A theory for the excitation mechanism of stratospheric equatorial waves is proposed. The theory states that the tropical atmosphere is under the marginally stable state with respect to wave-CISK mechanism and that equatorial waves are forced ones under such circumstances. It is shown from this theory that only the mode with the equivalent depth equal to that of the free wave in the marginal state or the slightly longer one is selectively excited, regardless of the profile of a forcing. Although the selected equivalent depth is shorter than the observed one when the Arakawa-Schubert's theory is used as the cumulus parameterization, the dominant periods in the stratosphere, at least, coincide with observed ones. Further considerations suggest that, under some devices of more complete parameterization, the longer equivalent depth seems to be selected. Then the dominant periods at the tropopause are close to those in the stratosphere, so that the vertical structure in the troposphere of the selected waves in the stratosphere may agree well with observations. Assuming a lateral forcing as the excitation source of mixed Rossby-gravity waves and imposing the forcing in the form of a body forcing confined in mid-latitudes (not a boundary forcing), the selectivity for wavenumber is examined. With large meridional scale forcing, the waves with wavenumber 1 or 2 are not dominant and the waves of middle wavenumbers (3-7) are selected corresponding to those observed. Concerning the horizontal structure of the dominant waves, they also show a phase difference of about 90°between meridional wind and geopotential in agreement with observations. It is difficult to specify the excitation source of Kelvin waves, but if thermal forcing is assumed to be the source at least, wavenumber 1 is selected. Thus, this theory seems to explain well the characteristics of stratospheric equatorial waves, with a more complete parameterization of cumulus ensemble.
A two dimensional numerical model is designed to investigate phenomena of urban heat islands under a steady condition. The model describes temperature and wind velocity distributions in the Ekman layer under a certain combination of factors. These factors are anthropogenic heat generation, evaporability, roughness and prevailing flow. The surface temperature is decided from the energy balance equation at the air-earth interface. The anthropogenic heat is given to the air at 50 m level instead of at the interface. Many facts pointed out in past studies are successfully simulated. The characteristics of this study and the results are following: 1) The diurnal condition including insolation is considered and the importance of the non-uniform evaporability is denoted. 2) The difference of influences between the anthropogenic heat and the evaporation whose each effect acts on the different level, becomes clear in the temperature distributions at the 50 m and the ground. (These two effects are referred to as the thermal effect.) 3) The effect of variation of the prevailing flow intensity on the wind pattern is investigated in detail within the extent from 0 to 10 m/sec in the flow intensity. 4) When the prevailing flow intensity increases, the non-uniform roughness becomes a main controlling factor instead of the thermal effect. In these two regimes, the direction of the perturbed wind is reverse with each other.
Comparison is made of the numerical solutions of the Rossby-Haurwitz waves by the shallow water equations on a sphere using staggered and non-staggered grid systems. Integrations are made with a high resolution grid net with the 2.50° grid size and a low resolution grid net with the 5° grid size for the two grid systems. The results of the high resolution grid nets of the two grid systems agree well with each other. These results also agree with those of other studies using a spectral method and a very high resolution latitude-longitude grid. Therefore, we may say that these solutions are converging. The results of the low resolution grid nets are considerably different from those of the high resolution grid nets. The solutions are also different depending on the grid system and the choice of the initial conditions. Truncation errors of the latitude-longitude grid and the skipped grid are also reexamined. As shown by Williamson and Browning (1973), in the latitude-longitude grid, the absolute value of the error of a second-order finite-difference approximation becomes of first order near the pole where cosφ(φ: latitude of a grid point) is of the same order as Δφ (the latitudinal grid size). However, it is shown that if Δφ→0 the area of the region of first order accuracy becomes smaller and hence its erroneous effect may become negligible. There is a possibility in some skipped grids that the error of finite-difference approximations is finite due to the interpolation of the variables. The error appears not only near the pole but also in lower latitudes. However, the error may become of smaller order if the flow has a very small deviation in the zonal direction (nearly zonal flow) and hence the solution may converge to that obtained with the latitude-longitude grid when Δφ→0. In the case of the cross-polar flow the error would not be smaller whatever high resolution grid net may be used.
By combining the ideas of the iterative time integration scheme and the time filtering, a time integration scheme for a primitive equations model is formulated. This scheme turns out to be identical with the generalized two time level iterative time integration scheme. However, it is shown that a weight parameter used at the corrector step of time integration is permissible to exceed unity. It is also shown that a weight parameter larger than unity has the character to damp high-frequency noises more efficiently than that less than unity. Along the Kurihara and Tripoli's idea, terms in the primitive equations are divided into two parts, that is, terms which contribute to the relatively slow temporal variation and those which yield the high-frequency noises. By adapting a weight parameter less than unity to the former terms and one larger than unity to the latter ones, it is shown that the amplitude of low-frequency meteorological waves are preserved fairly well while the high-frequency noises are damped effectively. Numerical examples corresponding to the differences of a weight parameter are presented and the results are compared with each other. The results of application of this scheme to the actual numerical prediction model are also presented.
The equation of motion on the unstably stratified PBL under stationary, horizontally homogeneous, and barotropic conditions is numerically solved with the use of so-called simple K-theory. The numerical predictions on the stability dependences of the geostrophic drag coefficient Cg and the surface cross-isobar angle α0 agree with the observational data of Wangara and AMTEX on the average. In addition, the present calculations predict that α0 decreases as the value of ratio of the actual height of PBL Zi to the dynamical scale height kU*/ƒ increases. The tendency is found in the data of Wangara but not found in those of AMTEX.