Figure V .l: Vertical profile o f any atmospheric param eter (solid line), such as wind and temperature, in the presence o f a propagating tide, at a fix e d moment in time. The horizontal tidal amplitudes rise exponentially (dashed line) due to the decrease o f density with height.
The vertical distances between extrema in Figure V .l are half the tide’s vertical wavelength. The occurrence of damping prevents amphtudes from growing continuously with height, and in the real atmosphere they reach a maximum value at an altitude, the dissipation height, above which the vertical and horizontal oscillations dissipate and release their energy- and momentum to the background atmosphere. Two categories o f factors are found to influence profiles such as that o f Figure V .l. One category includes all those parameters which influence the undamped tidal profile and the other category are those which affect the damping processes.
For quick reference, the findings o f the following sections are listed in simplified form in Table V .l Various background atmosphere- and wave parameters are listed along with terms describing their importance for semidiurnal tidal profiles o f winds and temperature. A distinction is made between three latitudinal regimes o f around 0° to 30°, 30° to 60° and 60° to 90°, denoted as “low”, “mid” and “high”, respectively. The terms “primary”, “secondary” and “negligible” have been used to express the degree o f influence of a listed parameter on the semidiurnal tidal profiles
Validation Chapter V
at various latitudes. The table is based on the findings described in more detail below, and thus on simulations from the CTIM.
low latitude mid-latitude high latitude
background wind negligible negligible primary
background temperature
primary primary secondary
tidal mode primary primary primary
tidal amplitude primary primary primary
tidal phase primary primary primary
molecular viscosit} coefficient
primary secondary secondary
molecular heat conduction coeff.
secondary- secondary- secondary
ion density negligible secondary primary
T a b le V .l : Ihe degree o f influence o f various parameters on the vertical profiles o f semidiurnal tidal amplitudes between 80 and around 200 km altitude. The findings were obtained from theoretical discussions as well as CTIM simulations.
V. 2. 1. TH E UNDAMPED TIDAL PROFILE
The profile in Figure V .l is influenced by the value of scale height and the altitude at which the tide is generated. It was showm in Chapter II that the vertical wavelength of a tide is expressed in terms of scale height, which itself depends on temperature. In a pressure coordinate frame, the profile of Figure V.l is to first a approximation invariant with changes of scale height or temperature, but when plotted in a height coordinate frame the curve is “ stretched” or “compressed” vertically when increasing- or decreasing the background temperature. For easier
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comparison with measured data all plots in this chapter use the height coordinate frame, and therefore differences o f background temperature need to be considered. It will be shown later that these also influence the momentum- and energy damping processes.
The other aspect which can, in theory, influence a tidal profile such as that in F igure V .l is the height at which a tide is generated. In CTIM the tides are generated at 80 km, in the TIGCM (see V.3 .1) at 97 km and in the other models used here as well as in the real atmosphere this forcing occurs below 50 km altitude. Comparisons of the CTIM with other models or data require the knowledge o f forcing amplitudes and -phases at its lower boundary height (80 km). However, another factor plays a role and potentially might influence the vertical amplitude profiles. In the CTIM and TIGCM, the external tides are generated by oscillating the lower boundary pressure levels. A vertical structure is not defined externally but follows from the background atmosphere properties. In the real atmosphere as well as in models at sufficient distance from the forcing level a tidal oscillation “knows” how far it has progressed from the region o f excitation. This can be understood from the finding in Classical Tidal Theory (see Chapter II) that the horizontal- and vertical profiles o f tides are coupled. This information cannot be specified when forcing tides externally in the manner used in CTIM and the TIGCM. A tide forced below CTIM ’s lower boundary will thus contain information about its further vertical progression which cannot be specified in the CTIM, and similarly a tide forced at 80 km in CTIM contains information at 97 km height which cannot be specified in the TIGCM 's forcing. In Figure V.2 the situation which might arise is illustrated for a simplified case o f an undamped tide.
Validation Chapter V Ah t -o 5
Parameter value
F ig u re V .2: Same as Figure V. 1., hut with a second tide
(dashed) being generated at an altitude higher by Aj^.
Although the tides have the same properties, both profiles are shifted vertically.
Here, the dashed curv e represents a tide which is identical in term s o f vertical w avelength and amplitude to the original tide (solid e u n e), but forced at a vertical distance o f Aj^ above the other. A result o f this shift, the am plitude m axim a do not occur at the sam e heights. At som e heights the tw o curves cross and give the sam e param eter values. W hen specifying forcing in horizontal d irection only, it is thus am biguous w hether the vertical progression will follow the solid or the dashed curv e. In principle, there are then an unlim ited num ber o f possible scenarios. In order to avoid tlie situation illustrated in F ig u re V.2, one would need to define a “ vertical p hase” o f the tide at C T lM ’s lower boundary N o num erical experim ents have yet been carried out to dem onstrate the effect under realistic atm ospheric conditions, and therefore it is at present a theoretical possibility which might play a role in the C TIM /T IG C M com parisons. A collaborative study with
M .Hagan is planned for the near future to carry out such a jo in t num erical experim ent w ith the
CTIM and G SW M models. When ignoring any in-situ forcing with w hich an upw ards propagating tide could interact, the vertical profile shift o f F ig u re V.2. is independent o f the choice o f h o rizo n tal phase since the am plitude at any height is independent o f phase as well. In the real atmosphere the horizontal phase does play a role, as outlined below, since interference between the upw ards propagating- and in-situ solar- and auroral tides occurs, affecting the total am plitude at
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each height, but nevertheless it is expected not to play an important role in this effect.
V. 2. 2. M O M EN TU M DRAG
The second category of factors influencing the vertical propagation profiles o f tides is linked to the damping processes which occur in the “real” atmosphere. The main damping terms for tidal momentum were found in Chapter IV to be vertical viscous drag at low-to mid latitudes and ion drag at mid- to high latitudes. Vertical viscous drag is in a pressure coordinate frame given by