Evidence of damping and overturning of gravity waves in the Arctic mesosphere: Na lidar and OH temperature observations

Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 867 – 879

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Evidence of damping and overturning of gravity waves in the Arctic mesosphere: Na lidar and OH temperature observations Richard L. Collinsa;∗ , Roger W. Smithb a Geophysical

Institute and Department of Electrical and Computer Engineering, University of Alaska Fairbanks, Fairbanks, AK, USA b Geophysical Institute, University of Alaska Fairbanks, Fairbanks, AK, USA Received 30 January 2003; received in revised form 15 January 2004; accepted 28 January 2004

Abstract Lidar observations of the mesospheric sodium (Na) layer have been made at Poker Flat Research Range, Chatanika, Alaska (65◦ N; 147◦ W) over a 4-year period. Long-period oscillations have been observed routinely in the bottomside of the Na layer. Simultaneous hydroxyl airglow temperature measurements have con:rmed that these oscillations are associated with upwardly propagating gravity waves. These lidar observations have yielded statistically signi:cant measurements of upwardly propagating gravity waves on 24 occasions. A gravity-wave model with pseudo-steady-state chemistry is used to determine the characteristics of the waves. These 24 waves have an average observed period of 6:9 h, average vertical wavelength of 14:2 km, average temperature amplitude of 8 K, and average horizontal velocity amplitude of 30 m=s. These waves appear to be damped over the altitude of the Na layer with a growth length of 216 km. The waves do not appear to be damped by viscous dissipation or linear instabilities in the waves themselves. However, 20 of the 24 wave events are accompanied by overturning structures in the bottomside of the Na layer. These wave-overturning events have the same characteristics as those observed at Urbana, IL (40◦ N; 88◦ W), that were interpreted as convective instabilities arising from the superposition of largeand small-scale waves. The current observations suggest that such convective instabilities are a relatively common feature at this high-latitude site and contribute to the damping of large-scale gravity waves. c 2004 Elsevier Ltd. All rights reserved.  Keywords: Gravity-wave dynamics; Resonance lidar; Hydroxyl temperatures; Mesospheric sodium layer

1. Introduction A wide variety of observational and theoretical studies have been conducted to study gravity waves in the middle atmosphere. These studies have attempted to better understand how these waves interact with other waves, tides, and mean winds in the middle atmosphere. It is through these interactions that gravity waves contribute to the observed general circulation and the turbulent mixing and diffusion of constituents (see the recent collections of papers in the monographs edited by Johnson and Killeen (1995) and Siskind et al. (2000), and the review article by Fritts and Alexander (2003)). While gravity waves can become

∗

Corresponding author. Tel.: +1-970-491-6554. E-mail address: [email protected] (R.L. Collins).

unstable through a variety of mechanisms, shear and convective instabilities are considered the primary mechanisms for turbulence production (Fritts and Rastogi, 1985; Fritts and Alexander, 2003). Convective instabilities are expected to dominate in high-frequency waves and dynamic instabilities in lower-frequency waves. Recent computational studies have modeled the wave-breaking process and provided new insights into the transfer of energy from waves to turbulence (Fritts et al., 1994). The multi-instrument observations of the recent Collaborative Observations Regarding the Nightglow (CORN) campaign (Hecht et al., 1997; Fritts et al., 1997) have shown that superposition of largeand small-scale waves is an important mechanism in wave breaking. In this study we present lidar measurements of the sodium (Na) concentration pro:les and hydroxyl (OH) airglow measurements of temperature from Poker Flat Research Range

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(PFRR), Chatanika, Alaska (65◦ N; 147◦ W). We use the measurements to identify statistically signi:cant oscillations in the bottomside of the Na layer as gravity waves. We then employ a gravity-wave model with a pseudo-steady-state chemical scheme to characterize the observations in terms of quasi-monochromatic gravity waves. We pay particular attention to how the wave amplitudes vary with altitude across the altitude range of the Na layer. We correlate the presence of these waves with overturning signatures in the bottomside of the Na layer. We compare these wave signatures with those measured during the CORN campaign. We :nd that large-scale gravity waves with associated overturning signatures are a relatively common feature at this site. Finally, we discuss these observations in terms of recent observational studies of wave breaking in the Na layer (Williams et al., 2002; Franke and Collins, 2003).

2. Experiment description 2.1. Na lidar The Na concentration pro:les are measured with a Na density lidar. (Na resonance lidars that are not capable of measuring temperature or wind are commonly called Na density lidars to distinguish them from Na wind/temperature lidars.) This Na lidar employs a Eashlamp-pumped dye laser and is capable of making measurements of the vertical concentration pro:le of mesospheric Na at a resolution of 100 s and 75 m (Collins et al., 1996a). The Na density lidar at PFRR is a broadband system with a laser linewidth of approximately 9 GHz. The power-aperture product is 0:04 W=m2 . The Na concentration pro:les are determined from the Na photon count pro:les with standard inversion techniques (e.g. Gardner et al. (1986), Tilgner and von Zahn, 1988). For this study the lidar measurements have yielded sequences of Na pro:les that are integrated over 15 min intervals and low-pass :ltered at 2 km. The observations over a 4-year period have yielded 68 observation sets of Na pro:les (totaling 720 h) that are of suGcient quality to study the gravity-wave activity in this region. The data were obtained between April 1995 and March 1999. Between mid-May and mid-August the sunlight reduced the data quality and thus summertime observations are not included in this study. The data sets have been screened for the presence of sporadic Na layers. Sporadic Na layers, also termed sudden Na layers, are narrow layers, typically 1–2 km FWHM, that form as an enhancement to the ambient or background Na layer (see Clemesha, 1995, and references therein for discussion). During sporadic layer events the Na chemistry is not in equilibrium and we cannot assume that the Na layer acts as a tracer of wave motions. Of the 68 data sets available, sporadic Na layers are observed on 16 occasions. Heinselman (2000) has modeled the inEuence of the aurora

on the gas-phase chemistry of the mesospheric Na layer and shown that during major auroral events, the aurorally induced ionization can alter the structure of the Na layer and produce sporadic Na layers. The occurrence of sporadic layers at PFRR is generally associated with active aurora and has been reported at PFRR (Collins et al., 1996a) and at other locations (Gu et al., 1995). During these events the auroral arcs have magenta lower borders indicating that the precipitating electrons are penetrating into the mesosphere (Vallance Jones, 1974). We limit our study to the remaining set of 52 observation periods when sporadic Na layers are not observed. The current study represents observations when the aurora is not expected to have a major inEuence on the upper mesosphere. Other studies at PFRR have focussed on the impact solar activity on the winds in the lower thermosphere and upper mesosphere (e.g. Johnson and Luhmann, 1993). For these 52 observations each observation period lasted between 4 and 16 h with an average of 9 h. The structure of the mesospheric Na layer can be characterized by the column abundance, centroid height and rms width (Gardner et al., 1986). Due to uncertainties in the laser linewidth, we do not report the column abundance in this paper. The seasonal variations of the centroid height and rms width are shown in Fig. 1. These measurements show a Na layer that is broadest and lowest in the winter. The wintertime structure of the Na layer is consistent with the wintertime observations at several polar sites (i.e. Andoya (69◦ N; 16◦ E) (Tilgner and von Zahn 1988), the South Pole (90◦ S) and Syowa (69◦ S; 39◦ E) (Collins et al., 1994) where the low centroid height (∼88 km) is associated with Na layer peak altitudes below 88 km. The seasonal variations of the Na layer at these high-latitude sites can be compared with the recent middle-latitude (40◦ N; 88◦ W) observations of States and Gardner (1999). States and Gardner reported seasonal variations in the centroid height and rms width of the Na layer that are smaller than at high latitudes. This behavior is consistent with current chemical models of the Na layer; in the warm winter mesosphere free Na atoms, rather than NaO2 and NaHCO3 molecules, exist on the bottomside of the Na layer (Plane et al., 1998). This increase in the Na concentration on the bottomside of the Na layer explains the observed wintertime decrease in centroid height and the increase in rms width. The larger seasonal variation at high latitudes than middle latitudes is consistent with the larger seasonal variation in mesopause temperatures. 2.2. OH Michelson interferometer The OH temperature measurements are made using a BOMEM DA8 Michelson interferometer operated in a Fourier Transform mode. The Michelson interferometer measures the airglow spectrum from 1.0 to 1:7
m with a resolution of 0:4 nm. The distribution of the rotational lines in the Mienel band of the OH spectrum is used to

R.L. Collins, R.W. Smith / Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 867 – 879

Poker Flat Research Range (65˚N, 147˚W)

84

92 90 88 86

83 82 81

J

F M A M J J A S Month

80 18

O N D

Poker Flat Research Range (65˚N, 147˚W)

20

22

00 02 Time (LST)

04

06

08

04

06

08

2-3 March 1997

220

6 Temperature (K)

Na Layer RMS Width (km)

2-3 March 1997

85

Altitude (km)

Na Layer Centroid Height (km)

94

869

5 4

210 200 190

3 J

F M A M J J A S Month

O N D

180 18

20

22

00 02 Time (LST)

Fig. 1. Centroid height (top) and rms width (bottom) of mesospheric Na layer as a function of month. The values represent a Gaussian :t to the observed Na layer for each observation period. The data does not include observations where sporadic Na layers were observed.

Fig. 2. Displacement of Na concentration contour (top) and OH layer temperature (bottom) as a function of time on the night of 2–3 March 1997. The contour and temperature are plotted as thin lines with crosses. The thick lines are the best-:t harmonics to the data. See text for details.

determine the rotational temperature. Measurements are made of the column OH temperature every 3 min with typical measurement accuracy of 2–3%.

chemistry of the Na layer on the amplitude of the oscillation in the Na layer.

3. Analysis of oscillations in the Na and OH layers

Hernandez (1999) has studied the question of signi:cance in the :tting of harmonics to observational time series. Hernandez showed that comparison of harmonics in diLerent geophysical data sets is of questionable merit without a quantitative measure of the signi:cance of the harmonic :t. Filtering methods can improve the apparent signi:cance of a given harmonic without changing the actual geophysical signi:cance (or insigni:cance) of the :t. In this study the oscillations are determined using a best :t to the constant concentration contours in the bottomside and topside of the Na layer. We choose the following constant concentration values: max =16, max =8, max =4 and max =2, where max is the Na concentration at the peak of the average layer over the observation period. A sequence of n points, zi (i = 0; n − 1),

3.1. Simultaneous oscillations in the Na and OH layers Simultaneous Na lidar and OH temperature measurements were made on the night of 2–3, March 1997 at PFRR. The altitude of a constant Na concentration level and the OH temperature are plotted in Fig. 2. Harmonic :ts to both data yield :ts with common periods. In analyzing these oscillations we consider the following factors: the statistical signi:cance of the harmonic :t; the relationship between the observed displacement and the actual wave amplitude; the inEuence of the structure of the Na and OH layer on the observed amplitude of the oscillation; and the inEuence of the

3.2. The statistical signi
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R.L. Collins, R.W. Smith / Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 867 – 879

de:nes the altitude of a given Na concentration contour as a function of time, ti . We assume that the contours can be modeled by the superposition of a linear trend and a single harmonic, fi , (1)

and a residual signal, ei , ei = zi − fi ;

(2)

that is modeled as noise that is uncorrelated with the :t. The best :t is determined by searching for the choice of !0 that minimizes the signal-to-noise ratio (SNR) of the :t. The SNR is de:ned as the ratio of the mean square amplitude of the harmonic to the mean square amplitude of the error signal erms , SNR = 0:5(a21 + a22 )1=2 =erms ;

(3)

where erms = ((1=n)

n


(ei )2 )1=2 :

10 1

(4)

i=1

The signi:cance of the :t is determined by calculating the probability that a white noise signal with the same number of points would yield the same SNR. Before calculating the SNR, we determine the autocorrelation function of the residual error signal, ei . If ei is a white noise signal the autocorrelation function should be zero for all nonzero lags and leads. If the autocorrelation function falls to zero at a lag of length of r, then we increase the rms error, erms , by a factor r 1=2 and accordingly reduce the measured SNR by the same factor. The estimate of the minimum, erms , has an associated uncertainty of erms =n1=2 . We determine uncertainty in the frequency and amplitude estimates from the range of :ts that yield residual rms errors within the uncertainty of the minimum error. We use a Monte Carlo approach to determine the signi:cance of the SNR as a function of the number of points in the sequence. For the purposes of this study, we have de:ned a harmonic :t as signi:cant if it has an SNR that is 95% signi:cant or better. The signi:cance level curves are plotted as a function of SNR and number of independent points in Fig. 3. We calculate the phase progression of the harmonic in the Na layer using a linear :t to the phase of the harmonics as a function of the mean altitude for each of the four Na concentration levels. Again we employ a Monte Carlo approach to determine the signi:cance of these results. For :tting to four levels, a phase progression with an associated error of 23% or less is signi:cant at the 95% level. 3.3. Perturbation of Na and OH layers by gravity waves We have developed a model for the interaction of gravity waves and the Na and OH layers. We employ the dispersion and polarization relations for a linear gravity wave (Hines, 1960). The model is initialized with an altitude concentration pro:le based on the Na layer averaged over the

0.95 SNR

fi = a0 + a1 ti + a2 cos(!0 ti ) + a3 sin(!0 ti )

Harmonic Fits to White Noise

0.90 0.50

10 0

10

15

20

25

30

35

40

45

50

Number of Points Fig. 3. Signi:cance level curves of a harmonic :t of a given SNR for a given number of points in a random series. A harmonic :t with an SNR of 1 is only ∼50% signi:cant if there are 15 points in the series, but ∼95% signi:cant if there are 27 points in the series. The curves are obtained using a Monte Carlo technique (see text for details).

observation period. The observed centroid height, topside rms width and bottomside rms width are calculated from the average pro:le. A background Na pro:le is then calculated as an asymmetric Gaussian pro:le with these measured parameters (Collins et al., 1997). This background pro:le, which is assumed to represent the unperturbed Na layer, is then divided into a series of altitude parcels. These parcels move with the gravity-wave wind perturbations and are compressed and rare:ed by the gravity-wave density perturbations. Thus the Na concentration pro:le is distorted as the gravity waves pass through the Na layer. The distorted concentration pro:le is then interpolated back to a uniform altitude series to model the Na layer as observed by the lidar. This model yields the Na concentrations where Na acts as a chemically inert tracer of the gravity waves [Na(t; z)]GW . We have developed a similar gravity-wave model for the OH layer. We average the temperature over the OH layer weighting the temperature in each parcel by the OH luminosity of the parcel as the luminosity increases with density (Swenson and Gardner, 1998). The model yields the temperature series that would be measured by the altitude-averaged OH airglow interferometer. 3.4. Na and OH layer chemistry Hickey and Plane (1995) have studied the eLects of Na chemistry in a chemical dynamic model of wave-driven Euctuations. These authors studied gravity waves with periods of 20 min to 3 h and found that the eLects of Na chemistry were negligible above 85 km. In this study we are interested in oscillations in the Na layer with a typical period of 6 h, which are longer than those periods considered by Hickey and Plane. The Na chemistry might amplify or

R.L. Collins, R.W. Smith / Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 867 – 879

S (z) = d(fNa (z)=fNa0 (z))=d((z) − 0 (z));

(5a)

S (z) = d(fNa (z)=fNa0 (z))d(((z) − 0 (z))=0 (z));

(5b)

where 0 is the unperturbed or mean temperature (K), 0 is the unperturbed or mean atmospheric density (kg=m3 ), fNa is the mixing ratio of Na, and fNa0 is the equilibrium, or unperturbed, mixing ratio of Na at temperature 0 and density 0 . S , the sodium temperature sensitivity, is the change in both fNa and [Na] as the total mixing ratio of all Na compounds (i.e. Na, NaO, NaOH, etc.) in the parcel is :xed. S , the sodium density sensitivity, is the change in fNa but not [Na] as the total mixing ratio of all Na compounds scales with the density. The sensitivities, S and S, are plotted as a function of altitude in Fig. 4. The chemistry is included in the gravity-wave model using the chemical sensitivities, S (z) and S (z). The change in [Na] is the product of the density change and the change in mixing ratio between the Na compounds. Thus, the Na concentration is varied as the density and temperature of a parcel evolves as follows: [Na(t; z)] = [Na(t; z)]GW ×[1+S (z0 )×((t; z)−0 (z))] ×[1 + S (z0 ) × (((z; t) − 0 (z))=0 (z))]; (6) where z0 is the initial or unperturbed altitude of the parcel. As the parcel moves the density and temperature of the parcel are calculated. In the chemically inert model, S = 0 and S = 0 and [Na(t; z)] = [Na(t; z)]GW . The change in Na concentration is determined from the sensitivities, S (z0 ) and S (z0 ) associated with the initial or unperturbed parcel altitude z0 . The chemical sensitivity of the OH layer is also determined using the chemical reactions given by Roble

TIME-GCM 65˚N 120

Altitude (km)

110 Winter Solstice Equinox

100 90 80 -1 10 -2 0 10 0 1 10-2 2 10 -2 Sodium Temperature Sensitivity TIME-GCM 65˚N 120 110

Altitude (km)

attenuate the Euctuations associated with a wave and thus the apparent attenuation of a wave with altitude in the Na layer could represent altitude variation in Na chemistry and not a variation in the characteristics of the wave itself. The eLects of changes in chemical equilibrium are modeled using two models. We model the Na chemistry using the model of Plane et al. (1998). We model the background atmosphere using temperature and concentration pro:les from the thermosphere–ionosphere– mesosphere-electrodynamics general circulation model (TIME-GCM) (Roble and Ridley, 1994). The speci:c chemical reactions are taken from Roble (1995). The TIME-GCM provides vertical pro:les of temperature and species concentrations for winter solstice and equinox conditions at PFRR. Na exists in chemical equilibrium with 10 other Na-containing species (e.g. NaO, NaOH, Na+ ). We determine the sensitivity of the steady-state Na mixing ratio pro:le to changes in density and temperature. The sensitivity analysis includes changes in the concentrations of the background oxygen and hydrogen species as well as the sodium species. The linear :ts to the relative change in Na as a function of temperature, , alone and density, , alone at each altitude yields the sensitivities to changes in temperature, S , and density, S , as a function of altitude,

871

Winter Solstice Equinox 100 90 80 -1.5

-1 -0.5 0 0.5 Sodium Density Sensitivity

1

Fig. 4. Sensitivity of Na to changes in temperarure, S , (top) and density, S , (bottom) as a function of altitude. The sensitivity pro:le is calculated for winter solstice (solid) and equinox (dashed). See text for details.

(1995). As the density and temperature of the OH parcels evolve the OH concentration in a similar fashion as for the Na parcels (Eq. (6)). This approach assumes that both the Na and OH reach chemical equilibrium over the period of the wave. 3.5. Characteristics of gravity wave on detected on 2–3, March 1997 Harmonic :ts are carried out for the Na contours and OH temperatures measured on the night of 2–3, March 1997 at PFRR. The harmonic :ts are signi:cant at or above the 95% level in both the contour on the bottomside of the Na layer and the OH temperature. We determine the best agreement between the observations and gravity-wave models of the Na and OH layers. We use the observed Na layer parameters and a range of wave and OH layer parameters. The altitude distribution of the OH airglow has been measured with rocket borne photometers (Baker and Stair, 1988) and

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R.L. Collins, R.W. Smith / Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 867 – 879

Table 1 Gravity wave characteristics on March 2–3, 1997 Na contour Period (h) Best :t Range Displacement (km) Temperature (K) Vertical phase Velocity (km/h) Signi:cance (%) Harmonic Phase :t

4.9 4.9–5.3 0.94 4.9 97 99

OH temperature 5.7 5.1–6.4 6.4

98

more recently with lidars (Brinksma et al., 1998). We consider a range of amplitudes (5–25 K), a vertical wavelength determined from the observed phase progression in Na data (23:9 km), a range of OH layer peak altitudes (84–94 km), and a range of OH rms layer widths (3–7 km). This analysis indicates that the oscillations on March 2–3, 1997 are associated with a gravity wave of temperature amplitude 7:5 K(±2:5 K). Furthermore, the observed phase progression is negative, indicating that the oscillation is associated with an upward propagating gravity wave. The results of the harmonic :tting for 2–3, March 1997 are presented in Table 1. 4. Damping of gravity waves in the Na layer 4.1. Characteristics of quasi-monochromatic waves We :nd that oscillations in the bottomside of the Na layer are a relatively common feature of these observations. Harmonic :ts at the 95% signi:cance level or greater are found in at least one of the bottomside Na contours on 37 of the 52 observations. For 25 of these 37 observations we :nd a linear :t to the phase progression that is signi:cant at or above the 95% level. Of these 25 observations, we :nd that 24 have negative phase velocities (i.e. downward phase progressions) and only one yields a positive phase velocity (i.e. upward phase progression). We focus on these 24 observations as representative of upward propagating gravity waves. The average altitude of the oscillations in the bottomside of the Na layer is 81:9 km and in the topside of the Na layer is 98:4 km. We :nd statistically signi:cant oscillations in the topside of the Na layer on only three of these 24 observation periods. Examples of these oscillations and their harmonic :ts are plotted in Fig. 5. The characteristics of these observations are listed in Table 2. The 24 observed oscillations have observed periods between 2.8 and 12:8 h (with an average value of 6:9 h), displacements between 0.5 and 2:3 km (with an average value of 1:2 km), and downward vertical phase velocities between 0.17 and 1:8 m=s (with an

Period (h) Vertical wavelength (km) Horizontal wavelength (km) Horizontal velocity (m/s) Vertical velocity (m/s) Vertical displacement (km) Temperature (K)

4.9 23.9 1470 19 0.27 0.76 7.5

5.7 23.9 1760 20 0.23 0.76 7.5

average value of 0:67 m=s). The associated vertical wavelengths are between 4.8 and 28:7 km (with an average value of 14:2 km). The observed wave characteristics are plotted in Fig. 6. We use the gravity-wave model to determine the amplitude of the gravity waves. For each wave observation the observed gravity wave and Na layer characteristics are used with the gravity-wave model to simulate the observations. A range of temperature amplitudes (2.5–25 K) is used and the temperature amplitude that yields the oscillation amplitude closest to the observations is taken as the amplitude of the wave. The simulated wave has constant amplitude over the altitude range of the Na layer. For these waves we :nd a range of temperature amplitudes between 5 and 15 K (with an average of 8 K), horizontal velocity amplitudes of between 12 and 91 m=s (with an average value of 30 m=s), and vertical displacement amplitudes of between 0.5 and 1:6 km (with an average value of 0:8 km). The ratio of the amplitudes of the best-:t-simulated displacement contours to the observed displacement contours is 1.0. To determine the propagation characteristics of these waves we calculate the ratio of the amplitude of each harmonic in the topside and bottomside of the Na layer, R0 , relative to the values determined from the gravity-wave model, Rm . The ratio of the observed value to the model value yields a damping ratio, Rg (=R0 Rm ), that is a measure of how the observed waves grow or decay with altitude. We :nd that the average value of this ratio is 1.2. We :t the values of Rg to the altitude diLerence between the topside altitude (z1 ) and bottomside altitude (z2 ) with an exponential model, that assumes that the waves would either (a) maintain constant amplitude with height or (b) maintain constant energy and grow with a growth length of Ha , Rg = exp((z2 − z1 )=Hg );

(7a)

Rg = exp((z2 − z1 )=Hg ) exp((z2 − z1 )=Ha

(7b)

and determine the scale height Hg . For these waves we :nd an average growth length of 216 km for the wave amplitude relative to constant amplitude waves (Eq. (7a)). In

R.L. Collins, R.W. Smith / Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 867 – 879 Table 2 Observed characteristics and derived gravity-wave parameters

March 7-8, 1996

85

Date

Altitude (km)

84 83 82 81 21

22

23

00 01 Time (LST)

873

02

03

04

March 7–8, 1996

Observations Period (h) 2.8 Signi:cance (%) 99 Vertical wavelength (km) 11.0 Amplitude (km) 0.95 Estimated gravity wave parameters Horizontal velocity (m/s) 23.4 Vertical displacement (km) 1.1 Horizontal wavelength (km) 377

January 11–12, 1997 5.8 98 15.6 1.0 27.3 1.0 1210

January 3–4, 1998 9.1 99 17.8 1.1 17.6 0.78 2670

January 11-12, 1997 80

Altitude (km)

79

conclude that these waves are damped across the altitude of the Na layer.

78

4.2. Viscous damping and linear instability

77

Following the analysis of Hines (1960), we determine that the vertical wavelength, z , of a gravity wave that is viscously damped, by an exponential amplitude factor, in p periods is related to the period, T , as follows:

76 75 18

20

22

00 02 04 Time (LST)

06

08

z = 2(pT(1 − 1=e))1=2 ;

January 3-4, 1998

80

Altitude (km)

79

78 77 76 18

20

22

00 02 03 Time (LST)

(8) 2

04

05

06

Fig. 5. Displacement of Na concentration contours as a function of time on the nights of 7–8 March 1996 (top), 11–12 January 1997 (middle), and 3–4 January 1998 (bottom). The contours are plotted as thin lines with crosses. The thick lines are the best-:t harmonics to the contours. See text for details.

comparison with waves are freely propagating and growing with a growth length (Ha ) of 12 km the observed ratio of 1.2 represents the inEuence of a damping process with a damping length (i.e. negative growth length) of 13 km. Thus we

where  is the kinematic viscosity (m =s). For a wave of a given scale (i.e. z and T ), we can determine how the wave is damped by determining the value of p for a given viscosity. As the viscosity increases the wave is damped more quickly and the value of p decreases. Thus, p represents the viscous lifetime of the waves (in numbers of period). The original analysis of Hines considered the problem in terms of how a wave is quenched in one period rather than decays exponentially over many periods. We consider the eLects of molecular viscosity and eddy kinematic viscosity. We consider viscous damping due to both molecular viscosity and eddy diLusion. To study the eLects of molecular viscosity we employ a kinematic viscosity of 4 m2 =s at 90 km (Pitteway and Hines, 1963) that is also consistent with the US Standard Atmosphere (NOAA, 1976). To study the eLects of eddy diLusion we employ an eddy kinematic viscosity of 100 m2 =s (LPubken et al., 1993). We note that while dissipation by molecular viscosity and eddy diLusion processes can be both modeled in the same way, molecular viscosity is a steady process while eddy viscosity is a function of the dynamics of the region and behaves more intermittently. For the molecular viscosity case we :nd values of p between 5.5 and 185 with an average value for p of 45 for these waves. The viscous damping length (i.e. the altitude over which the waves travel in one viscous lifetime) is the product of the vertical group velocity and the viscous lifetime. For these waves we :nd an average viscous damping length

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R.L. Collins, R.W. Smith / Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 867 – 879 Poker Flat Research Range (65˚N, 147˚W) 2.0

7 6

1.5

5 4

1.0

3 2

0.5

Observed Vertical Phase Velocity (m/s)

Observed Vertical Phase Velocity (km/hr)

8

1 0.0

0 0

4

6 8 10 12 Observed Period (h)

14

16

Poker Flat Research Range (65˚N, 147˚W)

40

Vertical Wavelength (km)

2

35 30 25 20 15 10 5 0 0

4

6 8 10 12 Observed Period (h)

14

16

Poker Flat Research Range (65˚N, 147˚W)

2.5

Observed Amplitude (km)

2

2 1.5 1 0.5 0 0

2

4

6

8

10

12

14

16

Observed Period (h)

Fig. 6. Characteristics of gravity waves measured at PFRR. Top: observed vertical phase velocity versus observed period. Middle: observed vertical wavelength versus observed period. Bottom: observed displacement amplitude versus observed period. The error bars represent the uncertainty in the measured parameters.

Orlanski and Bryan (1969) considered convective instability of oceanic internal gravity waves. When the horizontal parcel velocity (u ) approaches the intrinsic horizontal phase velocity (c) the wave becomes convectively unstable. More recently, Fritts and Rastogi (1985) have discussed convective and dynamic instability in atmospheric gravity waves. Following these studies, we use the ratio (u =c) to quantify the linear stability of these waves. For these waves we :nd an average value for (u =c) of 0.5 indicating that the waves are stable and the observed damping is not due to simple linear instability of these large-scale waves. 4.3. Doppler shifting of waves The above analysis assumes that the observed wave periods represent the intrinsic periods of the waves. Balsley and Riddle (1984) reported mean zonal and meridional winds of approximately 10 m=s at Poker Flat in mid-winter. To determine the inEuence of Doppler shifting by the mean winds we analyze the data in terms of viscous damping and linear stability by assuming the intrinsic wave periods are at least half the observed period (i.e. T = Tobs =2). This factor of two is a reasonable bound given that the average horizontal phase speed is over four times the typical mean wind speed. Given the long periods and horizontal wavelengths of the waves, we do not expect the observed waves to be Doppler-shifted waves with periods twice the observed period. We vary the period of the waves and keep the associated vertical wavelength constant and simulate the waves with the gravity-wave model. We :nd that the average value of the damping ratio, Rg is 1.2. For these shorter-period waves we :nd an average value for (u =c) of 0.5 and a damping length of 514 km under the inEuence of molecular viscosity and a damping length of 128 km under the inEuence of eddy viscosity. These damping lengths are much longer than the observed damping length of 13 km. Thus, we conclude viscous dissipation processes do not seem to be the source of the observed damping. These analyses suggest that the observed damping of the waves is an intrinsic property of the waves and is not due to viscous damping or linear instability in higher-frequency (and smaller-scale) waves that have been Doppler shifted to the observed periods. 5. Overturning in the Na layer

of 81 km, which is longer than the observed value of 13 km. For the eddy viscosity case we :nd values of p between 1.4 and 46 with an average value for p of 11.4 for these waves. For these waves we :nd an average viscous damping length of 20 km, which is again longer than the observed value of 13 km. If the wave growth was limited by viscous dissipation alone we would expect to measure larger damping ratio values, Rg . Thus, these observations indicate that the observed wave damping is not due to simple viscous eLects.

Given that the damping in the gravity waves does not appear to be due to viscous damping or instability in the waves themselves, we consider the observations in terms of wave breaking. During the CORN campaign, Hecht and co-workers (Hecht et al., 1997; Fritts et al., 1997) observed overturning in the Na concentration pro:les and showed that the scale of the overturning was consistent with the scale of the gravity waves that were observed. These observations were made at middle latitudes at the Urbana

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Atmospheric Observatory (UAO) (40◦ N; 88◦ W). Contour plots (Fig. 5 of Hecht et al.) of the Na concentration and temperature measured on the night of 27–28, September 1992 at UAO, showed a downward phase progression in both quantities. The overturning structure was visible in the bottomside of the Na layer in the altitude range 85–90 km during the period 2100–2300 LST. This feature had a depth of overturning of 2–3 km. The UAO Na concentration data for the CORN measurements is plotted in false-color in Fig. 7. The downward phase progression and overturning in the Na layer is clearly visible. False-color plots of the Na layer measured on the nights of 7–8, January 1997 and 16–17, January 1999, respectively, at PFRR are also plotted in Fig. 7. On the night of 7–8, January 1997 an overturning feature is apparent in the altitude range 80–85 km during 0400–0600 LST with a second weaker possible feature during 2200–2400 LST. On the night of 16–17 January 1999 an overturning feature is apparent in the altitude range 80–85 km during 0200–0400 LST. These features persist for about 1 h with a depth of overturning of 2–3 km. The evolution of the Na layer at PFRR with downward phase progressions accompanied by overturning structures in the bottomside of the layer shows the same features as that observed during the CORN experiment. We note that the quality of the lidar data is signi:cantly diLerent at both sites. The power-aperture product and eLective backscatter cross-section of the Na atoms determine the detection limits of the lidar system (Gardner et al., 1989). The UAO data were obtained with the Na wind/Doppler temperature lidar which has a power-aperture product of 0:08 W=m2 and a narrow laser linewidth (∼120 MHz FWHM). The PFRR data were obtained with broadband lidar which has a power-aperture product of 0:04 W=m2 and a broad laser linewidth (∼9 GHz FWHM). Thus, the UAO measurements are made with signal levels at least 20 times greater than the PFRR measurements. Despite the diLerence in measurement quality, similar overturning signatures and downward phase progressions are apparent in all three sets of observations (Fig. 7). Harmonic analysis of the UAO observations indicates a statistically signi:cant harmonic of period 5:7 ± 0:2 h in the bottomside of the Na layer consistent with the period of 5:5 h reported by Hecht et al. (1997). Using the characteristics of the wave and the Na layer, we :nd that this wave has a damping ratio, Rg of 1.5, which indicates a growth length of 32 km relative to constant amplitude waves. Analysis of the PFRR data also yields signi:cant waves in the data. On the night of 7–8, January 1997 we :nd a statistically signi:cant harmonic with an observed period of 8:0 h while on the night of 16–17, January 1999 we :nd a statistically signi:cant wave with an observed period of 5:8 h. On 7–8, January 1997 the characteristics of the wave and the Na layer indicate that the wave has a damping ratio, Rg of 1.0, which indicates an in:nite growth length relative to a constant amplitude wave. On 16–17, January 1999 the characteristics of the wave and the Na layer indicate that this wave has a damping

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Fig. 7. False color images of Na concentration plotted against time and altitude. The color scale runs from black (minimum of 0 atom=cm3 to yellow (maximum of several thousand atoms=cm3 ). Top: UAO on the night of 27–28, September 1992. Middle: PFRR on night of 7–8, January 1997. Bottom: PFRR on night of 16–17, January 1999.

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ratio, Rg of 1.2, which indicates a growth length of 108 km relative to constant amplitude wave. For the PFRR observations we :nd overturning events on 20 of the 24 days associated with upwardly propagating large-scale waves having observed periods and vertical wavelengths that are signi:cant at the 95% level. The overturning events are visible over 1–2 h periods with a typical depth of 2–3 km in the bottomside of the Na layer. 6. Discussion 6.1. Comparison with other Na lidar studies of monochromatic gravity waves The method we have used in this study to retrieve monochromatic gravity-wave parameters is diLerent from that used in previous Na layer studies of waves. Gardner and colleagues have determined gravity-wave parameters by measuring the vertical wavelength and vertical phase velocity of the wave in the Na concentration pro:les (e.g, Gardner and Voelz, 1987; Beatty et al., 1992; Collins et al., 1994, 1996b). The vertical wavelength is determined by identifying a notch in the vertical wave number spectrum of the Na concentration pro:le at the corresponding wave number. The vertical phase velocity of the wave is determined from the vertical phase progression in a sequence of Na pro:les. This method required coherence of the wave throughout the altitude of the Na layer so that a spectral signature is found in the vertical wave number spectrum. This requirement biases the method to :nd waves that are coherent throughout the height of the Na layer and are not being strongly modi:ed as they propagate through the Na layer. The use of a notch in the spectrum makes the method very sensitive to the quality of the lidar measurements. This sensitivity is clearly evident in the relative scatter in gravity-wave parameters estimated from UAO Na lidar data (e.g. Collins et al., 1996b) and Antarctic Na lidar data (Collins et al., 1994). The UAO measurements were made with signal levels at least 10 times larger than the Antarctic measurements. Waves that have been characterized with these methods have yielded systematic relationships between the wave parameters that indicate that the characteristics of the waves reported in these earlier studies are de:ned by diLusive and viscous processes. The current method requires coherence of the wave during the entire observation period to yield a statistically signi:cant :t and is biased towards longer period waves. Collins et al. (1992, 1994) noted the presence of long-period oscillations in the bottomside of the Na layer at the South Pole. The observed periods and amplitudes of the South Pole oscillations are similar to that observed at PFRR though the signi:cance of the :tting was not reported. On occasion, such as on 27–28, September 1992, a single large-scale wave that is coherent in time and altitude is detected by both the vertical wave number spectrum approach and the har-

monic :tting method. However, the waves detected by the harmonic :tting approach, as opposed to the vertical wave number spectrum approach, do not show systematic relationships between their wave parameters. This suggests that the waves reported in the current study are not de:ned by diLusive and viscous processes. 6.2. Comparison with CORN experiment The primary goal of the CORN researchers was to determine the type of instabilities (either dynamic or convective) that underlay airglow ripple structures (Hecht et al., 1997). The CORN observations included lidar measurements of temperatures and Na densities in the mesospheric Na layer, airglow imager measurements of OH intensities and MF radar measurements of winds. The key observations were as follows; overturning in the bottomside of the Na layer (lidar) in the presence of a large-scale quasi-monochromatic gravity wave (lidar measurements of Na density, airglow measurements of OH and O2 , MF radar measurements of wind); near adiabatic lapse rates in the temperature pro:le (lidar measurements of temperature); and ripple structures in the airglow layer during the overturning event (Hecht et al., 1997). These observations were then combined with a three-dimensional Euid dynamic model to determine possible physical scenarios consistent with these observations (Fritts et al., 1997). Fritts et al. concluded that they had observed a convective instability arising from the superposition of small- and large-scale gravity waves. The study indicated that the large-scale wave provided background lapse rates that induced overturning of the small-scale waves. The subsequent instability, seen as ripples in the OH images, extracted energy from the superposition and the ensuing turbulence preferentially dissipated the large-scale wave that had a slower wave speed. The PFRR observations presented in this study do not recreate the CORN campaign observations completely. The PFRR observations are limited to Na lidar measurements of quasi-monochromatic gravity waves and overturning structures. The Na layer signatures of these phenomena have the same characteristics at PFRR as those observed at UAO during the CORN campaign. The PFRR lidar observations show that overturning structures embedded in large-scale quasi-monochromatic waves are a relatively common occurrence in the wintertime Arctic mesosphere. The quasi-monochromatic waves are not propagating freely but appear to be damped over the altitude range of the Na layer. This damping does not arise from the linear instability or viscous damping of the large-scale wave. These observations suggest that similar to the CORN observations the overturning is the signature of a convective instability due to superposition of large- and small-scale gravity waves that generates turbulence. The turbulence then acts to dissipate the large-scale wave. A secondary goal of the CORN campaign was to study convective instabilities at longer horizontal wavelength and

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lower intrinsic frequencies than previously studied (Fritts et al., 1997). Linear theory suggests that the threshold for convective instability is constant with respect to the intrinsic frequency of the wave while the threshold for dynamic instability is lower. The threshold for dynamic instability decreases as the ratio of inertial frequency (f) to intrinsic frequency (!), f=! increases (see Fig. 8 of Fritts and Rastogi, 1985). Accordingly, the threshold for dynamic instabilities reduces as the latitude increases. At PFRR (65◦ N) the inertial frequency f is 1.4 times larger than at UAO (40◦ N). These PFRR observations support the view of Fritts and colleagues (Andreassen et al., 1994; Fritts et al., 1994) that while dynamic instability may be important in the early stages of wave breaking, the convective instability grows more rapidly and dominates the wave-breaking process. 6.3. Comparison with Na temperature lidar studies of wave overturning Two other studies have bee reported where Na resonance temperature lidar measurements have been used to study wave breaking and instability in the mesopause region. Williams et al. (2002) and Franke and Collins (2003) have reported lidar observations of wave breaking and overturning in the Na layer at Fort Collins (41◦ N; 105◦ W) and at Star:re Optical Range (35◦ N; 107◦ W). In both these studies the authors calculated the potential temperature from the temperature measurements (Fig. 3 of Williams et al., Figs. 2 and 3 of Franke and Collins) and showed that the wave :elds supported super-adiabatic conditions. Overturning in conserved quantities such as potential temperature has been modeled in gravity-wave instabilities (Walterscheid and Schubert, 1990). These superadiabatic conditions were accompanied by overturning structures in the Na layer that have the same characteristics as those observed at PFRR and during the CORN campaign. While the Na may not be perfectly conserved the Na contours will follow the overturning in the wave. Thus we conclude, that while the PFRR study is limited to measurements of Na alone, and not temperature and Na, the overturning events in Na represent wave-breaking and overturning events. 7. Conclusions Na density lidar observations of the mesospheric Na layer have yielded signatures of oscillations in the mesopause region at Poker Flat Research Range. Simultaneous OH interferometer and Na lidar measurements indicate that these oscillations are consistent with upwardly propagating gravity waves. While phase progressions are commonly observed the lidar data, our analysis has yielded statistically signi:cant measurements of the period and vertical wavelength of upwardly propagating gravity waves in 24 of 52 observation periods. These waves have observed periods between 2.8 and 12:8 h and observed vertical phase velocities be-

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tween 0.17 and 1:8 m=s. These waves do not appear to be propagating freely as their growth lengths are signi:cantly longer (216 km) than the growth length of freely propagating waves (12 km). Our analysis indicates that these waves are damped by a process with an eLective decay length of 13 km. Linear analysis of these waves indicates that the waves are neither viscously damped (by molecular or eddy diLusion) nor inherently convectively unstable. However, overturning structures are detected in the bottomside of the Na layer during 20 of these 24 events. These overturning structures are indicative of convective instabilities as reported in several recent studies (Hecht et al., 1997; Fritts et al, 1997; Williams et al., 2002; Franke and Collins, 2003). We conclude that the overturning arises from instabilities due to superposition of large- and small-scale waves, rather than breaking of the large-scale waves, similar to the interaction reported by Hecht et al. (1997) and modeled by Fritts et al. (1997). The turbulence generated by the instability dissipates the large-scale (long-period) waves and these waves appear damped on the topside of the Na layer. These PFRR observations support the view of Fritts and colleagues (Andreassen et al., 1994; Fritts et al., 1994) that while dynamic instability may be important in the early stages of wave breaking, the convective instability grows more rapidly and dominates the wave breaking process. This study suggests that such events are a common feature in the wintertime high-latitude mesopause region. Acknowledgements The authors acknowledge the eLorts of the following students that assisted in making the lidar observations; Justin Breese, Laura Cutler, Dominic deLucia, Keith Nowicki and Mark Piedra. The authors thank the staL at Poker Flat Research Range for their support over the course of this study. The authors thank Chester S. Gardner for providing the UAO lidar data and Raymond G. Roble for providing the NCAR TIME-GCM results. The authors thank Dirk Lummerzheim and Richard L. Walterscheid for helpful discussions and two anonymous reviewers for important review comments. The study was supported by the NSF CEDAR program (under grants ATM-9415767, ATM-9525787, and ATM-9612870) and by NASA (under grant NAG5-5218). Poker Flat Research Range is a rocket range operated by the Geophysical Institute of the University of Alaska Fairbanks with support from NASA.

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