A one dimensional semi-empirical model of the trade-wind inversion in a steady state is developed to predict the height of the inversion in terms of the external parameters such as the heat and moisture fluxes at the ocean surface, the large-scale subsidence and the radiative cooling rate. The cumulus cloud effects on the heat and moisture budgets are explicitely incorporated into the model using a simple entrainment cloud model. The atmosphere is divided into five layers with distinctively different characteristics: a mixed layer, a transition layer, a cloud layer, the trade-wind inversion and a layer above it. Both transition and inversion layers are assumed to be infinitesimally thin and only the vertically integrated properties in the cloud layer are considered. The lapse rates of static energy and moisture in the cloud layer are assumed to be linear and prescribed. All layers interact with each other through the vertical transports of heat and moisture due to cumulus clouds and condensation and evaporation processes. Thus the cloud mass flux at the cloud base is an important parameter to be determined internally by the model. Theoretical values of the characteristics of the trade-wind inversion, such as the height of the inversion and jumps of static energy and moisture across the inversion, are computed using observed values of the external parameters for the BOMEX region. Reasonal agreement is obtained between these theoretical values and the observed values. However, the sensitivity test of the model reveals some limitations of the applicability of the model.
The response of the stratospheric equatorial waves to thermal forcing is theoretically discussed, taking into account various factors such as the meridional distribution of heating and the vertical shear of the mean zonal wind. First we discuss analytically these effects based on normal mode models and then we treat a realistic three-dimensional model by numerical method. The horizontal structure of waves obtained in the models including the above effects indicates that the dominant wave modes are identified as Kelvin waves, mixed Rossby-gravity waves and n=1 Rossby waves, and that gravity waves are not prominent. The coexistence of gravity waves with the dominant modes, however, in the realistic model with maximum heating near the ITCZ makes the heating and vertical motion to be in phase, in agreement with observations, while in the single-component normal mode model they are in quadrature. It is concluded that mixed Rossby-gravity waves have the maximum response at wavenumbers 4-5 as observed, in view of the effect of vertical shear of the mean zonal wind on the selectivity of wavenumbers. In normal mode models hitherto treated the vertical wavelength of the dominant waves (resonant waves) was somewhat longer and hence the period was shorter, compared with observations. The defect still remains in the present model, though improved to some extent by introducing the realistic distribution of heating. Vertical structure of wind and temperature for predominant waves also shows different features from observed ones in the troposphere. Although some characteristics of observed equatorial waves are accounted for in light of the present model, these results suggest that the observed waves cannot be interpreted merely as the resonant waves by thermal forcing.
The stability of planetary waves in a two-layer fluid system is investigated in the small local Rossby number M limit. The problem presents a simple example of non-linear resonant instability discussed by Hasselmann (1967). The energy transfer mechanism of the instability is clarified. Some implications on energy and enstrophy cascade in planetary fluids are discussed. The analysis is complementary to the preceding paper of Yamagata (1976).
Dynamical structure of baroclinic waves are analysed under quasi-geostrophic assumptions. Except for regions near walls, following characteristics are observed. (1) The maxima of the amplitude of the pressure perturbation are both in the uppermost and the bottom layers, with its minimum around the middle layer. (2) The phase of the pressure perturbation retards with height (opposite to the direction of the container's rotation). (3) The vertical motion shows its maximum amplitude around (but a little below) the middle height, while its phase remains almost unchanged (but slightly tending to advance) with height. (4) Waves transport heat principally through the uppermost layer. These characteristics are similar to that of the wave of Eady type. Apart from the Eady type waves, another type of waves suggested by Green seems to develop in the bottom layer.
The Austausch coefficient K which is used in the so-called zonally averaged model for the discussion of climate change is usually considered as constant with time. However, K is regarded as time dependent variable in this paper. And the relation between the meanvalue of K(τ) averaged over the time intervalτ, K(τ), and the standard deviation of K(τ), √K' (τ)2, is discussed as a function of τ. The result shows that √K' (τ)2/K(τ) decrease as 1/√τ and it is necessary to take the longer time inverval more than τ=30 days if we wish to obtain the small value of √K'2/K that is less than 1/10. In the latter part of this paper, the seasonal change of zonally averaged surface temperature, To and mean temperature in the vertical column of the atmosphere, [T] is computed by making use of the zonally averaged model for the temperature. The value of K in the model is treated as a function of time with the assumed standard deviation of, √K'2(τ) (τ=1 day). The difference between [T] in case of K=const. with time and that in case of K=variable with time is compared. The difference is large in high latitude while the small value is obtained in the tropics. Taking the time average of the difference mentioned above over the period of τ=30 days, we compute the latitudinal variance of [T] for τ=30 days in the zonally averaged model and it is compared with the latitudinal so-called noise level of zonally averaged 1.5 km temperature forτ=29 days obtained by the NCAR GCM.
An analysis was made of zonal stationary waves in the Southern Hemisphere midlatitude zone (20°S-60°S) by the use of 3-monthly (90 day) average brightness charts for the two extreme seasons (summer and winter) and one intermediate season of 1969, produced from daily satellite cloud pictures. Harmonic analyses of average brightness along the four latitude circles reveal the predominance of stationary waves of wavenumber 1, 2, 3, and 4. At the main westerly zone (40°5-50°S), the maximum brightness, which corresponds to the trough of pressure wave, of wavenumber 1 stays in the eastern Atlantic through Indian Ocean, and at the subtropical latitudes (20°S-40°S), it stays in the central Pacific. Wavenumber 2 may be the fundamental mode through the mid-latitude zone with its maxima in the western Indian Ocean and the central Pacific. Wavenumber 3 is superior in the main westerly zone, and its maxima are located in the eastern parts of the three ocean. At the subtropical latitudes, wavenumber 4 is prominent, whose maxima are located in the extremely eastern parts of the three oceans and the central Pacific. These stationary waves (wavenumber 1 to 4) generally show NW-SE tilt. The features of wavenumber 1 and 3 are in good agreement with those depicted from 500mb monthly mean charts by van Loon and Jenne (1972), but the predominance of wavenumber 2 and 4 is also confirmed by the present analysis.
From the analysis of three medium-scale depressions which formed over the East China Sea during the AMTEX'75, the following characteristic features were drawn: (1) The medium-scale depression was a shallow disturbance with a warm core below 700mb. (2) The depression was thought to generate over the East China Sea. The sea-level cyclogenesis, however, commenced when a pre-existing cyclonic vortex at about 850mb moved over the sea from the continent. (3) The intensification of the system was largest in the lowest layer, and the deepening rapidly decreased with height. (4) The depression formed in the largescale frontal zone. The above-mentioned features suggested warming in the lowest layer was a primary factor for formation of sea-level medium-scale depression. Heat balances in the three layers between 1000mb and 500mb were evaluated by using the equation of thickness tendency. The result of evaluation showed the following three simultaneous dynamical processes were responsible for the formation: (1) warm air advection; (2) upward motion and small adiabatic cooling; (3) apparent heat source in the lowest layer. Sometimes such a shallow system seemed to develop into a strong cyclone. This was attributed to development of a synoptic-scale disturbance rather than to self-development of a mediumscale low.
Wind fields in the baroclinic, unstably stratified planetary boundary layer above the ocean have been analysed for the data of the AMTEX experiments executed during winter in the East China Sea. For the so-called cold air advection, the angle between winds and isobars increases as the height decreases at the lower half of the planetary boundary layer, while at the upper half layer the angles have negative values. The typical angles in the lower and upper layers are 20-50 deg. and -10- -40deg., respectively, when the horizontal temperature gradient is about 1.5°C per 100km. An empiric formula for the Rossby-number similarity theory is obtained, of which form is a modification of the AryaWyngaard's theoretical expression for the baroclinic, convective boundary layer model. The present result with respect to the baroclinicity dependence of the numerical constants of Rossbynumber similarity theory is slightly different from the empirical result derived from the Wangara data by Clarke and Hess.
The turbulence quantities such as the RMS of vertical wind speed σw, the dissipation rate of kinetic energy to heat ε, and the vertical diffusion coefficient KM in the planetary boundary layer under near-neutral stability are considered. In this layer, observations have shown that σw is proportional to the friction velocity u* and decreases approximately linearly with height. Based upon these observations, u* is approximated by u*=u*0ζ where u* is the friction velocity at height z, suffix 0 denotes the value at the surface and ζ=1- z/h, h is the characteristic scale height relating to the thickness of the boundary layer. The turbulence quantities are related to u* by replacing u*0 in the relations given by the similarity theory attributed to Monin and Obukhov (1954), for the constant flux layer, these are as follows; σw=Cwu*0ζ ε=u*03ζ3/(kz) KM+CK where C with suffix w or KM is constant, k is _??_ constant. The above relations hold fairly well with the observations taken in lower region of the boundary layer below the height of 700 to 1000m approximately.