Total hydrogen mixing ratio anomaly around the mesopause region

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. D22, 4692, doi: /2002jd003015, 2003 Total hydrogen mixing ratio anomaly around the mesopause region G. R. Sonnemann and U. Körner Leibniz-Institute of Atmospheric Physics, University of Rostock, Ostseebad Kühlungsborn, Germany Received 4 October 2002; revised 29 April 2003; accepted 13 August 2003; published 19 November [1] The strong turbulent mixing within the middle atmosphere should prevent a change of the value of the total hydrogen mixing ratio regardless of the transformation of the hydrogen species in one another within the homosphere. Within the heterosphere the corresponding mixing ratio should drastically increase due to the action of molecular diffusion. We show on the basis of a global three-dimensional model of the dynamics and chemistry of the middle atmosphere that the total mixing ratio decreases under certain conditions when an (escape) flux flows through the domain. The effect occurs particularly above and around the mesopause region, reaching a distinct minimum at about 108 km height. Hunten and Strobel [1974] also found a small reduction on the basis of simplified model calculations, but they stated that the total mixing ratio of hydrogen atoms remains nearly the same. The cause of this apparently paradoxical behavior lies in the fact that under the condition of a hydrogen flux just in the domain of transition of predominant turbulent diffusion to predominant molecular diffusion, a strong decomposition of the heavier H 2 O component into the light hydrogen constituents takes place, and the temperature increases strongly with height above the mesopause. The marked reduction of the total hydrogen mixing ratio within the extended mesopause region is extremely important for all questions concerning the physics and chemistry of this domain. INDEX TERMS: 0340 Atmospheric Composition and Structure: Middle atmosphere composition and chemistry; 0341 Atmospheric Composition and Structure: Middle atmosphere constituent transport and chemistry (3334); 0355 Atmospheric Composition and Structure: Thermosphere composition and chemistry; 3210 Mathematical Geophysics: Modeling; 3334 Meteorology and Atmospheric Dynamics: Middle atmosphere dynamics (0341, 0342); KEYWORDS: escape flux, hydrogen mixing ratio, mesopause region Citation: Sonnemann, G. R., and U. Körner, Total hydrogen mixing ratio anomaly around the mesopause region, J. Geophys. Res., 108(D22), 4692, doi: /2002jd003015, Introduction [2] In contrast to the lower atmosphere the upper atmosphere is dry, marked by water vapor concentrations of only few ppmv. The cold tropopause acts as trap for water vapor; it freezes out there leaving behind a mixing ratio of only about 4 ppmv. It is thought that a global net upward transport of water vapor takes place through the tropopause, as well as with methane, which contributes to the hydrogen escape flux from Earth. Currently its value is estimated at hydrogen atoms cm 2 s 1 [Bishop, 2001]. [3] A serious drawback is that the hydrogen carrying species are unmeasurable to a great extent, at least above about 80 km. Water vapor has been measured by means of microwave technique and occultation technique up to about 80 km and sporadically some kilometers higher yielding very controversial results (Bevilacqua et al. [1990], Hartogh and Jarchow [1995], Seele and Hartogh [1999], Nedoluha et al. [1999], Harries et al. [1996], Summers et al. [1996], Siskind and Summers [1998], Summers and Siskind [1999] and others; see also Körner and Sonnemann [2001] and Copyright 2003 by the American Geophysical Union /03/2002JD quotation there). There are some measurements of atomic hydrogen in the mesopause region and in the (lower) thermosphere [e.g., Vidal-Madjar et al., 1974; Breig et al., 1976; Thomas and Anderson, 1976; Breig et al., 1985; Sharp and Kita, 1987; Anderson et al., 1987; Sanatani and Breig, 1988; Yung et al., 1989; Thomas, 1990, 1993; Takahashi et al., 1992; Bishop, 2001; Bishop et al., 2001]. Rather few observations are available for molecular hydrogen [e.g., Fabian et al., 1979; Harries et al., 1996], which in this context is an extremely important constituent in the upper mesosphere and lower thermosphere. Harries et al. [1996], Summers et al. [1997] and Siskind and Summers [1998] inferred the concentration of molecular hydrogen from HALOE measurements of H 2 O and CH 4 under the assumption that the total number of hydrogen atoms is a conserved quantity. This is, however, questionable, at least in the upper domain of measurements close to 0.01 mb. Our general knowledge about molecular hydrogen in the mesopause region and thermosphere results from different photochemical model calculations. There are no measurements of H 2 within the mesopause region and thermosphere. Summarizing the present situation, we have only imperfect and incomplete knowledge in view of the hydrogen species, at least above the upper mesosphere. Owing to this lack of ACH 1-1

2 ACH 1-2 SONNEMANN AND KÖRNER: TOTAL HYDROGEN MIXING RATIO ANOMALY data one often has to use model data for investigations within the mesopause, but these data are only as good as the models are. [4] As opposed to water vapor, methane can cross the cold tropopause without freezing there. Its mixing ratio at the surface currently amounts to about 1.7 ppmv [Khalil et al., 1993; Kheshgi et al., 1999]. It is decomposed by OH and O( 1 D) primarily in the stratosphere, with the result that its mixing ratio monotonically decreases with increasing height so that methane becomes a constituent of secondary importance above the lower mesosphere. [5] As a result methane is finally oxidized to water vapor, although the formation of molecular hydrogen is possible. However, molecular hydrogen is also subject to oxidation by O( 1 D) so that, considering the net balance, the molecular hydrogen concentration does not change remarkably and CH 4 seems to be entirely converted into 2 H 2 O. Owing to the methane oxidation H 2 O increases and reaches a relative maximum of the mixing ratio above the stratopause. Above the maximum of H 2 O there is increasing photolysis. This photolysis results in the formation of H and the hydroxyl radical OH, but within the mesosphere H reacts with O 2 very quickly in a three-body reaction and forms HO 2. The constituents OH and HO 2 mostly return to H 2 O. Only reactions including H produce H 2 effectively and that requires that the three-body reaction of H becomes ineffective. Hence H 2 increases in the upper mesosphere, especially within the mesopause region where the air pressure is sufficiently low. H 2 is a relatively inert species so that it can accumulate, the H 2 -production and the diffusive transport balancing each other out. In even greater altitudes the H 2 -production becomes more and more inefficient, and as a consequence the concentration of atomic hydrogen increases and reaches an absolute maximum at around 85 km. Above that height the production of H is lower due to the strongly decreasing H 2 O concentration. Within the mesopause region the distribution of the major hydrogen carrying species H 2 O, H 2 and H is sensitively determined by the balance between chemistry and transport [Körner and Sonnemann, 2001]. [6] The domain of the mesopause is the transition region between predominantly turbulent diffusion (below) and predominantly molecular diffusion (above). The turbopause is defined by the equality of the eddy diffusion coefficient with the molecular diffusion coefficient. The height of the turbopause may be close to 100 km. However, the molecular diffusion coefficient roughly depends inversely on the molecular weight, and thus each species possesses its own turbopause. [7] The turbulent diffusion tends to mix the components in such a way that the total mixing ratio of all hydrogen bearing components remains constantly independent of chemical conversions between the constituents. The molecular diffusion tends to increase the mixing ratio of the lightest components such as the most important hydrogen containing molecules. Consequently, it seems to be a trivial statement that the total mixing ratio of the hydrogen components can only grow with increasing height above the turbopause. In this paper we will show that this picture is wrong under the condition of a sufficient high escape flux. We have termed this effect the total hydrogen mixing ratio anomaly (THYMRA). [8] In section 2 we give a brief model description of the model used for calculations. In section 3 we present the results of the calculations. The results will be discussed in section 4. The discussion also comprises an attempt to interpret the THYMRA on the basis of a simplified mathematical model. In this section we also appreciate the pioneering work of Hunten and Strobel [1974]. Some conclusions will be drawn and a short summary will be given in the closing section Brief Model Description [9] The model used for the calculations is a global 3-D model of the middle atmosphere (0 150 km) and consists of a dynamical and a chemical transport model. The chemical transport model considers both advective and diffusive transport. The diffusive transport is divided into the turbulent and molecular diffusion part. The dynamic model is based on a version of the COMMA-IAP model [Berger and Dameris, 1993; Ebel et al., 1995; Berger and von Zahn, 1999]. This acronym stands for Cologne Model of the Middle Atmosphere of the Institute of Atmospheric Physics in Kühlungsborn. It is a three-dimensional mechanistic grid point model with a current resolution of 128 height levels, 64 zonal and 32 meridional grid points. It considers gravity and planetary wave excitation and has been discussed in the work of Sonnemann et al. [1998], Berger and von Zahn [1999], Kremp et al. [1999], Körner and Sonnemann [2001]. It reflects both the real wind fields observed and the temperature fields very well. In the work of Kremp et al. [1999] it was shown, in comparison with radar wind observations, that the seasonal wind patterns are correctly calculated, and in the article by Berger and von Zahn [1999] even the two level mesopause was modeled correctly. A touchstone for the correctness of the important vertical wind is the calculation of the seasonal variation of the middle atmospheric water vapor concentration. Körner and Sonnemann [2001], among other things, computed the seasonal behavior of the water vapor concentration. The results mirror the seasonal variation observed, and even such special phenomenon as the areas of the possible occurrence of NLCs are sufficiently well calculated. The chemical model is based on a family concept and distinguishes between species and families which are subjected to transport, those which have only to time-integrate, and those which are instantaneously in equilibrium. It is important to note that the eddy diffusion profile is an external quantity in the chemical model, meaning to a certain extent the model output can be tuned by it, as is shown in the next section. The eddy diffusion coefficients are extremely variable, especially in the mesopause region where they take the absolutely highest values and are marked by the strongest scatter. Published eddy diffusion coefficients which have been measured, calculated or indirectly inferred vary in magnitude by more than two orders in the mesopause region (see also Hocking [1990] and Lübken [1993, 1997]. We use an idealized standard eddy diffusion profile which is based on results derived by Lübken [1997]. As displayed in Figure 1 this standard profile has been varied in the mesopause region by a factor and quotient of 5 in order to study the sensitivity. The constant thermospheric eddy diffusion profile is of no importance because the

3 SONNEMANN AND KÖRNER: TOTAL HYDROGEN MIXING RATIO ANOMALY ACH 1-3 Figure 1. Idealized eddy diffusion profiles used for calculations and profiles of the molecular diffusion coefficients of atomic oxygen D O and atomic hydrogen D H, calculated on the basis of the COMMA-IAP model. molecular diffusion dominates there. The figure also depicts the molecular diffusion coefficients for atomic oxygen and atomic hydrogen. They have been computed according to the air density and temperature resulting from the model. The constant eddy diffusion coefficient in the domain below is also an idealization. The values may be a little too high in the stratopause. This is, however, of no importance as the THYMRA emerges only above that region. A side effect is that the transients die away faster so that the system normally already enters its flowing equilibrium after about half a year. We will discuss further details in context with the results and again in section Results [10] Figure 2 shows the fluxes of the most important individual hydrogen compounds in H equivalents between 30 and 150 km. Positive fluxes are directed upward and negative ones downward. HX stands for H + OH + HO H 2 O 2. It is almost exclusively atomic hydrogen above about 85 km. The black line represents the balance of all fluxes. The different fluxes are global means, the wind has been switched off for this calculation and the middle standard eddy diffusion coefficient profile has been used. The total flux of hydrogen atoms amounts to nearly H atoms cm 2 s 1. In the lower model domain it is the balance of terms which are two orders greater in magnitude than this flux, indicating a high precision of the numeric procedure. The figure illustrates that the only carrier of H atoms from the lower atmosphere for the escape flux is methane. Below about 55 km the water vapor flux is directed downward on a global average. A small H 2 -flux below about 80 km is also directed downward. Only above 55 km is the H 2 O-flux directed upward due to the methane oxidation. Above about 80 km the H 2 -flux is directed upward as a result of the photolysis of H 2 O and the chemical conversion into H 2 which has a relative maximum of the mixing ratio there. From the peak of the mixing ratio of H, a negative flux takes place within a small height interval between about 75 to 90 km. Above the turbopause the hydrogen constituents H and H 2 only take on the hydrogen transport of the escape flux. [11] The general picture changes in detail under the condition of varying turbulent diffusion. The most marked alteration consists in a broadening, for high eddy diffusion, or a narrowing, for weak eddy diffusion, of the domain into which atomic hydrogen is transported downward. Another essential effect concerns the H 2 O-distribution around and above 80 km which grows with increasing eddy diffusion and this affects the formation of NLCs in high latitudes in summer. [12] Figure 3 displays the mixing ratios of the main hydrogen carrying components and the sum of them given in [ppmv] of an H 2 equivalent. The figure corresponds to

4 ACH 1-4 SONNEMANN AND KÖRNER: TOTAL HYDROGEN MIXING RATIO ANOMALY Figure 2. Fluxes without consideration of the winds of the most important hydrogen components for an escape flux of approximately H atoms cm 2 s 1 on 8 April. Positive fluxes (upward) are shown by solid lines, negative fluxes (downward) by dashed lines. HX = H + OH + HO 2 +2 H 2 O 2 consists mainly of atomic hydrogen above 90 km. The total flux (black line) is the difference of large terms (CH 4 upward flux and H 2 O and H 2 downward fluxes) in the stratosphere. The figure depicts results according to Figure 1 obtained with the mean standard eddy diffusion profile. Figure 2. The most marked feature is the deep minimum of the total hydrogen mixing ratio around 108 km. The mixing ratio is nearly halved and most clearly marked for weak turbulent diffusion. The eddy diffusion influences the mixing ratio especially around the domain of the strongest values of the eddy diffusion coefficient. Only CH 4 possesses a continuous negative gradient of the mixing ratio, indicating that CH 4 is the main carrier of H atoms from the lower atmosphere. The disregard of the winds results in an idealized picture. [13] Figure 4 exhibits the relation again under consideration of the full dynamics globally averaged. The general appearance is the same, it differs only in some details. The picture changes, of course, when a distinct latitude circle is considered. Particularly the fluxes are subjected to the seasonal wind system as shown in Figure 5a in case of the high latitude (72.5 N) in summer. Regardless of these specifications, the anomalous behavior of the total hydrogen mixing ratio close to the turbopause is maintained as Figure 5b demonstrates. The hydrogen flux is determined by the boundary conditions which result from both measurements (H) [Thomas, 1990, 1993; Roble, 1995; Bishop, 2001] and calculations (H 2 ) [Roble, 1995; Körner and Sonnemann, 2001]. [14] Reducing or enhancing the flux, the THYMRA is influenced in compliance with this flux alteration. An increase of the flux, which corresponds to a decrease of the upper boundary values, amplifies the anomaly and vice versa. Surprisingly, the escape flux is relatively insensitive to changes of the upper boundaries within certain real borders. An enhancement of the concentration at the upper boundary entails a weaker gradient and consequently, as mentioned before, a weakening of the anomalous behavior of the total hydrogen mixing ratio. An escape flux value of about cm 2 s 1 [Bishop, 2001], as already estimated by Maher [1980] or by Liu and Donahue [1974], seems to fit the middle atmospheric relations best, meaning the measured concentrations of the main hydrogen species. 4. Discussion of the THYMRA [15] Currently, the scientific community is not (or only insufficiently) aware of the qualitative fact that the total hydrogen mixing ratio can also decrease within the upper mesosphere/lower thermosphere region. This assertion is supported by different papers in which was assumed that the total hydrogen mixing ratio, also called potential water or potential H 2, is constant at least up to the mesopause region [e.g., Garcia and Solomon, 1983; Le Texier et al., 1988; Harries et al., 1996; Summers et al., 1997; Siskind and Summers, 1998; Thomas and Olivero, 2001]. The main reason for this may be that the 2-D model of Garcia and

5 SONNEMANN AND KÖRNER: TOTAL HYDROGEN MIXING RATIO ANOMALY ACH 1-5 Figure 3. The globally averaged total hydrogen mixing ratio anomaly THYMRA shown in H 2 equivalents according to Figures 2 and 1. Under the condition of an escape flux of H atoms cm 2 s 1 a marked minimum occurs at around 108 km. The change of the mixing ratios of the individual components with increasing height makes it clear that the mean molecular weight decreases strongly above the middle mesosphere. Solomon [1983] (and the following versions) which was constructed to investigate the middle atmosphere ( km) did not consider molecular diffusion and a hydrogen (escape) flux through the domain. They clearly shows a constant total hydrogen mixing ratio of about 7 ppmv H 2 equivalent within the entire model domain. [16] In a pioneering work, Hunten and Strobel [1974, p. 314] investigated the problem of the hydrogen flux flowing through the atmosphere. They showed that the escape flux is restricted by the limiting diffusion. The controlling factor is the total mixing ratio of hydrogen atoms at 100 km height. They stated that this quantity is maintained by eddy and molecular diffusion at nearly the same value that it has in the stratosphere. Their calculations result in a small reduction of the mixing ratio between 30 and 100 km. The authors wrote, Water vapor, methane and H 2 in the 30-km region diffuse and mix upward, and between there and 100 km are converted to H 2, with some H; the total mixing ratio of hydrogen atoms remains nearly the same, but with a small reduction. This result gives evidence for the possibility of a reduction, but seems to say that this effect is negligible. Hunten and Strobel [1974] obtained their results based on a simplified one-dimensional model using diurnal means for O( 1 D) and J H2 O, excluding the methane chemistry and considering the Jeans escape flux [Jeans, 1925] as the only escape flux mechanism which was estimated to have a preferred value of cm 2 s 1. Also the chemical reaction rates have changed since the early seventies. For example, for the important reaction H + HO 2! 2OH we use a value of cm 3 s 1 instead of cm 3 s 1. The odd hydrogen family is additionally subjected to diffusive transport in our calculations because the characteristic family time is sufficiently great. [17] Different global 2-D or 3-D models designed to model the stratosphere/mesosphere have their upper border just around the mesopause/turbopause meaning, within (or slightly above) the most sensitive region of the atmosphere [e.g., Garcia and Solomon, 1983; Smith and Brasseur, 1991; Bacmeister et al., 1995; Summers et al., 1997; Reddmann et al., 1999]. Hence it is important to know the relations at the upper border. Our model was specifically developed in order to investigate the mesosphere/lower thermosphere under particular consideration of the mesopause region. [18] Hunten and Strobel [1974] already proved that the mixing ratio of each constituent has to decrease monotonically under the condition of a constant flux if only eddy diffusion is considered. This statement is easy to prove. In order to get a feeling for this effect we solved the onedimensional continuity equation for the hydrogen family under simplified conditions of constant temperature, T(z) =

6 ACH 1-6 SONNEMANN AND KÖRNER: TOTAL HYDROGEN MIXING RATIO ANOMALY Figure 4. The globally averaged THYMRA under consideration of the full wind system using the standard eddy diffusion profile on 19 July. We note that the maximum of the H 2 O mixing ratio now occurs slightly above the stratopause and is somewhat stronger than in the cases without wind. constant, and constant eddy diffusion, K(z) = constant. The flux was labeled, the mixing ratio r, the air density n air, and the pressure scale height H. For the mixing ratio one obtains the expression: rðþ¼ z r 0 þ H K 1 n air ðz 0 Þ 1 : ð1þ n air ðþ z [19] The expression (1) becomes zero for a certain air density (the term in parentheses is negative for z > z 0 ) and would be negative for even smaller values of the air density. The escape flux has been fixed in our calculation, as mentioned in section 3, to about cm 2 s 1. At 65 km the air density amounts to about cm 3 according to Stickland [1972] and the total hydrogen mixing ratio is about 15 ppmv. We assume H/K = 1 cm 1 s 1 as a numerical example. In this case, according to equation (1), r(z) becomes zero for n air (z) = cm 3 and this value corresponds to a height of about 97 km. At 80 km altitude r(z) diminishes to about r(z = 80km) = ppmv. This value remains basically constant at 65 km and the strong decrease takes place above this height. A value for H/K equal to unity may be very roughly valid above about 80 km within the mesopause region. Below this height the ratio is clearly higher, meaning the effect is more marked. The calculations presented in section 3, using a constant diffusion coefficient of 10 4 cm 2 s 1 below 70 km (H cm), already show a strong decrease of r at 80 km. The decrease of r above 70 km is slowed by the increase of the eddy diffusion coefficient. We note again that equation (1) is only valid for a constant eddy diffusion coefficient, meaning it does not describe the behavior of an increasing coefficient. Regardless of this restriction, the consideration demonstrates the close connection of turbulent diffusion and the total mixing ratio of the hydrogen compounds under condition of a constant flux through the domain and it points to the cause of the THYMRA. We define n ¼ XN a i n i as the equivalent family concentration in view of a special sort of atom like hydrogen with n i concentration of member i of the family consisting of N members and a i number of atoms of this sort of the molecule. For the hydrogen-bearing family a j = 4 is valid for methane or a l =2forH 2 Oetc.IfP i is the chemical production term and L i n i the corresponding loss term of the constituent i the sum will be X N ð2þ a i ðp i L i n i Þ ¼ 0: ð3þ [20] The growing decrease of the total hydrogen mixing ratio is stopped if molecular diffusion is taken into consid-

7 SONNEMANN AND KÖRNER: TOTAL HYDROGEN MIXING RATIO ANOMALY ACH 1-7 Figure 5a. Zonally averaged fluxes of the individual hydrogen constituents considering the full dynamics at the particular high latitude of 72.5 N on 19 July. Compared with Figure 2 the fluxes, and especially the total flux, change drastically. Almost the entire mesosphere is marked by positive fluxes for all components and the stratosphere is characterized by negative fluxes according to the dominant vertical winds. eration. However, as the quantity of molecular diffusion coefficient depends on air density and temperature, an analytical solution of the continuity equation is only possible under very special assumptions. We have solved the equation under the condition T = constant and K = constant for an individual component i which was not subjected to any chemical loss or production neglecting the thermal diffusion coefficient a Ti and also disregarding a dependence of the acceleration due to gravity g on height. The derivation of the solution is relatively long-winded and awkward. That is why we will only mention the result here. The mixing ratio can only increase monotonically for 1 i < n i0 D i0 H 1 ; ð4þ H i or it decreases steadily for the greater sign reaching negative values at a certain height. Here D i0 stands for the molecular diffusion coefficient of the component i at height z 0 and H i is the scale height of this constituent. A minimum as obtained from the global calculations for the total hydrogen mixing ratio cannot be formed. This is also the common opinion in view of the behavior of a complete family. Consequently, such a simple and idealized model cannot solve the problem of the total hydrogen mixing ratio anomaly (THYMRA). [21] The most far-reaching restriction consisted of the consideration of only one chemically invariable component. The mean molecular weight of the hydrogen species can be calculated by the relation m H ðþ¼ z XN n i ðþm z i = XN n i ðþ: z Above the maximum of H 2 O in the mean mesosphere the mean molecular weight of the hydrogen species decreases dramatically. This is a consequence of the chemical conversion of the more complex hydrogen molecules into molecular and atomic hydrogen roughly below the turbopause and of the diffusive separation above this domain. [22] In case of more than one hydrogen species the following must be valid ¼ XN a i i : is the total flux, which agrees in global mean with the globally averaged escape flux. The sign of the individual fluxes i can be different, as Figure 2 indicated. The total flux, however, is directed upward. In order to search for the cause of the anomalous behavior we simplify the continuity equations strongly. We neglect the temperature ð5þ ð6þ

8 ACH 1-8 SONNEMANN AND KÖRNER: TOTAL HYDROGEN MIXING RATIO ANOMALY Figure 5b. The zonally averaged THYMRA at the particular high latitude of 72.5 N on 19 July. The effect is clearly marked, however, the mixing ratios of the individual components are strongly influenced by the local wind systems, especially as demonstrated by H 2 O having high upper mesospheric values (compare with Figure 4). depending terms n dt T dz and n i dt T dz in the continuity equation. With equation (2), n ¼ PN a i n i, we can write K dn dz þ n H þ D dn dz þ n H þ ¼ 0 ¼ 0 is assumed. An effective diffusion coefficient D and an effective scale height H of the family is defined by and D ¼ P N dn a i i dz Di dn dz 1 H ¼ P N a i ¼ XN D i n i n D H i dn i a i D i dn ð7þ ð8þ : ð9þ It is, of course, impossible to determine D and H without solving the entire system of the continuity equations coupled by the chemistry. What we can and will do is to consider the expressions (8) and (9) qualitatively and to solve (7) under highly idealized conditions. H is a function of the altitude z now. We approximate D(z) by D(z) = A(z)/n air (z). The magnitude A(z) also depends on z. According to Banks and Kockarts [1973]D i = A i T s /n air (z) is valid. The exponent s is a constant where 1/2 s < 1 is valid. A i depends on the species and, as mentioned above, increases normally with decreasing molecular weight. For instance A H2 = and A CH4 = cm 2 s 1. As the mixing ratio of the light constituents rises with increasing height A(z) also increases for a constant temperature T. In the real atmosphere the temperature grows strongly above the mesopause at about 87 km in summer so that the rising tendency of A(z)is even amplified there. An even stronger tendency is valid for H(z) ash i depends inversely on the molecular weight (e.g., the scale height of molecular hydrogen H 2 is nine times of that of H 2 O). [23] Performing model calculations under these assumptions, one finds that a slight minimum of the total hydrogen mixing ratio will occur around 110 km when only A increases with height. In this case it was impossible to obtain a marked minimum. A somewhat stronger minimum could be modeled when D also increased. The eddy diffusion coefficient and the temperature were held constant. Enhancing the effective molecular diffusion coefficient above the mesopause even stronger according to the rising amount of T S in the real atmosphere and decreasing the constant eddy diffusion coefficient very quickly above about 93 km, one can obtain a distinct minimum which, however, sensitively depends on the particular conditions. Figure 6 shows an example of a model calculation. The flux amounts to cm 2 s 1 and the eddy diffusion

9 SONNEMANN AND KÖRNER: TOTAL HYDROGEN MIXING RATIO ANOMALY ACH 1-9 Figure 6. Model calculation employing a very simplified model which considers an escape flux of H atoms cm 2 s 1, a strong decrease of the mean molecular weight influencing the scale height and the molecular diffusion coefficient, an increase of the temperature above the mesopause and a strong decline of the eddy diffusion coefficient with rising height beginning close by the turbopause and being constant below this domain. This simple model can mirror the most characteristic features of the THYMRA but it also reacts rather sensitively to small changes of the parameters. coefficient to about cm 2 s 1. The results are based on numerical computation using the adapted equation (7). There are some typical characteristics. The decline of the total mixing ratio has its start slowly in the mesosphere. The minimum occurs relatively high above the turbopause and increases with increasing flux. There is a maximum flux in each case. For flux values greater than this value, the mixing ratios becomes negative at a certain height. However, when a minimum is passed the mixing ratio can only increase with rising height. The model investigations make it clear that the THYMRA is caused by a number of very particular conditions: [24] 1. It supposes an escape flux or, at least, a flux through the model domain including the mesosphere and lower thermosphere. [25] 2. It also supposes the existence of the turbopause which is the transition region between predominant turbulent diffusion below and predominant molecular diffusion above. The profile of the eddy diffusion coefficient, including the strong reduction of the coefficient close by the turbopause, influences the effect. [26] 3. An apparently geophysically accidental condition is the chemical conversion of the heavier hydrogen species into the lightest constituents just in the domain of the anomaly. [27] 4. An additionally promoting condition consists in the strong temperature increase above the mesopause which also starts close by the turbopause within the region of the anomaly. [28] How strong the anomaly is marked depends on very particular conditions. Figure 3 exhibited the impression of a clearly existing effect. However, perhaps it is based on too high an escape flux. An escape flux of cm 2 s 1 H atoms seems to be the value most widely accepted [Bishop, 2001]. A smaller flux reduces the effect. Unfortunately, there are no appropriate measurements of the corresponding hydrogen species available which could confirm a drop of the total hydrogen mixing ratio. [29] Our 3-D calculations are based on a family concept. A serious problem consists in the partitioning of the family concentrations into the concentrations of the members of the family. In order to investigate the possibility that the THYMRA results from a wrong partitioning we have developed an 1-D model which calculates all individual species separately with highest time (0.025 s) and height (1 km) resolution. The calculation supply evidence that the THYMRA is really a robust effect. The total hydrogen mixing ratio is noticable affected at least above 65 km. The altitude of this minimum seems to be located close to the turbopause. [30] The effect could have a remarkable influence on some important processes around the mesopause, such as the occurrence of NLCs and PMSEs, depending on the water vapor concentration. The long-term observation of NLCs [e.g., Gadsden, 1985; Thomas et al., 1989; Gadsden, 1990; Thomas, 1995] yields an increase of the occurrence rate interpreted by the rise of the methane concentration [Thomas et al., 1989; Thomas, 1996; Thomas and Olivero, 2001]. A cooling of the thermosphere, as supposed by different groups [Roble and Dickinson, 1989; Berger and Dameris, 1993; Keating et al., 2000], may weaken the anomaly by a reduced temperature gradient and consequently it could enhance the water vapor concentration at NLC heights. This, of course, is only one way of thinking. In this context it must be emphasized that this region reacts very sensitively to changes of very different kinds which could also be subjected to a long-term trend. [31] The chemical heating rates depends on the distribution of the hydrogen species as, for example, the important reaction of ozone with atomic hydrogen. The entire thermic and dynamic system of this region depends rather sensitively on diabatic chemical heating [Berger and von Zahn, 1999]. In some recent papers employing HALOE measurements, the unmeasurable H 2 -concentration was determined by the difference of a constant total hydrogen mixing ratio minus H 2 O and CH 4 measured [e.g., Harries et al., 1996; Summers et al., 1997; Siskind and Summers, 1998]. The THYMRA is, however, small but not negligible below 70 km. Therefore the calculation of the molecular hydrogen concentration from the water vapor and methane concentration measured under the assumption of a constant total hydrogen mixing ratio in the middle atmosphere possibly requires a correction in the upper mesosphere. 5. Summary [32] The hydrogen escape flux depends on the transportation of hydrogen-bearing constituents in the middle atmo-

10 ACH 1-10 SONNEMANN AND KÖRNER: TOTAL HYDROGEN MIXING RATIO ANOMALY sphere. This region has been termed the bottleneck for the escape flux [Hunten, 1973; Maher, 1980]. The escape flux is determined by the total hydrogen concentration in this region but it is also influenced by special conditions of the upper mesosphere-lower thermosphere. In this domain an anomalous behavior of the total hydrogen mixing ratio can occur. This anomaly is characterized by a growing decrease of the mixing ratio reaching its minimum around 108 km. Above this minimum the mixing ratio increases again strongly due to the separation of light constituents by the molecular diffusion. The analysis of this phenomenon results in the conclusion that four conditions are the main supposition for this effect: [33] 1. The turbopause, as a transition region from predominant turbulent diffusion (below) to predominant molecular diffusion(above), is located around 100 km altitude. The eddy diffusion suddenly breaks down above this height. [34] 2. Beginning roughly in the middle mesosphere, the hydrogen bearing constituents are increasingly chemically transformed into lighter constituents, so that the mean molecular weight of the hydrogen bearing constituents strongly decreases. This effect is most marked within the mesopause region. [35] 3. Above the mesopause at 87 km in summer and at about 100 km during the other seasons as defined by the diurnally averaged temperature minimum, the temperature grows with a large gradient. These conditions entail a tendency that the mean scale height of the hydrogen bearing constituents increases and a mean molecular diffusion coefficient, independent of the inverse dependence on the air concentration, rises more strongly with growing height compared with the case of constant temperature. [36] 4. The last and most important necessary condition consists in the existence of a positive hydrogen flux through the domain given by the escape flux. [37] The anomaly influences and feeds back to the chemistry, particularly to that of the mesopause region. As the extent of the anomaly sensitively depends on all particular conditions, the (perhaps anthropogenic) longterm change of one parameter (such as the thermospheric cooling by CO 2 -increase) can result in a change of the chemical composition just in the mesopause region. The results also show that it is disadvantageous to place the upper border of a model in the vicinity of this domain. In first approximation the escape flux depends on the middle atmospheric total hydrogen concentration. As methane is not subjected to the freeze-dry process at the tropopause, the increasing methane concentrations due to increased rice cultivation in marshland and extensive keeping of cows and sheep [Khalil et al., 1993] should adequately enhance the escape flux. Another consequence of higher methane concentrations in the atmosphere consists in a change of the composition of the hydrogen species in the middle atmosphere. As methane is an extreme long-living constituent, the conversion to the lightest hydrogen species H and H 2 is delayed. It would be interesting to investigate the influence of varying methane mixing ratios on the distribution of the hydrogen-carrying constituents. In order to confirm the total hydrogen mixing ratio anomaly precise measurements of the major hydrogen species would be necessary, at least of atomic and molecular hydrogen at around 100 km height. [38] Acknowledgments. This work was supported by the German Research Community DFG, grants So 268/3-1 and -2. 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Sonnemann, Leibniz-Institute of Atmospheric Physics, University of Rostock, Schloss-Straße 6, D Ostseebad Kühlungsborn, Germany. (sonnemann@iap-kborn.de)