that there is more than 12 dB enhancement at 4 km, with enhanced values of just under 10 dB persisting beyond 10 km. Fig. 12B, for 30 Hz, shows a similar enhancement within 1 km of the source, after which the signal attenuates to zero enhancement at 10 km. The results for both frequencies contrast strongly with daytime super-adiabatic conditions, which show a rapidly falling enhancement reaching -20 dB by 4 km. The 12–50 dB difference in enhancement between evening and daytime conditions for distances beyond 2 km represents a four-to 300-fold increase in sound pressure. Comparison of the SEI calculations with results based on an adiabatic atmosphere show that, for SEI conditions, sound levels increase by 9–20 dB, a three-to tenfold increase in sound pressure beyond 2 km. The transition from adiabatic to SEI conditions takes place rapidly before and immediately following sunset.

Fig. 12.

Response of sound transmission to a standardized evening inversion (SEI) for frequencies of (A) 15 Hz and (B) 30 Hz, where an SEI consists of a 5°C inversion at the surface over a depth of 50 m. The effects of an SEI are compared with the effects of an atmosphere with super-adiabatic and adiabatic lapse rates on sound transmission.

Fig. 12.

Response of sound transmission to a standardized evening inversion (SEI) for frequencies of (A) 15 Hz and (B) 30 Hz, where an SEI consists of a 5°C inversion at the surface over a depth of 50 m. The effects of an SEI are compared with the effects of an atmosphere with super-adiabatic and adiabatic lapse rates on sound transmission.

Payne et al. (1986), Langbauer et al. (1989, 1991) and Poole et al. (1988) leave little doubt that elephants respond to low-frequency sounds in the range 14–35 Hz. They also demonstrate that elephants can generate sounds in these frequencies up to levels of 103±3 dB (mean ± S.D.) at 5 m from the source. Langbauer et al. (1991) show, from the studies carried out in the Etosha National Park, that under the conditions of that experiment, elephants responded to low-frequency sounds over distances of at least 2 km. They postulated from the Etosha study that the range of low-frequency sound communication was likely to be at least double the observed value, i.e. at least 4 km, since their broadcasts were made at half the sound pressure levels they had recorded from elephants making sounds of the same categories. Martin (1978) suggests that elephant groups in Zimbabwe communicate over distances of up to 5 km.

These workers have suggested that low-frequency calls are vital to elephant reproduction because females are typically in oestrus for only 2–4 days every 4 years and reproductive males may not be in close proximity to these females. Although reproduction is not confined to males in musth, dominant males in musth are the preferred partners, adding yet another variable to the reproduction cycle. Musth and oestrus both being limiting factors, the importance of long-distance communication is increased. Males in musth use low-frequency sounds to avoid encounters with each other. Matriarchs in herds and females in groups with calves use a range of sounds to remain in contact and to signal various events, including the approach of other elephants (Poole et al. 1988). Martin’s (1978) work suggests that elephant groups use low-frequency sound to maintain range separation and to minimize competition for resources. This suggestion has recently been strengthened by the results of a season in which W. R. Langbauer, R. A. Charif, R. B. Martin and K. B. Payne radio-collared 16 elephants from separated family groups. The collars were capable of transmitting the vocalizations of the animals as well as their locations (K. B. Payne, personal communication). It is of interest to note from our results that the distance over which such communications could be sent would increase as a function of drought. Clear, dry atmospheres with a low moisture content, typical of drought conditions, would produce the most pronounced and frequent (consecutive evenings) nocturnal inversions. This would maximize the distance between groups and minimize wasteful expenditure of energy in competing for severely depleted resources.

The results of our study suggest that the efficiency of elephant communication is a function of weather conditions. Communication is optimized during the dry season and on dry days in the wet season. A pronounced maximum in the frequency and effectiveness of the communications should be observed starting an hour or so before sunset and reaching a peak 1–2 h after sunset. This would happen with the greatest probability on clear, dry, calm and (relatively) cold evenings. Communication using low frequencies should work best at night. Nocturnal winds, which are often produced by topographic features, including modest and distant sloping land surfaces, increase surface wind speeds and turbulence, weakening or even breaking down the surface nocturnal inversion. Thus, optimum conditions might not prevail long into the evening or night. Nocturnal conditions, however, are predictably better than daytime conditions. Communication using low frequencies will not be as effective in daytime compared with nighttime conditions, particularly where the surface has a low heat capacity and warms rapidly to high temperatures. Under such conditions, super-adiabatic lapse rates prevail just above the surface and sound transmission is severely attenuated owing to the absence of inversion ducting and enhancement of turbulent fluctuations in temperature and velocity. J. H. Poole (personal communication) has noted an early evening peak in elephant social activity with associated levels of vocalization.

Under optimum inversion conditions, there is no reason why elephants cannot communicate over distances of 10 km. Inversion effects amplified the lower more than the higher of the two frequencies tested. Under typical inversion conditions, sound levels at 15 Hz are greater than those at 30 Hz for all distances greater than 1 km. For long-range communication, elephants might favour the lower over the higher end of the range of frequencies they have been observed to use (14–35 Hz).

The distance over which communication can be effected will be optimized in terms of time (year, season, day, time of day), place (terrain, vegetation, soils) and the relationship between the place and its weather. If behaviour is limited by the range of communication elephants can achieve, changes in weather on time scales greater than the diurnal should produce a change in behaviour that is commensurate with the effects of these weather changes on low-frequency sound propagation. Day-to-day storm or synoptic-scale changes as well as monthly to seasonal (wet and dry) differences in communication range induced by weather should be discernible in behaviour. Long period (decadal) and large spatial variations (regional to subcontinental) in climate patterns which produce alternating dry and wet conditions should result in changes in patterns of communication. The larger spacing of elephant groups under dry conditions is not only dictated by resources but is made possible by the meteorological conditions governing communication. The competition for localized resources, such as water, may also be influenced by enhanced long-range communication. Elephants in dry conditions might converge to drink most frequently in the early evening, as noted by K. B. Payne (personal communication) and many others. Kinship groups often assemble en route to waterholes or synchronize their arrivals at waterholes. The occurrence of this behaviour in the early evening or at night may be a response to the fact that low-frequency sounds propagate best under dry conditions at these times. Laws et al. (1975, p. 164) report observations from the Galana Ranching Scheme and the Tsavo National Park in Kenya, suggesting that elephants adopt a routine of drinking at night under dry conditions. One of the authors (M. Lindeque) has noted that, at the beginning of the rainy season, elephant herds leave the southern reaches of the Etosha National Park and migrate northeastwards up to 2 weeks before other herd animals initiate a similar migration. This observation raises the possibility that elephants are reacting to low-frequency sound generated by thunderstorms moving into northeastern Namibia at the end of the dry season.

A knowledge of the atmospheric controls on acoustic enhancement can be used in understanding, controlling and preserving elephants. It is possible that elephant range is in part related to the factors that control distance of communication, thus influencing the amount of territory occupied by the animals. Given the enhanced acoustic transmission conditions of early evening, the identification and tracking of individual animals may be possible. Certainly, the tracking of entire herds by infrasound should be feasible. A knowledge of the nocturnal enhancement of low-frequency sound transmission may help in attempts to develop acoustic fencing or warning systems. Similarly, a knowledge of infrasound could be used to minimize stress transmitted to neighbouring groups during culling operations.

Our findings suggest that the use of low frequencies as a means of communication by terrestrial animals should be treated in a broad biophysical context. The observation, interpretation and prediction of terrestrial animal communications can be greatly enhanced by the use of numerical models based on physical and biological field measurements.

The field work for this study was carried out within the framework of the Southern African Fire–Atmosphere Research Initiative (SAFARI), a multinational programme under the auspices of the International Geosphere–Biosphere Program. The field work was supported by Grant ATM-92-07924, awarded by the National Science Foundation to the University of Virginia, directed at the characterization of aerosols over southern Africa. Support of students in the field was also generously provided by the Eugene P. and William E. Odum Foundation. SAFARI was carried out with the approval and kind cooperation of the Namibian government. Field operations at Okaukuejo in the Etosha National Park were made possible by the generous support and cooperation of the Director and staff of Etosha Ecological Institute and the Chief Ranger and his staff. We draw, in an interdisciplinary study such as this, upon the talents and contributions of many groups and individuals. In particular, we wish to recognize the University of the Witwatersrand for their overall administration of SAFARI, the University of Natal for operating the surface meteorological tower and upper air sounding system, the Council for Industrial and Scientific Research of South Africa for the tethered balloon measurements and the South African and Namibian Weather Bureaux for overall support of weather observations. Not only were these contributions essential but they were also provided with the utmost enthusiasm. We are most grateful for this help. This paper draws upon a dissertation to be submitted by D.L. as part of the requirements of the PhD degree at the University of Virginia. Ideas central to this paper were initially discussed with Mr Richard Garstang.

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