Motivated by appearances of multiple equilibrium states in some models of atmospheric flows (Charney and DeVore (1979), Matsuda (1980)), we classify critical points (transition points) appearing in steady problems of fluid dynamics in connection with symmetry break-down in the velocity field. For this purpose, we rewrite the Navier-Stokes equations in a spectral form. In the expansion of the velocity field in terms of normal modes, we divide the modes into two groups; the first group consists of modes which have the same symmetry as the external conditions imposed on the system, while the second group consists of other asymmetric modes. By postulating that there exists always a steady solution which has the same symmetry as the external conditions in the system, we restrict nonlinear coupling between the two groups of modes in the spectral equations. Using the spectral equations obtained in this way, we examine structure of critical points. If the symmetry breaks down in the velocity field, critical points of two types can appear in a fluid system. The first type is the critical point at which a symmetric solution is destabilized and other solutions with lowered symmetry branch from it. The second type is the critical point at which a symmetric solution and an asymmetric solution exchange its stability. If the degree of symmetry is preserved, the critical point of another type can appear in a fluid system; this type of critical point is characterized by coalescence of a stable solution and an unstable one and its subsequent disappearence in the phase space as the relevant parameter is varied. By constructing a local potential in the vicinity of each critical point, we examine the correspondence of critical points examined in this study to Thom's (1972) elementary catastrophes. In the last section, in the light of our classification theory we re-examine multiplicity and stability of the equilibrium states obtained in Charney and DeVore's model (1979) of blocking phenomena.
Stability properties of a baroclinic zonal flow in the presence of surface topography are investigated by using 2-layer and 20-layer, quasi-geostrophic, low-order models. The effect of the topography is approximately incorporated into the model by using a rather simple lower boundary condition. Compared with the conventional baroclinic instability analysis, the present analysis has two differences: Inclusion of (1) effect of surface topo-graphy and (2) perturbation of zonal components. Two kinds of instabilities are obtained in both models. One is the modified baroclinic instability, which is essentially the conventional baroclinic instability. However, the growth rate, the phase speed and the vertical structure of the wave perturbation vary in time depending on the phase relation between the wave and the topography. The other is the topographic instability, in which the wave perturbation grows exponentially in time without phase propagation. In the 20-layer model the second modes of both instabilities, in which the perturbation has a nodal structure in vertical, are obtained in addition to the first modes similar to those obtained in the 2-layer model. Except for the time-dependency, however, the structure and energetics are similar in both instabilities. The eddy energy is supplied by the baroclinic conversion from the available potential energy of the basic zonal flow. The conversion rate of kinetic energy by the surface topography is small compared with the baroclinic conversion.
Thickness of turbulence layers, strictly speaking the distance between the breaking level and the critical level, in the stratosphere is calculated numerically based on an equation representing a marginal state of internal gravity wave breakdown. The results demonstrate that the turbulence layers thinner than approximately 300m, which are frequently observed in the lower stratosphere, can be caused by the breakdown of mesoscale internal gravity waves. Kinematic viscosity and Newtonian cooling suppress the activity of turbulence depending on the horizontal wavelength of internal gravity waves and altitude. In general, long waves are more affected by such dissipative processes than short waves. Detailed inspection shows that damping due to Newtonian cooling is more effective, particularly for longer waves. Maximum eddy viscosity coefficients in the lower stratosphere are also obtained theoretically based on the turbulence layer thickness and characteristic vertical scale associated with kinematic viscosity. The relation between the turbulence layer thickness and wave amplitude provides useful information on parameters of internal gravity waves at the bottom of the middle atmosphere, which propagate upwards and break into turbulence to modify the general circulation near the mesopause.
A 12-level hemispheric spectral model has been developed for operational purpose. The model has a horizontal resolution of triangular 42 truncation and incorporates full physical processes including diurnal variation of shortwave radiation and cloud effects. The model has been tested for nearly a year before introduction as an operational model, and compared with the grid point model which was operational at that time. It has been shown that the spectral model was superior to the grid point model in many respects. The reason is due to various factors, i.e., higher resolution, initialization, analysis etc., and not just due to the use of the spectral method. The useful predictability of the spectral model is found to be 5-6 days. The model forecast is quite useful in predicting sudden developments of baroclinic disturbances, typhoon movements and other important meteorological phenomena with reasonable accuracy.
In order to discuss the teleconnection in the zonally asymmetric height field during the Northern Hemisphere summer, the so-called one-point correlation map is used. In the map, the correlation coefficient between 700mb or 500mb zonally asymmetric height at the reference grid point and 700mb or 500mb zonally asymmetric height at every other grid point is computed, based on the data set consisting of monthly mean height for 34 summer months (July and August for the 17 summers 1963 through 1979). The discussion is mainly focused on the case where the reference point is over the eastern part of the Asian Continent in low latitude. Two types of teleconnection map, i.e., the teleconnection map due to the yearly change of monthly mean height with zonal wavenumber 1 or 2 and that due to zonal wavenumber 5 or 6, are obtained. In the latter case, a train of waves with positive and negative correlation coefficients predominates along the latitudinal circle around 45°N. These teleconnection maps are also examined in relation to the stationary waves which are excited by stationary heat sources over the subtropics.
This is an observational and diagnostic study exploring the interaction between the northeasterly cold surge from the Asian continent and deep cumulus convection over the South China Sea. Based on the data analyses (FGGE III-B), a physical mechanism, by which the cold surge affects deep cumulus convection, has been suggested. The northeasterly cold surge enhances deep cumulus convection in front of it by increasing the lower level convergence and weakens the deep cumulus convection afterwards by stabilizing the stratification through cooling and drying the lower-level air. As a response of deep cumulus convection to the cold surge, the upper level (200mb) outflow over the cluster area is clearly increased. It is also found that deep cumulus clouds always grow over the area where the stratification is conditionally unstable (θe5001000<-10°C), the lower levels large scale flow is convergent (Div. <-10-5s-1). The case study on 14 December reveals that there is a distinct local meridional circu-lation which cooperates with the cold surge and the deep cumulus convection. The circula-tion is enhanced due to the release of latent heat in cumulus clusters. The large-scale vertical velocity profile shows a similarity to the pattern occurring over the western Pacific. The diagnostic results show that the deep cumulus convection and its associated large-scale subsidence stabilizes the stratification in both the cumulus cloud clusters area and in the adjacent clnud-free area.
The nocturnal low level jet, which appears over the southeastern part of the Kanto Plain, is simulated using a three-dimensional numerical model of the local winds. The results agree well with observations of the horizontal and vertical distribuitons of the jet. The diurnal variation of the jet generally agrees with the observation. However, the amplitude of the diurnal variation is a little smaller and the maximum wind velocity appears a few hours earlier than the observation. From some additional numerical experiments, e.g., without the thermal effect of the ground, it is found that the primary factor of the low level jet formation is the mechanical effect of the mountains in central Japan upon the large scale wind. The thermal effect of the mountains enhances the low level jet and produces a diurnal variation. The turbulent stress is also important to the diurnal variation of the jet, but the inertia oscillation, which is generated by the large scale wind and the diurnal variation of the stress, is unlikely to be a primary factor of the jet formation.
Numerical simulations of photochemical air pollution under a theoretical two-dimen-sional local wind system are carried out in order to clarify the fundamental characteristics of the effects of local wind upon photochemical air pollution. The numerical model used here is divided into two steps. The first step is a local wind model which is constructed from the Boussinesq approximation and the hydrostatic equation, and the second step is a photochemical air pollution model in which concentrations of pollutants are calculated using the results of step one as the meteorological data. In the second step, the photo-chemical reaction system, which is actually very complex, is extremely simplified by a parameterization technique. Although this parameterized reaction model is simple, its results, especially the fundamental behaviors of the ozone concentration, are very close to the actual reaction system. The following results were found: 1) In the source area, the diurnal variation of the O3 concentration has a large peak at about noon, but the concentration of NOx has a bi-modal variation with two peaks, one in the morning and another in the evening; 2) The time of the maximum ozone concentration becomes later with an increase in distance from the source area which is located near the coast; 3) At night, a large amount of ozone still remains in the upper layer near the source area, but the concentration is very low near the surface; 4) The large-scale wind affects the distributions of pollutants, even if it is mild. Particularly, it strongly affects the remaining concentrations of pollutants which were formed on the previous day; 5) A mountain inland acts as a suction pump which transports the pollutants from the plain to the upper layer over the mountain.
The broad band spectral measurements of the incident and reflected shortwave radiation were carried out on the snow cover at Mizuho Station, East Antarctica under the POLEX-South program during 1979 and 1981. Diurnal, daily and seasonal variations of both the global solar radiation and albedo were analyzed against two spectral regions, solar zenith angle and cloud cover, with a special intention to the interaction between the global radiation and albedo. The global radiation was large compared to that at the normal mid-latitude station. The atmospheric transmittance was high about 0.75 to 0.80 in the average in summer months because of small amount of atmospheric molecules, aerosols and water vapor. The diffuse radiation from a clear sky, which was similar to the Rayleigh scattering, was about twice as large as that for the place of 0% albedo owing to the high surface albedo through the multiple reflection between the snow surface and atmospheric layer. The effect of clouds to reduce the global radiation was small also on account of the multiple reflection, especially in the visible spectral region. The effect of drifting snow was also examined. The snow albedo for the clear sky was about 0.8 on the daily average in the total wavelength region of the solar radiation. The albedo was higher than 0.95 in the visible region and about 0.66 in the near infrared under the clear sky. The cloudy sky albedo was higher than the clear sky albedo on account of the variation of spectral distribution of the incident solar flux. The solar zenith angle dependence of the albedo was various owing to the micro and macroscale snow surface conditions, however, mostly the albedo became high when the solar elevation became low. The measured albedo was compared to the theoretical albedo calculated from a radiative transfer model, and a good accordance was found on the average.
An entropy balance equation including radiative heating is developed to examine the principle of minimum entropy exchange hypothesized by Paltridge. It is shown that the thermodynamic dissipation (entropy production) due to latent and sensible heat transport cannot be negligible in the entropy balance model. The zonally averaged two-latitude and ten-latitude models with ten radiative heating levels are used to find climates at minima of the entropy exchange rate. The models are examined under two different conditions of the water vapor distribution: one is the case with a given distribution of absolute humidity and the other the case with a given distribution of relative humidity. Multiple minima are found in the former case, while no minima in the latter case. In the former case, one of the minima corresponds to a climate with distributions of temperature and cloud amount similar to those in the present climate. However, it does not correspond to the least minimum of the entropy exchange rate. It is demonstrated that climates at minimum entropy exchange are very sensitive to the parameterization of the humidity distribution.
A time dependent model for the rate of growth of electric field at various points at the ground surface due to a thundercloud of finite dimensions has been presented. Calculations have been made for various sets of paramters viz., precipitation intensity p0, vertical cloud motion U, rebound mean angle probability <p>, cloud radius W and the distance of the surface observation point D. The charge within the charging zone of the thundercloud is computed by the combination of both precipitative and convective charging mechanisms. We have obtained: (Eout)max≈-9×103 Vm-1 within 1200s at the ground surface (D=2km) due to a thundercloud (W=1.0km), if p0=10mmh-1 and U=3 ms-1 (taking H=0.5km, L=1.5km, h=5.0km, f1=f2=0.25, τ=100s, <p>=1), where H is the vertical length of both lower main negative and upper main positive charge regions; L is the length of charging zone on each side from the center of the cloud; h is the vertical height of the cloud base from the ground; f1, f2 are the fractional constants for screening charge density and electric field, respectively; and τ is the relaxation time. The obtained results are consistent with the observations of electric field due to a thundercloud at the ground surface.
The heating and moistening rates in the atmosphere over the Kuroshio region in winter are compared to each other for cases with different vertical resolutions of upper-air obser-vation data. The total sensible and latent heat flux at the sea surface calculated with a poor vertical resolution is overestimated by about 60W m-2 (-15% of the total flux)(-15% of the total flux) compared to that with a fine resolution due to the overestimation of the heating rate in the upper part of the convective mixed layer. Such discrepancies are remarkable when the wind in the mixed layer is strong (in an intense cold air outbreak situation). These errors are partly due to errors of the horizontal advection of heat in the use of a poor vertical resolution, but mainly due to the underestimation of the vertical p-velocity which is caused by the underestimation of horizontal divergence in the lowest layer. It is suggested that errors in budget computations in the mixed layer can be reduced if we properly treat wind speeds near the surface at land stations even in cases of poor vertical resolutions.