A. A. Krivolutsky, V. M. Kiryushov, and P. N. Vargin
Central Aerological Observatory, Dolgoprudny, Russia
It is widely known [Brasseur and Solomon, 1984; Khrgian, 1973] that the atmospheric ozone is the most sensible link in any analysis of the chemical, radiation, and dynamical processes in the middle atmosphere and also their interrelation. In particular, the solar ultraviolet radiation (UV) with the wavelength below 242 nm determines directly the photodissociation rate of molecular oxygen and so the ozone production rate. The UV radiation absorption in this atmospheric region leads to its heating which governs in its turn the temperature and dynamical regimes. Photochemical processes determine the ozone variations in the upper stratosphere and mesosphere due to the decrease of the ozone relaxation time with height. In the troposphere and lower stratosphere the contribution of dynamical processes to the ozone variability is determining. That is why the problem of separation of the part of the total ozone content variations which is caused by the solar UV radiation variations is rather complicate and had no unambiguous answer for a long time [Angell and Korshover, 1976]. At the same time the long-term ozone variations in the upper stratosphere in the solar activity cycle (10-12 years) are revealed fairly reliably based on satellite observation data [Chandra, 1994; Hood and McCormack, 1992; Hood et al., 1993]. The solar UV radiation variations contain not only the long-term variations (10-12 years) induced by the solar activity cycle but relatively shorter-term variations (about 27 days) related to the Sun's rotation around its axis [Chandra et al., 1995; Donelly, 1991]. These variations are due to the existence of so-called "active longitudes" (stable longitudinal intervals) on the Sun in which long-term activity centers are grouped [Vitinskiy, 1983]. The lifetime of such "active longitudes" may be comparable with the characteristic period of solar activity cycle, that is, considerably exceeds the lifetime of an individual activity center. Sometimes two "active longitudes" exist and that leads to a modulation of the observed solar radiation with a period of 13-14 days. In a general case when the angle difference between such longitudes is not equal to 180o, one can say about other harmonic components of temporal variations of the solar radiation flux subjecting the initial series of observations to a spectral analysis.
The use of numerical models may provide a possibility, for example, to check the photochemical ozone production theory which must be fulfilled at heights of the upper stratosphere and mesosphere. During the recent decade the simultaneous satellite observations of the temperature, ozone content, and ultraviolet radiation made it possible really to start solving such problem. Brasseur  and Brasseur et al.  used one-dimensional and two-dimensional numerical photochemical models to study the ozone response to solar UV radiation variations, including those with the period of the Sun's proper rotation (about 27 days). The comparison of the real ozone and temperature variations in the upper stratosphere detected in the satellite (Nimbus 7) measurements with the photochemical calculation results revealed a discrepancy. For example, the temperature response with the 27-day period at these heights proved to be underestimated by a factor of two in the model simulations. Actually (under the data analysis) the effect magnitude is about 0.1 K per 1% variations of the UV radiation flux at a wavelength of 205 nm. Hood  showed that the difference should be caused by the dynamical factors not taken into account in the one-dimensional model.
Krivolutsky  used the tide theory to show that in the terrestrial atmosphere there exists a possibility of intensification of induced variations of such type if there exist large-scale longitudinal irregularities in the ozone distribution which modulate the atmospheric heating and determine the corresponding horizontal length of the excited wave. The analysis of the aerological data shows [Krivolutsky, 1989] that the revealed structure of the 27-day waves in the lower stratosphere is close to the corresponding structure of one of the proper modes (the Hough functions) and that does not contradict the idea of solar rhythm resonant intensification in the atmosphere. Krivolutsky and Kiryushov  used a numerical two-dimensional model of planetary waves to study resonant properties of the terrestrial atmosphere when there is an internal source caused by irregularities of the heating due to the solar radiation temporal variations. A conventionalized structure of the excitation source was used. The calculations by Krivolutsky and Kiryushov  revealed the middle atmosphere selective response to periodical impacts of this type, one of the peaks of the resonant curve corresponding to a period of 23-27-days (external impact).
This paper presents a development of the work by Krivolutsky and Kiryushov . The nonzonal structure of the ozone heating source is studied in more detail using the global satellite information on the ozone distribution and the data on the solar ultraviolet radiation flux.
The planetary wave numerical model is based on the equation of potential vortex conservation. If a planetary wave propagates along a latitude circle, the longitude-temporal dependence of the wave parameters may be presented in the form
Here m is the zonal wave number, s is the oscillation frequency, the dashed values show the deviation from the zonal mean state, and the line means zonal averaging. For the wave amplitude which depends on latitude q and dimensionless height z = log(P0/P), where P0 is the pressure on the surface level, one can obtain the following equation [Shoeberl and Clark, 1980]:
is the potential vortex meridional gradient of the zonal mean flow;
a and W are the Earth's radius and angular rotation velocity, respectively; a is the Newton cooling coefficient; r is the Rayleigh's friction coefficient; u = u(q,z) is the zonal mean wind velocity;
S2 is the static stability parameter; R is the gas constant; T is the global mean temperature; Q = J/cp; and J is the nonadiabatic heating rate (degree per day). The wave amplitude Y is related to the geopotential disturbance amplitude F in the following way:
Equation (1) is a second-order equation in partial derivatives of the elliptic type with complex coefficients. The equation was solved on the hemisphere with the help of the finite-residual approximation by the method proposed by Madala . The nonleakage condition (the velocity vertical component w = 0 ) was assumed at the upper and lower boundaries of the integration region. The wave amplitude was assumed to be equal to 0 (Y = 0) at the side boundaries (the equator and pole). The upper and lower boundaries of the integration region were posed at heights of 90 km and 12 km, respectively. The altitude and latitude steps were approximately 2.5 km and 1.8o, respectively. The coefficients r and a parameterizing dissipative processes were chosen according to the recommendation by Garsia and Solomon  but were slightly increased in the vicinity of the upper boundary, thus reducing (in the author opinion) the solution dependence on the upper boundary condition. The calculations were performed for various oscillation frequencies s and fixed spatial structure of the internal excitation source Q which had a real physics sense for the periods close to 27 and 14 days caused by the periodic heating of the middle atmosphere as the result of the ozone absorption of the variable solar ultraviolet radiation.
Twelve various instruments were installed on board the UARS (Upper Atmosphere Research Satellite) satellite launched by the National Aeronautics and Space Administration (NASA) on 12 September 1991 and aimed to study from the space the atmospheric state global variations. Six out of them provide a monitoring of the global distribution of minor gas constituents (including ozone) in the atmosphere, and two are aimed at a monitoring of its dynamical regime (the wind). Four additional instruments provide a permanent observations of solar corpuscular fluxes. Two of these instruments (SOLSTICE, Solar Stellar Irradiance Comparison Experiment, and SUSIM, Solar Ultraviolet Spectral Irradiance Monitor) measure the UV radiation flux in the following spectral ranges: 119-420 nm (SOLSTICE, spectral resolution is 0.1-0.3 nm) and 115-410 nm (SUSIM, spectral resolution is 0.15-5 nm). The measurements of the solar UV radiation by the SUSIM instrument are used in this paper to analyze temporal variations (the instrument characteristics and methodical details are given by Reiser et al. ). The description of the UARS instrumentation is presented also on the UARS websites http://www-uars-science.html and http://daac.gsfc.nasa.gov/CAMPAIGN_DOCS/UARS_project.html.
To have the solution of the linear problem in the form of a running wave, the excitation source should be such a wave. The ozone heating function [Brasseur and Solomon, 1984; Khrgian, 1973] is the product of the solar ultraviolet radiation intensity outside the atmosphere and absorber (ozone) concentration. Thus the ozone heating function is a standing wave (the product of the temporal UV variations and longitudinal ozone variations) which may be formally presented as two waves running toward each other. However, the analysis of the proper curves of the Laplace tidal equation [Ivanovskiy and Krivolutsky, 1979] shows that the resonant conditions (close to the proper terrestrial atmosphere variations) may be fulfilled only for one of these waves and therefore under these conditions the standing wave would excite a running planetary wave in the atmosphere (in this case with the period close to 25 days and horizontal wavelength determined by the distance between the maxima of the ozone field irregularities.) In this case we are interested in quantitative evaluations of the Q' value (the excitation source) standing in the right-hand side of equation (1).
To study typical peculiarities and amplitudes of the nonzonal ozone distribution, at the first stage an analysis of the global satellite data on the total ozone content (TOC) measured by the TOMS instrument on board Nimbus 7 and Meteor satellites [McPeters and Beach, 1996] was carried out. The data are daily global fields of the total ozone content on the regular net with the latitudinal and longitudinal resolutions of 1o and 1.25o, respectively. The data are absent in the polar regions in winter period. Few gaps in the data available at lower latitudes were filled in with the help of a linear interpolation. Then the data were averaged over latitudinal (5o) and longitudinal (20o) intervals. The daily fields spatially averaged in this way were averaged for a month to filter out short-term variations of the total ozone content and to reveal quasi-stationary disturbances. The harmonic analysis of these monthly averaged data for each latitudinal zone allowed us to study the latitudinal structure of the TOC nonzonal deviations during 1979-1994.
Thus during some years the ozone field which governs the heating and temperature in the stratosphere, has a strong longitudinal irregularity. It should be noted that only the data of satellite measurements made possible a correct study of the nonzonal ozone distribution structure since the ozone ground-based observation network provide no possibility to obtain the global picture because of the strong irregularity in the station disposition. First of all, it is true for the ozone fields and spatial peculiarities of its distribution in the southern hemisphere.
Thus the analysis performed of the solar UV radiation variations and global ozone distribution irregularities makes it possible to evaluate quantitatively the magnitude of the external periodic source. However, we should bear in mind that we consider the maximum magnitude of that source equal to a product of the maximum nonzonal heating rate (1o per day) and relative UV radiation variations (of the order of 1%-2%). In the calculations, the maximum value (Q') of the periodic atmospheric heating was used and assumed to be 0.01o per day.
Thus the study carried out of the terrestrial atmosphere response to a periodic atmospheric heating with the period of the Sun's proper rotation (25-30 days) makes it possible to estimate possible efficiency of this mechanism. It is shown that the atmosphere has resonant frequencies in this range of the disturbance periods and thus the effect may be dynamically intensified by several times as compared with the purely zonal atmospheric heating. Such heating of the upper stratosphere should theoretically lead to the temperature variations with solar rotation period of ~0.1 K per each percent of the increase of the solar UV radiation at a wavelength of 205 nm [Brasseur et al., 1987]. The analysis of the temperature variations based on the measurements on board Nimbus 7 satellite [Hood, 1987] revealed the magnitude higher by a factor of 2. This discrepancy may be, as it has been already mentioned, related to possible dynamical effects. In this paper it is shown that, besides the possibility of a resonant intensification, the response depends significantly (linearly) also on the amplitude of the nonzonal part of the atmospheric heating. Under the UV variation magnitude of 1% chosen after the analysis of the magnitude of the temperature disturbance in the wave, is approximately 0.4 K.
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