Diurnal and semi-diurnal tidal structures due to O2,O3 and H2O heating Geeta Vichare∗ and R Rajaram Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410 218, India. ∗Corresponding author. e-mail: [email protected] Today with increased availability of data of middle atmospheric winds and temperature, modelling of middle atmospheric tides has acquired greater importance. The theory of atmospheric tides has two main parts: (i) Investigation of the sources of periodic excitation, and (ii) calculation of the atmospheric response to the excitation. Other than stratospheric ozone and tropospheric water vapour absorption, the thermal energy available from the absorption in Schumann–Runge (SR) continuum leading to photo- dissociation of O2 is important energy source for tides in the lower thermosphere. PHODIS radiative transfer model is capable of providing tidal forcing due to combined effect of solar and chemical heating in the wavelength region 116 to 850 nm. In this paper, we present an atmospheric tidal model based on classical tidal theory and the prime objective is to obtain the tidal structure due to conventional ozone and water vapour heating in conjunction with the O2 absorption. Mean wind and dissipation mechanisms are not considered. The present tidal model reveals that the diurnal amplitude peaks in mid to low latitudes, whereas semidiurnal component is stronger at higher latitudes. The semidiurnal tide is about an order of magnitude weaker than the diurnal tide. Also, semidiurnal wave has longer vertical wavelength than diurnal tide. The results of present model are qualitatively in good agreement with the other tidal models, which utilize more sophisticated parameterization. Thus, the salient features of the tidal structure are obtained using basic computations without considering the effects of background winds and dissipation processes. Further refinements to the model can serve as an inexpensive substitute to the presently available tidal models. 1. Introduction space-based observations (Vincent 1984; Sasi and Krishna Murthy 1990;Denget al. 1997;Rajaram The Earth’s atmosphere responds to gravitational and Gurubaran 1998; Vincent et al. 1998; Tsuda and thermal forces in a manner analogous to forced et al. 1999; Ratnam et al. 2002;Panchevaet al. mechanical vibrations. The thermally forced atmo- 2003;Rigginet al. 2003;Xuet al. 2009;Zhao spheric tides are excited by the periodic absorp- et al. 2012). Also, number of attempts has been tion of solar radiation connected with the apparent made towards the modelling of tides (Forbes 1982; sidereal motion of the Sun around the Earth. Lieberman and Leovy 1995; Miyahara and Miyoshi Characteristics of the diurnal and semi-diurnal 1997; Wood and Andrews 1997; Hagan and Forbes components of the tidal oscillations have been 2002, 2003; Grieger et al. 2002; Zhang et al. 2010). studied extensively using various techniques such The theory of atmospheric tides has two main as rocket sounding, radar, lidar measurements and parts: (i) Investigation of the sources of periodic Keywords. Atmospheric tides; atmospheric tidal model; Phodis heating; O2,O3 and H2O heating; diurnal tide; semi-diurnal tide. J. Earth Syst. Sci. 122, No. 5, October 2013, pp. 1207–1217 c Indian Academy of Sciences 1207 1208 Geeta Vichare and R Rajaram excitation, and (ii) calculation of the atmospheric perturbations in neutral wind derived from present response to the excitation. Therefore, in order model simulations are discussed in section 5.Scope to numerically simulate the Earth’s upper atmo- of the future work is outlined in section 6, and the spheric circulation, the accurate knowledge of the last section presents the summary. heat budget of the atmosphere is essential. During photo-dissociation of the absorbing species, sub- stantial portions of the incident energy may appear as internal energy of the excited species or as chem- ical potential energy of the product species. Thus 2. Heating rates obtained from ‘PHODIS’ the absorbed solar energy does not all immedi- ately appear as heat, rather heating is a multi- The solar ultraviolet radiation absorbed by ozone step process, which makes the accurate evaluation and molecular oxygen in the mesosphere and lower of the heating rates of the atmosphere more com- thermosphere produces heating through a series of plicated. Moreover, absorption in the atmosphere complex processes and it is strongly dependent on takes place by various atoms and molecules such wavelength of impinging solar radiation. Ozone is ∼ as O2,O3,H2O, N2,N,CO2, etc. However, con- the main absorber of wavelength 240–320 nm, sidering all of them together affects the clarity in O2 of ∼100–200 nm, and both O3 and O2 absorb arriving at the cause and effect discussions. The radiation of wavelength ∼200–240 nm. Absorp- main absorbing molecules responsible for thermal tion below ∼100 nm can occur by various other tides are O3 in the stratosphere and mesosphere molecules and atoms, such as N2,O2,N,O. (Butler and Small 1963), H2O in the troposphere PHODIS is a software package developed by (Siebert 1961)andO2 in the thermosphere. Exten- Arve Kylling (Kylling et al. 1995), to calculate sive work has been performed for first two com- photo dissociation rates for number of molecules ponents (Chapman and Lindzen 1970;Forbesand such as O2,O3,NO2,CO2 and also computes Garrett 1978;Groves1982; Groves and Wilson the heating rate due to O3 and O2 absorption 1982), whereas fewer efforts have been made for in the wavelength region 116 to 850 nm. Many the forcing due to oxygen molecule. The O2 heat- atmospheric models such as Finish Meteoro- ing is significant in the thermosphere and it is logical Institute’s FinROSE chemistry transport found that the heating in the Schumann–Runge model (FinROSE-ctm) (Damski et al. 2007), the (SR) bands is the dominant heat source between EMEP Eulerian photochemistry model (Simpson 88 and 96 km, while absorption in the SR con- et al. 2012), etc., use photodissociation coefficients tinuum is most important above 96 km (Strobel compiled by PHODIS radiative transfer model. 1978). Therefore, it is vital to simulate the atmo- Simpson et al. (2002) compared the PHODIS pho- spheric tides for oxygen heating too. In this paper tolysis rate coefficients of NO2 with observations we present modelling results of diurnal and semi- and found the agreement is good under clear sky diurnal tides in the atmosphere due to O3,H2O conditions. and O2 heating using classical tidal theory. Here we In PHODIS model, the radiative transfer cal- demonstrate that the simple computations of the culation is divided into three distinct regions: tides without considering the mean wind and dis- (a) 116.3–177.5 nm (SR Continuum), (b) 177.5– sipation mechanisms can also reproduce the broad 202.5 nm (SR Bands), which uses Minschwaner features of the atmospheric tides, and is qualita- et al. (1993) parameterization, and (c) 202.5– tively in good agreement with the other existing 850.0 nm. First two regions employ no multiple sophisticated tidal models. The aim of the present scattering (Beer–Lambert law), whereas multiple paper is to introduce our atmospheric tidal model. scattering is included in the third region. All three For the present tidal model, we use PHODIS regions take into account the ozone and molecu- radiative transfer model to reproduce the heat- lar oxygen absorption and Rayleigh scattering. To ing due to stratospheric ozone and lower thermo- handle multiple scattering in the 202.5–850.0 nm spheric oxygen absorption, which is discussed in region PHODIS provides an option of three dif- section 2. The tropospheric water vapour heating ferent radiative transfer solvers: (1) The general is computed separately using the well-established purpose discrete ordinate algorithm DISORT with Grove’s method (Groves 1982). The mathemat- plane parallel geometry (Stamnes et al. 1988), (2) ical description of the model is presented in spherical and pseudo-spherical version of DISORT section 3. The height profiles of the Hough com- (Dahlback and Stamnes 1991), and (3) two-stream ponents of diurnal and semi-diurnal waves have algorithm (Twostr) (Kylling et al. 1995). In the been discussed in section 4. Thus, sections 2 and 4 present work, we used first solver (DISORT) to take care of the sources of periodic excitation calculate the radiation field in a model atmosphere. and section 3 describes the computation of the For the present simulations, we have used a atmospheric response to the excitation. The tidal tropical (15◦N) atmosphere as a background Diurnal and semi-diurnal tidal structures due to O2,O3 and H2Oheating 1209 Figure 1. Height profile of neutral densities. Figure 2. Height profile of heating rates obtained from PHODIS during equinox at noon, at geographic equator. atmosphere, which is based on the Air Force Geo- wavelength grid specified by WMO (1986). Higher physics Laboratory’s (AFGL) Atmospheric Con- resolution of 1 nm is used between wavelength 300 stituent Profiles model (Anderson et al. 1986). In and 315 nm. this model, the vertical structure including tem- Figure 2 represents typical heating rates perature, pressure and density distributions, plus obtained from PHODIS at spring equinox, at the mixing ratio profiles of H O, CO ,O,NO, CO, 2 2 3 2 geographic equator during noontime. The meso- and CH , were initially taken from U.S. Standard 4 spheric heating, essentially due to Ozone absorp- Atmosphere. Altogether, vertical profiles of the tion peaks at around 45 km above the Earth’s number densities of 28 constituents (H O, CO ,O , 2 2 3 surface. Whereas, in the lower thermosphere, the N O, CO, CH ,O,NO,SO,NO, HNO ,OH, 2 4 2 2 2 3 heating increases considerably due to molecu- HF, HCl , HBr, HI, ClO, OCS, H CO, HOCl, N , 2 2 lar oxygen absorption, which normally maximizes HCN, CH3Cl , H O ,CH ,CH ,andPH)are 2 2 2 2 2 6 3 around 140 km.