### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Wave-Induced Vertical Flux of Na
- 3. Production Rate of Na Due to Flux Convergence
- 4. Impact of Wave-Induced Transport on the Na Layer
- 5. Theoretical Relationship Between Heat and Constituent Fluxes
- 6. Physical Interpretation of the Dynamical Constituent Flux
- 7. Vertical Transport Velocities for Heat and Constituents
- 8. Wave-Induced Chemical Transport of Na
- 9. Conclusions
- Appendix A: Estimating Mean Vertical Wind
- Acknowledgments
- References
- Supporting Information

[1] Extensive observations of winds, temperatures, and Na densities between 80 and 105 km at the Starfire Optical Range, New Mexico, are used to characterize the seasonal variations of the vertical flux of atomic Na and its impact on the Na layer. The largely downward Na flux and its convergence enhance the transport of Na from meteoric sources above 90 km to chemical sinks below 85 km, altering the height, width, and abundance of the Na layer. From theoretical considerations, it is shown that the effective vertical velocity associated with dynamical transport by dissipating waves is the same for all species and is about 3 times faster than the effective heat transport velocity. Dynamical transport is generally downward with velocities as high as −5 cm s^{−1} below 90 km in midwinter when and where gravity wave activity and dissipation are strongest. Chemically induced transport of atomic Na by both dissipating and nondissipating waves is also significant so that the total effective transport velocity for Na below 90 km approaches −8 cm s^{−1} in midwinter. The observations show that at the solstices, dynamical and chemical transport play far more important roles than turbulent mixing in transporting Na downward, while at the equinoxes the impacts of all three wave-induced transport mechanisms are comparable. These results have important implications for chemical modeling of the mesopause region.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Wave-Induced Vertical Flux of Na
- 3. Production Rate of Na Due to Flux Convergence
- 4. Impact of Wave-Induced Transport on the Na Layer
- 5. Theoretical Relationship Between Heat and Constituent Fluxes
- 6. Physical Interpretation of the Dynamical Constituent Flux
- 7. Vertical Transport Velocities for Heat and Constituents
- 8. Wave-Induced Chemical Transport of Na
- 9. Conclusions
- Appendix A: Estimating Mean Vertical Wind
- Acknowledgments
- References
- Supporting Information

[2] Wave-induced vertical transport of atmospheric species through mixing, displacement, chemistry and advection, plays a crucial role in establishing the constituent structure of the middle atmosphere. Eddy transport by turbulent mixing has been studied extensively by treating the mechanism as a larger-scale analog of molecular diffusion [e.g., *Colegrove et al.*, 1966]. Turbulent mixing leads to a net transport of constituents from regions of higher concentrations to those of lower concentrations. Gravity waves contribute to eddy transport by generating turbulence when they break [e.g., *Hodges*, 1967; *Lindzen*, 1981]. Dynamical transport arises when wind fluctuations associated with dissipating, nonbreaking waves impart a net vertical displacement in the constituent as they propagate through a region. The Stokes drift studied by *Walterscheid and Hocking* [1991] is an example of a wave-induced displacement mechanism that contributes to dynamical transport. Chemically induced transport of reactive species occurs when vertical advection by wave-induced winds alters the chemical production and loss of the species. Both dissipating and nondissipating waves contribute to chemically induced transport whenever there exists a nonzero correlation between the species fluctuations and the fluctuations in its chemical sources and sinks [*Walterscheid and Schubert*, 1989]. Gravity wave forcing of the meridional circulation system is a global phenomenon that induces a summertime upwelling and wintertime downwelling in the mesopause region [*Lindzen*, 1981; *Holton*, 1982, 1983; *Garcia and Solomon*, 1985], which can approach velocity magnitudes of several cm*s*^{−1}, especially at high latitudes. Vertical advection associated with this upwelling and downwelling, also contributes to the vertical fluxes of all mesospheric species. Although the physics of eddy, dynamical, chemical and advective transport are fundamentally different, all four processes can produce substantial vertical fluxes of middle atmosphere constituents which directly affect the structure of this region [e.g., *Garcia and Solomon*, 1985; *Walterscheid and Schubert*, 1989; *Liu and Gardner*, 2004].

[3] In this paper we explore the transport of atomic Na and its effect on the mesospheric Na layer using extensive observations conducted at the Starfire Optical Range (SOR), near Albuquerque, New Mexico with a Na wind/temperature lidar system. The data are used to characterize the seasonal variations of the vertical flux of atomic Na throughout the mesopause region, the concomitant Na production and loss rates arising from flux convergence and the resulting impact on the structure of the Na layer. From theoretical considerations, we use the measurements to infer the net displacement velocity associated with the dynamical transport by dissipating waves, which we show is the same for all species, and the chemically induced transport velocity associated with the advection of Na bearing species by both dissipating and nondissipating waves. We compare these measurements with the effective eddy transport velocity based upon commonly assumed values for the diffusion coefficient and with vertical drift velocities above SOR that were inferred from the mean meridional winds. We show that all four transport mechanisms are important for atomic Na but their altitude and seasonal variations are considerably different. Dynamical and chemically induced transport are generally directed downward throughout the year. In contrast, eddy transport is downward on the Na layer bottom side and upward on the top side, while advective transport is upward in summer and downward in winter. Each mechanism gives rise to velocity magnitudes as high as several cm*s*^{−1} or more, which make significant contributions to the total Na flux. These results have important implications for chemical models of the mesopause region.

### 2. Wave-Induced Vertical Flux of Na

- Top of page
- Abstract
- 1. Introduction
- 2. Wave-Induced Vertical Flux of Na
- 3. Production Rate of Na Due to Flux Convergence
- 4. Impact of Wave-Induced Transport on the Na Layer
- 5. Theoretical Relationship Between Heat and Constituent Fluxes
- 6. Physical Interpretation of the Dynamical Constituent Flux
- 7. Vertical Transport Velocities for Heat and Constituents
- 8. Wave-Induced Chemical Transport of Na
- 9. Conclusions
- Appendix A: Estimating Mean Vertical Wind
- Acknowledgments
- References
- Supporting Information

[4] For this study we employ 370 hours of mesopause region vertical and horizontal winds, temperature and Na density measurements conducted throughout the year with a steerable lidar system at the SOR (35°N, 106.5°W). *Liu and Gardner* [2004, 2005] and *Gardner and Liu* [2007] have described in detail this extensive data set and the processing techniques used to derive and validate the fundamental wind, temperature and Na density profiles.

[5] The wave-induced vertical flux of a constituent is defined as the expected value of the product of the fluctuations in vertical wind (*w*′, prime denotes a perturbation quantity) and constituent number density (*ρ*′_{C}). Wind, temperature and Na density profiles were derived from the SOR lidar measurements at 500 m vertical resolution and 90 s temporal resolution. Monthly mean profiles of Na density (_{Na}, overbar denotes sample average) and the vertical flux of Na () were computed according to the procedures used by *Gardner and Liu* [2007] for computing the heat and momentum fluxes. All the Na density and flux profiles measured during a given month were averaged and then smoothed vertically using a Hamming window of 2.5 km FWHM. Consequently, the monthly average flux profiles have a vertical resolution of 2.5 km and include the effects of all gravity waves (and atmospheric tides) with vertical wavelengths (*λ*_{z}) and observed periods (*τ*_{obs}) within the following ranges:

The small-scale wave limits are established by the resolution of the fundamental wind and Na measurements (0.5 km and 1.5 min), while the large-scale limits result from the finite vertical extent of the Na layer (∼15 km) and length of the nighttime observation periods (average = 7.4 h). The measured flux profiles include the effects of the important short vertical-scale, high-frequency waves that are most susceptible to dissipation and make the largest contributions to the vertical constituent fluxes. In particular, the measurements include the effects of dynamical and chemical transport by nonbreaking gravity waves. However, the flux measurements do not include the effects of eddy mixing or advective transport, which involve different physics and are derived using entirely different measurements and mathematics. Other approaches are used to estimate the eddy mixing and vertical advection of Na at SOR to assess the relative importance of all four wave-induced transport mechanisms.

[6] The dominant seasonal variations were determined by fitting the monthly mean densities and vertical fluxes to a model that includes the annual mean plus 12 and 6 month oscillations. To illustrate the seasonal variations, the Na density and vertical flux regression models are plotted in contour format in Figure 1. The fitted model parameters are plotted versus altitude in Figure 2, and their values are tabulated in Tables 1 and 2. The errors in the fitted parameters were calculated using the standard regression formulas for the harmonic model.

Table 1. Na Density ParametersAltitude (km) | Mean (cm^{−3}) | Amplitude (cm^{−3}) | Phase (Month) | Model Uncertainty (cm^{−3}) |
---|

12 Month | 6 Month | 12 Month | 6 Month |
---|

105.0 | 124 ± 3.7 | 81 ± 5.3 | 51 ± 5.3 | 10.8 ± 0.1 | 5.2 ± 0.1 | ±8.3 |

102.5 | 314 ± 9.5 | 234 ± 13 | 86 ± 13 | 11.0 ± 0.1 | 5.2 ± 0.1 | ±21 |

100.0 | 833 ± 25 | 554 ± 36 | 140 ± 36 | 11.3 ± 0.1 | 5.2 ± 0.2 | ±56 |

97.5 | 1902 ± 57 | 1054 ± 81 | 223 ± 81 | 11.3 ± 0.1 | 4.8 ± 0.3 | ±130 |

95.0 | 3251 ± 98 | 1773 ± 139 | 366 ± 139 | 11.5 ± 0.2 | 4.3 ± 0.4 | ±220 |

92.5 | 4326 ± 130 | 2123 ± 184 | 733 ± 184 | 11.3 ± 0.2 | 3.8 ± 0.2 | ±290 |

90.0 | 4316 ± 130 | 2316 ± 184 | 883 ± 184 | 11.2 ± 0.2 | 4.1 ± 0.2 | ±290 |

87.5 | 3255 ± 98 | 2175 ± 139 | 1098 ± 139 | 11.2 ± 0.1 | 4.4 ± 0.1 | ±220 |

85.0 | 1762 ± 53 | 1407 ± 75 | 1047 ± 75 | 10.9 ± 0.1 | 4.5 ± 0.1 | ±120 |

82.5 | 548 ± 17 | 470 ± 23 | 219 ± 23 | 10.9 ± 0.1 | 4.8 ± 0.1 | ±38 |

80.0 | 115 ± 3.5 | 141 ± 4.9 | 48 ± 4.9 | 11.1 ± 0.1 | 4.8 ± 0.1 | ±7.8 |

Table 2. Measured Na Flux ParametersAltitude (km) | Mean (cm^{−3} m s^{−1}) | Amplitude (cm^{−3} m s^{−1}) | Phase (Month) | Model Uncertainty (cm^{−3} m s^{−1}) |
---|

12 Month | 6 Month | 12 Month | 6 Month |
---|

100.0 | −11.6 ± 7.8 | 21.8 ± 11.0 | 22.6 ± 11.0 | 4.1 ± 1.0 | 2.8 ± 0.5 | ±17 |

97.5 | −47.5 ± 8.8 | 30.5 ± 12.5 | 11.0 ± 12.5 | 3.8 ± 0.8 | 2.4 ± 1.1 | ±20 |

95.0 | −59.3 ± 9.7 | 31.2 ± 13.7 | 12.1 ± 13.7 | 4.9 ± 0.8 | 2.9 ± 1.1 | ±22 |

92.5 | −70.1 ± 10.6 | 41.3 ± 15.0 | 27.3 ± 15.0 | 5.4 ± 0.7 | 3.6 ± 0.5 | ±24 |

90.0 | −101.0 ± 12.3 | 81.0 ± 17.4 | 58.2 ± 17.4 | 5.7 ± 0.4 | 2.8 ± 0.3 | ±28 |

87.5 | −106.6 ± 15.3 | 110.1 ± 21.7 | 64.1 ± 21.7 | 5.9 ± 0.4 | 3.2 ± 0.3 | ±34 |

85.0 | −50.5 ± 14.1 | 94.1 ± 19.9 | 33.5 ± 19.9 | 5.6 ± 0.4 | 2.9 ± 0.6 | ±32 |

[7] The Na profiles exhibit strong seasonal variations with minimum densities in midsummer and maximum densities in November. This well-known behavior is driven primarily by temperature-dependent chemistry and to a lesser extent by the meteoric input [*McNeil et al.*, 1995]. The Na flux also exhibits strong seasonal variations, which arise in part because of the seasonal variations of the Na densities. In fact the largest downward Na fluxes (∼ −280 m s^{−1} cm^{−3} at 88 km) occur just below the peak of the Na layer in midwinter when the densities are also largest. In general the Na flux is downward (negative) throughout the mesopause region except during the spring equinox when it exhibits small upwardly directed (positive) values. The annual mean Na flux is downward throughout the altitude range with a maximum value of 120 m s^{−1} cm^{−3} near 88 km. The amplitudes of the 12 month and 6 month oscillations have prominent maxima near 88 km of about 100 and 65 m s^{−1} cm^{−3}, respectively.

[8] The vertical structure and seasonal variations of the Na fluxes are consistent with the observed behavior in gravity wave activity reported by *Gardner and Liu* [2007]. The perturbation variances of temperature and winds and the atmospheric instability probabilities are greatest at the solstices. Furthermore, the vertical heat flux [see *Gardner and Liu*, 2007, Figure 6], which is a proxy for wave dissipation [*Walterscheid*, 1981; *Weinstock*, 1983; *Walterscheid*, 2001; *Gardner and Yang*, 1998], is largest just below 90 km at the solstices. Thus as expected, the Na flux is largest when and where the gravity wave variances and dissipation are also strongest.

### 3. Production Rate of Na Due to Flux Convergence

- Top of page
- Abstract
- 1. Introduction
- 2. Wave-Induced Vertical Flux of Na
- 3. Production Rate of Na Due to Flux Convergence
- 4. Impact of Wave-Induced Transport on the Na Layer
- 5. Theoretical Relationship Between Heat and Constituent Fluxes
- 6. Physical Interpretation of the Dynamical Constituent Flux
- 7. Vertical Transport Velocities for Heat and Constituents
- 8. Wave-Induced Chemical Transport of Na
- 9. Conclusions
- Appendix A: Estimating Mean Vertical Wind
- Acknowledgments
- References
- Supporting Information

[9] The direct effect of vertical constituent transport is local production or loss of the constituent. The production rate of Na due to vertical flux convergence is

The seasonal variations of the Na production rate at SOR are shown in Figure 3. The annual mean profile plus the 12 month and 6 month amplitudes and phases are plotted versus altitude in Figure 4, and their values are tabulated in Table 3.

Table 3. Measured Na Dynamical Production Rate ParametersAltitude (km) | Mean (cm^{−3} h^{−1}) | Amplitude (cm^{−3} h^{−1}) | Phase (Month) | Model Uncertainty (cm^{−3} h^{−1}) |
---|

12 Month | 6 Month | 12 Month | 6 Month |
---|

100.0 | −47.1 ± 7.9 | 10.8 ± 11.2 | 15.7 ± 11.2 | 5.1 ± 2.0 | 4.1 ± 0.7 | ±18 |

97.5 | −36.8 ± 9.0 | 29.8 ± 12.7 | 21.8 ± 12.7 | 4.3 ± 0.8 | 0.4 ± 0.6 | ±20 |

95.0 | −22.6 ± 9.9 | 35.8 ± 13.9 | 47.8 ± 13.9 | 9.1 ± 0.7 | 4.0 ± 0.3 | ±22 |

92.5 | −7.4 ± 10.8 | 60.6 ± 15.3 | 43.0 ± 15.3 | 5.3 ± 0.5 | 2.0 ± 0.3 | ±24 |

90.0 | −74.2 ± 12.5 | 56.9 ± 17.7 | 47.5 ± 17.7 | 6.6 ± 0.6 | 3.3 ± 0.4 | ±28 |

87.5 | 63.6 ± 15.6 | 18.6 ± 22.1 | 16.0 ± 22.1 | 3.8 ± 2.3 | 5.9 ± 1.3 | ±35 |

85.0 | 106.2 ± 14.4 | 73.4 ± 20.3 | 92.6 ± 20.3 | 11.5 ± 0.5 | 6.2 ± 0.2 | ±32 |

[10] The annual mean production rate exhibits local maxima on the bottom side of the Na layer with values of about 106 cm^{−3} h^{−1} at 85 km and −74 cm^{−3} h^{−1} at 90 km. The 12 and 6 month oscillations are also substantial. In particular the 6 month amplitudes reach peak values of 80 and 93 cm^{−3} h^{−1} at 92 and 85 km altitude, respectively. The strong semiannual oscillations are particularly apparent in the contour plot (Figure 4).

[11] These production rates are significant, even in comparison to the primary source of mesospheric Na, meteoric ablation. The meteoric input flux of Na averages about 2.5 × 10^{7} cm^{−2} h^{−1} [*Plane*, 2004]. The ablation profile depends on the entry speed of the meteoroids and their size, with the faster, smaller meteoroids ablating at higher altitudes. If we assume that the height and width of the meteoric ablation profile is similar to the mean Na profile, then the peak meteoric source rate near 92 km is about 25 cm^{−3} h^{−1}. Thus, the production and loss of Na associated with wave-induced transport is at least comparable to the meteoric input and at some altitudes during certain times of the year, it is many times larger.

### 4. Impact of Wave-Induced Transport on the Na Layer

- Top of page
- Abstract
- 1. Introduction
- 2. Wave-Induced Vertical Flux of Na
- 3. Production Rate of Na Due to Flux Convergence
- 4. Impact of Wave-Induced Transport on the Na Layer
- 5. Theoretical Relationship Between Heat and Constituent Fluxes
- 6. Physical Interpretation of the Dynamical Constituent Flux
- 7. Vertical Transport Velocities for Heat and Constituents
- 8. Wave-Induced Chemical Transport of Na
- 9. Conclusions
- Appendix A: Estimating Mean Vertical Wind
- Acknowledgments
- References
- Supporting Information

[12] Vertical dynamical transport of Na will affect the structure of the layer and its seasonal variations. The density changes associated with wave-induced transport are related to the production rate and the chemical lifetime of atomic Na (*τ*_{Na}), which varies with altitude:

[13] Above 95 km, ion chemistry predominates where ablated Na atoms are converted to Na^{+} mostly by charge transfer with ambient NO^{+} and O_{2}^{+} ions. Below 85 km, Na is converted to the stable reservoir NaHCO_{3}, via a series of reactions beginning with the oxidation of atomic Na by ozone. In both regions Na ions and compounds can be converted back to atomic Na on time scales that depend on the relevant reaction rates, ambient temperatures and minor species concentrations [*Plane*, 2004]. Below the peak of the layer during nighttime, the Na lifetimes vary from less than 1 hour at 80 km altitude to more than 10 hours at 90 km altitude (J. M. C. Plane, University of Leeds, private communication, 2010) so that the densities associated with transport can be large. For example, for a Na lifetime of 2 h at 85 km, wave-induced transport will enhance the average density by 200 cm^{−3} (see Figure 4a). The annual average Na concentration is about 1800 cm^{−3} at 85 km (see Table 1) so the mean transport contribution is about 11%.

[14] Another effect of downward transport is to reduce the density gradient on the bottom side of the Na layer. The vertical flux contribution to the Na gradient is related to the production rate and Na lifetime variation with altitude:

This contribution can be significant. For example, for the annual mean production rate profile we calculate an average value of ∂*P*_{Na}/∂*z* = −50 cm^{−3} km^{−1} h^{−1} at about 88 km where *P*_{Na} = 0 and ∂*ρ*_{Na}/∂*z* = 500 cm^{−3} km^{−1}. Thus if the Na lifetime is 5 h, the flux contribution to the density gradient is −250 cm^{−3} km^{−1}, which is opposite in sign to the total gradient and a substantial fraction of its magnitude.

[15] The seasonal variation of the mean Na density gradient between 88 and 90 km is plotted versus time in Figure 5 along with the seasonal variation of the transport contribution that was calculated from equation (3) by assuming a Na lifetime of 5 h, which provides the best match between the two curves. Also plotted in Figure 5 is the estimated Na density gradient in the absence of transport (difference of the two Na gradient curves). Wave-induced transport has a significant effect on the Na density gradient on the bottom side of the layer between 88 and 90 km, reducing its value by approximately 50% and introducing a strong semiannual oscillation.

[16] The largely downward transport of Na observed in Figure 1b, especially in midwinter below 95 km, results in a broadening of the Na layer, a downward displacement of centroid height and a reduction in the Na abundance because of the enhanced transport of atomic Na from meteoric sources above 90 km to stable chemical sinks below 85 km. Furthermore, the seasonal variations in the Na flux will introduce similar variations into the layer centroid height, width and abundance.

[17] The impact of wave-induced transport on the overall layer structure can be significant. To illustrate we make the following order-magnitude calculations. The annual mean Na flux between 85 and 100 km is about −64 ms^{−1} cm^{−3} and the average Na density is about 2800 cm^{−3}. The ratio yields an effective transport velocity of about −2.3 cms^{−1}. By comparison, the mean residence time for a Na atom in the layer after meteoricablation, including its time as an ion or an intermediate compound, before it is transported below 80 km by various mixing and advection processes and permanently removed in a stable chemical sink, is given approximately by the ratio of the mean Na abundance (5.2 × 10^{9} cm^{−2}) and to the mean meteoric source rate or about 200 h. The average transport distance from source (mean ablation altitude ∼92 km) to sink (∼80 km) is 12 km so that the average vertical transport velocity is slightly more than −1.6 cms^{−1}. Based upon these approximate calculations, wave-induced transport appears to be a substantial fraction of the overall transport velocity and as a result, will have a significant influence of the height of the Na layer and its abundance.

### 5. Theoretical Relationship Between Heat and Constituent Fluxes

- Top of page
- Abstract
- 1. Introduction
- 2. Wave-Induced Vertical Flux of Na
- 3. Production Rate of Na Due to Flux Convergence
- 4. Impact of Wave-Induced Transport on the Na Layer
- 5. Theoretical Relationship Between Heat and Constituent Fluxes
- 6. Physical Interpretation of the Dynamical Constituent Flux
- 7. Vertical Transport Velocities for Heat and Constituents
- 8. Wave-Induced Chemical Transport of Na
- 9. Conclusions
- Appendix A: Estimating Mean Vertical Wind
- Acknowledgments
- References
- Supporting Information

[18] All of the gaseous constituents in a region will be affected by wave-induced transport. Unfortunately, it is only possible to measure constituent fluxes for those species that can be observed simultaneously with the vertical wind. In the mesopause region, only the Na flux has been measured. However, if the chemical lifetime of a species is long compared to the periods of the important high-frequency gravity waves, the constituent fluctuations can be expressed in terms of the temperature fluctuations so that the vertical flux of the species can be inferred when the heat flux, temperature and species density profiles are known.

[19] The first attempt to relate the heat and constituent fluxes was published by *Liu and Gardner* [2004], who used a linear perturbation technique to express the constituent density fluctuations as a linear function of the temperature fluctuations. This approach is valid on the bottom and topside of a constituent layer where the linear layer response is dominant, but it breaks down near the peak of the layer where nonlinear effects are significant [*Gardner and Shelton*, 1985]. In the following, we extend those previous results by deriving an expression for the constituent flux that is valid even in regions where the nonlinear layer response to gravity wave fluctuations is important.

[20] The density response of the neutral atmosphere or of an atmospheric layer composed of a neutral constituent is governed by the continuity equation

where **V** is the velocity of the constituent and *P* and *L* represent the production and loss terms. We assume the effects of molecular diffusion are negligible in comparison to the wind fluctuations so that the constituent velocity is equal to the atmospheric velocity. This is a reasonable assumption because the effective vertical diffusion velocities in the mesopause region are typically less than a few mms^{−1} while the RMS vertical wind fluctuations are several hundred times faster [*Gardner and Liu*, 2007]. We also ignore chemical effects and other constituent sources and sinks so that *P* and *L* are zero.

[21] When the unperturbed constituent is horizontally homogeneous, *Gardner and Shelton* [1985] have shown that the density response to wind fluctuations may be written in the form

where *ρ*_{C} (**p**, *t*) is the perturbed constituent density at position **p** and time *t* and *ρ*_{C0}(*z*) is the steady state density profile in the absence of wind fluctuations. By substituting (5) in (4) with *P* = *L* = 0 and rearranging terms, it is easy to show that the parameters *χ*(**p**, *t*) and *ζ*(**p**, *t*) are solutions to the partial differential equations

where the atmospheric velocity field is given by

The parameters *u*, *v*, and *w* denote the zonal, meridional, and vertical wind velocities, respectively, with the angle brackets denoting the ensemble mean and the prime denoting the wind fluctuation.

[22] *Gardner and Shelton* [1985] showed that gravity wave winds, the dominant sources of wind fluctuations in the mesosphere, are small enough that second- and higher-order perturbation effects are negligible in (6). As a consequence, *χ* and *ζ* are accurately represented by the first-order perturbation solutions of these equations. We assume the mean vertical velocity 〈*w*(*z*)〉 and the divergence of the mean wind field ∇ · 〈**V**〉 are negligible so that

The constituent fluctuations given by (5) and (8) result from a multiplicative distortion *e*^{−χ} due to the wind divergence and a vertical displacement *ζ* caused by the vertical wind. Notice that these solutions include the effects of horizontal advection associated with the mean horizontal wind profile 〈*u*(*z*)〉 + 〈*v*(*z*)〉.

[23] By expressing the unperturbed constituent number density in terms of its spatial Fourier transform P_{C0}(*κ*), the perturbed density profile given by (5) and the constituent flux may be written as

and

To evaluate the expectation on the right hand side of (10), we assume that wind fluctuations are Gaussian distributed. Because *χ* and *ζ* are linearly related to the wind fluctuations through (8), *χ*, *ζ* and *w*′ are jointly distributed Gaussian random processes. Consequently, the expectation in (10) can be evaluated in closed form so that the constituent flux may be written as

where

Because *ζ* is equal to the vertical displacement, it is orthogonal to the vertical wind fluctuations so that 〈*w*′*ζ*〉 = 0 and (11) reduces to

We call this the dynamical flux to differentiate it from the additional wave-induced chemical transport that may be important for chemically active species.

[24] These expressions for the dynamical constituent flux and mean constituent profile were derived by making three crucial assumptions: (1) chemical effects and other sources are negligible on the time scales of the important wind fluctuations, (2) the wind fluctuations are small enough that *χ* and *ζ* can be accurately represented by the first-order perturbation solutions to equation (6), and (3) the wind fluctuations are Gaussian distributed random processes. Because of the first assumption, the results apply in the strictest sense, only to chemically inert constituents. For chemically active species like mesospheric Na, the observed flux will differ from the value predicted by (13), especially in regions where the chemical lifetime of the species is short. We address wave-induced chemical transport in section 8.

[25] *Gardner and Shelton* [1985] have shown that the second assumption is valid, even in the mesopause region where gravity wave amplitudes, the dominant source of wind fluctuations, frequently reach saturation levels. Finally, statistical analysis of measured mesopause winds and temperatures has also confirmed that the Gaussian assumption is valid [*Gardner and Yang*, 1998]. This is expected since the fluctuations in winds and temperature are the sum of contributions from many different sources, including waves propagating in different directions that were generated by different sources primarily in the lower atmosphere. According to the Central Limit Theorem, when the number of independent perturbation sources becomes sufficiently large, the temperature and wind fluctuations can be modeled as Gaussian-distributed random processes.

[26] We invoke the Boussinesq approximation and assume the wind fluctuations are much smaller than the speed of sound. In this case pressure fluctuations are negligible in comparison with the associated temperature and atmospheric density fluctuations (*ρ*′_{A}). Therefore, equation (5) and the ideal gas law can be used to show that

where

is pressure scale height of the atmosphere, *R* = 287 m^{2}K^{−1} s^{−2} is the universal gas constant, *g* = 9.5 ms^{−2} is the acceleration of gravity and 〈*T*(*z*)〉 is the mean temperature profile. According to the thermodynamic equation, the temperature change for a parcel of air that is displaced vertically by an amount *ζ* is *T*′ = −(Γ_{ad} + ∂〈*T*〉/∂*z*)*ζ* so that

where Γ_{ad} = *g*/*C*_{p} ≃ 9.5 K km^{−1} is the dry adiabatic lapse rate and *C*_{p} is the specific heat at constant pressure. By combining (14)–(16) and solving for *χ* we obtain

As a consequence of (13) and (17), the dynamical constituent flux is directly proportional to the heat flux

Because (18) is the flux that arises from partially correlated fluctuations in the vertical wind and constituent density, it does not include the eddy flux which results from turbulent mixing nor the advective flux associated with the mean vertical drift. We address wave-induced eddy and advective transport in section 9.

[27] The theoretical covariance between the temperature and constituent fluctuations can also be computed by simply substituting *T*′ for *w*′ in (11):

where

is the scale height of the mean constituent density profile. The term involving ∂〈*ρ*_{C}〉/∂*z* = −〈*ρ*_{C}〉/*H*_{C} in (19) arises because the temperature fluctuations are approximately proportional to vertical displacement. This term does not appear in the expression for constituent flux because the vertical wind fluctuations are orthogonal to the vertical displacement fluctuations, even when they are caused by dissipating waves. *Liu and Gardner* [2004, 2005] used (5), (16), and (17) to expand the constituent density in a perturbation series about *T*′. They then used the first-order term of the series to express *ρ*′_{C} as a function of *T*′. Their approach did not take into account the fact that *w*′ and *ζ* are orthogonal and as a consequence their expression for the constituent flux includes an additional, superfluous term involving ∂〈*ρ*_{C}〉/∂*z*.

[28] These simple relationships for the vertical constituent flux and constituent/temperature covariance are a direct consequence of the close relationships between the constituent and temperature fluctuations described by (5), (16), and (17). Although gravity waves are a major source of those fluctuations in the mesosphere, the theoretical derivations leading to (18) and (19) are general and the formulas apply to all wind, temperature and constituent fluctuations, with the exception of those related to the constituent chemistry, which has been ignored.

### 6. Physical Interpretation of the Dynamical Constituent Flux

- Top of page
- Abstract
- 1. Introduction
- 2. Wave-Induced Vertical Flux of Na
- 3. Production Rate of Na Due to Flux Convergence
- 4. Impact of Wave-Induced Transport on the Na Layer
- 5. Theoretical Relationship Between Heat and Constituent Fluxes
- 6. Physical Interpretation of the Dynamical Constituent Flux
- 7. Vertical Transport Velocities for Heat and Constituents
- 8. Wave-Induced Chemical Transport of Na
- 9. Conclusions
- Appendix A: Estimating Mean Vertical Wind
- Acknowledgments
- References
- Supporting Information

[29] The theoretical expression for the constituent flux has a simple physical interpretation. Dynamical transport and the resulting constituent fluxes arise when dissipating waves impart a net vertical displacement in the atmospheric constituents as they propagate through a region. The dynamical flux can be expressed as the product of the mean constituent density and an effective vertical transport velocity, which depends only on the heat flux and temperature profiles:

[30] The parameter *w*_{Dyn} may be regarded as the effective vertical velocity associated with dynamical constituent transport, while *w*_{Heat} is the effective velocity associated with heat transport. In the mesopause region, constituent transport velocities are generally directed downward (because the heat flux and hence *w*_{Heat} are negative) and vary from a few millimeters per second to almost 10 cms^{−1} in regions of strong wave dissipation. In an isothermal atmosphere, constituent transport is about 2.5 times faster than heat transport because the relative constituent fluctuations are larger than the relative temperature fluctuations. This is a consequence of (14) and the thermodynamic equation, which lead to (18). The dynamical transport velocity varies with altitude and time, depending on gravity wave activity and the stability of the atmosphere, but it is the same for all constituents. Therefore, *w*_{Dyn} is a universal parameter, similar to the eddy diffusion coefficient, that can be used to characterize the constituent transport associated with dissipating but nonbreaking gravity waves.

[31] It is instructive to compare the displacement velocities associated with dynamical transport with the effective constituent velocities associated with transport by turbulent mixing. The vertical eddy flux (EF) is derived from the continuity equation and is given by the well-known expression [*Colegrove et al.*, 1966]

where *K*_{zz} is the eddy diffusivity and *ρ*_{A}(*z*) is the atmospheric density profile. *H*_{C} is the constituent density scale height. Eddy transport of a constituent occurs only in the presence of a gradient in the constituent mixing ratio. In an isothermal atmosphere, it is downward whenever the constituent scale height is smaller than *H* and upward whenever *H*_{C} > *H*.

[32] Like the dynamical flux, eddy flux can also be expressed as the product of an effective constituent velocity and the constituent density profile:

In the mesopause region where the atmospheric scale height is about 6 km and *K*_{zz} is believed to be vary from a few tens to a few hundred m^{2} s^{−1} [*Lübken*, 1997; *Plane*, 2004; *Liu*, 2009], *w*_{Diff} varies from a few millimeters to a few centimeters per second. These values are comparable to the effective heat transport velocities associated with the heat flux *w*_{Heat}. The scale factor *α*_{C}, which depends on the constituent scale height, can reach magnitudes of 2–5 where the constituent volume mixing ratio exhibits steep vertical gradients so that the effective transport velocity associated with turbulent mixing (*w*_{Mix}) can be as large as the dynamical transport velocity (*w*_{Dyn}). In other words, the dynamical and eddy fluxes of atmospheric constituents reach comparable magnitudes in the mesopause region, however their profiles can be quite different. Significantly, dynamical flux depends only on the constituent density profile, while eddy flux depends on both the density profile and its vertical gradient. Furthermore, while the dynamical flux is generally downward, the eddy flux can have strong upward components in regions where the constituent scale height is small and positive, such as the topside of the Na layer.

### 7. Vertical Transport Velocities for Heat and Constituents

- Top of page
- Abstract
- 1. Introduction
- 2. Wave-Induced Vertical Flux of Na
- 3. Production Rate of Na Due to Flux Convergence
- 4. Impact of Wave-Induced Transport on the Na Layer
- 5. Theoretical Relationship Between Heat and Constituent Fluxes
- 6. Physical Interpretation of the Dynamical Constituent Flux
- 7. Vertical Transport Velocities for Heat and Constituents
- 8. Wave-Induced Chemical Transport of Na
- 9. Conclusions
- Appendix A: Estimating Mean Vertical Wind
- Acknowledgments
- References
- Supporting Information

[33] The effective transport velocities for heat and constituents observed at SOR were computed by substituting the measured heat flux and temperature profiles into equations (21), (23), and (24):

In addition, the observed Na transport velocity was computed by substituting the measured Na flux and Na density profiles into equation (22):

Contour plots of the seasonal variations of these three transport velocities are shown in Figure 6. The annual mean profile of the dynamical transport velocity (_{Dyn}) plus the 12 month and 6 month amplitudes and phases are plotted versus altitude in Figure 7, and their values are tabulated in Table 4.

Table 4. Measured Constituent Transport Velocity (*w*_{Dyn}) ParametersAltitude (km) | Mean (cm s^{−1}) | Amplitude (cm s^{−1}) | Phase (Month) | Model Uncertainty (cm s^{−1}) |
---|

12 Month | 6 Month | 12 Month | 6 Month |
---|

100.0 | 0.13 ± 0.23 | 1.92 ± 0.33 | 0.88 ± 0.33 | 1.2 ± 0.3 | 3.7 ± 0.4 | ±0.51 |

97.5 | 0.22 ± 0.20 | 0.26 ± 0.28 | 0.64 ± 0.28 | 2.3 ± 2.1 | 3.7 ± 0.4 | ±0.45 |

95.0 | 0.03 ± 0.20 | 0.05 ± 0.28 | 0.64 ± 0.28 | 5.5 ± 11 | 3.1 ± 0.4 | ±0.45 |

92.5 | −0.53 ± 0.23 | 0.58 ± 0.33 | 0.14 ± 0.33 | 6.0 ± 1.1 | 2.6 ± 2.3 | ±0.52 |

90.0 | −1.59 ± 0.22 | 1.08 ± 0.31 | 1.17 ± 0.31 | 6.4 ± 0.5 | 3.2 ± 0.3 | ±0.49 |

87.5 | −1.67 ± 0.19 | 1.04 ± 0.27 | 1.09 ± 0.27 | 5.8 ± 0.5 | 3.3 ± 0.2 | ±0.42 |

85.0 | −1.48 ± 0.20 | 0.68 ± 0.29 | 1.45 ± 0.29 | 3.0 ± 0.8 | 3.3 ± 0.2 | ±0.44 |

[34] Theoretically, dissipating gravity waves transport heat and constituents downward [*Walterscheid*, 1981; *Weinstock*, 1983; *Walterscheid*, 2001]. All three measured transport velocities are generally downward throughout the mesopause region. They vary strongly with altitude and exhibit prominent annual and semiannual oscillations. Weakest transport occurs at the equinoxes when the average values of _{Heat}, _{Dyn} and _{Na}, between 85 and 100 km, are nearly zero. The weak upward velocities, observed primarily at high altitudes during the equinoxes, suggest that the measured fluctuations are being influenced by other effects, in addition to gravity waves. The largest heat transport velocities, in excess of −1 cms^{−1}, occur in midwinter and midsummer between 85 and 90 km where static instabilities dominate the wave dissipation processes and above 97 km in midsummer where shear instabilities dominate [*Gardner and Liu*, 2007]. The inferred dynamical transport velocities exhibit a similar pattern but the magnitudes average about 3 times larger than _{Heat}, depending on the environmental lapse rate. The observed Na transport velocities (_{Na}), which were derived directly from the measured Na fluxes and densities, also exhibit the same general altitude and seasonal behavior as _{Heat} and _{Dyn}. However, _{Na} averages almost 3 times larger than _{Dyn} and about 9 times larger than _{Heat}.

[36] Plotted versus altitude in Figure 8 is the theoretical correlation between the temperature and density fluctuations for an inert species with a Gaussian shaped density profile that is similar to the annual mean Na density profile. The temperature and constituent fluctuations are positively correlated on the bottom side of the layer where they are in-phase and negatively correlated (180° out of phase) on the top side. As expected the correlation is nearly perfect (±1) on both sides of the layer where the density fluctuations are approximately linearly related to temperature through equations (5), (16), and (17). Near the peak of the layer around 92 km where nonlinear effects dominate, the correlation decreases as it transitions smoothly between the bottom and topside values.

[37] The observed correlation between the measured Na and temperature fluctuations is also plotted in Figure 8. Although the Na/temperature correlation is relatively high below 90 km, it reaches a maximum value of only 0.8, less than the theoretical value of +1 for an inert species for which the constituent and temperature fluctuations are linearly related. On the layer topside, the measured correlation is even lower, reaching a maximum value of just −0.4 compared to −1 for the inert species. These results suggest that chemical effects throughout Na layer have altered the simple linear relationships between the Na and temperature fluctuations predicted by (5). A further complication for Na is the importance of ion chemistry on the topside of the layer above 95 km. The theoretical results only apply to neutral species.

[38] Because the total amount of Na in all the Na bearing species is conserved, *w*_{Dyn} is the effective dynamical transport velocity associated with the total flux of all neutral Na species. This is true for all chemically active constituents and follows directly from the continuity equation and the law of mass action,

where *ρ*_{CT} is the total constituent concentration, *ρ*_{Ci} is the concentration of the *i*th specie containing the constituent and *P*_{i} and *L*_{i} are associated chemical sources and sinks. Because the sources and sinks are balanced in (33), chemistry plays no role in altering the fluctuations in *ρ*_{CT} and its vertical flux so that

Although the observed transport velocities of the individual species may differ because of coupled chemistry and dynamics, the effective transport velocity of the total constituent is identical to *w*_{Dyn}.

### 8. Wave-Induced Chemical Transport of Na

- Top of page
- Abstract
- 1. Introduction
- 2. Wave-Induced Vertical Flux of Na
- 3. Production Rate of Na Due to Flux Convergence
- 4. Impact of Wave-Induced Transport on the Na Layer
- 5. Theoretical Relationship Between Heat and Constituent Fluxes
- 6. Physical Interpretation of the Dynamical Constituent Flux
- 7. Vertical Transport Velocities for Heat and Constituents
- 8. Wave-Induced Chemical Transport of Na
- 9. Conclusions
- Appendix A: Estimating Mean Vertical Wind
- Acknowledgments
- References
- Supporting Information

[39] *Hickey and Plane* [1995], *Plane et al.* [1999], and *Xu et al.* [2003] analyzed the effects of chemistry on the Na and Fe fluctuations induced by monochromatic gravity waves propagating through these layers. They showed that the fluctuations can be larger or smaller than those expected for inert tracers because of chemistry. Chemical amplification and quenching of the constituent fluctuations depends on the gravity wave period, altitude and season. For the cases studied (wave periods of 90 min or shorter), the amplification (or quenching) in Na was greatest in June but reached values no larger than about ±20% at the extreme edges of the Na layer. In contrast, the amplification could be as high as a factor of 2–4 for Fe below 87 km. *Hickey and Plane* [1995] concluded that Na may be regarded as a conserved tracer of wave dynamics above 85 km. Our measurements of Na at SOR are consistent with these modeling results. Below 90 km the RMS Na fluctuations are 20%–30% less than expected for an inert species while above 98 km they are 10%–15% larger. Although chemistry plays a role, the small chemical amplification and quenching effects that we measured and that *Hickey and Plane* [1995] and *Plane et al.* [1999] calculated for Na, cannot explain the large differences we observe between _{Na} and _{Dyn}. Apparently, chemistry introduces other small amplitude Na fluctuations that are uncorrelated with temperature, contribute little to the total Na variance but are well correlated with the vertical wind fluctuations so that their contribution to the observed Na flux is significant.

[40] *Walterscheid and Schubert* [1989] calculated the dynamical fluxes of the chemically active species O, O_{3} and H induced by monochromatic gravity waves and analyzed their impact on the nighttime mesospheric OH layer. They showed that gravity waves significantly alter the mixing ratios of O_{3} and OH as a consequence of fast chemistry, which results in significant vertical fluxes of these species, even in the absence of wave dissipation. They called this effect chemically induced transport. Because O, O_{3}, and H also play important roles in Na chemistry [*McNeil et al.*, 1995; *Plane*, 2003], chemically induced transport by both dissipating and nondissipating gravity waves may be responsible for the large transport velocities observed for Na.

[41] Following the approach of *Walterscheid and Schubert* [1989], the rate of change of the mixing ratio caused by chemical reactions is

where *Q*_{C} is the net chemical production or loss of the constituent. The first-order perturbation form of this equation is

where (*Q*_{C}/*ρ*_{A}) is a consequence of the coupled chemistry and dynamics. After multiplying both sides of (36) by the perturbed mixing ratio, averaging and rearranging terms, we obtain for the mixing ratio flux

Chemistry has no impact on atmospheric density *ρ*_{A}, so that the relative atmospheric density flux in (37) may be replaced by *w*_{Dyn} (see (22) with *ρ*_{C} replaced by *ρ*_{A}). Solving for the relative constituent flux or equivalently, the total constituent transport velocity, we finally obtain

where

is the effective chemically induced transport velocity and *α*_{C} is given by (29). Although *w*_{Dyn} is zero in the absence of wave dissipation because the heat flux is zero, the chemically induced transport velocity can be significant even for nondissipating waves. It is nonzero whenever the net source fluctuations are partially correlated with the constituent or temperature fluctuations.

[42] The observed chemically induced transport velocity for Na is

which is plotted in Figure 9. _{ChemNa} is generally downward with values ranging from approximately zero to more than −8 cms^{−1} near 85 km in February. Chemical transport is especially strong during summer throughout the 85–100 km region when the vertical wind variance is also strongest [*Gardner and Liu*, 2007, Figure 4g]. In fact, the seasonal and vertical structure of _{ChemNa} is remarkably similar to that for the vertical wind variance, which suggests that the dominant chemically induced fluctuations in Na are approximately proportional to the vertical wind fluctuations. This is consistent with the less than perfect correlation between the Na and temperature fluctuations observed on the bottom and top sides of the layer in Figure 8. However, the effects of chemistry are complex as the results of time resolved chemical models of Na and Fe have demonstrated [*Hickey and Plane*, 1995; *Plane et al.*, 1999]. The Na fluctuations induced by coupled chemistry and dynamics depend upon the speed and temperature dependence of the key chemical reactions as well as the temporal frequency spectrum of the waves.

### 9. Conclusions

- Top of page
- Abstract
- 1. Introduction
- 2. Wave-Induced Vertical Flux of Na
- 3. Production Rate of Na Due to Flux Convergence
- 4. Impact of Wave-Induced Transport on the Na Layer
- 5. Theoretical Relationship Between Heat and Constituent Fluxes
- 6. Physical Interpretation of the Dynamical Constituent Flux
- 7. Vertical Transport Velocities for Heat and Constituents
- 8. Wave-Induced Chemical Transport of Na
- 9. Conclusions
- Appendix A: Estimating Mean Vertical Wind
- Acknowledgments
- References
- Supporting Information

[43] The vertical flux of any species is the sum of the wave-induced dynamical and chemical fluxes, the flux due to turbulent mixing, the molecular diffusion flux, which is small but not negligible in the mesopause region [*Chabrillat et al.*, 2002], and the flux due to advection by the mean vertical winds. For atomic Na, all wave-induced vertical transport mechanisms appear to be important. Our observations of the Na flux given by include only the effects of dynamical and chemically induced transport. Although the fundamental resolution of the lidar system (500 m and 90 s) was sufficient to observe all the important waves, it was not adequate to resolve even the largest-scale eddies responsible for turbulent mixing which are believed to be no larger than a few hundred meters. However, the eddy transport velocity can be estimated by assuming appropriate values for the eddy diffusivity and using our observations of the Na and temperature profiles to compute the Na scale height and temperature lapse rate to evaluate equations (26), (28), and (29). Unfortunately, the magnitude of the eddy diffusion coefficient in the mesopause region is uncertain.

[44] *Liu* [2009] used the momentum and heat flux observations at SOR to estimate the effective momentum and heat diffusivities and the related Prandtl number between 85 and 100 km. The annual mean momentum diffusion coefficient is about 400 m^{2}s^{−1} while the mean thermal diffusion coefficient decreases from 400 m^{2}s^{−1} at 85 km to 100 m^{2}s^{−1} at 100 km. Since the estimates were based on the observed momentum and heat fluxes, which include the effects of both breaking and nonbreaking waves, they do not represent the singular effect of turbulent mixing on constituent transport, hence the inferred diffusivity values are larger than expected for turbulent mixing only.

[45] *Plane* [2004] used a time-resolved chemical model to examine the combined impact of meteor mass flux and eddy flux on the abundance of the Na layer and found that *K*_{zz} was less than 50 m^{2}s^{−1}, which is consistent with other studies [e.g., *Chabrillat et al.*, 2002]. He concluded that 30 m^{2}s^{−1} was a sensible upper limit for the average diffusivity in the 80–90 km region assuming a global average meteoric mass input of 20 t d^{−1}. Since *K*_{zz} is related to the turbulence generated by breaking gravity waves, its value varies seasonally and increases with increasing altitude up to the turbopause just above 100 km. *Chabrillat et al.* [2002] used the atmospheric model SOCRATES to study the impact of turbulent mixing on the vertical profiles of CO_{2}. They obtained the best agreement between modeled and observed CO_{2} profiles for March at 40°N by using a *K*_{zz} profile generated from a gravity wave parameterization scheme with values of approximately 10, 30, and 60 m^{2}s^{−1} at 80, 90, and 100 km, respectively. For mathematical convenience we use the constant value of 30 m^{2}s^{−1} for *K*_{zz}. Since *H* is approximately equal to 6 km, we find that *w*_{Diff} = −0.5 cms^{−1}. This leads to average eddy transport velocities for Na of about + 0.55 cms^{−1} at 100 km, −0.65 cms^{−1} at 90 km and −1.5 cms^{−1} at 85 km.

[46] Gravity waves also exert a significant influence on the meridional circulation system, which induces a summertime upwelling and a wintertime downwelling in the mesopause region that is strongest over the polar caps [e.g., *Garcia and Solomon*, 1985]. Adiabatic cooling associated with the upwelling is responsible for the cold summer mesopause near 85 km at SOR [*Gardner and Liu*, 2007, Figure 2c]. In addition, the vertical drift induced by the meridional circulation system can result in significant advective fluxes (_{C}) for all mesospheric species. In fact above SOR, the mean vertical drift velocities are comparable to the dynamical, chemical and eddy transport velocities. Although the wind measurement accuracy was not sufficient to directly measure the small cm s^{−1} vertical velocities associated with advective transport, the seasonal variations in this vertical drift can be inferred from the measured meridional winds. If we assume that the monthly mean meridional winds measured by the lidar at SOR are approximately equal to the zonal mean meridional winds, then the two-dimensional continuity equation in spherical coordinates can be used to express the vertical drift in terms of the meridional wind field (see Appendix for details). Plotted in contour format in Figure 10 is the vertical drift velocity field above SOR that was inferred from the measured meridional winds [*Gardner and Liu*, 2007, Figure 2b]. The downwelling in winter reaches values approaching −2 cm s^{−1} below 90 km in Jan and Feb, while the summer upwelling exceeds +3 cm s^{−1} near the mesopause at 85 km in June and July. By comparing Figures 6b, 9, and 10, it is clear that wave-induced dynamical, chemical and advective transport make comparable contributions to the total vertical flux of Na.

[47] Plotted in Figure 11a versus altitude are the annual mean profiles of the dynamical, chemical, and eddy transport velocities for atomic Na. The annual mean vertical drift is expected to be negligible as the summer upwelling should be balanced by the winter downwelling. Indeed, for the inferred drift velocities plotted in Figure 10, the annual mean is less than ±0.2 cm s^{−1} throughout the height range. Dynamical and chemical transport are both downward throughout the altitude range, while eddy transport is downward below 95 km and upward above. Plotted in Figure 11b versus month are the seasonal variations of the Na transport velocities at 87.5 km, including the advective transport velocity (_{Adv}) arising from the mean vertical drift (Figure 10). The dynamical and chemically induced velocities exhibit strong annual and semiannual variations with maximum values up to −5 cm s^{−1} during the solstices and minimum values less than −0.5 cm s^{−1} at the equinoxes. Advective transport exceeds +2 cm s^{−1} in summer and is between −1 and −1.5 cm s^{−1} in winter. Although we employed a constant eddy diffusivity of 30 m^{2} s^{−2} throughout the year to estimate the effects of turbulent mixing, *w*_{Mix} varies between about −1 and −1.5 cm s^{−1} because the temperature and Na profiles vary seasonally. At the solstices below 90 km dynamical, chemical and advective transport play far more important roles than turbulent mixing in transporting Na. All four transport mechanisms exhibit comparable velocities at the equinoxes.

[48] These results have important implications for the modeling of Na and other minor species in the mesopause region. Existing models of the mesospheric metals generally fall into one of two categories. Steady state models have been developed by assuming that the gas phase chemistry is fast on the time scale of vertical transport so that all species are in chemical equilibrium at each height [e.g., *McNeil et al.*, 1995; *Plane*, 2003]. Time resolved models solve a system of coupled continuity equations for each species that includes the temporal effects of temperature perturbations and the dynamical effects of advection and divergence [e.g., *Hickey and Plane*, 1995; *Plane*, 2004]. In both cases, turbulent mixing, molecular diffusion and advection by the mean winds control vertical transport and all species are governed by the same eddy diffusion coefficient. The effects of dynamical and chemical transport are included only through the eddy mixing parameterization by adjusting the diffusion coefficient to produce reasonable species profiles.

[49] Our results demonstrate that for a chemically active species such as Na, dynamical and chemical transport processes are both important in the mesopause region. Furthermore, they are nondiffusive in character and cannot be accurately modeled using the eddy mixing parameterization. The dynamical transport of all species is governed by the same transport velocity, while the eddy transport is governed by the same diffusion coefficient. This leads to entirely different species fluxes for the two processes. Therefore, to simulate the effects of both turbulent mixing and dynamical transport in chemical models, the species fluxes should be calculated by adding the dynamical fluxes and the eddy fluxes. Chemically induced transport is more complex and can only be addressed using time resolved models with sufficient temporal resolution to resolve the important wave periods.