I. V. Karpov
Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Troitsk, Moscow Region, Russia
Tides in the upper atmosphere are determined as global wave perturbations of the hydrodynamic parameters with periods rigorously equal to 24 h/n ( n is integer) are meant. The longitudinal and latitudinal variations of the tides are described by the zonal harmonics and tidal modes: the Hough functions which are solutions of the tidal Laplace equation. This definition makes it possible to consider the observed variations of atmospheric parameters with the periods, which correspond to the tidal disturbances, as a superposition of the tidal modes. Therefore, the problem of determination of tidal parameter variations in the atmosphere is reduced to determination of the amplitudes and phases of the Hough functions.
Radar observations of the horizontal wind components are usually used to determine the mode composition of the tides in the lower thermosphere and mesosphere. The methods used to calculate the amplitudes and phases of the Hough functions are based on analysis of the vertical structure of the observed parameters [ Fakhrutdinova and Ishmuratov, 1991; Forbes and Salah, 1991]. However, due to difficulties of providing continuous observations and to inhomogeneous distribution of the ground-based stations, the parameters of the tidal variations in the lower thermosphere are not adequately studied and need specification.
The use of satellite observations, for example the winds measured
by UARS satellite, provides a significant expansion of the
experimental data on the tides in this atmospheric region. To
measure winds in the mesosphere and lower thermosphere, the HRDI
instrumentation (High Resolution Doppler Imager) is installed on
board the satellite and makes it possible to provide measurements
at altitudes of 50-115 km in the daytime and 90 km at
night. The detailed description of the HRDI and of its functioning
on board UARS was given by
Hays et al. .
The orbit parameters
provide measurements in the 72o latitude band. During 24
hours the measurements cover all the longitudes. The results of
observations of the wind tidal variations by the HDRI were
Burrage et al. [1995a, b\link
High horizontal resolution of the observations ( 500 km) made
it possible to obtain such combinations of data, which provide
determination of the mode composition of the tides from an analysis
of the latitudinal structure of wind variations. The aim of this
paper is to develop the method of determination of the amplitudes
and phases of the migrating tidal modes from the latitudinal
distributions of the wind components obtained in UARS measurements.
We hope that such method of tidal mode parameter determination
would make it possible to determine the global characteristics of
the zonally averaged tidal variations for shorter observation
period than it has been done by
Burrage et al. [1995a, b\link
Results of the observations of the horizontal wind components in the lower thermosphere on board the UARS satellite in February 1992 were presented by Hays et al. . During this observational period the satellite orbit parameters provided wind measurements in the latitude band from 60o in the northern hemisphere to 40o in the southern hemisphere. The experimental data were presented as zonally averaged values of the wind horizontal components at altitudes of 60-100 km at various LT moments.
Let us assume that the diurnal variations of the wind in the lower thermosphere are determined only by the tidal motions. The expression for the wind horizontal components may be written as
Here r and q are the height and colatitude, respectively; t is
the local time; n and m are the indices of the tidal modes; U is
the observed value of wind velocity; U
In the most cases it is sufficient to take into account the diurnal (n=1) and semidiurnal (n=2) tides at altitudes of the lower
thermosphere. The zonal averaging of the experimental data is taken
into account in (1), so the formulas do not contain any dependence
on longitude, and the indices of the tidal modes correspond to the
solar migrating tides, because the tidal modes with other relation
between the zonal wave numbers and frequencies disappear in the
averaging process. The U
Here sn = nW is the frequency of the tidal perturbation; W is the angular velocity of the Earth's rotation; N
Knowing the velocity components at various moments one can obtain from (3) a simple system of equations, solution of which determines the unknown amplitudes and phases:
The results of calculations of the amplitudes and local times of
the maximum of the geopotential semidiurnal tidal modes at
altitudes of 70-110 km are presented in Figure 1. The solid lines
show the tidal mode parameters, determined from the observations of
the wind meridional component, the dashed lines indicate the
parameters determined from the zonal component observations.
Unfortunately, a small volume of the experimental data presented by
Hays et al. 
prevents determination of the daily mean wind
directly from the UARS observations. This can be helped if the
measurements for a long observational period or modern models of
the mean parameters of the upper atmosphere are used. The results
in Figure 1 were obtained without taking into account the daily
mean wind (U0 = 0) . Such calculations contain some uncertainty in
determination of the amplitudes and phases of the tidal modes and
this uncertainty may be significant if the zonal wind component is
used. The results obtained (bearing in mind a small volume of the
experimental data and neglecting by the mean wind) are of an
illustrative character and merely demonstrate capacities of the
method of tidal mode composition determination based on an analysis
of the wind distribution mode structure. The tidal perturbations of
the geopotential in Figure 1 were recalculated from the
corresponding perturbations of the wind components using the
relations of the classic tidal theory. Deviations from the
values obtained due to the errors in the satellite measurements of
the wind ( 5 m s
It is worth noting that a significant increase of the (2,3) mode in comparison with the main symmetric modes, (2,2) and (2,4) , is found in the radar observations of Forbes and Salah . The same relationship between the inputs of various tidal modes is typical for our results. It can be seen in Figure 1b that at an altitude of about 97 km the phases of the tidal modes obtained in the radar observations at autumn equinox agree well with the phases determined by the measurements of the zonal wind component, and the phases of the tidal modes measured by Forbes and Vial  are closer to the phases determined by the measurements of the meridional wind component. Such a difference in the tidal mode phases can not be explained by a single reason. It is widely known that the equinox periods are characterized by a rapid change of the tidal phases [ Manson et al., 1989], therefore coincidences, as well as differences, based on a comparison to a small amount of data may be occasional. Moreover, the amplitudes and phases of the tidal modes determined from the ground-based observations depend on the number of stations used for the analysis, their geographic position and the instrumentation used [ Forbes and Salah, 1991]. Due to that, the UARS wind observations have a considerable advantage in determination of the tide mode composition as compared with ground-based measurements. The amplitude and phase differences of the semidiurnal solar migrated tides determined from the measurements of the zonal and meridional wind components observed on board the UARS are apparently due to the fact that in the calculations performed no daily mean wind has been taken into account. To evaluate influence of the mean flow on the semidiurnal tide mode structure. a calculation has been performed using the zonal component of the mean wind at altitudes of 70-80 km from the CIRA-65 empirical model. The results are shown in Figure 1 by the dashed line. Figure 1 demonstrates that taking into account of the daily mean wind alters significantly parameters of the principal tidal modes (2,2) and (2,3) and only slightly influence other tidal modes.
The mode structure obtained by satellite measurements was used to reconstruct the semidiurnal tidal parameters at middle latitudes. The amplitudes and phases of the tidal modes determined from observations of the meridional and zonal components of the wind velocity (Figure 1) were used to calculate the tides in these components. Figure 2 shows the results of calculations for the latitude of 50o and also the results of radar observations in February. The measurements at various stations were presented by Manson et al.  and are shown in Figure 2 in the following way: closed circles - Garchy (47o N, 3o E), open circles - Colm (52o N, 15o E), squares - Saskatoon (52o N, 107o W).
The tidal amplitudes based on the UARS measurements exceed those observed, especially for the zonal velocity component below 90 km (Figure 2b). Tidal amplitudes in the meridional velocity component below 100 km agree with the Saskatoon data (Figure 2a). The tide amplitudes in the horizontal wind components measured at Colm are significantly lower the ones obtained by us. The time of tide maximum derived from the observations of the velocity meridional component (Figure 2a) differs significantly from the observational data, whereas the calculated time of tidal maximum in the zonal wind component agrees well with the observations at altitudes of 80-100 km (Figure 2b).
The discrepancies in the parameters of the observed and calculated
tides may be due to the difference in methods used to determine the
wind in the lower thermosphere from satellite and radar data. It
should be noted that the UARS wind observations show that the wind
velocity measured by HRDI exceeds the velocities obtained by the
ground-based radar measurements
[ Burrage et al., 1996].
the question of determination of the wind in the lower thermosphere
by ion drifts measured in radar observations and by Doppler
measurements of the molecular oxygen spectra on board the UARS
satellite requires special consideration. Comparison of the
results obtained in this paper with the characteristics of the
semidiurnal tides derived from the HRDI measurements for two years
of UARS observations
[ Burrage et al., 1995b]
satisfactory agreement for the amplitude of the wind meridional
component and the time of a tide maximum in the wind zonal
component. At 95 km, the amplitude of the velocity meridional
component and the moment of the maximum of the velocity zonal
component are 30 m s
Similar calculations are performed to determine parameters of the diurnal tidal modes. It was assumed in calculations by (2)-(4) that the solar diurnal tides are determined by inputs of the (1,1) , (1,-1 ), (1,-2 ), (1,4) , and (1,3) tidal modes. The calculations performed demonstrate that the diurnal tide structure is mainly determined by the (1,1) mode. Some input into the diurnal variations below 90 km is also made by the (1,-1 ) and (1,-2 ) modes, their amplitudes decreasing rapidly with height. It is worth noting that the error of the method of mode input calculation for the (1,-1 ) and (1,-2 ) modes in the UARS observational period in question is rather high ( 50%) and thus the result obtained is merely of a qualitative nature. In the same way as for the semidiurnal tides, differences in tidal mode amplitude and phase, determined from different wind components, appear. Figure 3 shows the amplitudes and the time of maximum of the diurnal tide in the velocity horizontal components at an latitude of 50o calculated by the tidal mode parameters determined from the satellite measurements. The results of radar observations of the diurnal tides for February by Manson et al.  are also shown in Figure 3. The indexing is the same as in Figure 2. It should be kept in mind that the comparison of our results with the results obtained earlier is of a qualitative character. Moreover, the tide observations show significant interannual variation of the diurnal tide amplitudes (see Burrage et al. [1995b]). It can be seen that the amplitudes of the diurnal tide calculated in this paper exceed significantly the observed values. A significant depletion of the diurnal tide amplitude is seen above 90 km, which is due to the dissipative processes in the thermosphere. The time of tidal maximum determined for the meridional wind component differs significantly from that observed (Figure 3a). However, the tidal phase calculated for the wind zonal component agrees well with the observations above 80 km (Figure 3b). Possible reasons of such discrepancies between our results and observations were discussed above while analyzing the semidiurnal tides.
A new method to determine parameters of the solar diurnal and semidiurnal tides in the mesosphere and lower thermosphere from observations of the horizontal wind components on board the UARS satellite is suggested.
The method is based on an assumption that the temporal variability of the global distribution of parameters in this atmospheric region is governed by propagation of the solar migrating tides. The UARS measurements cover a wide latitudinal range and make it possible to determine the mode structure of the solar tides in the atmosphere, using the properties of orthogonal modes. Our method is a development of the idea of studying the tidal structure from the UARS observations applied to the diurnal tides by Hays .
The develop procedures of calculation of the tidal mode input and diurnal and semidiurnal mode parameters are applied to a limited set of the UARS observations in February 1991. The results of the calculations lead to the following conclusions:
1. The amplitudes and phases of the tidal modes determined by observations of the zonal and meridional components of the wind differ. Parameters of the above modes depend significantly on the daily mean wind. One of possible reasons of the difference in parameters of the tidal modes determined by different wind components may be related to not taking into account this factor in the above described calculations.
2. The semidiurnal tide structure is mainly determined by the (2,2) and (2,4) modes. The calculations reveal a significant increase of the mode (2,3) amplitude between 90 and 100 km. An increase of the input of this mode during equinoxes was also detected in the radar observations by Forbes and Salah . The diurnal tide structure is mainly determined by the (1,1) tidal mode.
3. Calculations of the midlatitude tidal parameters using the mode structure determined by the measurements on board UARS satellite show that the calculated tide amplitudes exceed the amplitudes obtained in the radar observations, especially for the diurnal tide. The times of tidal maxima in the meridional wind component differ significantly from the observational results, whereas the times of maxima of the diurnal and semidiurnal tides in the zonal component of the wind agree well with the observational data.
The results of the preliminary study show that the UARS measurements open broad possibilities to explore the tide morphology in the mesosphere and lower thermosphere.
The UARS measurements provide a possibility to improve significantly the accuracy of determination of the tidal mode structure, which is very important for theoretical modeling of the upper atmosphere. Attracting to tide analysis observations of other atmospheric parameters on board UARS (for example, the temperature) would improve tidal parameter determination and eliminate the uncertainties arising when the wind measurements are used.
Burrage, M. D., et al., Long-term variability in the solar diurnal tide observed by HRDI and simulated by the GSWM, Geophys. Res. Lett., 22, 2641, 1995a.
Burrage, M. D., et al., Latitude and seasonal dependence of the semidiurnal tide observed by HRDI, J. Geophys. Res., 100, 11,313, 1995b.
Burrage, M. D., et al., Validation of the mesosphere and lower thermosphere winds from the High Resolution Doppler Imager on UARS, J. Geophys. Res., 101, 10,365, 1996.
CIRA 1965, COSPAR Working Group IY, Amsterdam, 1965.
Fakhrutdinova, A. Ya., and R. A. Ishmuratov, Seasonal variations of the mode input into the semidiurnal tidal motions in the midlatitude lower thermosphere, Geomagn. Aeron., 31 (5), 904, 1991.
Forbes, J. M., and J. E. Salah, Mesosphere-thermosphere tidal coupling during the September 21-25, 1987, LTCS-1 campaign, J. Geophys. Res., 96 (A2), 1135, 1991.
Forbes, J. M., and F. Vial, Monthly simulations of the solar semidiurnal tide in the mesosphere and lower thermosphere, J. Atmos. Terr. Phys., 51, 649, 1989.
Forbes, J. M., R. G. Roble, and C. G. Fesen, Acceleration, heating and composition mixing of the thermosphere due to upward propagating tides, J. Geophys. Res., 98 (A1), 311, 1993.
Hays, P. B., et al., Remote sensing of mesosphere winds with the High Resolution Doppler Imager, Planet. Space Sci., 40 (12), 1599, 1992.
Hays, P. B., et al., The High Resolution Doppler Imager on the Upper Atmosphere Research Satellite, J. Geophys. Res., 98, 10,713, 1993.
Hays, P. B., et al., Observations of the diurnal tide from space, J. Atmos. Sci., 51, 3077, 1994.
Manson, A. H., et al., Climatologies of semidiurnal and diurnal tides in the middle atmosphere (70-110 km) at middle latitudes (40-55o), J. Atmos. Terr. Phys., 51 (7/8), 579, 1989.