wave–photochemistry coupling and its effect on water vapor, ozone and airglow variations in the...

Icarus 189 (2007) 136–150www.elsevier.com/locate/icarus

Wave–photochemistry coupling and its effect on water vapor, ozone andairglow variations in the atmosphere of Mars

Xun Zhu ∗, Jeng-Hwa Yee

Applied Physics Laboratory, The Johns Hopkins University, 11100 Johns Hopkins Road, Laurel, MD 20723-6099, USA

Received 15 August 2006; revised 23 December 2006

Available online 14 February 2007

Abstract

A one-dimensional photochemical–transport model for the martian lower atmosphere has been developed to study the diurnal cycles of wave–photochemistry coupling. The model self-consistently calculates water vapor mixing ratio profiles, which exhibit strong vertical and diurnalvariations mainly due to the high sensitivity of the saturation vapor pressure to temperature variation. The dynamical coupling of water vaporcaused by the temperature variation induced by tidal waves, vertical transport parameterized by eddy diffusion, and linear relaxation introducedin condensation–sublimation processes all have similar timescales of diurnal variation. This leads to a significant asymmetric distribution of watervapor concentration as a function of local time. As a result, the net effect of the temperature variation by tidal waves depletes the water vaporconcentration in its diurnal mean. The coupling processes also deplete the diurnally averaged HOx concentration, which in turn leads to significantenhancements of both ozone concentration and the associated airglow emissions in the martian atmosphere. The model also shows explicitly theimportance of photochemical–transport coupling to the airglow emissions and its implications in species retrievals when the photochemical timesof the excited states are comparable to the timescale of diurnal variation.© 2007 Elsevier Inc. All rights reserved.

Keywords: Mars; Photochemistry; Atmospheres, composition; Atmospheres, dynamics

1. Introduction

The dynamical–photochemical coupling in an atmospherehas emerged as one of the most active research areas in So-lar System comparative aeronomy in the last two decades,partly due to the fact that many fundamental physical processesinvolved are closely related to both the short-term variabil-ity and long-term evolution of planetary atmospheres (e.g.,Luhmann et al., 1992; Mendillo et al., 2002). The interac-tion among different physical processes of dynamics, radiation,chemistry, and transport in an atmospheric system becomesimportant to the short-term variability when the timescales ofvarious processes are of about the same order of magnitude(e.g., Zhu et al., 2000; Brasseur and Solomon, 2005). Under-standing the physical mechanism of coupling is also impor-tant for the correct interpretation of measurements by remote

* Corresponding author. Fax: +1 443 778 1641.E-mail address: [email protected] (X. Zhu).

0019-1035/$ – see front matter © 2007 Elsevier Inc. All rights reserved.doi:10.1016/j.icarus.2007.01.006

sounding techniques (e.g., Fox, 1992). Furthermore, the escapeof lighter gases that is largely determined by photochemistryand transport has a profound effect on the long-term evolu-tion of planetary atmospheres (e.g., Lewis and Prinn, 1984;Yung and DeMore, 1999). The dynamical–photochemical cou-pling in the martian atmosphere in particular is critically im-portant because water vapor (H2O) concentration and thus theHOx photochemistry of ozone (O3) is very sensitive to the localtemperature in a large part of the martian atmosphere.

Because temperature and H2O partial pressure are near thesublimation point in a large part of the martian atmosphere,H2O concentration is very sensitive to the local temperaturevariation. The dominant role of HOx-catalyzed destruction ofozone naturally leads to an overall anti-correlation betweenMars O3 and its H2O variations. For example, the seasonalvariation in O3 abundance can be largely explained by the anti-correlated variation in H2O abundance and its vertical distri-bution as derived from both measurements (e.g., Jakosky andFarmer, 1982; Clancy et al., 1999; Lebonnois et al., 2006; Fastet al., 2006a) and photochemical models (e.g., Nair et al., 1994;

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Wave–photochemistry coupling of the martian atmosphere 137

Clancy and Nair, 1996; Fast et al., 2006b). Likewise, the diurnalvariation of O3 is predicted to be anti-correlated with the corre-sponding HOx that is derived from the H2O photodissociation(e.g., García Muñoz et al., 2005). Note that the sensitivity ofO3 abundance to H2O concentration in the martian atmosphereprovides an important observational constraint to O3 and H2Omeasurements, due to their interrelated photochemistry involv-ing HOx (e.g., Novak et al., 2002). However, this kind of anti-correlation is not always well defined, and there exist significantdepartures from the H2O–O3 anti-correlation (e.g., Lefevre etal., 2004; Krasnopolsky, 2003, 2006), possibly due to the cou-pling among different timescales for processes of dynamics,photochemistry and H2O condensation–sublimation.

Recently, Krasnopolsky (2006) systematically investigatedthe photochemistry of the martian atmosphere for its seasonal,latitudinal, and diurnal variations. A hierarchical approach wasadopted by Krasnopolsky with three types of one-dimensional(1D) models for Mars photochemistry that also include hetero-geneous loss of odd hydrogen species on water ice aerosol.They are: (i) a steady-state global model that provides thebackground long-lived species, (ii) a steady-state local modelthat simulates the latitudinal, and seasonal variations, and (iii)a local model forced by diurnally varying photolysis that in-duces significant variations in O3 and dayglow at 1.27 µm.All three types of the models used fixed temperature profilesfrom the Thermal Emission Spectrometer (TES) onboard theMars Global Surveyor (MGS), the same vertical eddy diffu-sion coefficient and the same type of boundary conditions. Themodels were able to reproduce the observed main features ofthe O2 dayglow at 1.27 µm and O3 and H2O2 abundances(Krasnopolsky, 2006).

This paper investigates the coupling of tidal waves and pho-tochemistry due to variations in temperature and H2O and its ef-fect on O3 and airglow emissions in the martian atmosphere, us-ing a 1D photochemical–transport model. Specifically, we willfocus on the sensitivity of O3 abundance and airglow emissionto H2O concentration, which in turn are very sensitive to thevariation in local temperature. While there have been extensivestudies on wave–photochemistry coupling in the Earth’s mid-dle atmosphere (e.g., Craig and Ohring, 1958; Strobel, 1977;Zhu and Holton, 1986; Zhu et al., 2000), similar studies couldalso be conducted for planetary atmospheres. Recently, Melo etal. (2006) investigated the effect of upward propagating grav-ity waves on the model response of airglow emission in themartian atmosphere. The H2O sensitivity to the local temper-ature variation is also included in their model, because H2Ois self-consistently calculated by parameterized condensation–sublimation. In this paper, we will focus on the coupling be-tween migrating tidal waves and photochemistry. Since both thetidal waves and photolysis rates change with the changing rel-ative Sun position at the same phase speed, there exits a phaselock between the two (Zhu et al., 2000). We will also emphasizethe diurnally averaged effects of such a coupling, in addition tothe instantaneous variations as shown in Melo et al. (2006) forgravity waves. Section 2 describes the basic model physics andthe specification of boundary conditions. Section 3 presents themodel results that show the effect of strong asymmetric fea-

tures in the diurnal variations in H2O, HOx , O3, and airglowemissions, despite the symmetric temperature variation by tidalwaves, indicating a significant nonlinear response. The net ef-fects of such an asymmetric nonlinear influence turn out to bea diurnally averaged depletion in HOx and corresponding en-hancements in diurnally averaged O3 and airglow emissions.Concluding remarks are given in Section 4.

2. Description of photochemical–transport model

2.1. Model formulation and boundary conditions

If we denote χi (= ni/N) as the mixing ratio of an at-mospheric species i with number density ni and total numberdensity N , then the one-dimensional continuity equation de-scribing mass conservation can be written as (Zhu et al., 2000;Strobel, 2002)

(1)∂χi

∂t= 1

ρ

∂

∂z

(ρKi

zz

∂χi

∂z

)+ 1

ρ

∂

∂z(ργiχi) + (Pi − Liχi),

where t is time, z is altitude, ρ is the background atmosphericdensity, and Pi and Liχi are the chemical production and lossterms for species i, respectively. Ki

zz (= Kzz + Di) is the sumof the eddy (Kzz) and molecular (Di ) diffusion coefficients, andfinally, γi is the effective velocity of advection by moleculardiffusion:

(2)γi ≡ Di

(1

Hi

− 1

H

)+ αiDi

T

∂T

∂z.

In Eq. (2), T is temperature and Hi and H are the scale heightsof species i and the atmosphere, respectively. αi is the thermaldiffusion factor, which is equal to −0.25 for H and H2, and 0 forthe other species in the current model (Krasnopolsky, 2002). Wetake the approximate expression for Di (in m2 s−1) suggestedby Banks and Kockarts (1973, p. 39):

(3)Di = 1.52 × 1020[

1

mi

+ 1

m

]1/2T 1/2

N,

where the molecular mass of species i (mi) and the meanmolecular mass (m) are expressed in atomic mass units, T isexpressed in Kelvin and N in m−3. Mathematically, the con-tinuity equation (1) in terms of mixing ratio (χi ) is identi-cal to the standard form of the continuity equation writtenin number density (ni ) (e.g., Chamberlain and Hunten, 1987;Nair et al., 1994). Similar to the continuity equation in terms ofnumber density, Eq. (1) can also be written in a more compactform

(4)∂χi

∂t+ 1

ρ

∂

∂z(ρψi) = Pi − Liχi

with the flux for the mixing ratio given by

(5)ψi = −Kizz

∂χi

∂z− γiχi .

Since advective transport by meridional circulation and large-scale tidal waves is often expressed in terms of mixing ratio

138 X. Zhu, J.-H. Yee / Icarus 189 (2007) 136–150

(e.g., Andrews et al., 1987; Zhu et al., 2000), the chemical mod-ule formulated in Eq. (1) with an explicit advection term is moreeasily adapted into multi-dimensional transport models.

The JHU/APL photochemical module for simulating theO3–HOx photochemistry in the Earth’s upper stratosphere andmesosphere (Zhu et al., 1999, 2000) is adopted here directlyfor simulating martian atmospheric photochemistry. The cur-rent photochemical model includes 14 chemical species and50 photochemical reactions listed in Table 1 that are importantfor simulating the wave–photochemistry coupling in the mar-tian atmosphere. Among the 14 chemical species included inthe current model, O(1D), O(3P), O2, O3, OH, H, H2, HO2,H2O, H2O2, CO, CO2, H2O(ice), and O2(a1�g), the last twospecies have been added to account for the temperature sensi-tivity of water vapor condensation and for the computation ofairglow emissions in the martian atmosphere. Most of the pho-tochemical reactions shown in Table 1 have been directly takenfrom Zhu et al. (1999) with the rate coefficients taken form theJet Propulsion Laboratory (JPL) compilation of chemical ki-netic and photochemical data (DeMore et al., 1997). The 11new reactions, underlined in Table 1, have been added mainly toaccount for special characteristics of martian atmospheric pho-tochemistry: (i) the major species of the atmosphere is CO2,meaning that three-body reactions of atomic oxygen with CO2or CO become important and have to be included; (ii) H2Ocondensation–sublimation as described by two first-order re-actions, R02 and R03, plays an important role in determiningthe water vapor concentration and its variation because temper-ature and water vapor partial pressure are near the sublimationpoint in a large part of the martian lower atmosphere; and (iii)explicit calculation of the O2 electronically excited state a1�g

is required for simulating the airglow emission by the O2 in-frared (IR) atmospheric band. Following García Muñoz et al.(2005), we have explicitly adopted the quantum yields in pho-tolysis calculations that produce O2(a1�g).

A critical issue in calculating photolysis rates is to accu-rately account for the opacity effect. In the Earth’s middleatmosphere, the atmospheric opacity for calculating photoly-sis rates is mainly from O2 absorption (Zhu et al., 1999). Thephotolysis calculations for the martian atmosphere need to in-clude the opacity by both CO2 and O2, with CO2 being themajor contributor. In addition, the opacity and scattering ef-fect by airborne dust in the martian atmosphere could con-tribute to 10–50% increases in O3 abundances (Lindner, 1988).Since the strong temperature dependence of the CO2 crosssection leads to a significant impact on the photolysis ratesin the martian atmosphere (e.g., DeMore and Patapoff, 1972;Parisot and Zucconi, 1984; Nair et al., 1994), the temperaturedependence of the CO2 cross section is also included in thecurrent model. We find a significant impact from the CO2 crosssection temperature dependence on species distributions, espe-cially below 40 km, due to both opacity and absorption whencalculating CO2 photolysis rates J08 and J09 in Table 1. Inthe current model, we adopt the temperature-dependent CO2cross sections compiled by García Muñoz et al. (2005). Thethree-body reaction rate coefficients shown in Table 1 with CO2as the major species have been updated according to Nair et

Table 1Photochemical reactions in the model

PhotolysisO2 + hν → O(3P) + O(3P) (J01)O2 + hν → O(1D) + O(3P) (J02)O3 + hν → O(1D) + O2 (J03)H2O + hν → H + OH (J04)H2O + hν → O(3P) + H + H (J05)H2O + hν → O(1D) + H2 (J06)H2O2 + hν → OH + OH (J07)CO2 + hν → O(1D) + CO (J08)CO2 + hν → O(3P) + CO (J09)O3 + hν → O(3P) + O2 (J10)O3 + hν → O(1D) + O2(a1�g) (J11)O3 + hν → O(3P) + O(3P) + O(3P) (J12)H2O2 + hν → HO2 + H (J13)HO2 + hν → OH + O(3P) (J14)

First-order reactionsO2(a1�g) → O2 + hν (1.27 µm) (R01)H2O → H2O(ice) (R02)H2O(ice) → H2O (R03)

Bimolecular reactionsO(3P) + O3 → O2 + O2 (R04)O(1D) + H2O → OH + OH (R05)O(1D) + H2 → OH + H (R06)O(1D) + O2 → O(3P) + O2 (R07)O(1D) + O3 → O2 + O2 (R08)O(1D) + O3 → O2 + 2O(3P) (R09)H + O3 → OH + O2 (R10)H + HO2 → H2O + O(3P) (R11)H + HO2 → H2 + O2 (R12)H + HO2 → OH + OH (R13)O(3P) + OH → H + O2 (R14)O(3P) + HO2 → OH + O2 (R15)O(3P) + H2O2 → OH + HO2 (R16)OH + HO2 → H2O + O2 (R17)OH + O3 → HO2 + O2 (R18)OH + OH → H2O + O(3P) (R19)OH + H2O2 → H2O + HO2 (R20)HO2 + HO2 → H2O2 + O2 (R21)H2 + OH → H + H2O (R22)HO2 + O3 → OH + O2 + O2 (R23)CO + OH → CO2 + H (R24)O(3P) + H2 → OH + H (R25)O2(a1�g) + CO2 → O2 + CO2 (R26)O(1D) + CO2 → O(3P) + CO2 (R27)

Termolecular reactions

H + HM→ H2 (R28)

O2 + O(3P)M→ O3 (R29)

OH + HM→ H2O (R30)

OH + OHM→ H2O2 (R31)

H + O2M→ HO2 (R32)

HO2 + HO2M→ H2O2 + O2 (R33)

O(3P) + O(3P)M→ O2 (R34)

CO + O(3P)M→ CO2 (R35)

O(3P) + O(3P)M→ O2(a1�g) (R36)

al. (1994) and García Muñoz et al. (2005). The effect of air-borne dust is not included in this work for studying the wave–photochemistry coupling but will be included in a follow-up


paper examining the seasonal and latitudinal variations of air-glow emissions.

The programming details of the chemical solver and thetransport formulation are described by Zhu et al. (1999, 2000).The photochemical solver of the JHU/APL 1D model efficientlyderives the solution for the stiff set of ordinary differential equa-tions by evaluating the needed Jacobian matrix analytically.Both the vertical grids and the numbers of tabulated chemi-cal species and reactions are adjustable for the convenienceof code testing, numerical experiments, and coupling with thetransport module. Current research is mainly concerned withwave–photochemistry coupling, where the system of equationsis solved in a time-dependent fashion with diurnally varyingphotolysis rates for which the chemical timescales of certainspecies are often much smaller than the transport timescale.Therefore, it is worth briefly discussing the specifications ofboundary conditions.

Two types of boundary conditions commonly used in photo-chemical–diffusive models are fixed values of concentration(χi ) and fixed values of fluxes (ψi ) for a set of chemical species.Physically, the specification of these two types of boundaryconditions implicitly assumes that diffusive transport is thedominant process near the boundary so that the specificationof χi or ψi at the boundary will lead to a unique and well-behaved solution (e.g., Sneddon, 1957; Courant and Hilbert,1962). Krasnopolsky (1995) examined the effect on the unique-ness of a solution for a steady-state photochemical model whenthe values of different numbers of species were fixed at bound-aries with the rest of the species having fixed fluxes. Note that,photochemically, a near photochemical steady state is equiva-lent to a system consisting of only slowly varying states (Zhu etal., 2000) with much longer timescales, such that the diffusiveprocesses could be dominant. It is well known that, mathemat-ically, a consistent specification of the boundary condition isdetermined by the term(s) of the highest order of the deriva-tive in a partial differential equation (e.g., Courant and Hilbert,1962). In the present model, it is the first term on the right-handside of Eq. (1) that describes the diffusive processes and deter-mines the specification of the boundary conditions. However, ifthe first term becomes significantly smaller than the other terms,such as when the photochemical production and loss termsare forced by diurnally varying photolysis rates, an appropriateboundary condition is expected to be determined by those termsthat make the major contributions to the species concentrations.Note that many minor species have much shorter photochemicaltimescales than the transport timescales, and they can be con-sidered locally in photochemical evolution or equilibrium withother species. Under such a circumstance, we propose a photo-chemical boundary condition for species with short timescales:the species at the boundaries are determined by directly inte-grating the photochemical equation

(6)∂χi

∂t= Pi − Liχi at z = z0 and z = zT .

A photochemical model often includes many chemicalspecies, with only a few that are able to be specified appro-priately or accurately at the boundaries, based either directly

or indirectly on observations. Previous models often assumea boundary condition for the majority of the rest species ofzero flux at both boundaries. However, the derived solutionoften shows non-vanishing fluxes of some minor species atthe boundaries. This leads to an inconsistent solution to thespecified boundary condition, although the inconsistency cor-responding to those minor species at the boundaries may makesmall or negligible contributions to the overall results. Theadoption of photochemical boundary condition (6) as proposedin this paper is expected to lead to a more self-consistent result,especially when there exist strong diurnal variations of thoseminor species that are truly determined locally by the photo-chemistry.

In this paper, we are mainly concerned with the effectof wave–photochemical coupling that has a relatively shorttimescales of diurnal variation. Therefore, the mixing ratios offive species, CO2, CO, O2, H2, and H2O, are prescribed at thelower boundary (z0 = surface), whereas a slightly different setof six species, CO2, CO, O2, H2, H, and O, are prescribed atthe upper boundary (zT = 120 km), according to the derivedmeasurements and other photochemical models of climatology(Nair et al., 1994; Fox, 1992; Krasnopolsky, 2002), as shown inTable 2. We also set a vanishing flux of H2O(ice) mixing ratioat both lower and upper boundaries. The boundary conditionsfor the remaining species are specified according to our newlyproposed photochemical boundary condition (6).

2.2. Model specifications

The baseline temperature used in this study, T0(z), is themean temperature of the nominal model based on Viking data(Seiff, 1982). In order to study the coupling between thecondensation–sublimation processes and HOx photochemistry,two types of temperature perturbations, with and without localtime variation, are superimposed on T0(z) representing seasonaland diurnal variations of the temperature structure, respectively.Fig. 1 shows five temperature profiles, with T1(z) and T2(z)

being the mean temperature superimposed with steady tem-perature perturbations and representing seasonal variation andT3(z, t) and T4(z, t) representing background steady tempera-ture profiles perturbed by upward propagating tidal waves. Inthe numerical experiments, we set T1,2(z) = T0(z) ± �T (z),with the peak temperature perturbation �T of 8 K located at55 km, and T3(z, t) = T0(z) + δT (z, t) and T4(z, t) = T2(z) +δT (z, t), with δT (z, t) emulating both diurnal and semidiurnaltidal waves of the characteristic amplitudes and phases simu-lated by GCM numerical experiments (Wilson and Hamilton,

Table 2Boundary conditions of fixed mixing ratio

Lower boundary (surface) Upper boundary (120 km)

CO2 0.953 CO2 0.940CO 5.0 × 10−4 CO 4.2 × 10−3

O2 1.1 × 10−3 O2 1.0 × 10−3

H2 1.5 × 10−5 H2 2.0 × 10−5

H2O 2.4 × 10−4 H 9.0 × 10−6

O 1.0 × 10−2


Fig. 1. Five temperature profiles used in the numerical experiments. T0(z) isthe mean temperature of nominal model based on the Viking data (Seiff, 1982).T1(z) and T2(z) represent mean temperatures superimposed with steady tem-perature perturbations. T3(z, t) and T4(z, t), plotted at mid-night in the figure,represent background steady temperature profiles perturbed by upward propa-gating tidal waves.

Fig. 2. Diurnal variation of temperature at the equator by plotting T3(z, t) atselected altitudes.

1996; Wilson and Richardson, 2000). In Fig. 2, we show the di-urnal variation of temperature at the equator by plotting T3(z, t)

at select altitudes. The maximum variability occurs near 50 km,with the semi-diurnal variation being the dominant tidal com-ponent, leading to a typical dynamical timescale from minimumto maximum of about 6 h.

To illustrate the H2O sensitivity to temperature variation inthe martian atmosphere due to the near saturation state of H2Oconcentration, we show in Fig. 3 the corresponding saturationH2O number densities for the five temperature profiles shown inFig. 1. Noticing that the horizontal axis is in logarithmic scale,the figure indicates significant changes dependent on the dif-ferent temperature profiles. If we were also plotting five linesthat correspond to the total number densities in the same figure,

Fig. 3. Saturation H2O number densities corresponding to the five temperatureprofiles shown in Fig. 1.

those lines would be closely packed and indistinguishable be-cause changes in atmospheric density with respect to differenttemperature profiles is much smaller. Combination of the re-sults from both Fig. 2 and Fig. 3 suggests that H2O number den-sity would experience a huge change of several orders of mag-nitude within about 6 h near 50 km if the H2O concentrationremained near saturation as a temperature tidal wave passedthat altitude. In reality, there exist finite relaxation times in thesublimation or condensation processes, even if adequate waterice or water vapor is always available in the atmosphere for thesublimation–condensation to occur. Some photochemical mod-els assume instant adjustment toward saturation when the localtemperature drops or H2O convergence leads to supersaturationof water vapor (e.g., Lefevre et al., 2004). The latest photo-chemical model for the martian atmosphere by García Muñozet al. (2005) assumes a linear relaxation of finite time for bothcondensation (τsat = 30 min) and sublimation (τsubl = 15 sols).As a result, their model allows for the supersaturation of H2Oand excess water vapor produced by diffusive transport in theirmodel that approximately depend on the ratio of the two timeconstants (τsat/τsubl). We will follow the approach of GarcíaMuñoz et al. (2005) in our model so that the microphysics andphotochemistry are more naturally coupled.

Often, the greatest uncertainty that significantly affects theresults in a 1D photochemical–transport model is the verticaleddy diffusion coefficient. In principle, the eddy diffusion coef-ficient can be derived either directly through atmospheric mo-tions or indirectly through vertical tracer distributions, both re-quiring observations. In reality, however, the uncertainty comesnot only from the lack of observations that show how vigorousthe atmospheric motions are or how well the minor species aremixed by eddies but also from the definition itself that differenttypes of 1D models use to physically define different eddy dif-fusion coefficients. For example, Kzz in a 1D photochemical–transport model that simulates the climatological state averagedglobally represents vertical transport by motions of all scales,especially including those by the large-scale meridional circula-


tions. On the other hand, Kzz in a localized 1D model that sim-ulates the short-term temporal variations of chemical speciesmainly represents the vertical transport by small-scale eddiesthat are often unresolved in large-scale general circulation mod-els. In this study, two significantly different Kzz profiles, Kzz−A

from García Muñoz et al. (2005) and Kzz−B from Nair et al.(1994), are used to examine the effect of vertical transporton wave–photochemical coupling. Vertical profiles of Kzz−A

and Kzz−B will be given later together with the O3 enhance-ments in Fig. 10. The model by García Muñoz et al. (2005)is mainly concerned with the diurnal variation of the photo-chemistry whereas, the model by Nair et al. (1994) concernsthe long-term stability of the martian atmosphere. Therefore,Kzz−A will be the nominal eddy diffusion coefficient used inthis study.

3. Results

Previous photochemical models for the martian atmospherewere mainly concerned with the chemical stability of the at-mosphere for which HOx catalytic chemistry plays an essen-tial role (e.g., Yung and DeMore, 1999). Because HOx con-centration is directly related to both O3 and H2O, with H2Ovariability being sensitive to the change of temperature in themartian atmosphere, it follows that the seasonal and diurnalvariations of photochemistry in the martian atmosphere is pri-marily driven by H2O variability. Clancy and Nair (1996) foundthat the seasonal variation of O3 photochemistry in the mar-tian atmosphere was mainly determined by the vertical dis-tribution of H2O. The small thermal capacity of the martianatmosphere leads to a large diurnal variation in its temperature(e.g., Chamberlain and Hunten, 1987). Recent models of thephotochemistry of the martian atmosphere have also explicitlysimulated the diurnal variations of O3 and other related short-lived species (Lefevre et al., 2004; García Muñoz et al., 2005;Krasnopolsky, 2006). In addition, airglow is an important emis-sion feature of a planetary atmosphere, which characterizesthe atmospheric photochemistry and energetics. Combining the

modeled photochemistry with the measured airglow emissionsprovides a stringent test of our basic understanding to boththe modeling theories and experimental designs. Depending onthe photochemical timescale of the excited species, the calcu-lation of the airglow emission is done either off-line throughpost-processing the derived chemical species or on-line, fullycoupling the photochemical and transport processes.

In the present study, we compare the differences in distri-butions of species and airglow emissions under the diurnallyvarying photolysis rates with and without the diurnally varyingtemperature perturbations. For a given temperature profile andinitial species distributions, our photochemical–transport modelis first integrated to a steady-state solution under a fixed solarzenith angle corresponding to a 9:00 local time. The model isthen integrated with the presence of diurnally varying photol-ysis rates and also temperature variation to a state of diurnalrepeatability.

3.1. Effect of wave–photochemistry coupling on chemicalspecies

Fig. 4 shows the modeled diurnal variation of O3 numberdensity at selected altitudes under two different settings of tem-perature profile conditions: (i) the baseline temperature T0(z)

and (ii) a perturbed profile T3(z, t), respectively, as shown inFigs. 1 and 2. The model has been run by assuming an equinoxcondition of Ls = 0 (Read and Lewis, 2004) and a geographiclocation at the equator. Above about 20 km, the major char-acteristics of the diurnal variation of O3 concentration withouttransient temperature perturbations are similar to those for themesospheric O3 in the Earth’s atmosphere, for which the HOx

photochemistry produces the daytime O3 depletion (e.g., Allenet al., 1984; Zhu et al., 1999). The day–night difference in O3generally increases with altitude in both the martian atmosphereand Earth’s mesosphere as more HOx is produced at higher alti-tudes due to larger photolysis rates. The relative day–night dif-ference in O3 concentration in Fig. 4a is about a factor 3 to 10,which is consistent with similar factors in the Earth’s upper

Fig. 4. Modeled diurnal variations of O3 number density (cm−3) at selected altitudes under two different settings of temperature profile: (a) the baseline temperatureT0(z) and (b) a perturbed profile T3(z, t), respectively, as shown in Figs. 1 and 2.


mesosphere. In addition, there exists an asymmetry of O3 vari-ation between sunrise and sunset, with the variation near sunsetbeing slightly slower than that near sunrise. However, whena transient temperature profile that includes the effect of tidalwaves is introduced (Fig. 4b), additional variations of similarmagnitude of a factor 3 to 10 within the day and night periodsare present above about 40 km. Especially, the enhanced vari-ations in O3 concentration due to transient temperature pertur-bations are much greater than those in the Earth’s mesosphere,where a maximum of ∼50% enhancement in O3 concentrationmay occur mainly due to the temperature dependence of therate coefficients (Zhu et al., 2000). Near the surface, the muchmore efficient Ox production by the photodissociation of themajor species CO2 during daytime produces a daytime peak inO3 concentration. Although we have specified different tem-perature profiles to represent its seasonal variability, we haveassumed Ls = 0 in photolysis calculations in all the runs be-cause the main focus of this paper is to explore the mechanismof wave–photochemistry coupling rather than to produce clima-tological maps of the important species and airglow emissions.

In Fig. 5 we show the corresponding OH number density,which can be used to characterize the concentration and varia-tion of HOx in a large altitude range (Zhu et al., 1999; GarcíaMuñoz et al., 2005). The figure without transient temperatureperturbations (Fig. 5a) shows again a pattern of diurnal varia-tion similar to that in the Earth’s mesospheric photochemistry(Zhu et al., 1999). For example, the daytime OH number den-sity is higher than its nighttime value in the lower atmospherewhen the dissociation of H2O by photolysis processes dom-inates the HOx production rate. On the other hand, H + O3becomes a dominant process that depletes O3 and produces OHat the nighttime in the higher altitude region, leading to a largerOH concentration during nighttime than daytime. Similar tothe enhancement of O3 variation due to the presence of tidalwaves, as shown in Fig. 4, the enhancement of its diurnal varia-tion of OH concentration with the transient temperature profile(Fig. 5b) is also comparable to the variation caused by the diur-nally varying photolysis rates. This is consistent with the results

shown in Fig. 4b because O3 variability at the diurnal timescaleis partially or primarily caused by HOx variability in a HOx-dominated photochemical model.

In contrast to O3 and OH, the O concentration is largely de-termined by photodissociation of CO2 and O2 as sources andtermolecular recombinations with O and O2 as sinks, which arenot strongly influenced by the temperature perturbations of thetidal waves. Fig. 6 shows the corresponding O number densitysimilar to O3 and OH shown in Figs. 4 and 5 under two tem-perature profiles T0(z) and T3(z, t), respectively. There is littlenoticeable difference between two panels of Figs. 6a and 6b.The enhanced variations in O concentration due to transienttemperature perturbations reach ∼20% around 70 km when theamplitude of tidal waves becomes significantly large.

The much stronger enhancement of the diurnal variationsin O3 and OH in the martian atmosphere due to the presenceof tidal waves is caused by the sensitivity of H2O concentra-tion to the temperature variation. Note that the condensation–sublimation processes occur at the same timescales of minutesto days as the diurnally varying photolysis rates do. Hence, asignificant impact on the H2O variation is expected as a result ofa strong coupling between the two processes. Fig. 7 shows themodeled diurnal variations of H2O number density with a tran-sient temperature profile T3(z, t). The figure shows that there islittle variation in H2O near the surface (1.5 km) because the pre-scribed lower boundary condition of nH2O = 5.17 × 1013 cm−3

(corresponding to the H2O mixing ratio χH2O = 2.4 × 10−4 asshown in Table 2) is much less than the saturation number den-sity near the surface (García Muñoz et al., 2005), due to therelatively higher surface temperature that is only slightly modi-fied by the small surface diurnal temperature variation as shownin Fig. 3. Water concentration starts approaching saturationaround 30 km as the background temperature T0(z) decreaseswith altitude. Above this level, significant diurnal variations inH2O occur when a passing tidal wave further lowers the localtemperature to below the saturation point. Note that the temper-ature perturbations shown in Fig. 2 vary symmetrically in timewith a sinusoidal form. On the other hand, H2O variations in

Fig. 5. Same as Fig. 4 except for OH.


Fig. 6. Same as Fig. 4 except for O.

Fig. 7. Modeled diurnal variations of H2O number density (cm−3) at selectedaltitudes with the transient temperature profile T3(z, t).

Fig. 5 show strong asymmetric features, with a much shortercharacteristic timescale in depleting H2O concentration than inrecovering it.

The introduction of a linear relaxation of finite times ofcondensation–sublimation processes allows a supersaturationof H2O when the condensation–sublimation processes are notfast enough to thermodynamically equilibrate to the excessamount of H2O resulting from its vertical transport (GarcíaMuñoz et al., 2005). In the current study, the presence of thetransient temperature greatly enhances the fluctuations of H2Orelative to its local saturation concentration. The linear relax-ation of the finite times of condensation–sublimation processescoupled with the vertical transport leads to a significant asym-metry in H2O variations, as shown in Fig. 7.

The asymmetric distribution of H2O in the presence of tidalwaves further contributes to the coupling of O3–HOx photo-chemistry; as shown in Figs. 4 and 5, the additional variationsoccur within the daytime and nighttime periods. To illustratethe effect of the additional enhancement on O3 distributions

Fig. 8. Diurnally averaged O3 number densities (cm−3) for three different tem-perature profiles: T0(z) (solid line), T2(z) (dashed line), and T3(z, t) (solid linewith circles) shown in Figs. 1 and 2.

due to tidal waves, we show in Fig. 8 the modeled O3 numberdensities averaged diurnally under three different temperatureprofiles shown in Figs. 1 and 2: the baseline temperature T0(z),a steady-state temperature T2(z) = T0(z) − �T (z) that repre-sents a colder climate, and a transient temperature profile thatadds wave perturbation to the baseline temperature T3(z, t) =T0(z) + δT (z, t). First, the figure shows a consistently greaterO3 number density above ∼20 km for the colder temperaturefile T2(z). This is expected based on previous studies (e.g.,Clancy and Nair, 1996), where the colder temperature reducesthe overall H2O concentration in the atmosphere, which in turnreduces the catalytic destruction of O3 by HOx when the diurnalvariation of O3 is mainly caused by HOx catalytic chemistry.Second, however, Fig. 8 shows that the diurnally averaged O3

number density has also been systematically enhanced in thesame altitude range when a temperature perturbation inducedby tidal waves is added to the baseline temperature. The corre-


Fig. 9. Diurnally averaged (a) H2O and (b) OH number densities (cm−3) for three different temperature profiles: T0(z) (solid line), T2(z) (dashed line), and T3(z, t)

(solid line with circles) shown in Figs. 1 and 2.

sponding diurnally averaged H2O and OH profiles are presentedin Fig. 9, which indicate significantly and consistently the lowernumber densities in H2O of T2(z) and T3(z, t), as one wouldhave expected. The reduction in OH occurs above 20 km in re-gions of large OH concentration when its day–night variationas shown in Fig. 5b is not extremely great. We have shown pre-viously that by introducing tidal wave perturbations in tempera-ture the additional coupling among condensation–sublimation,transport, and photochemistry greatly increases the diurnal vari-ability and also produces significant asymmetry in variations ofO3, H2O, and OH. The noticeable enhancement of O3 in its di-urnal mean and the corresponding depletions in H2O and OHare mainly caused by the asymmetries induced by the wave–photochemistry coupling.

We have adopted the vertical eddy diffusion coefficientKzz−A from García Muñoz et al. (2005) as the nominal pro-file in our standard model runs. To examine the effect of thevertical transport on the diurnally averaged enhancement of O3concentration we show in Fig. 10 the ratios of the diurnallyaveraged O3 number densities modeled with T3(z, t) to thosewith T0(z) for two different vertical eddy diffusion coefficients,Kzz−A from García Muñoz et al. (2005) and Kzz−B from Nairet al. (1994), respectively. Note that below 20 km and above110 km, there is little difference in O3 enhancement due to tidalwaves, primarily because H2O never gets saturated in the modelin those regions. At intermediate altitudes, O3 enhancement asmeasured by the ratio of the two diurnally averaged O3 con-centrations decreases with the increasing vertical eddy diffu-sion coefficient. Such a decrease is expected from our analysisabove because the supersaturation in the model is mainly in-duced by colder temperature disturbances of the passing tidalwaves that lower the saturation H2O pressure to a much smallervalue. A more efficient vertical mixing by a greater eddy dif-fusion coefficient alleviates the degree of supersaturation byremoving the excess H2O through the transport process, whichultimately reduces the effect of O3 enhancement as shown inFig. 10.

Fig. 10. Ratios of the diurnally averaged O3 number densities modeled underT3(z, t) to those under T0(z) for two different vertical eddy diffusion coeffi-cients, Kzz−A from García Muñoz et al. (2005) and Kzz−B from Nair et al.(1994), and for the standard Kzz−A but with an increased τsat/τsubl, respec-tively. The units of Kzz in the horizontal scale of log10(Kzz) are m2 s−1.

To test the model sensitivity to the parameterized condensa-tion–sublimation we also vary the magnitudes of the relaxationtimes for condensation and sublimation. Fig. 10 also shows theO3 enhancement when (τsat, τsubl) is changed from (30 min,15 sol) to (60 min, 3 sol), which corresponds to a factor of 10 in-crease in τsat/τsubl. The figure shows that the O3 enhancementis significantly increased above 40 km and slightly decreasedaround 30 km, mainly due to the increased and decreased asym-metry in the H2O distribution realized by the coupling betweenthe parameterized condensation–sublimation and vertical trans-port.

In the current version of the 1D photochemical–transportmodel as defined by Eq. (1), the effect of the advective trans-port by tidal vertical velocity has been excluded from theoriginal version of the JHU/APL 1D photochemical–diffusive–


advective model (Zhu et al., 2000) mainly for the following tworeasons: (i) we do not have a martian tidal wind field that isself-consistently derived from the tidal temperature field and (ii)the effect of species advection is expected to be much smallerthan the saturation effect caused by the temperature variation.Our future modeling of martian photochemistry will exam-ine this effect with the extracted tidal temperature and windcomponents from the assimilated Mars Climate Database fromLaboratoire de Meteorologie Dynamique de CNRS (Lewis etal., 1999). In addition to the diffusive and advective transportby atmospheric motions, H2O(ice) is also subject to down-ward advective transport caused by sedimentation. In this paper,we have adopted a simple parameterization scheme of a lin-ear relaxation for the condensation–sublimation microphysicalprocesses. Furthermore, there exists greater uncertainty in a Kzz

that characterizes the vertical transport in a 1D model. There-fore, sedimentation of H2O(ice) is also neglected in the currentpaper.

There are some implications about the enhancements in O3and depletions in H2O and HOx in their diurnal means. First,both H2O and O3 are measurable quantities for the martianatmosphere, and the measurements are usually not made si-multaneously (e.g., Clancy et al., 1996; Novak et al., 2002;Lebonnois et al., 2006). A typical climatological state of an at-mospheric species is defined in general as a spatial and temporalmean of the available measurements. Second, both H2O and O3are key species for understanding the long-term evolution ofthe martian atmosphere. Specifically, the photochemical sensi-tivity of O3 to H2O as generally reflected in the O3–H2O neg-ative correlation provides an important observational constrainton the measurements of O3 and H2O. Third, photochemicalmodels used to study the chemical stability or long-term evo-lution often assume a globally or diurnally averaged physicalstate with a fixed temperature profile and solar zenith angle forcalculating the photolysis rates. Fourth, however, those photo-chemical models are usually constrained and guided or refinedby the measured climatology of O3 and H2O for the martianatmosphere. Now, Fig. 10 suggests that the more realisticallymodeled diurnally averaged O3 with the presence of tidal wavesdiffers by ∼50% from its modeled climatology by assuming afixed temperature profile. Therefore, a rectification factor due towave–photochemistry interactions needs to be considered in theabove mentioned four consequences on measurement-modelcomparisons and interpretations. Because tidal waves are ubiq-uitously extant and are a major component of the variability inthe martian atmosphere (Read and Lewis, 2004), understandingand appropriately incorporating such a difference or rectifica-tion thus become important.

3.2. Effect of wave–photochemistry coupling on airglowemissions

Airglow emissions can be used to remotely retrieve the abun-dances of atmospheric species (e.g., Fox, 1992; Slanger andWolven, 2002). They can also be used as a proxy to infer thewave motions in the Earth’s and planetary atmospheres (e.g.,Hecht et al., 1994; Melo et al., 2006). Because the strength

of airglow emissions is proportional to the populations of theexcited states of those species, the accuracy of the airglowmodeling depends critically on the photochemical timescales ofthose excited states (e.g., Rees, 1989; Sica, 1991). Furthermore,when the radiative relaxation timescales are comparable to thetimescale of the diurnal variation, the wave–photochemistrycoupling among the radiative relaxation of the excited states,the photochemistry of the ground-state chemical species and thedynamical transport is expected to become important. An air-glow model not including these coupling processes could leadto non-negligible errors in species retrieval.

It is known that quickly varying photochemical processesare indirectly coupled with transport by slowly varying pho-tochemistry. Several coupling techniques used in models arediscussed by Zhu et al. (2000), with the most familiar fam-ily species approach as a special case. The quickly varyingspecies within a family can be assumed to be in photochemicalequilibrium and be calculated independently from the transportprocesses. Similarly, given the modeled chemical compositionsof various species, the airglow emissions by vibrationally ex-cited molecules can be calculated off-line by assuming a localchemical equilibrium of those species at different vibrationalstates. This is because the timescales of those strong or the fun-damental vibrational transitions that primarily contribute to theairglow emissions are usually much shorter than the transporttimescale, with the relevant chemical timescales comparableto the transport timescale. For example, the calculation of air-glow by the OH Meinel bands requires the concentrations ofthe vibrationally excited OH that are mainly produced from theBates–Nicolet mechanism:

(7)H + O3R10−→ OH(ν � 9) + O2,

where 0 � ν � 9 denotes the vibrational energy level. Due tovery short timescales of ∼0.01 s for the vibrational relaxationwe can consider all the OH(ν) with different ν as a family ofspecies that are in local chemical equilibrium. The populationof OH(ν) and the volume emission rate at different energy lev-els that determine the strengths of different Meinel bands arecalculated by a rate equation that consists of terms for chemi-cal production, spontaneous emission and collisional deactiva-tion (e.g., García Muñoz et al., 2005). For airglow originatingfrom metastable electronic transitions, the spontaneous relax-ation times are usually much longer than those of the vibrationaltransitions and could be comparable to the transport timescale.For example, the radiative relaxation time of O2(a

1�g) thatcorresponds to the O2 IR atmospheric band airglow is 1.24 h(Lafferty et al., 1998). Therefore, O2(a

1�g) is listed as a chem-ical species that is calculated on-line in the coupled model, asshown in Table 1. The chemical schemes for calculating airglowemissions by the OH Meinel bands and O2 IR atmospheric bandmostly follow the approach of García Muñoz et al. (2005).

The calculations of airglow emissions by the OH Meinelbands include two extreme models, the collisional cascade andsudden death, regarding the specifications of the collisional de-activation coefficients (García Muñoz et al., 2005). The colli-sional cascade model relaxes the vibrationally excited OH onequantum energy level at each transition, whereas the sudden


death model directly deactivates OH(ν) of any ν > 0 to itsground level of ν = 0. Because the strength of the airglow emis-sion is directly proportional to the populations of the excitedstate that yield the spontaneous emission, the collisional cas-cade model and the sudden death model give the theoreticalbounds of the maximum and minimum emissions, respectively.

In Fig. 11, we show the altitude profiles of airglow emis-sions of the OH Meinel bands at midnight for the sudden deathmodel under two temperature profiles of T0(z) and T3(z, t),respectively. The maximum emissions occur around 55 km,which is slightly lower than those shown by García Muñozet al. (2005). The magnitudes of the volume emission ratesare about a factor of 2 greater than by García Muñoz et al.(2005). Note that the current model adopts a different alti-tude range than García Muñoz et al. (2005) in order to usethe concentrations of some of the measured species (Fox, 1992;Krasnopolsky, 2002) while specifying the upper boundary con-ditions. Comparison between the two panels indicates that the

temperature transient induced by tidal wave enhances the air-glow emission by ∼20%. Fig. 12 shows the similar volumeemission rates corresponding to the collisional cascade model.Comparison with Fig. 11 shows that the overall emission ratesare increased by a factor of 4 due to a much slower process ofthe relaxation of OH excited states to ground state. The relativeenhancement of ∼20% due to the temperature transient is thesame as that in Fig. 11.

We have already shown that wave–photochemistry couplingcauses an asymmetric variation in H2O, which leads to a deple-tion in HOx and an enhancement in O3 in their diurnal means.Since the strength of the airglow emission of the OH Meinelbands produced by the Bates–Nicolet mechanism (7) is propor-tional to both H and O3 number densities, one expects partialor near-equal cancellations of the depletion and enhancementfor the airglow emission in its local time mean. In Fig. 13,we show the nighttime averaged OH Meinel airglow emission,which is the major component for the diurnal mean, for the

Fig. 11. Airglow emissions (photons cm−3 s−1) of the OH Meinel bands at midnight for the sudden death model under two temperature profiles: (a) T0(z) and (b)T3(z, t).

Fig. 12. Same as Fig. 11 except for the collisional cascade model.


same three temperature profiles as in Figs. 8 and 9. The figureshows that, in most regions, the net effect of either decreas-ing the steady-state temperature (T2(z)) or adding a transienttemperature perturbation (T3(z, t)) is to enhance the emissionrate. However, the relative magnitudes of the enhancement inemission are smaller than those for O3 enhancements shown inFig. 8, mainly due to the partial cancellation by HOx depletionshown in Fig. 9.

The airglow emissions by the O2 IR atmospheric band arecaused by the electronic transition of a1�g → X3�−

g , which

has a relatively long lifetime. Therefore, O2(a1�g) is consid-

ered as an individual chemical species and calculated alongwith other species in the photochemical–transport model thatfully couples various processes. Fig. 14 shows the vertical pro-

Fig. 13. Nighttime averaged airglow emissions (photons cm−3 s−1) of the OHMeinel bands for the collisional cascade model for three different temperatureprofiles: T0(z), T2(z), and T3(z, t), respectively.

Fig. 14. Airglow emissions (kilo-photons cm−3 s−1) of the O2(a1�g) infraredatmospheric band at midnight (squares) and noon (circles) as for two tempera-ture profiles: T2(z) (solid lines) and T3(z, t) (dashed lines), respectively.

files of dayglow and nightglow for the two temperature pro-files of T0(z) and T3(z, t), respectively. The dayglow is muchstronger and peaks at much lower altitude than the nightglow.Introduction of transient temperature perturbations leads to sig-nificant enhancement in dayglow but little or no enhancementin nightglow. We show in Fig. 15 the vertically integrated emis-sions by the O2 IR atmospheric band as a function of normal-ized local time for three temperature profiles of T0(z), T2(z),and T3(z, t), respectively. The figure shows a significant en-hancement for the dayglow emission for either T2(z) or T3(z, t).Since the dayglow of the O2 IR atmospheric band is mainlyinduced by O3 photolysis (J11 in Table 1), such an enhance-ment is a direct consequence of the O3 enhancement discussedabove, as shown in Fig. 8. Note that for the upward propagatingtidal waves, the effect of averaging over altitude is similar tothat of averaging over the local time because they both approx-imately correspond to an average over a wave cycle. Duringthe nighttime, the only chemical production for O2(a

1�g) isthe three-body reaction R36 in Table 1, which only producesvery weak airglow emissions. Since the spontaneous emissionby the electronic transition of O2(a

1�g) → O2(X3�−

g ) has arelative long timescale, the column emission extends well intothe nighttime as shown in Fig. 15, which is consistent withGarcía Muñoz et al. (2005). Because O3 photolysis is the mainsource for O2(a

1�g) it is also worthwhile showing the localtime dependence of column integrated O3 number densities(Fig. 16) that correspond to the airglow emissions shown inFig. 15. Fig. 16 shows that the enhancement in column inte-grated O3 during daytime due to the introduction of tidal wavesis no longer significant anymore. This is due to the fact thatdaytime ozone number density peaks near the surface (Fig. 4),where H2O saturation in the atmosphere is low. The nighttimeO3 number density peaks above 30 km (Figs. 4 and 7) wherethe coupling between tidal waves and photochemistry throughsaturation vapor pressure becomes significant. Under such acircumstance, the enhancement in column integrated O3, as in-

Fig. 15. Column integrated airglow emissions (106 Rayleigh) of the O2(a1�g)

infrared atmospheric band as a function of normalized local time for three dif-ferent temperature profiles: T0(z), T2(z), and T3(z, t), respectively.


dicated in Fig. 16, is nearly doubled. Note from Figs. 7 and 9athat H2O number density peaks near the surface where it haslittle diurnal variation. As a result, the corresponding columnintegrated H2O number densities for T0(z), T2(z), and T3(z, t)

are 15, 14, and 13 µm of perceptible water, respectively. Thesevalues are near the high end of H2O profiles used in Nair et al.(1994).

Traditional modeling of airglow emissions in either plane-tary atmospheres or in Earth’s upper atmosphere often assumeslocal photochemical equilibrium (e.g., Novak et al., 2002;Krasnopolsky, 2003; Mlynczak et al., 1993). Use of such anassumption potentially introduces two types of errors in cal-culating airglow emissions: (i) errors due to the inappropri-ate treatment of chemical coupling between species in excitedstates and those in the ground state and (ii) errors due to the ne-glect of transport processes. The magnitudes of both types of

Fig. 16. Column integrated O3 number densities (in µm-amagat) as a functionof normalized local time for three different temperature profiles: T0(z), T2(z),and T3(z, t), respectively.

errors are expected to be dependent on timescales of the spon-taneous emissions of those excited states. When the airglowemissions, such as the 1.27 µm O2(a

1�g) dayglow emission,are used to remotely retrieve the abundances of atmosphericspecies, such as O3 concentration, it is worthwhile examiningthe errors resulting from the steady-state assumption in airglowmodeling. We have already indicated that the relatively longtimescale of 1.24 h for O2(a

1�g) radiative relaxation could af-fect its number density if O2(a

1�g) were calculated off-lineby assuming a local photochemical equilibrium. In Fig. 17, weshow the fractional errors in daytime O2(a

1�g) at five differentaltitudes for the baseline temperature T0(z) and the perturbedtemperature T3(z, t) when its number density is calculated off-line based on the modeled O, O3, and CO2 and by assuminga local photochemical equilibrium of photochemical reactionsJ11, R01, R26, and R36 in Table 1. Since the O3 photolysisby J11 makes the major contribution to O2(a

1�g), a near con-stant O3 concentration above ∼50 km without tidal waves asshown in Fig. 4a leads to the very small errors in O2(a

1�g)

shown in Fig. 17a, except near sunrise. At the lower altitudes orwhen the temperature perturbations due to tidal waves are in-cluded, Fig. 17 shows that the errors in O2(a

1�g) are generallysignificant and non-negligible, mostly due to both errors men-tioned above that lead to the inaccurate calculation of airglowemissions if O2(a

1�g) were calculated off-line by a model as-suming local photochemical equilibrium. The fractional errorsin O2(a

1�g) will be transformed into errors in the retrieved O3concentration if a steady-state model is used.

To summarize, we emphasize that the airglow emissionsvary as driven by their excitation mechanisms. Both OH Meinelbands and O2 IR atmospheric band vary with time as the at-mospheric temperature, photolysis rates, and transport varywith time even if the corresponding relaxation times may bevery different. The major difference between a relatively shorterand a longer relaxation time for the OH Meinel and O2 IR at-mospheric band is that the population of the excited states in theformer case can be derived by post-processing the model output

Fig. 17. Fractional errors (%) in O2(a1�g) due to the assumption of local photochemical equilibrium of O2(a1�g) with the rest of the species for two temperatureprofiles: (a) T0(z) and (b) T3(z, t).


whereas the excited states in the latter case need to be includedin the integration of the time-dependent model.

4. Conclusions

We have developed a one-dimensional photochemical–transport model for the martian atmosphere to study the di-urnal cycles of wave–photochemistry coupling in the loweratmosphere. We have also proposed a new set of the photo-chemical boundary conditions (6) for species whose photo-chemical timescales are much less than the transport timescale.The newly proposed boundary conditions can be and should beapplied to species with photochemical timescales shorter thanthe transport timescale in any photochemical–transport modelwith a transient photolysis rate. The model self-consistently cal-culates the time-dependent profiles of important species such asH2O and O3 and airglow emissions. We show explicitly that thespecies at the excited states with relatively long timescales fortheir spontaneous emissions need to be modeled on-line to fullyaccount for the photochemical–transport coupling processes.Because of a saturation vapor pressure high sensitive to tem-perature variation and the coupling among photochemistry,transport, and condensation–sublimation processes, H2O con-centrations show strong and asymmetric variations with respectto local time as the transient temperature perturbations repre-senting tidal waves are included in the modeling. The asym-metry of H2O variation leads to the net effects of a depletedHOx , an enhanced O3 and enhanced airglow emissions in theirdiurnal means. Since a typical climatological state of an at-mospheric species is generally defined as a spatial and temporalmean of the available measurements, the diurnally averagedenhancement or the depletion due to the existence of tidalwaves suggests that a rectification factor is needed when accu-rate or precise measurement-model comparisons are requiredfor understanding the martian atmospheric climatology and thelong-term evolution of its atmospheric species. The effect of thecoupling on the retrieval of O3 based on steady-state modelingof the 1.27 µm airglow emission by O2(a

1�g) is also examinedand shown to be generally significant and non-negligible.

Acknowledgments

This research was supported by NASA Grant NNG05GG-57G to The Johns Hopkins University Applied Physics Labo-ratory and JHU/APL internal research fund. The authors thankA. García Muñoz for providing us with the compiled CO2 crosssection and William H. Swartz for making constructive com-ments on the original manuscript. Constructive comments fromtwo anonymous reviewers are also greatly appreciated.

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