Atmospheric propagation modeling indicates homing pigeons use loft-specific infrasonic ‘map’ cues

After more than 50 years of intensive study, how homing and migratory birds navigate over great distances remains an open question (Kennedy and Norman, 2005). Kramer’s (Kramer, 1952) early work on avian orientation with circular cages showed that many birds use the Sun’s azimuthal position as a time-compensated compass, and he proposed a simple ‘map-and-compass’ model to explain their navigational behavior (Kramer, 1953). Support for this model has come from experiments in which homing pigeons have had their internal clocks shifted prior to release: pigeons depart release sites generally in the homeward direction, but those with their biological clocks shifted slow (or fast) with altered light:dark cycles will depart clockwise (or counterclockwise) off the homeward direction in the northern hemisphere (Schmidt-Koenig, 1958; Wiltschko et al., 1994). Apparently, the clock-shifted birds have correctly determined their location relative to home (‘map’ step) before incorrectly interpreting the homeward bearing from the Sun’s azimuth within a shifted time frame (‘compass’ step). Other avian compasses are known to depend on rotation of the stars (Emlen, 1975), inclination of the geomagnetic field (Wiltschko and Wiltschko, 1995) and patterns of skylight polarization (Muheim et al., 2006), but the long-range avian ‘map’ has yet to be understood.

Although the sensory basis of the avian map has been rigorously investigated, no consensus has been reached on which sense or senses are involved (Semm and Beason, 1990; Wiltschko, 1996; Wallraff, 2005). The possibility of birds using visual landmarks for crucial long-range map cues has been eliminated because pigeons fitted with frosted lenses can return from unfamiliar sites >100 km away to within a few kilometers of their loft; sight, however, is required for their final approach (Schmidt-Koenig and Schlichte, 1972; Schmidt-Koenig and Walcott, 1978). Natural infrasounds (low-frequency acoustic waves below the range of human hearing; <20 Hz) have also been considered as possible map cues (Griffin, 1969; Yodlowski et al., 1977; Quine, 1982), but no perennial geographic sources were recognized, and no clear evidence of their use by birds was found (Walcott, 1996). Laboratory tests, however, show that homing pigeons can detect sounds down to at least 0.05 Hz (Kreithen and Quine, 1979), and infrasonic cues remain an attractive option for long-range homing because these signals can travel thousands of kilometers in the atmosphere with little attenuation.

Other experimental results have been interpreted in support of the alternate concepts of birds using either olfactory (Papi, 1989; Wallraff, 2005) or magnetic cues (Walker et al., 2002; Wiltschko and Wiltschko, 2009) as sources of map information. It is difficult to envision, however, how birds can accurately navigate over great distances using as yet unidentified odors that would have to form stable gradients within a turbulent atmosphere. Moreover, empirical evidence indicates that such gradients are unlikely to exist (Becker and van Raden, 1986; Waldvogel, 1987; Waldvogel, 1989). It has also been suggested that birds use gradients of the geomagnetic field (Wiltschko and Wiltschko, 2009), but the poleward gradient in total intensity (<4 nT km^–1), for instance, would likely be obscured by commonly observed crustal magnetizations (∼10–50 nT km^–1) and/or diurnal field variations (∼20–30 nT day^–1) of equivalent or greater magnitude. One or more additional ‘geophysical’ gradients with E–W orientation, necessary for bicoordinate navigation, are also unknown and likely non-existent on large scales. Because the olfactory and magnetic map hypotheses are unresolved, it is possible that birds are using a different set of map cues. Furthermore, birds might not be using a bicoordinate map at all (Gould, 2008), and could be employing some other means of determining their homeward orientation (the term ‘map’, however, will be used here throughout for convenience).

Both Kramer (Kramer, 1959) and Keeton (Keeton, 1973) believed that release-site biases and sites of long-term disorientation are related to irregularities in the avian navigational map. Release-site biases are regular deviations in the orientations of departing birds off the geographic homeward direction and are found at most sites to varying degrees. Moreover, they tend to be consistent at any one site for pigeons from a given loft (Keeton, 1974; Wallraff, 2005). Although generally stable through time, the biases can also change on an hourly, daily or yearly basis (Wallraff, 2005). Additionally, at some release sites pigeons can be completely lost, departing year after year in random directions (Keeton, 1974; Walcott and Brown, 1989). Schmidt-Koenig (in Brown, 1971) pointed out that sites of disorientation are not uncommon, and suggested that at least one such site exists at varying directions and distances to all lofts.

In his investigations of avian navigation, Keeton (Keeton, 1973; Keeton, 1974) concentrated pigeon releases at three sites in upstate NY (Fig. 1) that he felt had particular significance to understanding the avian map: the Jersey Hill fire tower, 120 km W of the Cornell loft in Ithaca, where Cornell birds vanished randomly (Keeton, 1974; Walcott and Brown, 1989); the Castor Hill fire tower, 143 km NNE of the Cornell loft, where birds consistently showed large westward or clockwise biases (∼50 to 90 deg) from the homeward direction (Keeton, 1973; Keeton, 1974); and a site near Weedsport, 74 km N of the Cornell loft, where the birds regularly vanished ∼15 deg clockwise off the homeward direction (Keeton, 1974; Keeton et al., 1974; Larkin and Keeton, 1976).

To determine whether release site biases could be due to atmospheric and/or topographic influences on the transmission of infrasonic cues to pigeon release sites, as suggested previously (Hagstrum, 2000), atmospheric propagation modeling incorporating daily meteorological profiles was undertaken for those days birds were released at Jersey Hill, Castor Hill and Weedsport using a ray-tracing program [Hamiltonian Acoustic Ray-tracing Program for the Atmosphere (HARPA)] (Jones et al., 1986). Ray-tracing theory, in particular, was selected so that propagation directions of the modeled infrasound could be compared with departure bearings of the experimental birds. After Bill Keeton’s untimely death in 1980, an extensive database containing most of his published and unpublished pigeon (Columba livia) release data was made available to all researchers upon request (Brown et al., 1984).

Infrasounds can travel great distances through the atmosphere with little attenuation. Acoustic absorption increases as the square of frequency, so, for example, 90% of the energy of a 1000 Hz tone is absorbed by 7 km (at sea level), and the distance for 90% absorption of a 1 Hz tone of equivalent initial energy is 3000 km, whereas at 0.01 Hz this distance exceeds the circumference of Earth (Bedard and Georges, 2000). In addition, pressure waves from exceptionally powerful explosions (e.g. the Krakatau eruption in 1883, the Tunguska meteorite in 1908 and nuclear tests during and after 1945) have been recorded after traveling several times around Earth (Evers and Haak, 2010). At lower frequencies, wavelengths become longer, and are ∼340 m for 1 Hz and ∼3.4 km for 0.1 Hz tones (Bedard and Georges, 2000).

The static sound speed (C_t) is proportional to the square root of air temperature in K (Fig. 2), and travel directions of infrasonic waves (ray paths) are controlled primarily by temperature and horizontal wind (Norris et al., 2010). Adding or subtracting the horizontal wind speed to C_t in the direction of propagation determines the effective sound speed (C_eff), which is calculated by HARPA and accounts for the combined refractive effects of temperature and wind. Refraction of rays from a ground source back towards the surface occurs at heights in the atmosphere where C_eff is greater than the surface value and can be caused by increasing wind speed (wind shear), temperature (inversions) or both (Evers and Haak, 2010). Horizontal winds also create a moving medium by which sound waves are translated through advection. The normal temperature structures of the troposphere and mesosphere bend infrasonic waves upward, whereas those of the stratosphere and thermosphere refract them back towards the surface (Fig. 2). Sounds refracted upward can cause ‘zones of silence’ or acoustic ‘shadow’ zones up range at ground level that end where the waves return to the surface from either stratospheric or thermospheric ‘reflections’. Atmospheric conditions affecting infrasound propagation can change rapidly (Norris et al., 2010), and seasonal and geographic changes in atmospheric structure are also known to complicate the travel paths of infrasounds from distant sources (Bedard and Georges, 2000).

Between 1968 and 1987, 984 experimentally untreated or control birds from the Cornell loft were individually released on 81 days under sunny skies at the Jersey Hill fire tower (Fig. 1). In almost all cases, the birds departed randomly or nearly so (Fig. 3A) (Walcott and Brown, 1989). Moreover, homing performance was poor: Cornell pigeons released at Jersey Hill had longer flight times and much higher attrition rates than birds released at other sites in NY and PA (Keeton, 1974; Walcott and Brown, 1989). Airplane tracking of pigeons released from Jersey Hill showed that they flew aimlessly about the area for at least 45 min (Keeton, 1974).

Birds returned to and released at Jersey Hill a second and third time had no improvement in homing performance, unlike birds repeatedly released at other sites (Keeton, 1974). Groups of pigeons with small magnets or brass bars attached to them (Keeton, 1971) were also similarly lost at Jersey Hill (supplementary material Fig. S1A,B), and aeromagnetic maps and magnetic surveys made at Jersey Hill showed no indication of an anomalous field there (Brown, 1971; Walcott and Brown, 1989). Remarkably, birds from other lofts located at various directions and distances from Jersey Hill (N, 97 km; ENE, 113 km; W, 121 km; SE, 354 km) were able to orient there and return home to these lofts (Walcott and Brown, 1989), even on those days when Cornell birds were disoriented and homed poorly (e.g. Fig. 3B,C). Walcott and Brown (Walcott and Brown, 1989) conducted a series of experiments at Jersey Hill and concluded that it was not the genetic stock of the birds, but the location of their loft, that determined whether or not they could orient at Jersey Hill.

Results for one release at Jersey Hill on 13 August 1969 stand out: on this day Cornell pigeons were well oriented (Fig. 3D), and their vanishing bearings were tightly clustered to the NE (Keeton, 1974). The next day the birds were returned to Jersey Hill, but they again departed randomly (Brown, 1971). Disorientation of Cornell birds was not restricted to Jersey Hill, but also occurred at other release sites in its vicinity (supplementary material Fig. S2, Table S1). The bulk of the releases made from this region were at Jersey Hill due to the excellent visibility in all directions from its fire tower.

Although departure bearings from a single release at the Castor Hill fire tower (Fig. 1) have relatively little scatter, deviations of mean vanishing bearings under both sunny and overcast skies were mostly large (>50 deg) and clockwise (Keeton, 1973). Pigeons released at Castor Hill and followed by airplane flew 25 to 32 km W before they changed course and headed S toward the Cornell loft (Walcott, 2005). Young birds new to Castor Hill showed greater deviations from the homeward bearing (Fig. 4A) than older, more experienced birds familiar with the release site (Fig. 4B). There was an unusual group of birds, labeled the ‘no-bias’ or F₀ birds, that exhibited lower within-release scatter and substantially smaller mean biases at Castor Hill (Fig. 4C). The offspring of these birds behaved similarly, indicating that their enhanced ability was an inherited trait (Walcott, 2005). Young birds and F₀ birds released on the same day at Castor Hill departed in significantly different directions, consistent with the mean directions for their two groups (Fig. 4D). Control birds released at other sites near Castor Hill showed similar clockwise deflections of their departure bearings off the homeward one (supplementary material Fig. S3). On one day, 22 July 1970, Cornell pigeons released at Castor Hill departed in near random directions (Fig. 4E) and appeared lost (Keeton, 1973).

The most releases of Cornell pigeons at any one site (295) were made from a drumlin just N of Weedsport (Fig. 1). Releases of K birds made up the largest share of these (236). K birds, named after the K index of geomagnetic activity, were experienced Cornell pigeons repeatedly released at single sites under sunny conditions to test for any correlation between their initial bearings and the daily K index at the Fredericksburg Geomagnetic Observatory (VA, USA) (Keeton et al., 1974; Larkin and Keeton, 1976). Groups of K pigeons with magnets or brass bars attached to them were also released at Weedsport, but again the magnets produced no significant effect (supplementary material Fig. S4).

Although the pigeons released at Weedsport were remarkably well grouped and consistent in their departure bearings (Fig. 5B), an extraordinary shift in this bearing occurred on 6 June 1974 (T. Larkin, personal communication). On 5 June 1974 (release 1106) the released birds departed with a mean bearing of 175 deg (Fig. 5C), on 6 June (release 1110) they departed with a mean bearing of 127 deg (Fig. 5B,D) and on 7 June (release 1113) their mean departure bearing was 179 deg (Fig. 5E). Both the K (Fredericksburg, VA, USA) and Kp (planetary) indices indicate that the geomagnetic field was relatively quiet during this period of time (J. L. Gannon, written communication; http:/www.ndgc.noaa.gov/stp/geomag/kp_ap.html).

Sources and characteristics of the experimental pigeon release data, meteorological data and ray-tracing program HARPA are described below. The Keeton database is currently available from C. Walcott at Cornell University (Department of Neurobiology and Behavior, Ithaca, NY, USA), and a program that sorts and displays the database (Keeton) is available from T. Larkin (Abstract Tools, Brooktondale, NY, USA). Unfortunately, not all of the Cornell pigeon release data for Jersey Hill are in the Keeton database, and the full data set shown in Fig. 3A is no longer available. The Keeton database contains a total of 2545 releases, and 40 of these were made at Jersey Hill (42.3519°N, 77.8845°W). Of these, 30 releases of mostly control birds (N=511), which were made on 26 days, were selected for this study (supplementary material Fig. S1C, Table S1). The selected releases also include untreated ‘no-bias’ or F₀ birds (Fig. 3E), and others wearing magnets and brass bars (supplementary material Fig. S1A,B). The data used here are for clearly disoriented birds (supplementary material Fig. S1C), and, because of the normal geomagnetic field at Jersey Hill, it is inferred that the magnetic (or brass) bar treatments were not the cause of their disorientation.

For the Castor Hill fire tower (43.6492°N, 75.8422°W), a total of 62 pigeon releases are in the Keeton database, and 49 releases of control birds (N=678) on 39 days are used here (supplementary material Table S2). Of the 134 releases at Weedsport (43.0965°N, 77.5469°W) involving untreated K birds, 78% had mean vectors with lengths (r) >0.900. From these, releases on 51 days with N≥6 and r≥0.950 were selected for this study, although release 1106 on 5 June 1974 was also included with a r of 0.944 (Fig. 5A, supplementary material Table S3).

Updated meteorological data are available in the lower atmosphere from more than 800 stations worldwide (Parker and Cox, 1995), and are available online from the NOAA/ESRL Radiosonde Database (http://www.esrl.noaa.gov/raobs/). The rawinsonde profiles (including wind direction and speed) used in this study are from the Albany (WMO #72518; 42.45°N, 73.48°W) and Buffalo (WMO #72528; 42.56°N, 78.44°W) weather stations in upstate NY. These data were obtained daily at 00:00 and 12:00 GMT from instrument packages carried aloft by weather balloons that measured various atmospheric parameters and generally reached the lower stratosphere (∼16 km). The 12:00 GMT data (08:00 EDT) were collected closest in time to the Cornell pigeon releases and are used here. The atmospheric HWM-07 wind (Hedin et al., 1996; Drob et al., 2008) and NRLMSIS-00 temperature (Picone et al., 2002) models with global coverage from ground to thermosphere are also used to represent atmospheric conditions above the daily rawinsonde profiles. These two models provide statistical mean estimates for a given date, time and location that are based on data from satellite, radar, ground-based optical observations and rocket probes (Norris et al., 2010).

HARPA is available at http://cires.colorado.edu/~mjones/raytracing/. The program traces three-dimensional paths of acoustic rays through inhomogeneous atmospheres and accounts for both vertical and horizontal refraction, as well as advection (Jones et al., 1986). Zero amplitude is predicted within shadow zones, however, because the propagation effects of diffraction and scattering are not determined (Norris et al., 2010). In this study, the simplest characterization of the atmosphere is made: atmosphere conditions over the entire propagation path are modeled from a single set of profiles, and it should be noted that this representation does not include fine-scale atmospheric structure or define the range-dependent environment. Topographic profiles between the virtual transmitter and receiver (release site), defining the reflecting terrain’s height (Jones, 1982), can also be entered into the program. HARPA accepts only terrain models having smooth surfaces with continuous slope and curvature, and both weather and topographic profiles were represented in HARPA by fitted sequences of linear segments, joined with hyperbolic functions, which effectively smoothed the data sets (Jones et al., 1986).

HARPA launches rays at any azimuth and elevation (angle from horizontal), and program runs were generally made between ±90 deg of the direct azimuth to a given release site at 5, 10 or 20 deg intervals. Within a run, rays were launched at elevations between 0 and 90 deg at 1, 0.5 or 0.1 deg steps. For this investigation, HARPA’s virtual acoustic source was placed initially at the Cornell loft (42.4360°N, 76.4319°W), based on the hypothesis that Jersey Hill sits within an acoustic ‘shadow’ zone relative to the loft area (Hagstrum, 2000). The grounds for selecting this scenario will be discussed more fully in the Discussion.

Ray-tracing runs for the selected days birds were released at Jersey Hill were made using the 12:00 GMT (08:00 EDT) rawindsonde data from Buffalo, NY, and show two modes. In most cases (17 of 26 runs), rays launched westward from the loft are refracted upward above the troposphere as a result of the atmosphere’s daily temperature and wind fields forming an acoustic shadow zone at Jersey Hill (Fig. 6A). For the second mode (eight of 26 runs), rays launched above elevation angles of 4 to 16 deg are similarly refracted upward, but below this angle rays were channeled by wind shear and/or temperature inversions within an ephemeral duct at the surface (Fig. 6B). The ducted infrasound would be expected to arrive at Jersey Hill on these days, but reflections from the actual terrain have not been taken into account. The terrain rises from 313 m at the loft to 679 m at Jersey Hill, and is quite irregular across the N–S grain of the Finger Lakes (Fig. 1). A smoothed topographic profile based on a digital elevation model (DEM) of upstate NY was subsequently included in the HARPA runs (Fig. 6C), and ducted rays were mostly reflected off the terrain at large enough angles to pass upward through the duct (reflected launch angles >4 deg; Fig. 6B). Thus, it appears that little or no sound emanating from the loft area would normally have arrived at Jersey Hill on the release days.

On 13 August 1969, however, Cornell birds were unusually well oriented at Jersey Hill, and the ray-tracing results are distinctly different. Fig. 7A depicts a HARPA run for this day with rays launched directly at Jersey Hill along a 265 deg azimuth; the rays are neither refracted upward above the troposphere nor ducted at the surface. Rays launched at azimuths less than 265 deg are refracted upwards beyond a few tens of kilometers (Fig. 7B), but those launched along azimuths between 275 and 315 deg (e.g. Fig. 7C) are refracted back to the surface NNE of Jersey Hill where, according to Huygens’ principle, the surface-reflected rays would form secondary sources. The location of these secondary sources is generally consistent with a NE departure of birds from Jersey Hill on 13 August 1969 (Fig. 3D). By the next day, 14 August 1969, HARPA runs show that atmospheric conditions had returned to ‘normal’, again placing Jersey Hill within an acoustic ‘zone of silence’ relative to the loft (Fig. 2, Fig. 7D).

To determine how unusual the wind and temperature fields were on 13 August 1969, HARPA runs were made for an additional 122 days, arbitrarily selected between 1 June and 30 September 1978. In the results for modeled days (148 total), rays directed at Jersey Hill (265 deg launch azimuth) were refracted upward above the troposphere on 77 days (e.g. Fig. 6A), formed near-surface ducts as well on 64 days (e.g. Fig. 6B,C), and were similar to the 13 August 1969 result on only 7 days (e.g. Fig. 7A–C). Thus, atmospheric conditions like those on 13 August 1969 in upstate NY are relatively rare, and based on the modeled data would occur ∼5% of the time. Cornell birds were released at Jersey Hill 3 days per year on average, so encountering conditions like those on 13 August 1969 would be unlikely, which is consistent with Keeton’s group having encountered them only once.

Propagation modeling for the Castor Hill release days was performed using the 12:00 GMT (08:00 EDT) rawinsonde data from both the Buffalo and Albany weather stations. Overall, results from the two stations are similar, but those based on the Buffalo rawinsonde data are reported here because the Buffalo station, for the most part, is closer to the acoustic transit paths between the loft and the release site. Rays launched directly at Castor Hill (20 deg azimuth) from the Cornell loft show ephemeral ducting along the surface on 26 of 39 total days, and refraction upward through the troposphere on 13 remaining days. Intervening topography, reaching a maximum elevation of ∼560 m, also tends to reflect the ducted rays upward (Fig. 8A), effectively forming a barrier to ducted infrasound transmission between the Cornell loft (313 m) and Castor Hill (450 m).

A DEM of upstate NY including Castor Hill and the Cornell loft is shown in Fig. 9, along with the mean departure bearings for young birds; older, more experienced birds and F₀ birds released at Castor Hill (Fig. 4A–C). The mean vector for the F₀ birds has been extended by a dashed line to show that it points to a topographic gap in the Appalachian Highlands of southern NY State made by the Lake Cayuga valley (1 in Fig. 9, Fig. 1). Near-surface ducting of rays traveling northward along Lake Cayuga from the loft would form secondary sources for rays traveling directly across the lowlands to Castor Hill once the highlands had been cleared. Propagation runs show that ducted rays along Lake Cayuga (320 deg azimuth) were strongly favored on most of the Castor Hill release days (34 of 39) and on all but two of the 13 days that F₀ birds were released there (Fig. 8B). Near-surface ducting of rays between northern Lake Cayuga across the lowlands to Castor Hill (Fig. 8C) was favored less frequently by the Buffalo and Albany rawinsonde data sets, and, for example, occurred on 22 of the 39 total days control birds were released and on 7 of the 13 days F₀ birds were released at Castor Hill.

Rays launched to the NW from the Cornell loft also show near-surface ducting on 36 of the 39 Castor Hill release days (Fig. 8D), stratospheric reflections on those release days occurring during October and November (10 days; Fig. 8E), and thermospheric reflections on 37 of the 39 release days. Acoustic signals, however, are much more highly attenuated in the thermosphere because of its lower density, so these signal paths will not be considered further. For the stratospheric reflections, return rays intersect the surface at between ∼200 and 300 km from the loft area, far enough to also reach, along with the near-surface ducted rays, potentially return-reflecting terrain along the NE-trending northern shore of Lake Ontario. Infrasonic signals originating from secondary sources at land-surface reflections and returning across Lake Ontario to Castor Hill (Fig. 8F) could explain why young birds, in particular, depart Castor Hill to the W (Fig. 4A). Signals returning to Castor Hill from these secondary sources along the mean departure bearings for each of the release days could have been ducted near the surface of Lake Ontario on 18 days and reflected from the stratosphere on 22 days. On all but eight of the release days, near-surface and/or stratospheric return paths to Castor Hill existed for these westerly secondary sources (e.g. Fig. 8F).

The day Cornell pigeons appeared lost at Castor Hill, 22 July 1970 (Fig. 4E), was one of 8 days that HARPA runs showed weak to no near-surface ducting or stratospheric reflections of rays to the W of Castor Hill. Apparently, near-surface ducting of infrasound from the loft along Lake Cayuga and across to Castor Hill was also problematic on this day: runs using weather data from Albany support ducting along Lake Cayuga (320 deg azimuth) but not across to Castor Hill (40 deg azimuth), and runs with Buffalo weather data indicate near-surface ducting along a 40 deg azimuth, but not a 320 deg azimuth. Thus, it is likely that no infrasonic cues were transmitted to Castor Hill from the Cornell loft area on the one day that released Cornell pigeons appeared lost there.

HARPA runs for the Weedsport release days were also made using the Buffalo 12:00 GMT (08:00 EDT) rawinsonde data. The results for 21 May 1974 have been selected as representative of pigeon releases at Weedsport (supplementary material Table S3), and Fig. 10A shows a HARPA run for this day along the direct azimuth (353 deg) from the Cornell loft (Fig. 9). As the modeling shows, infrasound was most often transmitted along this azimuth within near-surface ephemeral ducts, with some rays having been reflected upward by prominent topographic features; therefore, a diminished number of rays and weakened homeward signal likely reached the release site. Ducting (e.g. Fig. 6A, Fig. 7D, Fig. 10D) was observed along the 353 deg azimuth on 47 of the 51 days selected for this study (supplementary material Table S4). Similar to Castor Hill, modeling results show that near-surface ducting along the 320 deg azimuth, aligned with the southern Lake Cayuga valley (1 in Fig. 9), was also favored (49 of 51) on the Weedsport release days (Fig. 10B). On most days (43 of 51), infrasound was ducted across from Lake Cayuga to Weedsport with little or no attenuation of rays by surface reflections along the 7 deg azimuth (Fig. 9, Fig. 10C). Thus, although some level of infrasound from the loft area was often transmitted directly to Weedsport, more intense levels likely arrived there from a path along Lake Cayuga and across to Weedsport that avoided the direct azimuth’s higher intervening topography (Fig. 9).

Generally, near-surface ducting of rays launched from the Cornell loft along the Fall Creek valley (40 deg azimuth) was not favored (Fig. 9, Fig. 10D), and little to no ducting occurred along this azimuth on 29 of the 51 Weedsport release days (supplementary material Table S4). Again, 6 June 1974 appears to have been an exceptional day (see Fig. 5D), here in terms of weather conditions. Although ducting occurred along the 40 deg azimuth from the Cornell loft on this day (Fig. 10E), it did not occur along the 353, 320 or 7 deg azimuths (Fig. 11). Infrasound ducted NE from the loft would tend to pass through the lower elevation valleys, and could have traveled along the Fall Creek, west branch of the Tioughnioga River and Tully valleys (5, 6 and 7 in Fig. 9) before arriving at Weedsport from near the observed 127 deg mean departure bearing (Fig. 5D).

Propagation modeling using Buffalo meteorological data, however, indicates that infrasound transmitted N through the Tioughnioga River and Tully valleys, with azimuths similar to 7 and 353 deg, respectively, would have been refracted upwards on 6 June 1974 (Fig. 9). The propagation of infrasound through these valleys would likely have involved diffraction and/or scattering of the acoustic waves, which, unfortunately, cannot be determined by HARPA. In addition, ducted rays traveling across to Weedsport from the northern end of Tully Valley along a 307 deg azimuth were reflected upward by intervening topography (Fig. 10F). Departure bearings of Cornell pigeons released on 6 June 1974 from Weedsport were somewhat spread out, but a significant number of birds selected a more easterly bearing (∼120 deg) than the mean (Fig. 5D, Fig. 10E,F), which corresponds to more topographically subdued and non-obstructive terrain (Fig. 9). Thus, even though HAPRA runs indicate that infrasound from the loft area would not have arrived at Weedsport from the SE on 6 June 1974, this result is probably inaccurate because of an incorrect azimuth (307 deg) and the limitations of HARPA.

That pigeons from other lofts in upstate NY, even those from a loft just 24 km W of Ithaca, could regularly orient at Jersey Hill (e.g. Fig. 3B,C) when Cornell birds could not indicates that a loft’s direction and distance from a release site are of crucial importance to the map function (Walcott and Brown, 1989). This is supported by observations that release-site biases tend to be consistent for birds from a given loft (Keeton, 1974; Wallraff, 2005). Moreover, the rare occurrence of Cornell birds orienting and homing directly from Jersey Hill, or departing Weedsport in an extraordinary direction to the SE, both coincident with unusual atmospheric conditions (Fig. 3D, Fig. 7C, Fig. 10E), shows that the atmosphere is likely an integral factor in the avian map. The generally observed hourly to daily changes in release-site biases (Wallraff, 2005) also point to processes acting on atmospheric time scales as the probable cause of these changes.

A map cue that can be absent at some sites while present at others, be available at a single site for birds from one loft but not others, and change rapidly depending on atmospheric conditions is in all likelihood an acoustic one, and, because of the distances involved, must be infrasonic. Thus, disorientation of Cornell birds at Jersey Hill can be readily explained by a shadow zone in the region relative to a single source area associated with the Cornell loft (Fig. 6A,C). An avian acoustic map consisting of multiple sources of infrasonic signals at various directions and distances from Jersey Hill can be ruled out because it would be highly unlikely, under variable atmospheric conditions, for multiple shadow zones to consistently overlap there over a 20-year period (Fig. 3A).

In a previous study (Hagstrum, 2000), I suggested that infrasonic signals possibly used by homing pigeons could come from the ubiquitous ground-to-air coupling of microseismic waves in steep-sided terrain. Microseisms are composed mostly of surface waves continuously generated in the solid earth by non-linear interactions of oceanic waves with similar frequencies traveling in nearly opposite directions. These seismic waves have frequencies that range from ∼0.1 to ∼0.5 Hz with a spectral peak at ∼0.2 Hz (Rind, 1980; Arrowsmith et al., 2010). Microseisms are recorded globally by seismic stations, even within deep continental interiors, and often define the background noise levels on seismic recordings. The average ground displacement due to microseisms ranges from ∼0.5 to ∼5 μm, and can be related to dominant sources in the North Atlantic and Pacific Oceans that follow the seasonal pattern of oceanic storms in the northern and southern hemispheres (Rind, 1980; Kedar et al., 2008; Arrowsmith et al., 2010).

Although continuous acoustic radiation coupled with the land surface has not been isolated in records from infrasound arrays, the ground-to-air coupling of higher amplitude earthquake-generated surface waves in mountainous terrain has often been observed at arrays distant to these sources (Young and Greene, 1982; Le Pichon et al., 2002; Le Pichon et al., 2003; Le Pichon et al., 2006; Arrowsmith et al., 2009). For example, a magnitude (M_L) 4.3 earthquake occurred on 28 April 2007 near Folkestone, UK, in a region of relatively subdued topography. Infrasound from the coupling of surface waves proximal to the epicenter was recorded at a station (FLERS) located ∼284 km to the SSW in France. Modeling of a 23 km stretch of 75-m-high coastal cliffs between 1 and 18 km from the epicenter as a series of 305 pistons independently generating acoustic waves produced synthetic microbarograms in close agreement with the FLERS station’s recordings (Greene et al., 2009).

Acoustic wavelengths are inversely proportional to frequency, and an infrasound tone of 0.2 Hz has a wavelength in air of 1.7 km at room temperature (e.g. Bedard and Georges, 2000). The total ground area needed, vibrating in unison with 1 μm amplitude at 0.2 Hz, to generate an overall signal that pigeons can hear at a 1 km range at ∼120 dB SPL (Kreithen and Quine, 1979), would be on the order of 1 km² (B. Thigpen, written communication; A. J. Bedard, Jr, written communication). Dimensions of the infrasonic source areas can also be inferred from the accuracy of pigeon homing: experiments in which frosted lenses were fitted over pigeons’ eyes prevented them from seeing landmarks in the loft’s vicinity needed for their final approach (Schmidt-Koenig and Walcott, 1978). Even so, these birds were able to return within 0.5 to 5 km of their loft (supplementary material Fig. S5). Regions of subdued terrain might result in larger acoustic source areas surrounding the loft, resulting in less accurate homing at close range in the absence of sight. The switch to sight navigation by pigeons near their loft would presumably occur once the birds had entered the acoustic source area.

Thus, birds distant to their home terrain could be identifying its characteristic acoustic radiation from steep-sided facets, normal to their position, continuously excited within a narrow frequency band by microseismic energy. Because sound intensity from a given source follows the inverse-square law, birds at distances increasingly beyond ∼1 km from their loft area would probably be listening to acoustic radiation from an expanded area of steep-sided terrain oriented toward their position and generating sound pressure levels that they could hear. However, the acoustic energy from intervening horizontal surfaces would be directed vertically upward and appear acoustically transparent to birds at distant points. Homing pigeons must be trained at varying directions and increasing distances from their loft area in order to develop and hone their navigational abilities. During this process the birds may be learning to recognize their loft area’s changing acoustic signature from the different release locations.

Another plausible source of characteristic infrasound from the loft area could be the scattering of direct microbaroms off topographic features (M. Haney, written communication); only those features with dimensions similar to or larger than the infrasonic wavelengths would cause significant scattering. Microbaroms are continuous atmospheric waves generated by the same oceanic sources as microseisms, and have a similar frequency band and peak. Moreover, they generally show amplitudes of a few microbars and are readily detected by infrasonic arrays worldwide (Rind, 1980; Willis et al., 2004). The sources of microbaroms are of large aerial extent, and these sound waves measured at distance rapidly de-correlate spatially, compared with point sources, which could possibly mask scattering effects (A. Bedard, Jr, written communication). Microbaroms, although conventionally regarded as sources of ambient noise, are prevalent within the atmosphere, and would most likely have higher amplitudes than locally coupled microseismic radiation. Moreover, these atmospheric oscillations might contain useful information concerning the nature of their origins, characteristics of their propagation and, for surface-reflected waves, terrain features between source and receiver locations (Arrowsmith et al., 2010).

A fundamental question raised by this acoustic hypothesis for the avian map is how pigeons, having a binaural distance of only a few centimeters, can detect the directionality of infrasonic cues that have wavelengths of ∼1.7 km. The problem of characterizing long-wavelength signals with much smaller, but transportable, antennae is solved in radar signal processing by placing the receiver on a movable platform (e.g. airplane, spacecraft) relative to the target area (ground surface). Flying birds can thus produce simulated or ‘synthetic’ apertures from their flight paths that are equivalent to those for stationary infrasonic arrays of similar dimensions that incorporate multiple sensors (Curlander and McDonough, 1991). In addition, Doppler shifts are particularly useful in synthetic aperture techniques for accurately determining target azimuths, and Quine and Kreithen (Quine and Kreithen, 1981) have shown that laboratory pigeons can detect frequency shifts of infrasonic signals designed to simulate natural Doppler shifts resulting from changes in their flight paths (e.g. 7% at 1 Hz). Homing pigeons flying in circles or other patterns at constant velocity prior to departing release sites (supplementary material Fig. S6) could be forming the synthetic apertures necessary to determine homeward directions using their loft area’s low-frequency acoustic signals.

Cornell pigeons were perhaps disoriented at Jersey Hill because of its location within a stable acoustic shadow zone relative to the loft area (Fig. 6A,C) that was caused by prevailing atmospheric conditions and obstructing terrain. Apparently, sites surrounding Jersey Hill were also within this shadow zone, because Cornell birds released there had similar problems determining their homeward bearing (supplementary material Fig. S2). The disorientation of Cornell birds at Jersey Hill indicates that the missing signal, most likely a map cue, is crucial to their navigational system. Presumably the pigeons’ solar and magnetic compasses were functioning at Jersey Hill during the experimental bird releases there under sunny skies, but apparently no alternative map cue was available for their use in homing. Cornell pigeons leaving Jersey Hill and returning to Ithaca might have flown off in random directions until they encountered (or did not encounter) acoustic signals from the loft area that were no longer deflected from the birds’ position by intervening topography and/or atmospheric wind and temperature fields. Similarly, pigeons released at Castor Hill on 22 July 1970 that appeared lost might have lacked an acoustic signal from the loft area until after they had disappeared from view.

At Castor Hill, Cornell pigeons were possibly detecting two separate acoustic signals that traveled along different paths from the loft area, and this could explain why groups of young birds and older, more experienced (i.e. F₀) birds departed in two significantly different directions on the same day. The signals from acoustic rays traveling along Lake Cayuga (1 in Fig. 9) and across to Castor Hill in near-surface ducts would have been attenuated by repeated reflections from the irregular ground surface (Fig. 8C) as irregularities comparable in size to the acoustic wavelength would scatter the waves, diminishing their acoustic intensity. Acoustic signals traveling within near-surface ducts or by stratospheric reflection to the W of Castor Hill at ranges that included the N shore of Lake Ontario, and possible reflection back across the featureless lake (Figs 1, 9), were likely of higher intensity and therefore more easily detected by the younger birds (Fig. 4A). The older, more experienced birds might have been able to detect both infrasonic signals from the loft area, but could have had difficulty selecting between them, and thus chose to depart in intermediate directions (Fig. 4B, Fig. 9). The F₀ birds, for whatever inherent reason (signal detection, processing), might have been able to recognize the direct, but possibly more attenuated, homeward signal from the SSE after it had been channeled a significant distance (∼100 km) across the ground surface from the Lake Cayuga valley (Fig. 8B,C, Fig. 9).

Similar to Castor Hill, the clockwise release-site bias at Weedsport probably resulted from the pigeons’ response to higher intensity infrasonic signals arriving there from the Cornell loft area after traveling along the Lake Cayuga valley (1 in Fig. 9) and around the intervening highlands. Some signals, however, do travel directly to Weedsport from the loft area, and this could explain why a significant number of birds released at Weedsport departed in the homeward direction. The brief and dramatic shift in atmospheric conditions that occurred on 6 June 1974 apparently favored transmission of homeward infrasonic signals NE of the loft along major valleys; these signals ultimately could have arrived at Weedsport from the SE. The details of this transmission are problematic, however, because of the inability of HARPA to model diffraction and scattering of acoustic waves. The spread in individual pigeon departure bearings from Weedsport along intermediate azimuths on 6 June 1974 (Fig. 5D, Fig. 10E,F) might have been caused by the transmission of additional homeward signals to Weedsport through the Otisco, Skaneateles and Owasko Lake valleys (4, 3 and 2 in Fig. 9).

Through modeling and other factors described above, it is inferred that Cornell pigeons released at Jersey Hill, Castor Hill, Weedsport and elsewhere were able to recognize the directionality of infrasonic signals from their loft area using Doppler shifts while flying in circular or other patterns at constant velocity immediately after release (e.g. supplementary material Fig. S6). Having thus established the homeward direction, it would then be necessary for the birds to register it as a compass bearing for use during the return flight home. Presumably, this would involve the magnetic rather than the sun compass, because the magnetic compass is available under both clear and overcast skies. Moreover, young pigeons apparently use their innate magnetic compass to learn their time-compensated sun compass (Wiltschko and Wiltschko, 1981), indicating its fundamental role in the pigeon’s navigational system.

The sun compass, after its acquisition, might then serve to calibrate the magnetic compass in a manner similar to how some migratory birds calibrate their magnetic compass using patterns of skylight polarization at sunset (Muheim et al., 2006). During this calibration, clock-shifted pigeons could rotate their magnetic compass, and the registered homeward direction, into the shifted solar reference frame and thus depart in a shifted direction. Older, more experienced clock-shifted birds, however, usually depart in directions with less than the predicted shift (Wiltschko et al., 1994), and may be compromising between the homeward (magnetic) direction and the shifted sun direction, perhaps based on the perceived strength of the homeward infrasonic signal. Many clock-shifted birds arrive at their loft on the day of release, indicating that at some point they correct for their initial compass error (Wiltchko et al., 1994). Returning pigeons might at any point begin circling or flying back and forth (zigzagging) in order to check their orientation, and, if necessary, re-establish the homeward compass course.

Microseisms and microbaroms are the highest-amplitude ‘noise’ continuously generated within the Earth and atmosphere (Rind, 1980), and the terrain-coupled or scattered signals from these sources, respectively, would be of approximately the same frequency (∼0.2 Hz peak). The annual decline in homing performance during winter months observed with European pigeons (Gronau and Schmidt-Koenig, 1970; Wallraff, 2005) could be caused by jamming of the ground-based navigational signals by direct microbaromic waves from winter storms in the North Atlantic channeled eastward by westerly stratospheric winds. Similarly, the reluctance of pigeons to fly over large bodies of water (Wagner, 1972) could be caused by obscuring noise directed upward from ocean and lake surface waves (Hagstrum, 2000). Furthermore, pigeons in Switzerland were able to home below but not above atmospheric temperature inversions (Wagner, 1978), and this could be explained by the inversion trapping ground-based infrasonic signals below it (Hagstrum, 2000).

HARPA runs using contemporaneous meteorological data from the Buffalo and Albany weather stations show similar results, indicating that atmospheric conditions were relatively stable across the acoustic transit paths between the Cornell loft and Keeton’s release sites in upstate NY. Differences between data sets for the same day and time are most commonly seen, however, in the presence or absence of near-surface ephemeral ducts. The interaction between terrain and prevailing weather patterns is likely responsible for the stable nature of release-site biases, and rapid shifts in atmospheric conditions (Norris et al., 2010) could be the cause of short-term changes observed over hours to days (Keeton, 1974; Wallraff, 2005). Propagation modeling with HARPA using available meteorological data from the late 1960s and 1970s apparently can resolve the most significant changes in acoustic signal transmission that might, for example, indicate whether pigeons can orient, or depart in unusual directions, at a given site on a given day.

More accurate modeling that could resolve the more subtle variations in signal transmission and resulting pigeon behavior would require more detailed meteorological data. Furthermore, HARPA uses one set of rawinsonde profiles to represent the entire atmosphere, and because, for example, Castor Hill is relatively far from either the Buffalo (243 km) or Albany (233 km) weather stations, any local and/or short-term (<12 h) changes in conditions between weather station and transit path cannot be determined. Ideally, for this type of analysis, detailed atmospheric data along the entire acoustic transit path between transmitter and receiver sites would be available. Even so, the propagation modeling presented here provides useful approximations of infrasound transmission across upstate NY coincident with the Keeton pigeon releases.

I am most grateful to M. Jones for providing HARPA and guidance in its use, L. Baker for his indispensable help in getting HARPA up and running on USGS computers, W. T. Keeton and his co-workers for producing the Cornell pigeon-release database and making it available to other investigators, C. Walcott for sending me the Keeton database, T. Larkin for providing the program Keeton and other information concerning the Keeton database and Weedsport releases, and P. Spudich, W. Wiltschko, R. Wiltschko, A. Bedard, Jr, B. Thigpen, M. Haney, D. Norris, M. McKenna, D. Drob, J. Spritzer and R. Blakely for enlightening discussions. Many thanks are also due A. Bedard, Jr, D. Fee, M. Haney, M. Jones, T. Larkin, H. McIsaac, P. Muffler, J. Phillips, V. Tsai, C. Walcott, W. Wiltschko and R. Wiltschko for commenting on early versions of the manuscript. The final manuscript also benefited from reviews by A. Bedard, Jr, and an anonymous referee.