Tracking near-surface atmospheric conditions using an infrasound network

Acoustic waves with frequencies below 20 Hz, or infrasound, can propagate long distances with minimal intrinsic attenuation or dispersion (Diamond, 1963). This characteristic makes infrasound a powerful remote sensing tool for probing the atmosphere (Drob et al., 2003; Herrin et al., 2008). Previous studies of the atmospheric properties using volcano infrasound (Antier et al., 2007; Fee and Garcés, 2007), and the experiment presented here, have utilized intense, continuous infrasound, which can be detectable at tens to hundreds of kilometers. Some sources of infrasound, natural and man-made, are sporadic, including hurricanes, avalanches, earthquakes, and most volcanic eruptions (Johnson et al., 2004).

Some volcanoes, such as Kilauea, are active for years (Heliker and Mattox, 2003) and produce high amplitude infrasound that can be recorded locally and regionally (Fee and Garcés, 2007; Garcés et al., 2003) and can be used as a tool to track changing atmospheric conditions. This study takes advantage of a particularly ‘loud’ and persistent infrasound source, the Halema`uma`u crater at the summit of Kilauea, which became active on March 12, 2008. This vent hosts an active convecting lava pond with prodigious and continuous degassing and intermittent explosive events (Patrick et al., 2008). Corresponding infrasound radiation has been reliably intense (more than 10 Pa when reduced to 1 km) and provides an ideal opportunity to probe the atmosphere near a volcanic vent.

We deployed a three-station network around the rim of Kilauea Caldera, HI from July 7–9, 2008. Over the course of 45 h, the network operated continuously. Each infrasound station had an infrasonic microphone, which utilized an AllSensors MEMS differential pressure transducer that operated in a quasi-absolute mode. A capillary tube with $50μm$ diameter and 2 cm long equilibrated barometric changes, this tube created a mechanical filter with frequency cutoff around 0.02 Hz, which was well below the primary band of volcanic sound, which was between 0.25 and 20 Hz. The rms noise floor of the sensors between 1 and 10 Hz was 5.75 mPa, which was about three orders of magnitude below the typical recorded signal levels. Data were acquired continuously to 24-bit Reftek RT130 digital acquisition systems and sampled at 100 Hz.

The three infrasound stations (VOL, ARR, and HVO) were deployed at various azimuths (45°, 85°, and 350°) and comparable distances (3.5, 2.4, and 2.1 km respectively) around the Halema`uma`u vent (Fig. 1). During our study, interval infrasound records are characterized by continuous signals with peak amplitudes up to 15 Pa when scaled to 1 km (using an inverse pressure falloff with distance). The spectral analysis of the records shows two pronounced energy bands, the highest intensity between 0.5 and 1.5 Hz and another between 2.5 and 3.5 Hz. Infrasound recorded across the network shows very high coherency, especially in the lower band [see Fig. 2(b)].

The relative delay times of acoustic phases at pairs of stations (⁠$ΔtARR-HVO$ and $ΔtVOL-HVO$⁠) and the corresponding correlation coefficient (⁠$rARR-HVO$ and $rVOL-HVO$⁠) is determined by comparing 3 min infrasound tremor windows with 2 min overlap. Delay times correspond to the peak correlation coefficient. Figure 2(a) shows the relative delay times for 5 h of continuous activity as a function of band-limited infrasound signal and Fig. 2(b) shows the time evolution of the corresponding correlation coefficients (cross correlogram). Regions of no data (shown as white) correspond to window comparisons with low correlation coefficients (below 0.5). High correlation is generally evident at low frequencies (0.5–1.5 Hz) suggesting either higher source energy and/or lower ambient noise in this band. Low values of $rARR-HVO$ for intermediate frequencies (2–4.5 Hz) may be related to propagation phenomena, potentially associated with crater rim diffraction. The relative arrival times for peak correlated phases was found to vary by up to 0.2 s in $ΔtARR-HVO$ and up to 0.4 s in $ΔtVOL-HVO$⁠, which is about 3% to 4% of the estimated time of flight from source to receivers.

Kilauea Caldera is at 1200 m above sea level and located about halfway between windward and leeward coasts. Trade winds from the east-northeast with magnitudes between 6 and 9 m/s tend to characterize the daytime summer conditions (Chen and Nash, 1994). The caldera is located to the south of the 4169 m Mauna Loa Volcano. At night the mountain breeze prevails and forces the trade winds away from the island. The mountain breeze is characterized by northwest wind with magnitudes of 3–5 m/s (Chen and Nash, 1994).

Records of air temperature, wind direction and speed are archived from two local weather stations, KEAUMO (11.5 km northwest of the vent and 1706 m), and the HVO weather station (2.1 km north and 1250 m). KEAUMO is operated by the Western Regional Climate Center and the HVO weather station is operated by the Hawaiian Volcano Observatory. KEAUMO station was located on the flanks of Mauna Loa, 500 m above the Kilauea’s rim within the influence of the mountain breeze.

The weather station operated by the Hawaii Volcano Observatory was located at the rim of Kilauea Caldera near to our infrasound station HVO. Although the HVO weather station was located at the periphery of the area sampled by our infrasound network it is important to note that its anemometer was near ground level and provided only a point source observation of the wind field. The technique described here is able to recover average atmospheric conditions between the infrasound source at Halema`uma`u Crater and infrasound recording sites 2.3 to 3.6 km from the vent. This spatially averaged wind field arguably has greater utility for meteorologists and volcanologists interested in macro-scale wind field properties.

Atmospheric temperature and winds affect the propagation of acoustic waves. The sound speed $(C)$ is proportional to the square root of the absolute temperature (⁠$T$ in kelvin) of the atmosphere, i.e., $C=γRT$⁠, where $R$ is the molar gas constant $(R=8.3145J/mol/K)$⁠, $γ$ is the adiabatic index (1.4 for diatomic gas). The speed of acoustic waves $(V)$ in a horizontally moving medium is (Diamond, 1963)

where $u⃗$ is the mean wind, and $n⃗$ is the unit vector normal to the wavefront. Using Eq. (1) under the assumption of homogeneous atmosphere (non-refracting atmosphere) and mean wind $u⃗=uxi⃗+uyj⃗$⁠, the equations that determine the relative delay times at pair of stations in our network are

where $dARR$⁠, $dHVO$⁠, and $dVOL$ are the distances from the vent to stations ARR, HVO, and VOL respectively. $n⃗ARR=axi⃗+ayj⃗$⁠, $n⃗VOL=bxi⃗+byj⃗$⁠, and $n⃗HVO=hxi⃗+hyj⃗$ are the unit vectors (and their Cartesian components) between source and respective stations.

Considering the typical atmospheric conditions at Kilauea, wind speed is less than 3% of the intrinsic sound velocity. An approximation using the first terms of a Taylor series expansion can then be applied to Eqs. (2) and (3) as follows:

Calculating the sound speed $(C)$ from the temperature record of the HVO weather station, Eqs. (4) and (5) form a system of two linear equations with two unknowns (⁠$ux$ and $uy$⁠), which can be solved algebraically.

Equations (4) and (5) were solved for the Cartesian components of wind $ux$⁠, and $uy$ using the delay times determined from the cross-correlation analysis in the 0.5–1.5 Hz bandwidth. The sound speed used in this inversion was determined using the temperature records from the weather station located at HVO. Figure 3 shows the results of the inversion for wind magnitude and direction along with the meteorological station records from Keaumo and HVO weather stations. Our inversion shows two main weather regimes defined by prevailing winds. The first regime, occurring during the daytime, is characterized by wind speeds of 7–9 m/s originating from azimuths between 90° and 120° and is consistent in magnitude and direction with summer trade winds. The second regime occurs at nighttime and is characterized by wind speeds of 3–5 m/s and more scattered azimuths between 60°–100°.

In this inversion, we assumed the point measurements of temperature at weather station HVO was representative of the entire area and used it to estimate the intrinsic sound velocity. We tested this assumption and its influence in the results by performing a sensitivity analysis of this parameter. In this analysis, we inverted the system using fixed values of sound speed, i.e., 320 $(−19°C)$⁠, 343 $(18°C)$⁠, and 355 $(40°C)m/s$⁠, corresponding to various fixed temperatures. Comparing with previous results (sound speed varies with temperature), modeling results show that inferred wind magnitude and direction are only affected by extreme choices of intrinsic sound velocity. Future studies could use a network of four or more stations to solve simultaneously for the wind field and a homogeneous temperature.

We assumed that the propagation in our model is non-refractive. With our source-receiver geometry (vertical distances less than 150 m and horizontal distances between 2.4 km to 3.5 km), the vertical gain influences less than 2% in the total propagation distances. The elevation angles are lower than 2°. In this geometry, the horizontal propagation is predominant. For longer distances (e.g., outside of the caldera), a refractive atmosphere should be considered.

The results of our inversion (wind magnitude and azimuth) are consistent with the two main wind fields that affect the summit region of Kilauea. The day time winds (hours: 15–28 and 40–48 in Fig. 3) are consistent in magnitude and direction with summer trade winds (Chen and Nash, 1994). The night time wind field (hours: 5–15 and 29–40) is characterized by wind speeds between 3–5 m/s originating from more scattered azimuths between 60°–100°. This second period is related to the low-speed down-slope mountain breeze (coming from the northwest). In general, the trade winds have a more consistent direction than the mountain breezes, which are influenced by uneven cooling of terrestrial surfaces at night.

Although the results of our wind inversion are in agreement with observations by Chen and Nash (1994) there are some substantial differences between the inferred wind fields from infrasound and the meteorological weather observations from the closest anemometer at HVO [compare Figs. 3(c) and 3(d)]. The HVO anemometer measures trade winds originating from about 60° (as opposed to 90°–120°) and detects wind speeds with an average velocity of only 4 m/s [as opposed to 7–9 m/s; see Figs. 3(c) and 3(d)]. We speculate that the point wind speed observations at HVO are influenced by local topography and vegetation and that the winds measured close to the ground are lower than the winds that are sampled by the infrasonic ray paths.

We suggest that meteorological station weather data are biased by a very localized site response and that in certain cases an ‘infrasound anemometer’, such as the one outlined in this paper, can provide a more robust measure of a spatially averaged winds above the ground-atmosphere boundary layer, which extends few hundred meters (Stull, 1988). Such spatially averaged wind fields are of particular interest to volcano studies and monitoring where plume dispersal modeling and gas flux calculations are made (e.g., Williams-Jones et al., 2006). For example, remote-sensing techniques, such as, COSPEC and FTIR, use the ambient wind as a proxy for plume velocity to calculate gas emission rates (Doukas, 2002).

During July 7–9, 2008, we recorded 45 h of continuous, high amplitude infrasound from activity of Halema`uma`u Vent. These continuous signals were used to identify relative acoustic phase delays, which varied over time with local winds and temperatures. Using data from three stations we demonstrated that it is possible to quantify time-dependent horizontal uniform wind direction and magnitude, which matched both the prevailing trade winds and intermittent mountain breezes in the area. This inversion of infrasound provided averaged constraints on weather conditions between the vent and infrasound network stations over a $∼5km2$ region. Such spatially averaged wind data can provide import input into atmospheric transport models, which are especially important for modeling volcanic ash and gas dispersal.

Future inversions will benefit from a greater number of infrasound stations with azimuthal and distance distribution. Because Halema`uma`u has proven to be such a reliable and continuous fixed radiator of infrasound it should be possible to map both spatial, as well as temporal variations in weather conditions toward the goal of performing 4-D tomographic studies of the atmosphere. Such studies could be accomplished near persistent volcano acoustic radiators and other reliable sources of infrasound.