Lunar tides in the Thermosphere-Ionosphere-Electrodynamics General Circulation Model

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. A1, PAGES 1-13, JANUARY 1, 1999 Lunar tides in the Thermosphere-Ionosphere-Electrodynamics General Circulation Model R. J. Stening School of Physics, University of New South Wales, Sydney, Australia A.D. Richmond and R. G. Roble High-Altitude Observatory, National Center for Atmospheric Research, Boulder, Colorado Abstract. Lunar semidiurnal tides are introduced at the lower boundary of the National Center for Atmospheric Research Therrnosphere-Ionosphere-Electrodynamics General Circulation Model (TIEGCM). The tides are derived from the model of Vial and Forbes [1994] and interesting properties of these tides are found when they are subjected to Hough decomposition; there is considerable hemispherical antisymmet in the September tides, and the March and September modal compositions are significantly different. A differencing method is used to isolate the lunar tidal effects in the TIEGCM, and these are compared with lunar tidal analyses of ionospheric data. The model reproduces the broad feature s of the lunar tide in fof2 (maximum frequency of the F region) with phase changes around 7 ø magnetic dip latitude during daytime. The model and data analysis both give variations of the amplitude and phase of the lunar tide with local time. Near the equator the variation of phase with local time changes with latitude as the equatorial anomaly develops during the day. Comparison between the model predictions and analyses of data at observatories midlatitudes produces mixed results. Here the effects of the lunar components of both electrodynamic drifts and of neutral winds need to be taken into account. Several cases of day to night changes in the phase of the lunar tide in fof2.are noted. Large nighttime amplitudes of the lunar tide in hmf2 (height of the maximum density), more than 4 km, seem to be due to inphase action of the electrodynamic and neutral wind effects while during daytime they are out of phase. The lunar tide in the ratio of oxygen to nitrogen density [O]/[N2]is estimated and found to be of relatively minor importance. Amplitudes of the lunar tide in fof2 may be measured at more than 0.4 MHz at some local times, but the model values are less than this. Comparison is also made with ion drift measurements made by the San Marco D satellite. The several uncertainties which underlie this work are discussed in detail. 1. Introduction presence of a phase anomaly in the geomagnetic variations [Stening and Winch, 1979; Schlapp and Malin, 1979] also In recent years our knowledge of the lunar tide in the upper suggested the possibility of such asymmetries, and these were atmosphere has been expanding. New methods of analyzing confirmed by further wind observations [Stening et al,, 1994]. data sets to extract the tide have yielded some intriguing Over the years there have been many determinations of the results [Winch and Cunningham, 1972; Stening and Winch, lunar tide in the F region by analysis of tabulated ionospheric 1979; Malin and Schlapp, 1980; Schlapp et al, 1996]. At the parameters. Those most frequently analyzed are the height of same time, more sophisticated atmospheric tidal models have the maximum density hmf 2 and the corresponding maximum been developed [Forbes, 1982; Vial and Forbes, 1994]. The basic tidal theory is presented by Chapman and Lindzen [1970] but the most complete tidal model published to date is that of Vial and Forbes [1994]. In this model, not only is the critical frequency fof2. Matsushita [ 1967] has summarized the early work. In most determinations, hourly values of the parameters are analyzed using some form of the Chapman- Miller method [Chapman and Miller, 1940]. More recent gravitational forcing of the moon on the atmosphere included, studies include those of Rastogi [1968], Rush and but also forcing due to the vertical movement of the oceans Venkateswaran [1968], Handa [1978], Rastogi et al. [1985], and of the Earth's land surface at the lower boundary. The and Stening [ 1986]. Few of these studies examined the local realistic atmosphere and inclusion of zonal mea n background time dependence of the lunar tidal effect in the ionosphere, and winds in the model give rise to some unexpected so we have performed some new analyses to compare with the hemispherical asymmetries at the September equinox, but results of the TIEGCM model. these results are broadly in accord with observations of the lunar tide in winds at the 80 to 100 km region as determined by Stening et al. [1987] and Stening and Vincent [1989]. The Many of the earlier calculations of the lunar tide in the F region of the ionosphere have concentrated on the low-latitude behavior and have been able to correctly simulate the phase reversal that occurs in the lunar tide in fof2 at ~ 8 ø dip latitude Copyright 1999 by the American Geophysical Union. [Dunford and Lawden, 1969; Anderson et al, 1973; Abur-Robb and Dunford, 1975]. In each of these studies the continuity Paper number 98JA /99/98JA equation for the ions has been solved with a simple electric field imposed to drive the lunar variation. At low latitudes the

2 STENING ET AL.: LUNAR TIDES IN A GENERAL CIRCULATION MODEL effect of the electric field clearly dominates that of neutral winds, so the latter are not include in the calculations. There are fewer theoretical studies of the ionospheric lunar tide at higher latitudes, partly because here one does need to include the lunar tide in the neutral winds, and, even now, this is poorly known at F region heights. The higher latitude calculations of Handa and Maeda [1978] had only limited Success. 2. Model The National Center for Atmospheric Research (NCAR) Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIEGCM) is a Eulerian model in which the neutral atmosphere and the ionized components are solved on the same grid. Other authors have outlined the evolution of this model from earlier versions [Roble et al., 1988; Richmond et al., 1992]. The neutral atmosphere (TGCM) part of the model calculates winds, temperatures, and densities from the input solar radiation and background atmosphere. Diurnal and semidiurnal tides are generated by processes within the model [Fesen et al., 1986]. Ion drag effects are included. Ion densities are derived from the continuity equation with the usual production and loss terms and movement by neutral winds along magnetic field lines and electric fields perpendicular to field lines [Roble et al., 1988]. The neutral and ion densities are used to determine the electric conductivities, the neutral winds yield the dynamo emfs, and the dynamo equation can then be solved for the electrostatic fields and thence the electric currents derived [Richmond et al., 1992]. The electric fields react back on the ion densities by providing electrodynamic drift, which, in turn, may affect the neutral winds by ion drag. A magnetospheric electric field in the form of a constant cross-polar cap potential of 30 kv is imposed on all the simulations considered here and the solar flux F lo. 7 is set to 150. We report here runs that started in March (day 80) and September (day 262). The lunar age was calculated for the year 1968, so that the lunar age at the start of the March run was ø. The lunar tides are introduced at the lower boundary of the model at an altitude of 97 km. They then propagate upward and are subject to the influences of the winds and temperatures that they encounter and so may be subject to such effects as mode coupling. Solar semidiurnal tides propagating up from lower in the atmosphere are also introduced at this lower boundary, in the manner of Fesen et al., [1986] but now using the improved model of Forbes and Vial [1989]. Their presence is not expected to affect the behavior of the lunar tides but should give rise to a more realistic ionosphere upon which the lunar tidal effects can be superposed. The simulations of Vial and Forbes [1994] provided the amplitude and phase of the lunar tide in geopotential height as a function of height and latitude for each of the months of the year. These authors also perform calculations including nonmigrating modes with zonal wavenumbers running from s = -3 to +5. These are mostly generated by vertical movement of the ocean at the lower boundary, and their inclusion yielded a better agreement with the observations of the longitudinal variation of the lunar tide in the air pressure at sea level. Vial and Forbes also compare results from their model with observations of lunar tides in upper atmosphere winds in the 80 to 100 km height region. They compare model results with s = 2 only and also with all the modes included. The differences between the two model results in the upper mesosphere are small, and the more complex model with all the tidal modes included does not give a significantly better agreement with the observations, so the simpler s = 2 only model has been adopted in this study. Using the Hough function dependence on colatitude given by Chapman and Lindzen [1970, Table 3.7], these results were analyzed to determine the amplitude and phase of the various lunar Hough modes, yielding the results shown in Table 1. The differences between the March and September equinoxes in these results are worth noting. In March the dominant mode is the symmetric (2,2) mode, as might be expected, but in September the antisymmetric (2,3) mode is the largest. Also, a symmetric mode is largest in December, while an antisymmetric mode clearly dominates in June. These effects ultimately arise from the lag in response to solar heating of the ozone concentration lower in the atmosphere. The asymmetric distribution of ozone between the northern and southern hemispheres during equinox is shown by Teitelbaum and Cot [1979]. This distribution causes asymmetric heating of the ozonosphere, leading to asymmetric wind distributions. The latter are probably mainly responsible for modulating the propagation of the lunar tide to yield the effects shown in Table 1. The model was run for ~ 11 days with the lunar tides included and then run again for the same period without the lunar tides. The lunar effects were determined by subtracting the results of the two model runs. Figure 1 shows the resulting output for zonal winds at 52øN latitude (location of Adak) in September at 97 km. Here an almost perfect lunar tide is reproduced because the lunar tide in geopotential heights is introduced at this height. The solid line has points plotted every 2 hours and clearly shows the semidiurnal nature of the tide. The dashed line connects points at the same local time each day and shows the semimonthly character of the tide. It is this feature that is used to determine the phase and amplitude of the tide as it varies with local time. The series of points from different days but the same local time is subjected to a least squares fit to a wave of period days, and the amplitude and phase of the fit are determined. In the case of Figure 1 these results can be compared with those input at 97 km as a check. Table 1. Geopotential Heights for Different Lunar Hough Modes at a Height of 97 km. March June September December Mode Amplitude Phase Amplitude Phase Amplitude Phase Amplitude Phase 2, , , , , Amplitudes are in meters and phases are the lunm' time of maximum.

3 ß. STENING ET AL.: LUNAR TIDES IN A GENERAL CIRCULATION MODEL O Tirne (hours) Figure 1. Zonal neutral wind output from the Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIEGCM) at a height of 97 km and location of Adak (51.9øN, 183.4øE). Points are plotted every 2 hours. The dashed line joins points at the same local time to show the semimonthly tide. the results of the TIEGCM calculation, while the dashed curve 3. Data Analysis Method is obtained from an analysis of fof2 values over 9 years Because few others have derived the local time dependence of the lunar tide, we have performed several analyses of ionospheric data to compare with the TIEGCM predictions. For this purpose we have used the method of Winch and Cunningham [1972], which takes hourly values and derives a series of Fourier coefficients representing the diurnal and ( ) using the method of Winch and Cunningham [1972] described above. The long-dashed line indicates the amplitude level of 2 standard errors in the Winch and Cunningham analysis. An amplitude equal to this will imply a corresponding error in phase of 1 lunar hour. When the amplitude falls below this level, then the phase errors will be seasonal variations of the lunar semidiurnal tide. From these larger and the values less reliable (this "2 or" level is indicated coefficients the local time variation of the tide may be in several of the following diagrams). In this particular reconstructed. This method is elaborated further by Stening example the raw fof2 data from Singapore had to be and Vincent [1989]. Values of hmf 2 for lunar analysis were derived from tabulated interpolated when there were one or two successive missing values. The analysis method requires a complete set of 24 values of M(3000)F2 using the "Shimazaki formula" values for each day. If there are more than two successive [Shimazaki, 1957] missing values, then that day is excluded from the analysis. The method uses four daily Fourier harmonics, and this may be hmf 2 = { 149,000/M (3000)F2} partly responsible for the shape of the "observed" curves. However, looking at the two times of maximum amplitude at 4 4. Results and Discussion and 13 hours, good agreement is obtained for the phases at these times of around 1 and 5 hours respectively. At times 4.1. Comparison with ionosonde data and other when the observed amplitude is low, the errors in the phase models will be large and the agreement between the determined values is correspondingly worse. This example shows that, at this Least squares fitting to the model output provides an amplitude and phase for each local time. The TIEGCM model location, there is at least a day to night change in the phases of the lunar tide in fof2 and that, in this respect, the modeled has the capability of presenting values of fof2 (maximum results are consistent with observation. frequency of the F region, corresponding to the maximum ion density of that region) and of hmf2 (the height of this A more global picture is seen in Figure 3, where the lunar tide in the neutral temperature is contoured in a longitude-height maximum density). Both of these have been extensively profile. The vertical propagation of the tide is evidenced analyzed from ionosonde records and so are useful parameters between 100 and 200 km with a vertical wavelength of over for comparison between the model and observations. 100 km and a maximum value at a height of- 160 km. The A typical plot is given in Figure 2, where the fof2 values at Singapore (1.3øN, 103.8øE) are used. The solid line represents variation of the phase and amplitude of the lunar tide in temperature in the model of Forbes and Gillette [1982] is

4 4 STENING ET AL.: LUNAR TIDES IN A GENERAL CIRCULATION MODEL 10 - observed. - \ I - I, I, 'i I, I J I 0.25 j i i / 0.05 ' - / Figure 2. (top) Phase and (bottom) amplitude of the lunar tide in maximum frequency of the F region fof2 at Singapore for March. Dashed line is the result from analyzing data. Solid line is the TIEGCM prediction. The long-dashed line indicates the 2 level for the observe data curve. shown in Figure 4, and this yields an average vertical wavelength of ~ 78 km between 100 and 180 km, somewhat calculation begins on day 80 of the year The calculation has reached day 90 at the time of the output in these figures. At shorter than the TIEGCM. In this height range and at low 0000 UT on this day the lunar age t) is ø. The largest latitudes, Forbes and Gillette show a maximum amplitude of maximum in Figure 3 at F region heights occurs at-60 ø 5.8 K in the lunar tide in temperature at ~ 115 km, decreasing longitude or 2000 LT. Combining this with the lunar age, the to a minimum of 1.6 K near 160 km and then reaching very lunar time is slowly varying values above 200 km around 2 K and a nearconstant phase of 7 hours. The relevant lunar phases in t = /15 = Figures 3 and 5 may be determined by noting that the or 7.25 hours for a semidiurnal variation. i i ii i i i i i ii i i i i i.i i 4, ',,, 2 i i i i i i i i i i i i i i i ß i i i i i i i i i i 1 I ' / "r-'ill// \/ Ii.'$,, \'., ; 1oo LONGITUDE Figure 3. Height-longitude profile of the lunar tide in neutral temperature at 2.5 ø latitude in March.

5 ,.. STENING ET AL.: LUNAR TIDES IN A GENERAL CIRCULATION MODEL 5 4OO oo 400, l,,, _, I.b _,, Temperature Amplitude (K),,, [ =----T, I ' ' [ ' ' oo lo 15 Temperature phase (lunar hr max.) Figure 4. Variation with height of the (top) amplitude and (bottom) phase of the lunar tide in temperature from the model of Forbes and Gillette [ 1982] for equinox at the equator., I 20 It is noted that there are, in fact, three maximums rather than two at these heights. We have chosen the largest-amplitude feature that connects with the more regular semidiurnal variations seen below 200 km. The two models can thus be seen to have fair agreement above 200 km. At lower heights the propagation properties differ but similar amplitudes are obtained. The Forbes and Gillette [1982] model differs from the TIEGCM in that the tides are computed from the ground all the way up to 400 km. In the TIEGCM modeling presented here the lunar tide is derived from Vial and Forbes' [1994] model, where updated background atmosphere conditions are used and the additional lunar forcing from the lower boundary is included. This additional forcing acts against the gravitational forcing to yield a lower resultant tidal amplitude. The Vial and Forbes model does not extend to F region heights. Figure 5 shows contours of zonal neutral wind amplitude in a latitude-longitude section near a height of km. While the maxima and the propagation characteristics in Figure 3 show the influence of the (2,2) mode component, there is evidence of considerable asymmetry in Figure 5, with larger wind amplitudes in the southern hemisphere. Such a lack of symmetry at the March equinox is not represented in the earlier models such as that of Forbes and Gillette [ 1982]. The worldwide plot of the lunar tide in fof2 given in Figure 6 was obtained after the model had run for 6 days. The lunar time Figure 5. Latitude-longitude contours of lunar tide in zonal neutral wind speed in March at a height of ~ 120 km.

6 _ 6 STENING ET AL.' LUNAR TIDES IN A GENERAL CIRCULATION MODEL LONGITUDE LOCAL TIME (HRS) Figure 6. Contours of the lunar tide in fof2. Contour interval is 0.03 MHz. at 2400 UT is 11.8 hours. This plot reveals several important features. In daytime a phase change is seen between values surrounding the dip magnetic equator and those at higher latitudes, while at nighttime this phase change is not present. This is typical of observations of phase changes in the vicinity of the dip equator where the F 2 region of the ionosphere is under the influence of the fountain effect, producing the equatorial anomaly during the 0900 to 2000 LT period. The maximum/minimum near the equator can be seen to roughly follow the line of the magnetic dip equator. The properties of the tide near the equator were further investigated by plotting the phase of the lunar tide in fof2 at 1 ø latitude intervals. It should be noted that the TIEGCM grid spacing is 5 ø of latitude, and so interpolation must be used to obtain these results. Figure 7 shows the phase reversing in daytime but not at night. These calculations were performed at 150øE longitude. For the daytime result a vector average was performed over all hours between 0700 and 1700 LT. All the other hours, 1800 through to 0600 LT, were used in the nighttime average. The reversal occurs between 5 ø and 8 ø dip latitude in March and between 8 ø and 10 ø in September. Comparison with lunar analyses of ionosonde data by earlier workers is complicated by several factors. Many of the analyses derive only one amplitude and phase, in that they average over all local times. Some also average over several months; there is a known variation with season of the phase of the lunar component of the electric field driving the equatorial anomaly [Tarpley and Balsley, 1972]. I ' ' ' ' I t,,, [,,, - ' daytime ß....- '...,,.,,.- -'""'... ; -...< <!.g?_ l,.m..e.... "-< , nighttime... _ -.,...,<... < ,... <--. = 10 - _ h daytime 6 I I, J I,, Dip Latitude Figure 7. Variation of the phase of the lunar tide in fof2 with latitude as derived from the TIEGCM showing (top) daytime and (bottom) nighttime results for March and September.

7 _ STENING ET AL.: LUNAR TIDES IN A GENERAL CIRCULATION MODEL 7 ///'/ - 10 /,/. c 0 ø 4. ø 0 - " '" Figure 8. Variation with local time of the phase of the lunar tide in fof2 from the TIEGCM for latitudes of 0% 4 ø, 8 ø, and 12 ø in September. Examination of the TIEGCM results shows that, at latitudes nearest the equator, there is a very considerable variation of phase with local time during daytime, as can be seen in Figure 2. A similar variation is found in the September calculation. When analyses of ionosonde data include local time variations, there are usually some local times when the lunar tidal amplitude is too small to be statistically significant [see for example, $tening, 1986]. So it is not possible to make a one-to-one comparison at all local times because all the data are not statistically reliable. There does appear to be a real local time variation at equatorial latitudes. For example, at Huancayo (12øS, 285øE) in March we found the lunar phase for fof2 varied from 3.7 hours at 0800 UT to 5.9 hours at 1700LT (derived from data). Rastogi [1968] analyzed data from Huancayo and, averaging over the whole year, found the phase varied from 1.1 hours at 0800 LT to 5.2 hours at 1700 LT. Rush and Venkateswaran [1968] show several stations with this change in lunar phase of fof2 with local time. In order to examine this further, we have plotted the local time variations of the phase for different latitudes, as determined by the TIEGCM, in Figure 8. Note that separate vector averages of these for daytime and nighttime are used for the results in Figure 7. An explanation of the daytime phase changes in Figure 7 is given by Dunford and Lawden [1969]. The vertical ion drift produced by the lunar semidiurnal tide is superposed on the drifts produced by all other sources. These latter drifts give rise to the equatorial anomaly, in which ionization is lifted up and away from the dip equatorial region and transported to higher latitudes, giving rise to a crest near 15" dip latitude. An extra upward drift from the lunar tides will give rise to a smaller fof2 near the equator as more ionization is moved away, and this will lead to a higher fof2 near the crest as that region receives / / -5,,, I,,, I,,, I, I,, Local time 0.4, TIEGCM calculation -- observed 0.1 x,,/ Local time Figure 9. Variation of (top) phase and (bottom) amplitude of the lunar tide in fof2 with local time at Manila in September. Solid line is TIEGCM model; dashed line is observed data,

8 8 STENING ET AL.: LUNAR TIDES IN A GENERAL CIRCULATION MODEL 15 lo I ", I, I I,,, I,, Local time I,, I,,,, I,, I m, I Local time Figure 10. (top) Phase and (bottom) amplitude of the lunar tide in fof2 for September at Yamagawa. Dashed line is analysis of data. Full line is TIEGCM prediction. more ionization by transport. Somewhere between 0 ø and 15 ø, there is a crossover, appearing around 8% on average. At night the background drifts are downward; the equatorial fountain does not operate, and so there is no phase change. We may now interpret Figure 8 as showing how the effects of the equatorial fountain vary with local time. At the equator the effects start at 1000 LT and persist up to 2000 LT, while at 12 ø latitude the ionosphere appears to be in the equatorward depletion region after only about 1400 to 1600 LT. Thus a daytime average at 12 ø will give a phase around 0.0 hours. In between 0 ø and 12 ø we can see that the lower is the latitude, the longer is the period of time that the ionosphere is in the depletion region of the anomaly. In Figure 9 we present another comparison between the model and observations for Manila (14.7øN, 121. IøE, 7.4 ø dip latitude). The TIEGCM phase varies much like the 8 ø curve in Figure 8, as expected. The observed curve more resembles the lower-latitude curve in Figure 8. We note here also that the TIEGCM gives a phase of 10 lunar hours for the vertical ion drift at Manila for all local times and a phase of 11_+1 hours for hrnf2 at Manila. The observed phase of hrnf2 at Manila is 10.5, with a local time variation of +1.5 hours and so is in good agreement. We should also note that the TIEGCM variation of phase with local time at Singapore in March, shown in Figure 2, is similar to the September variation at 0 ø in Figure 8. We conclude by showing some more examples of comparisons between the TIEGCM prediction and results obtained from analyzing ionospheric data. Figure 10 shows fof2 at Yamagawa (31.2øN, 130.6øE). Here the phases agree fairly well (largest difference is ~ 2 hours), but the observed amplitudes are sometimes much larger. Sometimes this analysis method yields amplitudes that are too large, particularly when the phase is also varying, as here. Figure 11 shows fof2 at Vanimo (2.7øS, 141.3øE, dip latitud e 10.9øS). In this example, at some local times, the least squares fitting to the TIEGCM output had problems. The error in the fit is inspected for each time, and here the errors were of similar magnitude to the amplitudes at 0200, 1100, 1600, 1800 and 1900 LT. In these cases the associated phases would also be unreliable. This is a comparatively rare occurrence, and it can be seen that there is a good phase fit at local times where this problem did not occur. This example also shows that the observed amplitudes were often below the 2 o' reliability line but not below the 1 o' probability line. The TIEGCM phase excursion near 16 hours is rather similar to that at 1'2 ø in Figure 9. This does not appear in the observations. Apart from this there may be a small variation of phase with local time, and the model agrees with observations to within the errors of measurement. The final selection is from Maui (20.8øN, 203.5øE) in Figure 12, and it demonstrates some of the problems associated with this work. Two different data set analyses are shown, one from and one from The latter data set has been interpolated for missing values, as for Singapore. The two data sets give remarkably similar results, except that the phases diverge when the amplitudes fall below the 2 o' level. When the model amplitudes become small compared With those observed, then the modeled phases also fail to yield the observed values. It is instructive to look at other outputs of the model which are likely to affect the lunar tides in fof2 and hmf2. The two most significant effects are (1) the vertical component of the electrodynamic drift due to the electrostatic field (the E x B drift), designated v i, and (2) the vertical component of the neutral wind measured parallel to the magnetic field, designated Wpa r. The lunar tides in these parameters, together with hmf 2 are plotted in Figure 13. At 1400 LT, the ion and neutral velocities have similar

9 ,,. STENING ET AL.: LUNAR TIDES IN A GENERAL CIRCULATION MODEL i! i [--L i i i i I! i i i I i i i '-':-. o ,.n <: _ 0 ' I,,,, I, i, I,,, I,,, I,,,, Figure 11. (top) Phase and (bottom) amplitude of the lunar tide in fof2 at Vanimo for March. Observedata are from Long dashed line is the 2 o' level d 12 e 10 I ' I I I I ' I I I I I, I ' I ' ' I " ' 8 6 _ / observed \ - _///2'/' - observed / _ ',,,, I,, I,,, I,,, I,, O Figure 12. (top) Phase and (bottom) amplitude of the lunar tide in fof2 at Maui for September. Dashed line is from analysis of data, dot-dashed line is from analysis of data, solid line is from the TIEGCM. The 2 o' level indicated is for the data. The 2 o' level for the data is 0.18 MHz.

10 10 STENING ET AL.: LUNAR TIDES IN A GENERAL CIRCULATION MODEL o Figure 13. (top) Phase and (bottom) amplitude of various parameters from TIEGCM at Maui for September. Solid line is fof2, long dashed line is hrnf2, dot-dashed line is vertical ion velocity, and short dashed line is the vertical component of the neutral wind parallel to the magnetic field. magnitudes (1 m/s) but opposite phases, giving some cancellation, so the amplitude of the modeled lunar tide in fof2 is very small at that time (and the phase may be unreliable). The lunar tide in hmf2 is also small at this time. As the modeled values depart from the observed values at this time, it might be surmised that either the effect of the neutral winds is too large or the ion drifts are too small. At 2400 LT the lunar tide in Wpa r is 1.3 m/s and phase is 8.4 hours while v i is 1.7 rn/s with phase 8.6 hours. So we have two relatively large effects acting inphase to give a large tide in fof2 and also in hrnf2 (4.4 km). In general, it can be seen in Figure 13 that, at this location, v i and Wpa r are inphase during nighttime from 2000 LT onward and out of phase during daytime. The phase of the hmf2 tide is similar to that of v i at night but several hours later during the day. This situation where there is a phase change in the modeled Wpar between day and night is common at midlatitudes and gives rise to largeramplitude lunar tides in hmf2 at night compared with daytime. We should note that the electrodynamic drifts vary little in phase and amplitude with height, while the neutral winds relate to the local vertical structure of the lunar tide. This means that Wpa r may have a considerable phase variation with height, and,c 6 4 v 2 i i i a Figure 14. TIEGCM predictions for the (top) Phase and (bottom) amplitude of the lunar tide in the neutral meridional wind (positive equatorward) in March at Concepcion (Chile) and Canberra (Australia).

11 _ STENING ET AL.: LUNAR TIDES IN A GENERAL CIRCULATION MODEL 11 [ i 1 i! i i ] i i i _ \ / \ / \ \ Figure 15. TIEGCM predictions for the (top) Phase and (bottom) amplitude of the lunar tide in zonal ion drifts at the magnetic equator and 150øE longitude in September at 400 km altitude. because the height of the F region maximum density hrnf 2 varies by more than 100 km during the course of a day, the phase of Wpa r in the vicinity of the maximum density height will also vary with time of day. It is realized that changes at lower levels will also influence effects near the layer peak, but these relations start to give some insight into the changes observed. We also examined model output for Australian stations such as Townsville (19.3øS, 146.7øE) and Darwin (12.45øS, øE) and found different behavior in March and September, presumably owing to the different modal structure of the lunar tides in these 2 months. In March the phase of W pa r varies with local time from 7 to 10 lunar hours. The phase also varies considerably with height and the model hrnf2 phase varies with local time from 5 hours at night to 10 hours in daytime. The observed hrnf2 phase ( ) at Townsville varied from 6 hours at night to 8.6 hours in daytime, which is reasonably good agreement, considering that the observed tides are only just statistically significant and that there is also some year-to-year variability. In September the phase of Wpa r has very little variation with local time at these stations (10-11 hours). It does vary with height and has a larger amplitude at night. The modeled hrnf 2 also has little daily phase variation (values of 7-8 hours) and a larger amplitude at night. The observed phases are around 4 hours at night (disagreeing) and 7.5 hours during the day (agreeing). Furthermore, the largest observed daytime amplitude is 2.7 km, and the average modeled daytime amplitude at Townsville is 2.9 km. These Australian observations further demonstrate the complexity of the problem. We may not have the tidal mode structure adjusted exactly correctly for the average observation. The variability of the observed lunar effect in the ionosphere indicates that there is also variability in the atmospheric tides. Examination of geomagnetic variations at midlatitudes will show similar variability, and so this is to be expected. We must comment on the consistent differences in the observed and modeled amplitudes. The lunar tide in fof2 may be > 0.4 MHz at Maui during a particular time of the day. This is 10 times the standard error in the measurements. The same results, when vector averaged over the day, give an amplitude of 0.2 MHz, which is more in line with previous determinations. In several of the results presented above there is a maximum amplitude near 1500 LT. This is true for Yamagawa, Manila, and Maui. We have been unable to explain why the model does not reproduce this, but note that this is the local time near which the background value of fof2 is often maximum. Another factor that can affect the F region ionization density is the ratio of atomic oxygen density to molecular nitrogen density [O]/[N2]. There is a lunar tide in this density ratio, which leads to lunar tides in fof2. We used the model to estimate this effect and found that, at midlatitudes, the lunar tide in [O]/[N 2] is ~ 0.6%, on average, which is to be compared to a lunar tide in the ionization density of ~ 2%. So we see that the neutral density ratio is not a dominant contributor to the lunar tide in the F region, maybe contributing about one quarter of the effect. At equatorial latitudes its relative significance is even less. Although the impressed lunar tide includes longitudinal wavenumber s = 2 components only and so has no longitude dependence, it is of interest to inquire whether the Earth's magnetic field structure causes any longitude dependence on the model. Some idea of longitudinal similarities and differences may be gleaned from Figures 3 and 5, in which only minor differences can be discerned, but these may be due to local time effects. Figure 14 compares the model results for the meridional neutral wind velocity at two stations with similar geographic latitudes but different geomagnetic

12 12 STENING ET AL.: LUNAR TIDES IN A GENERAL CIRCULATION MODEL latitudes. Concepcion has coordinates 36.6øS, 287øE geographic and 25.1øS geomagnetic, while Canberra has coordinates 35.3øS, 149.0øE geographic, and 44.0øS geomagnetic. Figure 14 shows that the diurnal variations of amplitude are very similar at the two locations. The values of phase are also similar at nighttime. The daytime phase values at Canberra are probably meaningless when the accompanying amplitude is so low. The model shows variations in hrnf2 similar to the meridional wind for both locations, and these can be compared with analyzed hrnf2 data. Unfortunately, the analysis does not yield a statistically significant result for Canberra in March. The Concepcion results do show a large tide in hrnf2 at night [see also Stening, 1986] with a phase agreeing at 6.5 lunar hours Comparison With Satellite Measurements Recently, Maynard et al. [1995] isolated a lunar tide in the zonal ion drifts near the equator as determined by the San Marco D satellite. Figure 15 gives the TIEGCM predictions for the phase and amplitude of this lunar tide at a height of 400 km. Maynard et al. examined the lunar tide by subtracting the average daily variation at various lunar ages. Their largest extremum [Maynard et al. 1995, Figure 10] is a negative deviation of over 30 m/s at 1100 LT at full moon. This translates into a lunar hour of maximum of 5 hours which compares well with the average daily phase (vector average) of the TIEGCM tide of 4.7 hours. However the average amplitude of the TIEGCM tide is only 2.1 m/s. One should therefore view these results with caution. The amplitude and phase of the TIEGCM lunar tide in zonal ion drift varies little with height above 300 km. If one takes only the daytime vector average, the result is 3.3 hours, not such a good agreement. 5. General Discussion and Conclusions The comparisons between the modeling of the lunar tide in the ionosphere by the TIEGCM and results obtained by analyzing data are subject to several uncertainties: 1. The accuracy of the lunar tide input into the model has been checked against upper atmosphere winds data by Vial and Forbes [1994]. They obtained reasonable but not perfect agreement. 2. The performance of the TIEGCM model itself has not been validated in all situations. The model sometimes experiences problems when hrnf2 is very high, as at the dip magnetic equator. 3. The accuracy of the analysis of lunar tides from ionospheric data varies with the data set. Sometimes a statistically significant lunar tide cannot be derived from the data. 4. In most cases the effects of magnetic disturbances have not been removed from the data analyzed. In one trial the 5 "disturbed days" of each month were excluded. The results were similar to those when these days were included, except the statistics were not as good. 5. The tide itself may vary to some extent from year to year. It is generally considered desirable to use a large data set comprising many years when deriving lunar tides, but, if there is year-to-year variability, a vector average of the tides from different years is obtained. Such a result may yield a lower amplitude, possibly statistically insignificant, and, at worst, a phase value that never actually occurs. Uncertainty 5 makes the comparison task particularly difficult but opens up questions as to what factors give rise to these year-to-year changes and whether some relationship can be found between lunar tidal behavior at a particular time and the properties of the background atmosphere, for example. Stening et al. [ 1997] have begun such an investigation. We therefore conclude that the simulation of lunar tides in the TIEGCM is broadly successful, though there remain some discrepancies when details are examined. It is not yet clear whether these discrepancies arise from problems with the model or the data analysis or from the variability of the tide itself. There is the possibility of performing further modeling runs during other seasons and different phases of the solar cycle. It would also be interesting to see whether there is any correlation between year-to-year changes in the ionospheric lunar tide and the geomagnetic lunar tide. Acknowledgments. This work was commenced when R. Stening was working as a visiting scientist at the High-Altitude Observatory, NCAR. He expresses gratitude to HAO and its staff for their support and assistancee The lunar tides were programmed into the TIEGCM model by E. C. Ridley. Ionospheric data were supplied by Ray Conkright of the WDC-A for Solar Terrestrial Physics, Boulder. 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