A Spectral Model for the Study of the Atmospheric General Circulation I. Preliminary Long-Term Integration for the Terrestrial Atmosphere

Abstract

A three-level linear-balance model for studies of the general circulation using the spectral method is presented with some preliminary results of time integration of the model for a specified terrestrial atmospheric condition.The model is, firstly, integrated for 180 model days under a specified condition to obtain a quasi-steady state without eddies, starting from a calm atmosphere.The zonally symmetric state thus obtained is unstable for the disturbance with zonal wavenumber 5 or 6, according to the linear theory of baroclinic instability. Secondly, after adding disturbances with small amplitudes to the above results of zonally symmetric model, the model integration is continued for another 180 model days to obtain a quasi-steady state with including eddies. The baroclinic instability appears to be released around the day 40, and thereafter the near-equilibrium state is obtained. The results are illustrated mainly for the zonal mean field averaged during either the period of the last 100 days or that of release of baroclinic instability (the day 30-50), and for the time evolutions of energy components and energy conversion terms. The results are not necessarily realistic, because somewhat large values are used tentatively for a part of several parameters, such as the vertical eddy mixing coefficient. Nevertheless, reasonable results are obtained and they are consistent under the model assumption.In order to study extensive problems concerning the general circulation and the climate of the planetary atmospheres, such a numerical model as is simple, economical and easy to handle is useful and worth-while to construct. So far as the preliminary results are concerned, we may say that the present model is one of powerful tools for further studies on the above subjects.

A spectral model of the atmospheric general circulation of Mars: A numerical experiment including the effects of the suspended dust and the topography

“…For example, Trenberth [1973] successfully performed numerical experiments of general circulation for the terrestrial atmosphere by using a model similar to ours. Furthermore, our model is also enough to resolve the meridional circulation although there are, of course, influences because of the limitation of expansion to some extent [see, Trenberth, 1973;Iwashima et al, 1979]. The model is certainly not suitable for dealing with vertical propagating tidal components, but it may be reasonably adequate for the trapped components of the diurnal tide.…”

“…The use of this method easily enables us to introduce some complex physical processes, such as the radiative process owing to dust suspended in the atmosphere, into the model. With regards to details of the model, its appropriateness, and its experimental results for a specified terrestrial atmospheric condition, another paper by the present authors is available for reference [Iwashima et al, 1979]. Our numerical model is useful to study the general circulation and the climate of the planetary atmospheres because it is simple, it is economical, and it is easy to handle as was stated in our previous paper [Iwashima et al,, 1979], although our results might not be necessarily realistic because of our use of tentative values for a part of several unknown parameters, such as the vertical eddy mixing coefficient.Section 2 is a description of the model, that is, governing equations, boundary conditions, numerical values of parameters, transformation into the spectral form, calculation of radiative process owing to dust, and methods of computation and of time integration.…”

“…With regards to details of the model, its appropriateness, and its experimental results for a specified terrestrial atmospheric condition, another paper by the present authors is available for reference [Iwashima et al, 1979]. Our numerical model is useful to study the general circulation and the climate of the planetary atmospheres because it is simple, it is economical, and it is easy to handle as was stated in our previous paper [Iwashima et al,, 1979], although our results might not be necessarily realistic because of our use of tentative values for a part of several unknown parameters, such as the vertical eddy mixing coefficient.…”

Time-Space Spectral General Circulation Model I. Time-Space Spectral Model of Low-Order Barotropic System with Periodic Forcing

“…Recently space-spectral and timedifference (time-integrating) models have been constructed, and used for study of climate. We also made a simple space-spectral and time-difference scheme model in order to study extensive problems concerning climate (Iwashima et al, 1979). The model based on time integration method is, of course, useful for some cases, such as in dealing with transient cases with wavewave interactions between many scales.…”