Seasonal variations of the semi-diurnal and diurnal tides in the MLT: multi-year MF radar observations from 2 to 70°N, and the GSWM tidal model

Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 809±828

Seasonal variations of the semi-diurnal and diurnal tides in the MLT: multi-year MF radar observations from 2 to 708N, and the GSWM tidal model Alan Manson a,*, Chris Meek a, Maura Hagan b, Chris Hall c, Wayne Hocking d, John MacDougall d, Steven Franke e, Dennis Riggin f, David Fritts f, Robert Vincent g, Mark Burrage h a

Institute of Space and Atmospheric Studies, University of Saskatchewan, 116 Science Place, Saskatoon, SK, S7N 5E2, Canada b NCAR, Boulder, CO, USA c Auroral Observatory, University of Tromsù, Tromsù, Norway d Department of Physics and Astronomy, University of Western Ontario, London, Canada e Space Science and Remote Sensing Laboratory, University of Illinois, Urbane, USA f Colorado Research Associates, Boulder, CO, USA g Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, Australia h Space Physics Research Laboratory, University of Michigan, Ann Arbr, USA Received 12 December 1998; received in revised form 3 June 1999; accepted 6 June 1999

Abstract Continuous observations of the wind ®eld have been made by six Medium Frequency Radars (MFRs), located between the equator and high northern latitudes: Christmas Islands (28N), Hawaii (228N), Urbana (408N), London (438N), Saskatoon (528N) and Tromsù (708N). Data have been sought for the time interval 1990±1997, and typically 5 years of data have become available from each station, to demonstrate the level of annual consistency and variability. Common harmonic analysis is applied so that the monthly amplitudes and phases of the semi-diurnal (SD) and diurnal (D) wind oscillations are available in the height range of (typically) 75±95 km in the upper Middle Atmosphere. Comparisons are made with tides from the Global Scale Wave Model (GSWM), which are available for 3-month seasons. The emphasis is upon the monthly climatologies at each location based upon comparisons of pro®les, and also latitudinal plots of amplitudes and phases at particular heights. For the diurnal tide, the agreement between observations and model is now quite excellent with modelled values frequently lying within the range of yearly values. Both observations and model demonstrate strong seasonal changes. This result is a striking improvement over the comparisons of 1989 (JATP, Special issue). In particular, the phases and phase-gradients for the non-winter months at mid- to high-latitudes are now in excellent agreement. Some of the low latitude discrepancies are attributed to the existence of non-migrating tidal components associated with tropospheric latent heat release. For the semi-diurnal tide, the observed strong transitions between clear solstitial states are less well captured by the model. There is little evidence for improvement over the promising comparisons of 1989. In particular, the late-summer/autumnal tidal maximum of mid-latitudes is observed to be larger, and with strong monthly variability. Also the summer modelled tide has unobserved short (20 km) wavelengths at high latitudes,

* Corresponding author. Tel.: +1-306-966-6401; fax: +1-306-966-6428. E-mail address: [email protected] (A. Manson) 1364-6826/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 4 - 6 8 2 6 ( 9 9 ) 0 0 0 4 5 - 0

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and much smaller amplitudes than observed at all extratropical locations. Possible improvements for the GSWM's simulations of the SD tide are discussed, which involve migrating tidal modes due to tropospheric latent heating. # 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction The special issue of the Journal of Atmospheric and Terrestrial Physics (July/August 1989) on ``Atmospheric Tides'' represents the most substantial published accumulation of observed tidal winds in the Mesosphere and Lower Thermosphere (MLT). A variety of radar types were used for these studies, including EISCAT (European Incoherent Scatter), Meteor Wind (MWR) and Medium Frequency (MFR) radars. The most substantial papers included assessments of high-latitudes (Avery et al., 1989), middle-latitudes (Manson et al., 1989), and low-latitudes (Vincent et al., 1989), using climatologies (height vs months) of tidal amplitudes and phases. The clear and strong seasonal variations of tidal structures were very clear in these climatologies, and had already encouraged the modelling of tides in realistic atmospheres. The issue also included the ®rst monthly simulations of the solar semi-diurnal (SD) tide in the MLT (Forbes and Vial, 1989). The new COSPAR International Reference Atmosphere (Rees, et al., 1990) was used for winds, temperatures and pressures; and gravity wave (GW) saturation climatologies for eddy di€usivities (Garcia and Solomon, 1985). The model reproduced the main observed characteristics of the tide: larger amplitudes in winter than in summer; a bi-modal behaviour of the phase with rapid transitions in the equinoxes; and generally longer wavelengths in summer than in winter. Modelling of the diurnal (D) tide (Forbes and Hagan, 1987) also allowed for comparisons of seasonal variations at that time. The modelled low latitude tide (dominated by the S11 mode), and high latitude tide (dominated by the S1ÿ1 mode), showed some useful general agreements with observations; but the modelled seasonal variations at these latitudes and the mid-latitude modelled tide evidenced signi®cant discrepancies from observations. Since that time considerable advances have been made in both observations and modelling. The number of radars, especially MFR, has increased and these have allowed more global coverage. Data have been gathered for the campaigns of STEP (Solar Terrestrial Energy Programme) and its parts e.g. MLTCS (Mesosphere Lower Thermosphere Coupling Study). In the case of the MFRs, data sets are now often continuous due to design improvements in the systems. A selection of these data is being used here for the ®rst time, to include common systems (MFR) in the

Northern Hemisphere's US/Canada and Paci®c sections. The major impact upon the observational knowledge of the thermal tides has of course been the analysis of data from the UARS satellite-systems HRDI (High Resolution Doppler Imager) and WINDII (Wind Imaging Interferometer) (Burrage et al., 1996). These have con®rmed the general global and seasonal tidal structures found by ground based radars (MFR and MWR), but have added useful details (there is truly global-coverage (0±708) and height-coverage which extends into the thermosphere (McLandress et al., 1996)). This is a magni®cent data set. One problem with observational data which has been noted in these new studies, is that radar-tides often display smaller amplitudes (by 20±50%) than do the UARS tides, in the 90±100 km range (Manson et al., 1989, Burrage et al., 1996). This discrepancy is discussed in Section 2. Disadvantages of some of the UARS tidal data which have been published thus far, have been that particular tidal (Hough) modes have been selected from the data. For example the S11 mode has been used for the D tide; and the SD tide has been studied following the removal of the S11 mode, therefore assuming its dominance in the D wind ®eld. Time resolution for the UARS tidal variability studies has also usually been limited to samples at 1±2 month intervals. However, such limitations are not serious providing appropriate care is taken in the conclusions reached, and if continued comparisons are made between alternate UARS analysis schemes and other measurements. The value of the present radar study is that no such assumptions about the tide are made. The wind ®eld is sampled every 2±5 min for a variety of latitudes (2± 708N) and the analysis automatically includes the e€ect of all the global migrating tidal modes upon the winds. However, the in¯uence of local non-migrating tidal waves will also be embedded in these results. In this study a monthly resolution is used Ð subsequent studies will assess intra-monthly variability and spatial coherences, as well as trends over intervals as long as a solar-cycle. Here also, several years of data have been analysed to assess the magnitude of inter-annual variabilities over 5±6 years. The SD and D tides are discussed, respectively, in Sections 3 and 4. Finally the sophistication of global tidal models has continued to grow. In particular the GSWM, a Global-Scale Wave Model, allows comparisons within the MLT for D and SD tides on a seasonal basis.

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GSWM is a two-dimensional linearized model that solves the extended Navier±Stokes equations for tidal and planetary wave perturbations as a function of latitude and altitude for a speci®ed wave periodicity and zonal wavenumber (Hagan et al., 1993, 1995). MSISE90 zonal mean temperatures (Hedin, 1991), with Groves (1985, 1987) and Portnyagin and Solov'era (1992a, 1992b) zonal-mean zonal winds are used to specify GSWM results presented herein and attributable to migrating tidal sources of tropospheric (Groves, 1982) and strato-mesospheric (Strobel, 1978; Keating et al., 1990) origin. The model accounts for molecular and eddy di€usivity e€ects, gravity wave stress on the diurnal tide, and parameterizations for ion drag and Newtonian cooling e€ects. The reader can ®nd a detailed description of the model and migrating tidal results on the GSWM web site (http:// www.hao.ucar.edu/public/research/tiso/gswm/ gswm.html) and in reports by Hagan et al. (1993, 1995, 1999). Here we shall use D and SD pro®les of amplitudes and phases from the model for the radar locations, as well as latitudinal variations at two heights, in both Sections 3 and 4. There is speci®c discussion of the comparisons, from the point of view of the model, in Section 5. 2. Analysis of the radar data The initial analysis applied to the radar data is the full-correlation analysis (FCA) for spatial antenna systems. The variant developed by Meek (1980) is used for the more northern stations (Tromsù 708N, Saskatoon 528N, London 438N, Urbana 408N), partly due to its usefulness in dealing with correlograms that are noisier or multi-peaked; while a more classical Brigg's method is used at the other stations (Isler and Fritts, 1996): Hawaii 228N, Christmas Island 28N. Comparisons have shown no signi®cant di€erences exist between these methods (Thayaparan et al., 1995). The radars provide samples of wind every 2 or 3 km (circa 70±100 km) and 2 or 5 min on a continuous basis. Although it is beyond the scope of this paper, it should be noted that very thorough comparisons exist between winds and tides measured by the MFR and other ground based systems: MWR and MFR radars at 408N (Hocking and Thayaparan, 1997); MFR and Fabry±Perot Interferometers (`green line' and hydroxyl) at 528N (Manson et al., 1996; Meek et al., 1997); and MFR, EISCAT and VHF radars (Manson et al., 1992) at 708N. In all of these studies the phases of the tides, or directions of the winds, have been quite satisfactorily consistent, as assessed by the respective authors. `Satisfactory' is often taken to indicate that mean phases agreed within the standard errors, or indi-

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vidual determinations from one instrument lay within the range of values from another (a similar use of `satisfactory' will be used later in this paper). The reader is encouraged to read these important and detailed studies. The amplitudes of the tides, or wind speeds, were in good agreement (typically within 10%) in some cases e.g. the optical and radar comparisons, but not in others. In particular, at 708N, the tidal amplitudes and wind speeds from the MFR were 0.65 of those from the VHF radar and rockets. This result is similar to the di€erences found between HRDI-UARS and MFR systems; e.g. at Saskatoon the MFR speeds are 0.75±0.8 of those from HRDI (Meek et al., 1997). As the reason for this is not fully understood at this time, we will simply bear this is mind when later comparisons are made in this paper. A common analysis has been used at each radar location to obtain the amplitudes and phases of the monthly D and SD oscillations in the wind ®eld. First, hourly means were formed. Then for each month of available years (1989±1996) an harmonic analysis was applied to the entire 28±31 day time series of hourly values (zonal, E±W; meridional, N±S), for the 12 and 24-h oscillations (amplitude and phase). We required that for each ®t there were data for 16 h or more of the 24 possible for each height over the month; and then also weighted the hourly means in the ®t according to the number of values therein. Values of the amplitudes and phases from the completed ®ts were retained when the standard deviations (sd) of the mean phases were less than 2.5 and 5-h, respectively; this choice eliminates noise and generally provides smoothly varying phase pro®les. The minimum height then possible to meet these criteria varied from 70 to 85 km, while the maximum height was restricted to values below the local estimates or calculations of total re¯ection of the radar pulse. This latter is generally between 90 and 100 km. The intention of the following commentary on the data presentations is to focus brie¯y upon the main features of agreement or disagreement between the observations and the model. The ®gures have been designed to provide easy appreciation of these features. Those interested in much greater detail, especially on the monthly evolution of the tide at particular latitudes, are encouraged to obtain a report (Manson et al., 1999) or to contact the authors. In the following, certain descriptive words will be used to typify the main features of the comparisons. Although these adjectives are widely used in the literature it is useful to de®ne our use of them. Also, given the possible bias associated with MFR amplitudes above 90 km, the adjectives will be applied mainly to the phase-data. However, when the modelled amplitude lies within the range of observed values over much of the height range, the word `good' will be

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Fig. 1. Winter (January) semi-diurnal (SD) tidal pro®les for the MF radars (thin lines) on available years (1989±1996) and for the GSWM (thick lines). In the phase plots, increasing time is toward the right, and local solar times are UT minus 10, 11, 6, 5, 7, +1 h in order of increasing latitude. N is for the north±south direction (N±S), meridional component; and E is for the east±west (E±W), zonal component. A negative phase slope is consistent with an upward (energy) propagating tidal wave.

used; if the spread of values is also small and the amplitude gradients are very similar the word `excellent' would apply. When a phase-pro®le for the model lies within the range of observed (annual) phase values for much or all of the height range, the words `very good' or `excellent' will be used. If the model pro®le is within p/2 of the medians (3 h for the SD tide, 6 h for the D tide) `good' will be used. Beyond that di€erence in phase, `disagreements' will be noted. Regarding slopes of the phase pro®les, the `phase-gradients' will be discussed on occasions, but for reasons of brevity the inverse of those, the `wavelengths', will be used more frequently. The latter are vertical wavelengths, but they are simply called `wavelengths' hereafter. When the modelled `wavelength' is very similar (within 10%) to that of the envelope of observed phases the

agreement will be typi®ed as `excellent' or `very-good.' (The former when the observed envelope is small). A strong disagreement will be noted when the modelled `wavelength' lies beyond the range of observed values. It is considered that the above will be most appropriate given the nature of the comparisons e.g. longitudinal variations of the observed tide are likely to be signi®cant at certain latitudes, but are not addressed here. Further, the sensitivity of the GSWM to changes in background conditions, such as the global wind ®eld, are not yet quanti®ed. And ®nally, the nature of the model is such that changes in background conditions for some given latitude range may a€ect the tides beyond that range i.e. the responses to change are global due to tidal Hough-mode coupling. In other words, the model cannot simply be improved at a par-

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Fig. 2. As for Fig. 1, but for the summer (July).

ticular location by arbitrarily adjusting one of the tidal modes. When PSMOS (Planetary Scale Mesopause Observing System Ð a program of SCOSTEP 1998± 2002) campaigns begin to provide a larger range of data (with more latitudes and longitudes) data assimilation processes may be used to gain insights into the di€erent tidal modes present in the observations and in the model. 3. Semi-diurnal (SD) tides 3.1. Pro®les for particular months of the seasons; and latitudinal variations We have chosen to plot the season's pro®les for each of the six stations, along with the GSWM pro-

®les, in a 3  2 block. A selection has had to be made, and so the E±W and N±S wind components are shown for the solstices, but only the E±W for the Equinoxes. The amplitudes and phases are in Fig. 1 for Tromsù, Saskatoon, London, Urbana, Hawaii, and Christmas Island for winter (January), in Fig. 2 for summer (July), and Fig. 3 for spring (April) and autumn (September). The SD tide is usually close to circular, with 3-h time di€erences (or phase shifts) between the N±S and E±W components of the clockwise rotating tides (hereafter described as `in quadrature'). The times shown in the phase-plots are for maximum perturbations in the northward and eastward directions. Because of the tidal circularity, the N±S wind components usually contain little additional information. However on occasion there are interesting di€erences in amplitude and even phase, which indicate that the

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Fig. 3. As for Fig. 1, but for pro®les of the E±W components for the spring (April) and autumn (October).

local tidal oscillations are due to the superposition of several tidal modes, and are not simple `classical tides.' For simplicity and clarity the individual years have not been marked; annual trends in the SD tide will be discussed elsewhere in a study of tidal coherence over small to large time scales. We simply note here, that generally speaking, the largest tides are seen in the same year at all locations, and are therefore indicative of a hemispheric pattern. We begin in winter at higher latitudes for our comments. The observed phases are quite close to the model, although leading it consistently by 1±2 h at most heights from Tromsù to Urbana. There is a rather small range of observed phases (typically 2 h) over the 05 years. The observed phase gradients are greater (smaller l ) than the model at Saskatoon (40 vs

60 km) and Urbana (40 vs 85 km) in particular; the observed gradients (and phases) at Saskatoon and Urbana are indeed closer to each other than the model, which has clearly smaller gradients at 408N. The observed Hawaiian phases have a large spread in the E±W (4±5 h), with the model pro®le lying in the middle of the observations; while there is a very small spread of phases in the N±S (1±2 h). The observed wavelengths are longer than modelled (70 vs 50 km). At the equator there is also a large spread of annual phases (2±6 h), which is evident in both components; the observations are centred near the model pro®le. Both the observed and modelled values have quite di€erent values for each component at Christmas Island. Considering now the amplitudes, the observed and modelled values are quite similar at most locations

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Fig. 4. Monthly observed and seasonally-modelled zonal SD amplitudes as a function of latitude for the two observed heights and the nearest modelled heights.

and heights. Distinctive features of the comparisons are that observed values at Saskatoon are generally smaller than the model above 75±80 km, while at Urbana they are generally larger. There is a general tendency at all locations for observed values above 85± 90 km to be smaller than the model. This may well be due to the bias in the MFR measurements as discussed earlier, since the model shows increasing amplitudes toward 95 km, whereas observed amplitudes often decrease or show no increase toward 95 km. An alternate data presentation (Figs. 4±6) shows the monthly amplitudes and phases as a function of latitude at two heights (81.5 and 90.5 km, see caption) for the E±W component, and also the wavelength l values (based on phase gradients between values from three height gates) over 6 km near 87 km. The advantages of this presentation are that observed trends within a season may be considered, and that latitudinal di€er-

ences between observations and model for a given season may be more easily discerned. This is important to consider here, as very strong monthly trends would bring into question the value of 3-month seasonal representations. Continuing with our consideration of the winter season, and looking at the amplitudes (Fig. 4), agreement is best achieved in January as observed values are already decreasing by February. Agreement with the model is generally quite good at both heights; although the Saskatoon and London values are consistently lower than the model. There is rather good phase agreement (Fig. 5) at both heights, although the observations consistently lead the model at 90.5 km (as noted already). The l values are based upon a phase gradient near 85 km, which usually gives a wellbehaved value. On occasion negative slopes (crosses or negative model values) do occur, which may be just

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Fig. 5. As for Fig. 4, but for the zonal SD phases (local solar time is used).

Fig. 6. As for Figs. 4 and 5, but for the zonal SD wavelengths. The phase gradients are from a 6 km layer centred on 87 km. Stars are for negative observed slopes, while negative modelled slopes are shown as such.

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local features in the phase gradients. Overall however, the winter agreement between observations and model is quite good; although as noted in Fig. 1 the observed values are often smaller than those obtained from the model. The summer solstice is now considered (Figs. 2 and 4±6). The most obvious feature in the July phases (Fig. 2), is the observed dominance of very long wavelengths or evanescence at all locations north of Christmas Island. In contrast the model, beginning at Saskatoon, demonstrates the in¯uence of a small wavelength structure (020 km). The resulting strong contrasts between observed and modelled structures at Tromsù are also evident for the other summer months (June, August) [not shown]. Again, the observed and modelled phases (Fig. 2) do not agree well at Urbana, London, or Saskatoon. There are several other distinctive features: observed phases generally have a very small spread (1± 2 h above 80 km) over the 5 years (except for Christmas Island); the agreement between observations and model at Hawaii is excellent; and there is evidence for smaller observed l below altitudes near 85 km at London (<30 km) and Saskatoon (55 km). This last feature has been shown in mid-latitude climatologies (Manson et al., 1989). The tide shows its largest spread of values at Christmas Island, where the phase gradients (although not the phases) are similar to the model. These di€erences in phase are discussed elsewhere (Vincent et al., 1998), but are related to the relative positions of the equatorial nodes for the model and the planetary atmosphere. If Christmas Island moves into the other (southern) tidal-hemisphere during the summer, then 1808 changes in phase can occur relative to the model. This has apparently occurred for the N±S phase during each of the observed years. Regarding amplitudes, the observed values are generally and substantially larger than those modelled (typically 10 vs less than 5 m/s near 85 km). These features are also evident in the latitudinal E± W amplitude, phase and l plots of Figs. 4±6. Continuing to focus on the summer months of June± August, the observed amplitudes are generally larger than the model for all sites and both heights (81.5 and 90.5 km). Notice that in August the observed amplitudes, especially for latitudes greater than 228N, are the largest of the summer, and are increasing toward the autumn maxima (Manson et al., 1989). Looking toward the autumn in the model, there is only a modest indication of such an increase. The observed phases for these three months show good agreement with the model at 90.5 km with di€erences typically less than 3 h, but with observations often leading the model. There is also good agreement at 81.5 km for the lower latitudes. Beyond 458N, the model's change of dominant mode is revealed by the strong latitudinal phase

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shift at 81.5 km. The l values of the model (Fig. 6) are either very large or negative between 0 and 458N, before assuming the small (020 km) high latitude value. The observed values are generally large (0100 km) or indeterminant, consistent with earlier climatologies (Avery et al., 1989; Manson et al., 1989). The equinoxes are times of considerable change, both in the tidal forcing and in the changes in background winds and temperatures. However the mid-season months of April and October should show fair agreement with a model based on average seasonal characteristics. In Fig. 3 we show the E±W component of those tides, which evidences much larger interannual variability of the phases than was noted during the solstices, consistent with these being intervals of greatest seasonal change. The range of observed phases is typically 2±3 h, rather than the solstitial 1±2 h. In April the observed and modelled phases (80±90 km) are in good agreement at 52 and 708N, although observed and modelled phase-gradients do di€er throughout the 70±95 km height range. Above 80 km, the observed amplitudes are much larger (>10 vs <5 m/s). There is a trend, increasingly evident from London (438N) as one moves to lower latitudes, for the observed phases to lead the model by up to 4 h. Observed amplitudes are again larger than the model (80±90 km), but these do not increase as strongly with height as does the model from 90 to 95 km. Christmas Island observed phases are within 1±2 h of the model above 80 km, although phase-gradients are much larger than modelled below 85 km. The observed amplitudes are similar to the model, although for the N±S-component (not shown) the modelled values increase strongly above 90 km to near 20 m/s, while the observations remain near 10 m/s. The latitudinal plots (Figs. 4±6) also demonstrate the observations made above, although only two heights are sampled; it is clear that the observed l are smaller than modelled results. The trends through the spring are relatively subtle, and not always easily seen in the selection of Figures shown Ð unfortunately space precludes showing all the monthly pro®les at each site. As previously noted, they are available in a report (Manson et al., 1999). Brie¯y from these and Figs. 4±6 we can say that at Saskatoon and Tromsù the phase structures (values and slopes) in March are still winter-like, and in May have the best overall agreement with the spring model. The amplitudes also suggest di€erent wave-mode mixtures in the model and in the real atmosphere, as the observed May values are the largest of the season, and they change systematically from March to May. At mid-latitudes (London, Urbana), the phase structures systematically change from the shorter l of winter to the longer l of summer, but in no month agree particularly well with the model. The amplitudes of spring are similar to the April sample of Fig. 3, with no

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strong trends. Hawaii's observed variations are clear and interesting; March is still winter-like, and by May the phase and amplitude agreement is very good with the model. May is still a time of strong change however, as June's N-S phase structure (l>100 km) is quite di€erent from May's (l 2 15 km at 85 km). Finally, the monthly changes at Christmas Island are quite small, with generally fair to good agreement in phase (2- to 4-h di€erences above 80 km) and amplitude (<90 km). These comments are all con®rmed by attention to Figs. 4±6, but they were easier to generalize from monthly pro®les. Finally we comment on October's tides (Figs. 3 and 4±6). At 52 and 708N the observed and modelled phases are in fair agreement (3- to 5-h di€erences), with quite large inter-annual variations (2±5 h). The observed l above 80 km altitude are much larger than modelled (75 vs 20 km). Also the observed amplitudes are much larger (r10 m/s near 85 km compared to R5 m/s). This is true for the N±S component also. At middle and lower latitudes (43±228N) the observed phases (which also vary considerably (3±6 h) interannually) di€er strongly from the model (typically 6 h), while still showing similar phase-slopes. Amplitudes are comparable there, although the amplitude gradients again di€er, and Hawaii's observed amplitude values are much larger than modelled (5±12 vs 2 m/s at 85 km). Christmas Island observed phases and amplitudes are in good to fair agreement with the model for the E±W component (Fig. 3) with phase di€erences of less than 3 h, but the N±S phases often show strong inter-annual variability. The latitudinal plots (Figs. 4±6) reinforce these comments. The mid-latitude observed amplitudes are seen to be even greater in September than October, while agreement with the model is almost achieved in November. The strong phase di€erences from the model (Fig. 5) are seen to exist throughout the autumn, especially at mid-latitudes. The phase gradients or l (Fig. 6), are in fair agreement, with common values ranging from 35 to 70 km. The trends in the pro®les from summer to winter are substantial, as has been shown from Figs. 1±6 and are nicely shown in the monthly pro®les (Manson et al., 1999). Generally one is moving from the long l of summer to the shorter values of winter. For Tromsù and Saskatoon there is no 1 month of excellent agreement between observations and model (October in Fig. 3 is typical). At mid-latitudes (London and Urbana) the phases come into best agreement in November, after which there is little change in observation or model before the winter (December). Amplitudes agree best in October. At Hawaii no one month agrees well (or better than October in Fig. 3). For Christmas Island the monthly trends are not strong, and October is typical of the seasonal state.

3.2. Summary The agreement between model and observations varies strongly throughout the year. There are many months/seasons with good agreement of amplitude and phase structures, and many with poor agreement. The results are summarized in Table 1. Clearly in some seasons the modes excited by the modelled sources, and modes existing and developing at mesopause heights from modal coupling within the model, di€er quite strongly from those observed. A new study of the SD tide using HRDI (UARS) data is also being prepared (Burrage, 1998). In this the D tide is assumed to be dominated by the S11 mode, and residuals are assigned to the SD tidal oscillations. A detailed discussion and comparison lies beyond the scope of this paper, but some results from Saskatoon and Tromsù are included (Fig. 7). The radar observations and the GSWM results are also shown. Useful agreements in phase structures are seen, especially in the solstices and in autumn. However amplitudes from HRDI are larger by factors of 2±10 in the equinoxes; there is fair agreement in the solstices. These factors of 2±10 are larger than any MFR speed bias found in detailed instrument comparisons (Section 2). Further comparisons involving HRDI tidal analysis will be pursued elsewhere. 4. Diurnal tides 4.1. Pro®les for particular months; latitudinal variations The data presentations are the same as for the semidiurnal tide. Figs. 8±10 show pro®les for the mid-season months of winter, summer, spring and autumn respectively, and Figs. 11±13 show the latitudinal variations of amplitude, phase and wavelength by month for the two height ranges 81±82 and 90±91 km. Earlier tidal studies (Avery et al., 1989; Manson et al., 1989) have shown relatively poor agreements between observations and model at middle to high latitudes. At low latitudes where the S11 mode is dominant the comparisons were somewhat better (Vincent et al., 1989). Beginning with winter, the model demonstrates a strong change of the wavelengths l from short values (030 km) at tropical latitudes, to longer values (40± 75 km) at middle latitudes, and evanescence at 708N. The observations do likewise, although there is strong inter-annual variability at mid-latitudes e.g. the spread of phases reaches 8±12 h at Urbana, London and Saskatoon. Phases and/or phase-slopes vary from excellent to very good agreement e.g. E±W for Christmas Island, Hawaii, Urbana, to poor e.g. Christmas Island (N±S), London, Saskatoon (N±S). At Saskatoon, where there appears to be a modelled tran-

a `Good' is when the modelled pro®les lie within the range (or for phases within p/2) of observed values. If the agreement is better than that (`very good'; `excellent', Section 2), the modelled phases also lie within the range of observed values, and amplitude gradients compare well. `Poor' may be used when phase di€erences are large (the order of p or greater), and modelled amplitudes consistently lie beyond the range of observed values. `Fair' may be a mixture of `good' and `poor' comparisons.

l0 (040 km) < lm (080 km) at extratropical latitudes (r228N)

A0 (10±15 m/s)>Am (5 m/s) at extratropical latitudes (r228N) at 90 km lm very small (020 km) or irregular at higher latitudes (r528N) A0 (020 m/s) < Am (030 m/s) at higher latitudes (r438N)

A0 (15±30 m/s)>Am (5±10 m/s) at middle/high latitudes (r528N) at 90 km l0, lm similar (35±70 km)

Fair to good agreement of A and f. f0 leads by several h at low/middle latitudes (22±438N) A0 (10±15 m/s)>Am (5 m/s) at middle/high latitudes (40±708N) at 90 km l0 smaller (20±70 km) than lm (>70 km) Generally good agreement of f and l at low/middle latitudes (22±438N) Generally good agreement of A and f

Generally poor agreement of A and f

Summer Winter

Observed and modelled amplitudes, wavelengths and phases A0, Am, l0, lm, f0, fm

Table 1 Summary of the comparisons between the modelled and observed semi-diurnal tidea

Autumn

Spring

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819

sition from short wavelengths (London) to long wavelengths or evanescence (Tromsù), the observed phases and their gradients (N±S) di€er quite signi®cantly from the model above 85 km (8±12 h), suggesting a regional di€erence in the mixture of modes within the model and the atmosphere. The amplitudes and their variations with latitude are very similar for observations and model, especially in the E±W component where the model pro®les frequently lie within the range of observed pro®les. The monthly variations of the E±W amplitudes during the winter season are shown in Fig. 11. At the lower height (81.5 km) the curves of modelled values generally pass through the range of observed values. This is also true at the upper height (90.5 km) in December and January; but in February the amplitudes for Hawaii and Urbana are above the modelled curve, as these locations have begun to show the spring-time increases which are very evident in March and April. For the phases (Fig. 12) the observed latitudinal phase gradient from 2 to 438N is steeper in both layers than in the model. The observed wavelengths calculated for January (Fig. 13) are consistent with those of Fig. 8: the wavelengths for London are larger than those for Urbana despite their proximity; the wavelengths for Saskatoon are smaller than the model; and Hawaii's are often larger than the model. Those generalizations also apply to the months of December and February. It is also clear that the range of observed wavelengths (phase-gradients) is larger than for the SD tide e.g. in January the mid-latitude l vary from 20 to 70 km for the group of Hawaii, Urbana and Saskatoon radars, rather than 30±50 km. (The monthly wavelengths for the N±S component, which are not shown, are similar to those evident in Fig. 8, and are somewhat less regular than for the E±W component.) The summer solstice is featured in Figs. 9 and 11± 13. For this season, and compared with the winter (Fig. 8), the model shows a more rapid transition with latitude to the long wavelengths and evanescence of the higher latitudes. The observed phase structures generally follow the model very well and the spread of phases (except for Christmas Island and London) is very small (2±3 h) when compared with the winter. There is a tendency (mainly in the N±S) for most of the annual observations at low to middle latitudes to lag the model. However the agreements between observations and model generally range from excellent (phases overlapping, e.g. Saskatoon) to good (model within p/2 of the medians, e.g. Urbana, Hawaii). The strong exception is Christmas Island (E±W). Hawaii's observed (median) wavelength is smaller than in winter (45 vs 95 km for the N±S components), and closer to the modelled value (30 km). The agreement of phases between model and observations at Saskatoon is con-

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Fig. 7. Semi-diurnal (SD) zonal tidal pro®les for the four seasons and for January, April, October and July as observed. The thin lines are for the MF Radars, the thick lines for the GSWM, and the dotted-lines are for HRDI observations.

A. Manson et al. / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 809±828

821

Fig. 8. Winter (January) diurnal (D) tidal pro®les for the MF radars (thin lines) on available years (1989±1996) and for the GSWM (thick lines). Otherwise, as in Fig. 1.

sidered remarkable. The observed interannual variability is small (2±3 h at most heights), as is the monthly variation (June±August, not shown). The relative phases between N±S and E±W components are such as to favour quadrature below 85 km, and linear polarization above (as in Manson and Meek, 1986; Manson et al., 1989). It is most satisfying to at last see a model reproduce those strong and consistent features, which are certainly not those of a `classical tide'. It was noted earlier, in the discussion of the winter tide, that the modelled amplitude pro®les frequently lay within the range of observed pro®les (for 9 out of 12 `site-component' plots in Fig. 8). In the summer season (Fig. 9), in contrast, the modelled pro®les for heights above 80 km lie beyond almost all of the annual pro®les for 9 of the 12 `site-component' plots. The di€erences between the observed median-pro®les

and the modelled pro®les vary with latitude and component, but there is often a factor of two evident, e.g. at London (N±S) the observed values are near 5 m/s while the model values reach 17±20 m/s. These di€erences are often larger than the MFR speed biases found in the detailed instrument comparisons referred to earlier; in Section 2 other systems were reported as providing speeds or tidal amplitudes greater than the MFR by factors of 1.25±1.55. The latitudinal monthly plots of Figs. 11±13 are consistent with the observations shown in Fig. 9, as there are small trends in the observed amplitudes and phases over the 3 months. The comments made regarding the amplitudes and phases in Fig. 9 are therefore also appropriate here. For example, the observed E±W amplitudes at 90.5 km (Fig. 11) and for 40±708N are smaller than the model (except for one point at

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Fig. 9. As for Fig. 8, but for the summer (July).

London in June). This relationship is also true for the N±S amplitudes (not shown), where the generalization also includes Hawaii. With regard to phases, the model at 90.5 km has a steeper latitudinal gradient than do the median points of the observations (Fig. 12). However, for the N±S phases (not shown), the latitudinal gradients of model and observations are very similar, and the only minor disagreement is a general tendency for the observations to lag the model by 2± 3 h This is one of the few cases when the two components (N±S, E±W) have modestly di€erent characteristics (this was evident from Fig. 9 also). It is consistent with the superposition and coupling of tidal modes. Fig. 13 con®rms the general similarity of l values between observations and model; the apparently small observed l at London and Urbana appears to be a local height gradient e€ect at 87 km (see Fig. 9). For the equinoxes (Figs. 10 and 11±13) we show the

E±W component for the April (spring) and October (autumn) months. It is worthy of note that the modelled pro®les (Fig. 10) and the modelled latitudinal curves (Figs. 11±13) generally show little di€erence between the spring and autumn months. The most noticeable di€erence (Fig. 11) is in the 90.5 km altitude amplitudes near the peak of the curve (0258N), where the autumn values (25 m/s) are larger than in spring (17 m/s). The modelled amplitudes also demonstrate a semi-annual oscillation (SAO) near 258N, with maxima in the equinoxes; and an annual oscillation at higher latitudes, with a summer maximum. The SAO has been observed in the low latitude radar studies referenced earlier (Vincent et al., 1989, 1998). The observed phase structures (Fig. 10) generally follow the model well in spring; the agreement varies from good for London (the model is within p/2 or 6 h of the observed median) to excellent for the other lo-

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823

Fig. 10. As for Fig. 8, but for pro®les of the E±W components for the spring (April) and autumn (October).

cations (the model lies within the range of observed pro®les). The spread of phases is generally small (2± 3 h), but is larger at London and Christmas Island (3± 6 h). These values are very similar to those noted in the summer season. Similar remarks apply to the autumn months which are also shown in Fig. 10. Given the generally good to excellent phase agreements between model and observations, the phase-gradients (and wavelengths) are also very similar, and the agreement is described as `very good' (the modelled pro®le slopes lie within the range of observed pro®les, or their envelope). An exception is London in the autumn, where the model wavelength is near 30 km, and the observed value is near 100 km. Considering amplitudes, the agreement is considered good in the spring as the modelled pro®les lie within the range of observed values; there is increasing inter-annual varia-

bility below 528N. However, observed values are often smaller than modelled in the autumn (London and Saskatoon); the two equinoxes are clearly not observed to be the same (Hawaii and Saskatoon); and the modelled and observed amplitude gradients often di€er, especially above 85 km (likely an instrumental e€ect), and near 80 km. The latitudinal monthly plots (Figs. 11±13) show some additional features. The observed and modelled phases show good agreement in the spring, at both heights, as the modelled curves lie within the range of observed values. In contrast, in the autumn, the agreement at 90.5 km is good only in October. This is due to a strong trend in phase from September to November with values moving to earlier times (a change of 06 h). For amplitudes, the observed `springlike' values (90.5 km) at lower latitudes in February

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Fig. 11. Monthly observed and seasonally-modelled zonal D amplitudes. Otherwise as for Fig. 4.

are a precursor to the large March values, which are generally larger than modelled, (2±408N). April is the month of best agreement between model and observations. In the autumn, the middle month (October) of observations is again in best agreement with the model, with observed amplitudes often lying below the model in September and November. For wavelengths (Fig. 13), the phase slopes of Fig. 10 are shown to be typical of the 3-month seasons. In spring the observations are centred on the model for the higher latitudes, but Hawaii and Christmas Island often have longer observed wavelengths. Finally in the fall, while October observations are centred on the model, the September wavelengths are often longer than modelled. 4.2. Summary In general, the agreement between model and observations is very good, with modelled pro®les and curves frequently lying within the range of observations. This

is most encouraging. For the earlier MAP comparisons, the model of the day failed seriously at middle to high latitudes, especially in summer months. Even at that time, the observations were very consistent over several years, and yet strongly non-classical. The comments upon the modelled and observed tides are summarized in Table 2. The agreement between observations and model in summer months at these middle to high latitudes is now very good i.e. modelled values frequently lie with the (small) range of observed values. The winter higher-latitude tide demonstrates the highest inter-annual variability and not surprisingly, it is not as well modelled. It is likely that this variability is due to other e€ects, such as planetary waves (associated with the Stratospheric Warmings) interacting with the global tidal ®elds, and perhaps also creating non-migrating modes. Otherwise, the lower latitudes continue to be well modelled (with of course the signi®cant di€erences noted in the Table 2), probably due to the relative simplicity of the tidal structure. A detailed study of low latitudes (Vincent et

A. Manson et al. / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 809±828

Fig. 12. As for Fig. 11, but for the zonal D phases.

Fig. 13. As for Figs. 11 and 12, but for the zonal wavelengths.

825

`Good' is when the modelled pro®les lie within the range (or for phases within p/2) of observed values. If the agreement is better than that (`very good'; `excellent', Section 2), the modelled phases also lie within the range of observed values, and amplitude gradients compare well. `Poor' may be used when phase di€erences are large (the order of p or greater), and modelled amplitudes consistently lie beyond the range of observed values. `Fair' may be a mixture of `good' and `poor' comparisons.

l0 (150 km)>lm (30 km) at London

a

A0 (10±30 m/s)>Am (10±15 m/s) at low (<438N) latitudes in February± March (early observed `spring') at 90 km l0 (050 km)>lm (025 km) at low latitudes A0 (05 m/s) < Am (010 m/s) at middle/high latitudes (43±708N) at 90 km

l0 (070 km)>lm (040 km) at middle latitudes (September)

Generally good (or better) agreement of A, f and l at 90 km

Generally good (or better) agreement of f and l at 90 km f0 lags fm by several h at low/middle latitudes above 80 km. Agreement excellent at Saskatoon, Tromsù A0 (5±10 m/s) < Am (10±15 m/s) at low/middle latitudes above 80 km Generally good agreement of A, f and l f0, fm and l0, lm di€er most at middle latitudes (43±528N). Strong inter-annual variability For N±S component; A0 and Am di€er at Hawaii, and f0 and fm di€er at Christmas Island

Autumn Summer Winter

Observed and modelled amplitudes, wavelengths and phases A0, Am, l0, lm, f0, fm

Table 2 Summary of the comparisons between the modelled and observed diurnal tidea

Generally good (or better) agreement of A, f and l at 90 km f0 shows a strong trend September± November at 90 km

A. Manson et al. / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 809±828

Spring

826

al., 1998) revealed similar characteristics to those discussed and shown in the Figures for Section 4.1. 5. Considerations of GSWM results and comparisons with observations While the current migrating tidal forcing schemes preclude GSWM predictions of interannual or monthly tidal variability (Hagan, 1996), GSWM captures the salient features of the tidal harmonics observed by the MF radar suite. In particular, the observed seasonal variability of the diurnal tide is generally reproduced by GSWM (Figs. 8±13). One notable exception are the diurnal amplitudes (N±S) that are observed over Hawaii and which appear to be systematically overestimated by GSWM. Hagan et al. (1997a) recently discussed this discrepancy and provided illustrative GSWM non-migrating tidal results. In a follow-on report, Hagan et al. (1997b) included an analysis of UARS WINDII data to show that the di€erences were at least partly attributable to longitudinal variability of the diurnal tide associated with non-migrating components forced by tropospheric latent heat release. More recently, Forbes et al. (1997) quanti®ed the migrating tidal signatures due to this tidal source. Their diurnal and semidiurnal tidal forcing scheme is based on 7-year monthly averaged global cloud imagery data (Forbes et al., 1999). Their results suggest that GSWM results reported herein neglect an important migrating tidal source. That is, the model does not account for latent heat e€ects associated with meridional diurnal tidal amplitudes that approach 20 m/s near 108N and 100 km during October, 10 m/s during January, but remain within 5 m/s during April and July. Perhaps more relevant to the interpretation of the model/ observed semidiurnal tidal discrepancies reported herein, the semidiurnal tropospheric latent heating e€ects at middle latitudes (488N) are comparatively more persistent and extensive. Forbes et al. (1999) report semidiurnal meridional wind amplitudes of 5± 10 m/s between 100 and 115 km throughout the year. Above (115±150 km), they report even larger amplitudes (approaching 20 m/s) during February±May. Additional GSWM calculations which account for the latent heat tidal source and an improved heating scheme to account for the absorption of infrared solar radiation using monthly averaged data are needed to fully understand the comparative importance of the tidal sources in the upper mesosphere and lower thermosphere (MLT). As previously noted the relative phase coherence between the tidal components determines whether the inclusions of an additional source will result in a net increase or decrease of the aggregate tidal signature in the MLT (Hagan, 1996; Hagan et al., 1997a, 1997b; Forbes, et al., 1997, 1999). Further, the

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phase relationships vary with latitude, altitude, season and harmonic component, so it is currently premature to suggest the GSWM shortcomings described herein will be recti®ed by the new latent heating scheme. A GSWM-98 has been developed and recently discussed (Hagan et al., 1999). This incorporates an extended GW stress scheme and an updated background atmosphere. Brie¯y, a somewhat larger equinoctial Diurnal tide at low and middle latitudes is demonstrated, enhancing the modelled semi-annual oscillation already evident in Fig. 11. The generally good agreement shown there is not strongly a€ected. Otherwise however, the semi-diurnal tidal discrepancies between observations and model noted in Section 3 are still not well explained. Further comparisons involving other radars at a variety of latitudes and longitudes, and new models such as the GSWM-98 will be the subject of later studies.

827

are by factors of 4 or more at heights where groundbased observations and model are in good agreement. In a new study (Jacobi, et al., 1999) using radars, the climatology of the SD along latitude circles near 548N provide evidence for modest but signi®cant variations with longitude; in particular amplitudes vary by 010 m/ s in winter and autumn, and phases by 1±2 h, although the vertical phase gradients are very similar. Further comparisons between developments of the GSWM and data from these, and more recently developed radars at other latitudes and longitudes, will also proceed.

Acknowledgements The authors gratefully acknowledge grants from their national agencies: NSERC Canada, NSF USA, ARC Australia. The ®rst authors also thank the University of Saskatchewan and ISAS for support.

6. Conclusions The detailed assessment of the monthly trends in the tidal climatologies has revealed striking and regular changes at each of the six MFR sites. The range of phases over the 6 years, for a particular location, month and height, are typically less than 2±4 h (for the SD/D tides) suggesting that successful tidal modelling (using seasonal atmospheric properties) is indeed possible. The agreement between the observed D tide and the GSWM is now quite excellent. While some modest di€erences exist between amplitudes, phases and wavelengths at particular locations for some months, the model now appears to encompass the dominant tidal modes present in the global tide. This represents a strong improvement over the 1989 comparisons (JATP, Special issue). The agreement of phase and phase structures at mid-latitudes in nonwinter months is now excellent, at a time when the tide is a complex combination of many modes, and is evidently ``non-classical''. However the situation regarding the SD tide is less satisfactory, with little evidence for improvement over the promising comparisons of 1989. The agreement is best in winter. In summer the model has unobserved short (20 km, 708N) wavelengths and small amplitudes (5 vs 10±15 m/s, 90 km). Again, although the wavelengths of autumn are reasonably reproduced, phase gradients do di€er at heights near 90 km where the modelled amplitudes are much smaller than observed (5±10 vs 10±30 m/s). Initial comparisons with the HRDI SD tides are encouraging, with seasonal phases being quite similar to the ground-based radars. In some months however the HRDI amplitudes are also much larger than both the radars and the GSWM. This will require further investigation as the di€erences

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