Wavelike features suggesting gravity waves were revealed by lidar observations (from El Segundo, California) of smoke layers produced by large wildfires in the Southern California region during a Santa Ana event. Unique features of the observations were multiple thin layers that enabled precise determinations of wave frequency, amplitude, and vertical structure. The data revealed persistent wavelike oscillations that showed no phase variation with altitude, an amplitude of 20 m, and a period near 12 min. The observations were averaged over 1.5 min with a vertical resolution of 3 m and were obtained over a period of 5 h on 25 October and 8 h on 26 October 2007. Vertical profiles of temperature and winds from the Aircraft Communication Addressing and Reporting System (ACARS) of commercial aircraft departing Los Angeles International Airport (LAX) were selected for temporal and spatial coincidence with the lidar observations. In addition, satellite images of the smoke distribution over the Los Angeles Basin and the coastal areas (including coastal waters) to the south were obtained from Moderate Resolution Imaging Spectroradiometer (MODIS) data from overflights 5.5 h prior to the lidar observation window. The images show wavelike features with horizontal wavelengths of ∼10 km or less. The temperature data showed an inversion layer topped at 500-m altitude. The wind data were consistent with a residual sea breeze near the surface and Santa Ana easterlies above. A simple model of wave ducting showed that the observed features were the evanescent extension of resonant waves ducted in the lower stable inversion layer. These are the first detailed observations, including vertical structure, of ducted waves associated with Santa Ana conditions. It is suggested that such waves should be a common feature in conditions occurring during Santa Ana events.
Highly periodic oscillations in the earth’s planetary boundary layer and neighboring atmosphere are well established (Metcalf 1975; Stull 1976). Lidar scattering from aerosols such as smoke particles, which act as air parcel tracers, is the most sensitive and direct means of observing oscillations of the lower troposphere in detail. Previous lidar data on smoke layers have revealed short-term height oscillations of the smoke layer edges near the boundary layer height, attributed to penetrative convective instabilities (Pahlow et al. 2004).
This study reports on a multi-instrument study of wavelike oscillations during a 5-day period from 21 to 26 October 2007 when wildfires over Southern California consumed more than a half million acres and destroyed over 3200 structures. Lidar data were obtained simultaneously from multiple smoke layers over a period of 5 h on 25 October and 8 h on 26 October. These layers enabled precise determinations of wave frequency, amplitude, and vertical structure. Temperature profiles and wind data were obtained for the lidar operational period from the Aircraft Communication Addressing and Reporting System (ACARS) of commercial aircraft data. Profiles obtained for aircraft departing and arriving at Los Angeles International Airport (LAX) were selected for temporal and spatial coincidence with the lidar observations. In addition, satellite images of the smoke distribution over the basin were obtained from Moderate Resolution Imaging Spectroradiometer (MODIS) data on the National Aeronautics and Space Administration (NASA) Aqua satellite overflight 5.5 h prior to the start of the first lidar observation window. This unique dataset of lidar observations, detailed aircraft temperature and wind profiles, and satellite images, overlapping in time and space, allowed a study of new aspects of atmospheric dynamics associated with such fires. Foremost is that the data were consistent with the presence of wavelike feature associated with the smoke produced by the fires.
The comprehensive dataset allowed for the first time a study of the nature of these waves. In particular, the following considerations form the focus of this report:
The meteorological conditions, including a strong low-level temperature inversion associated with Santa Ana winds, have not previously been studied with respect to wave formation. The presence of an inversion layer capped by an abrupt change in the Brunt–Väisälä frequency is ideal for the formation of ducted waves below the region where the smoke occurred. The existence of a distinct trapping layer and a precise determination of wave characteristics above are well suited for assessing the possibility that the observed waves are the upward extension of waves ducted below.
The smoke was vertically distributed throughout the 1–5-km altitude range in optically thin layers. This allowed a characterization of vertical structure. The vertical phase variation, in particular, allows insight into the question as to whether these waves are freely propagating or evanescent above the inversion.
The vertical structure and persistence of the waves suggest that the waves are ducted. The data lend themselves well to the use of a simple model of wave ducting to assess this suggestion. The meteorological conditions and wave structure above the inversion are well characterized. The temperature data show that there are two distinct layers: a lower stable layer and an upper layer close to neutral stability. The wind data likewise are suitably layered.
2. Instrument and model description
First, we present a description of the instrument used to obtain the main data for this paper. This is followed by a description of a basic model for ducted gravity waves that is used to analyze the lidar data.
a. Lidar system
The lidar system was originally developed for measuring water vapor profiles using Raman scattering (Wessel et al. 2000). The transmitter is a neodymium-doped yttrium–aluminum–garnet (Nd:YAG) laser whose output is frequency tripled to 355 nm. It delivers 70-mJ, 10-nsec-wide pulses at 20 Hz. The transmitter beam is directed vertically with a steering mirror mounted on the backside of the secondary mirror of the receiver telescope. The receiver consists of a 0.7-m-diameter Cassegrain telescope. For these studies the output of the telescope is collimated and directed through a 0.2-nm full-width half-maximum (FWHM) interference filter and detected by a photomultiplier tube. The analog signal was amplified and digitized. This setup allowed daytime as well as nighttime operation. The vertical resolution of the lidar was set by the digitization interval to 3 m. Individual lidar profiles were normalized for laser power fluctuations, averaged for 1.5 min. and stored as a single profile. Three datasets were collected, each comprising approximately 6 h of continuous lidar data. Only a single lidar observation period is reported.
Figure 1 shows the lidar data obtained for the period of approximately 0200–0700 UTC 25 October. In this set of data the lidar was optimized to record signals no lower in altitude than 1 km. Throughout this observation period multiple smoke layers are evident, extending from 1.5 km to nearly of 5 km in altitude. The lower layers have vertical spatial extents of roughly 400 m whereas higher layers become wispy, some having vertical thickness of less than 10 m. The overlaid white line in the figure is a lidar profile for one specific time, 0400 UTC. The profile emphasizes the highly structured and defined vertical layering of the smoke distribution. Most of the smoke layers are persistent as distinct layers that do not vertically mix throughout the 5.5-h observation period.
An interesting high-frequency sinusoidal height oscillation is observed in all of the layers. The ability to see the same wave in several layers simultaneously is a unique and highly significant aspect of the observations. It allows us to characterize the vertical phase and amplitude variation of the waves.
Figure 2 shows a blow-up of the higher-altitude portion of Fig. 1, clearly showing these oscillations. The amplitude and phase of the oscillations are approximately constant throughout the altitude range of 2 to 5 km. The amplitude of the oscillation is about 20 m, peak to valley (±10 m). This amplitude, although small, is nearly twice as large as the vertical thickness of some of the upper layers and so is unambiguous. Several of the layers show small gaps between layers, and these gaps persist even in the presence of oscillations in the layer heights larger than the separation. The layers are not mixed by these oscillations, showing that the air is moving in a coherent fashion. The oscillations range in period from 12 min for the time interval of 0200 to 0430 UTC to about 8 min, later in the evening, from 0500 to 0600 UTC. Between those two time intervals, some process is occurring that disrupts the periodic oscillations and induces some mixing of the layers.
The winds during the entire 5.5-h observation period were light throughout the 0–5-km-altitude range of interest. Prior to this period the prevailing winds had been strong and easterly. Strong Santa Ana conditions had prevailed during the initial phases of the fires and continued for several days.
Figure 3a shows a MODIS image of the Los Angeles Basin on 24 October, one day prior to the start of lidar data collection, showing the smoke plumes carried over the Pacific by the easterly Santa Anas. The following day, the winds turned light and variable direction, as can be observed from the bottom MODIS image, Fig. 3b, obtained on 25 October, the same day the lidar data was obtained. This image shows smoke plumes consistent with light variable direction winds. Trajectory calculations indicate that to a significant extent the smoke layers observed on 25 October by lidar had been previously resident over the ocean for approximately 24 h before being blown back onshore.
4. Model calculations
Ducted gravity waves are vertically trapped internal gravity waves that can be sustained with little diminishment in the absence of forcing. We examine waves trapped by evanescence above and the earth’s surface below.
We assume waveform solutions of the form ψ = ψ̂(z) exp i(kx − ωt), where ψ is any dependent variable, ω is frequency, x and z are the horizontal and vertical coordinates, respectively, and t is time. Primes denote perturbation (wave) quantities. The familiar Taylor–Goldstein equation gives
where m is the vertical wavenumber, N is the Brunt–Väisälä frequency, and U is the mean (background) horizontal wind in the direction of wave propagation. When m2 < 0, the wave is evanescent and there is no vertical propagation; when m2 > 0, the wave is freely propagating. Equation (1) is valid when k ≫ 1/2H (k is the horizontal wavenumber and H is the scale height). This is well satisfied a posteriori.
The Brunt–Väisälä frequency is given by
where θ = T(p0/p)κ is potential temperature and where T is temperature, p is pressure, p0 is 1000 hPa, and g is gravity. The quantity κ = R/Cp, where R is the gas constant for air and Cp is the specific heat at constant pressure.
For a basic state where U and N 2 are constant, m is a constant. Note that if N 2 is constant but the atmosphere is not isothermal, m2 is more complex than (1). However, (2) with (3) is a good approximation to the more general form (Einaudi and Hines 1971). It is the vertical wavenumber if m2 > 0 and an inverse attenuation scale if m2 < 0.
b. Two-level model
We adopt a two-layer model with constant N 2 and U in each layer. For convenience we set z = 0 at the top of the inversion. The earth’s surface is at z = −D. In layer 1 (−D ≤ z ≤ 0) the solution has the form
and in layer 2 (z > 0) it has the form
where w is the vertical velocity,
We require ŵ = 0 at z = −D and also require that the wave satisfy continuity conditions at z = 0—namely, continuity of ŵ (kinematic condition) and p̂ (dynamic condition). The latter implies continuity of (c − U)ŵ. The characteristic equation obtained from (3) and (4), subject to the boundary condition and the continuity conditions, is
where μ ≡ (c − U)m. When ω is specified, k is the eigenvalue, and when k is specified ω is the eigenvalue. Because we have measurements of ω, we solve for k. The eigenfunctions satisfying boundary and continuity conditions have the form
in layer 1 and
in layer 2. The coefficient A is arbitrary.
c. Background state
We composited ACARS data from four flights at 0237, 0336, 0343, and 0409 UTC 25 October 2007. The data were for flights departing LAX and were selected for spatial and temporal proximity to the lidar site and the period of observation. LAX is approximately 4 km distant from the lidar site. The composited data were then smoothed to eliminate noiselike variations in the profiles due to spatial and temporal noncoincidence and discretization noise in the wind profiles due to the fact that winds are reported to the nearest knot (∼0.5 m s−1). The smoothing was performed by first employing a median filter and then smoothing using least squares linear fits. Smoothing over the main part of the profiles was performed with seven- to nine-point filters and seven- to nine-point linear least squares fits centered on each data point, except for temperature, where a five-point median filter was used. The smoothed and unsmoothed data are shown in Fig. 4 (temperature), Fig. 5 (zonal wind component), and Fig. 6 (meridional component). The zonal winds are positive eastward and the meridional winds are positive northward.
The temperature profile shows a low-level inversion topped near 500 m. The temperature decrease above the inversion is rather steep, being close the adiabatic lapse rate (9.8 K km−1). We have calculated N 2 based on the smoothed T profile. The result is shown in Fig. 7. The results show a low-level maximum in N 2 with a very steep decrease to near 500-m altitude where the decrease slows. There is a minimum near 700 m where N 2 is slightly negative (unstable). Above the minimum N 2 becomes weakly positive and remains so until the top of the plot at 6 km. The very large differences between values of N 2 below and above the inversion allow the possibility of waves that are internal below ∼500 m and evanescent above (i.e., trapped waves).
The winds are shown in the next two figures. The zonal winds (Fig. 5) show a low-level maximum below 500 m with peak eastward (onshore) winds near 3 m s−1 (somewhat less in the smoothed profile). There is a wind reversal near 500 m, increasing in speed to a broad maximum between ∼1 and 2.5 km where winds are close to −3 m s−1 (offshore) before decreasing to zero again near 3-km altitude. The meridional winds in the same altitude range (Fig. 6) are weak, varying between −1 m s−1 at the ground to 2 m s−1 near 500 m and less than ∼1 m s−1 above. The zonal winds are consistent with weak Santa Ana conditions. The onshore winds below the inversion are most likely a residual sea breeze when the land is still comparatively warm (the local times covered are between 1837 and 2009 PST).
These zonal winds are favorable for ducting for waves that are propagating close to zonally in an onshore sense. For such waves, m is Doppler shifted to larger values below the top of the inversion and to lower values above. Larger values of m below indicate waves with smaller vertical wavelengths; thus, it is easier to find waves that fit the duct without requiring very short horizontal wavelengths. Smaller values of m above the top of the inversion mean a higher degree of trapping. The meridional winds should not be substantially different from zero winds in their effect on ducting.
d. Model results
We applied the two-layer model with the background and wave parameters given in Table 1 for three cases corresponding respectively to zero winds, eastward propagation, and westward propagation. For westward propagation, solutions were not possible for the nominal winds and temperature profile. This is because the winds in the upper level caused the evanescence in the upper level to disappear. For this case we considered two subcases; one with reduced N 2 and slightly weaker winds (model 1, denoted M1) and the other with N 2 further reduced and nominal winds (M2). Both subcases seem realizable within the variability and uncertainty in the winds and temperature. We normalized the solutions to give the observed vertical displacements at 3-km altitude (±10 m), assuming the smoke is a tracer of the time scale of a wave period.
Table 2 gives the eigenvalues k and properties of the corresponding eigensolutions. Only data for the fundamental are shown. The eigenfunctions for case 1 are shown in Fig. 8. The wave amplitude peaks just below the top of the inversion and is much greater than at altitudes where the wave is observed by lidar. This behavior is common to all of the solutions (not shown).
We have also examined the second-gravest mode for cases 1 and 2. These waves are double peaked within the internal wave region (lower layer). One maximum is again found near the interface; the other is found about midway between the interface and the lower boundary. They have horizontal wavelengths about a factor of 2 smaller than the fundamental and are correspondingly slower in terms of phase speed. They decay much faster above the interface (∼factor of 3 in terms of e-folding attenuation scale). Therefore, to match the observed amplitudes where the smoke layers are observed, the waves in the internal region are required to be much stronger (vertical velocity ∼ 10s of m s−1) and have surface pressure amplitudes of several hPa. Solutions for case 3 could not be found.
5. Discussion and conclusions
The lidar observations show long-lived variations in the height of smoke layers with a well-defined periodicity. The periods are ∼12 min. These oscillations are seen simultaneously in several layers in the approximate altitude range 2–5 km. There is no discernible phase variation with altitude. This is consistent with the waves being evanescent at these altitudes. MODIS visible imagery from the afternoon pass on 24 October 2007, approximately 5.5 h before the lidar observations on 25 October (Fig. 9), shows a number of periodic spatial modulations of smoke density, consistent with wave activity. The superimposed black lines indicate the position of the local peak in smoke density and wave phase front. The wavelength of the modulation for the wave fronts closest to the lidar position is approximately 9 km. This is very close to the wavelength calculated for case 2 in the model and tabulated in Table 2. There is also some indication of wave features much smaller than this.
The background temperature variation shows that in the altitude regions where the waves are observed the observed period τ is less than the Brunt–Väisälä period (τB∼20 min). All gravity waves are evanescent for τ less than τB. However, below the top of the inversion near 500-m altitude τ ≫ τB (see Table 1) and internal waves are likely. This situation is favorable for ducting.
Winds can strengthen or diminish wave ducting by changing the intrinsic frequency (Jones 1972; Schubert and Walterscheid 1984; Walterscheid et al. 1999; Chimonas and Hines 1986). Stronger ducting is favored by winds that increase the intrinsic frequency in the evanescent layer and decrease it in the internal wave layer below. The observed winds indicate that waves propagating predominately eastward satisfy this condition (Fig. 3). Waves propagating in the north–south direction should be little affected by winds.
We use a simple two-layer model of wave ducting to explore the characteristics of ducted waves for windless conditions (case 1) and for waves propagating eastward (case 2) and westward (case 3). The model comprises a lower layer of thickness D = 500 m where the waves are internal and a semi-infinite upper layer when the waves are evanescent. We solve for the horizontal wavelength λ and vertical structure of ducted waves given the observed period. We find that for windless conditions (or very weak wind conditions, such as for meridional propagation) the fundamental (i.e., gravest) mode λ ∼ 6 km. For eastward (roughly onshore) propagation, λ ∼ 8 km. For westward propagation, λ ∼ 4 km. The vertical wavelength in the duct is approximately the same for the first two cases, being ∼3.5 times the duct thickness, whereas for westward propagation it is ∼4D. All waves reach their maximum value of vertical velocity near the top of the duct. Cases 1 and 2 decay with an e-folding length of ∼2.3D and 2.3D, respectively, with roughly similar values for case 3.
Sources for ducted waves include flow over rough or hilly terrain and a change in surface roughness, such as at a land–sea boundary. There is no reason to believe that any of these sources excite waves preferentially at the observed frequency. Most likely these sources are rather broadband. The observed waves would thus be the result of resonant selection on the part of the duct.
It appears that eastward or meridional propagation gives results that are closer to the predominate wavelengths observed in the MODIS imagery. Meridionally propagating waves could originate in flow over topography located to the north or south of the lidar site. Eastward waves could originate at the coast or the off-shore islands (Santa Catalina and San Clemente). There is some evidence of curved wave fronts emanating from San Clemente Island, indicating offshore islands as a possible source. There is a suggestion of waves propagating in an arc that extends westward over the coastal waters south of the Palos Verdes peninsula, then northwestward and northward between Santa Catalina and San Nicolas islands and then northeastward and eastward over Santa Monica bay. The directions used here are inferred from the normal to the wave crests and are ambiguous to 180°.
We note that the Brunt–Väisälä profile indicates a thin layer of convective instability just above the inversion layer (Fig. 7). Convective instabilities can excite waves close to the Brunt–Väisälä frequency and one might be tempted to explain the oscillations in these terms. However, we believe this is unlikely. First and foremost, instabilities are not long lived, usually lasting a few buoyancy periods. Moreover, they should show some evidence of overturning. We see no such behavior. Also, the instabilities are confined to the unstable region, which is only ∼100 m in thickness, whereas the observed oscillations are much more extensive.
It is interesting to estimate the surface pressure oscillation. From Walterscheid and Hecht [2003, their Eq. (6)] we obtain for the waves of interest (waves that are slow compared to the speed of sound)
where ωI is the intrinsic frequency and cI = ωI/k = c − U. This gives a pressure amplitude of ∼0.2 hPa at the surface for cases 1 and 2 and much smaller values for case 3 (see Table 2). The case 3 subcases are much less owing to the smallness of cI. The estimate of 0.2 hPa is much smaller than the surface pressure oscillations reported by Tsai et al. (2004) (∼1 hPa). These authors speculated that such waves might be excited by Santa Ana events. Tsai et al. (2004) referred to the events they observed as instances of morning glory events. These are spectacular wave events and are nonlinear in nature (Clarke et al. 1981; Porter and Smyth 2002). Although the waves we infer from these calculations are much weaker, it is possible that at other times and places much stronger waves were generated during a Santa Ana event. In fact, the lidar observations reported here were obtained at the end of the Santa Ana event and the winds were light by then.
The solutions are sensitive to the values of N 2 in the two layers. It is possible that within uncertainties due to spatial and temporal variability realizable values of N 2 could give much stronger waves; so too could a greater weighting for values of N 2 just above the inversion layer where values of N 2 are very low and where local wave attenuation might reduce the sensitivity of waves to the higher values of N 2 above.
Although 4.9 m s−1 seems large, the corresponding fractional density perturbation is rather modest (∼3%). We note also that the second-gravest mode can have very large values for surface pressure oscillations (on the order of several hPa). Under favorable N2 conditions, this mode might explain the waves reported by Tsai et al. (2004). It is possible that the events seen by Tsai et al. (2004) could be explained by ducted waves less dramatic than morning glories.
Finally, we note that wavelike structures very similar to the waves seen in the MODIS imagery for the Santa Ana wildfires in October 2007 were seen in MODIS imagery for the Santa Ana wildfires 2 yr before. We believe that waves such as we observed are common events during Santa Ana conditions when hot stable air underlies much cooler marine air above.
This work was sponsored by The Aerospace Corporation under the Independent Research and Development program. JHH and RLW were supported by NSF Grants ATM-0737557 and ATM-0436516, and by NASA Grant NAG5-13025. We thank A. M. Kishi and L. O. Belsma for satellite data retrieval.
Corresponding author address: Steven Beck, The Aerospace Corporation, M2/253, P.O. Box 92957, Los Angeles, CA 90009. Email: email@example.com