A numerical model for gravity wave dissipation in the thermosphere

Two simplified models of internal gravity wave dissipation due to viscosity, thermal conduction and ion-drag, in a multilayered, isothermal thermosphere are developed. Each of these models uses the WKB approximation, ray theory and the time-averaged equation of energy conservation, but whereas one of the models (A) employs all of the gravity wave equations appropriate to a dissipative atmosphere, the other (B) does not. Results derived from these models for one particular wave are compared to each other and also to some previously published results of Klostermeyer, which employed a full-wave, model. A breakdown of the WKB approximation in the lower, non-isothermal thermosphere leads to models A and B underestimating the total dissipation there. In the middle thermosphere model A estimates the dissipation reasonably well, while model B grossly overestimates the dissipation. In the upper thermosphere model A underestimates the total upward energy flux, probably as a result of the neglect of coupling into the dissipative waves at these levels, while no energy remains in model B. Results from model A show that when dissipation due to viscosity and thermal conduction are included correctly and simultaneously, the dissipation due to viscosity can exceed that due to thermal conduction by a factor of three. It is argued that ray theory may either overestimate or underestimate the energy flux reaching the upper boundary of a thermospheric model depending on both its height and the particular thermospheric model used.