The melting experiment has been carried out on freshly fallen snowflakes supported on a nylon net in a vertical wind tunnel at an airstream of 100cm sec-1 in wind velocity and of 5.5°C in temperature. The morphological variations of snowflakes by melting were shown in a series of photographs taken every ten seconds. Examinations of the melting process with eyes and through a camera revealed that most of water produced at snowflake surface by melting was not accumulated on the surface but penetrated into the inside, and this is markedly different from the melting processes of ice spheres and crystals. A simple microphysical model was proposed for the melting process of snowflakes. Using the model, it was shown that the rate of decrease in snowflake radius R by melting, assuming spherical symmetry, could be expressed as -dR/dt=εa(KΔT+LvDΔσ)/L_??_σiR in connection with the problem of heat transfer. a is a kind of adjustable parameter to bridge the gap between the experiment and the theory, and was evaluated experimentally as 1.75. a is a ventilation coefficient of spheres determined by Yuge (1960) which is given by a=1+0.275 P1/3r R1/2e.
A theoretical and observational approach was made to elucidate the phenomena of melting of snowflakes below freezing level in the atmosphere. A main purpose of the theoretical approach was to examine the effect of relative humidity of air on snowflake melting that has never referred so far. It is based on the consideration that latent heat accompanied with sublimation or condensation of water vapor from or on snowflake surface exerts a significant influence on the melting rate of snowflakes in addition to heat transfer due to heat diffusion from the ambient air to snowflakes. In the theoretical calculations, we used an empirical formula of the melting rate of snowflakes proposed previously by Matsuo and Sasyo (1981) as the basic equation. Snowflake diameter, liquid water content, and fall velocity as a function of distance below freezing level were obtained by the calculations using parameters such as relative humidity of air, snowflake sizes, and densities. In saturated air below freezing level, snowflakes commenced melting from just below freezing level and snowflakes with equivalent diameter 1-5 mm in raindrops completed melting within several hundred meters. The width of the melting layer thus formed increased with increasing sizes and densities of snowflakes contained. In subsaturated air below freezing level, on the other hand, melting of snowflakes did not take place as far as a considerable distance below freezing level because of cooling of snowflakes by sublimation of water vapor. The width of the non-melting layer thus formed increased nearly linearly as relative humidity decreased; for example, it was about 120 m for relative humidity of 90%, and 700 m for RH=50%. Under the non-melting layer, snowflakes commenced melting because of increase in heat transfer from the ambient air due to increase in air temperature and water vapor density. The width of the melting layer decreased as the layer became dryer. Fall velocity of snowflakes decreased slightly in the non-melting layer and increased rapidly in the melting layer with increasing distance below freezing level. In the observations, simultaneous measurements were carried out for snowflake water content, fall velocity, mass, and cross-sectional area. The observational results showed that fall velocity and liquid water content of snowflakes as a function of their mass were dependent on surface air temperature above 0°C and relative humidity. Especially at high surface air temperature (>1°C), fall velocities were almost constant with respect to their masses and some of them in small mass range were higher than those in larger mass range. This finding shows a different tendency from the results observed by Magono (1953) and Langleben (1954). These observational results were interpreted well by the present theoretical calculations.
The analyses of the meteorological surface data at Wajima, Matsumoto, and Nikko Weather Stations in Japan were made in order to examine the effect of relative humidity of air on melting of snowflakes below freezing level in the atmosphere. The results showed that the types of precipitations (rain or snow) observed on the ground were closely dependent on surface relative humidity as well as surface air temperature. When surface relative humidity was below a certain critical humidity, even at a higher surface air tempera- ture above 0°C precipitations were snow. Using the regression analysis, the relations of the critical relative humidity RHcri to surface air temperature T could be obtained at each Weather Station in the following forms, RHcri=-7.5T+93, ............... Wajima, RHcri=-7.3T+96, ............... Mtsumoto, RHcri=-6.2T+91, ............... Nikko. The relations thus obtained agreed well with that obtained previously from the theoretical calculations by Matsuo and Sasyo (1981).
Observations of continental aerosols were carried out in Canada in winter season. The horizontal distribution of aerosol concentrations in an area for approximately a 100km radius showed the characteristic features of dispersion over land. It was seen that the horizontal distributions of aerosol concentrations in a city were influenced by the emission rate and meteorological conditions. The ratios N7.0/N1.5 representing vertical distributions of aerosol concentrations were greater than 1.0, that is to say, the aerosol concentrations at 1.5m were lower than those at 7.0m. The ratio N7.0/N1.5 became larger, as the atmospheric stability became more stable. It is considered that the characteristic features result from inactive diffusion with the ground sink under the stable condition.
Some of the characteristic features of the 1978-79 winter mean circulation over and around the Tibetan Plateau were investigated by using twice-daily wind, temperature and geopotential height data at eight standard pressure levels. Surface pressures and winds were estimated over a smoothed topography (determined by Berkofsky and Bertoni, 1955) from the 2.5° latitude by 2.5° longitude resolution, standard pressure level data for the period from 1 December 1978 through 28 February 1979. Winter mean surface winds tend to flow around, rather than cross over, the high mountains of the Tibetan Plateau. Thus, forced vertical motions do not appear to be very strong along the periphery of these mountains. A local direct Hadley cell is present in this region with updrafts (downdrafts) to the south (north) of the Tibetan Plateau. West of the Tibetan Plateau, the winter mean flow patterns at 700 and 500mb tend to split into two major streams with axes at 25°N and 45°N. These two westerly flows then converge approximately 1000km downstream (east) of the Tibetan Plateau. In association with this circulation pattern, pairs of anticyclonic and cyclonic vorticity cells occur at the western and eastern borders of the Tibetan Plateau. These vorticity pairs are dominant in the lower troposphere below about 500mb and are indicative of strong surface frictional effects. A comparison of observed and geostrophic winds suggests that the planetary bound- ary layer extends to a height of about 1.5km above the earth's surface. At 200mb, a strong jet stream flows along the southern boundary of the Tibetan Plateau. This jet stream is characterized by pronounced eastward acceleration that is primarily associated with strong, nongeostrophic, southerly winds. Momentum fluxes due to transient disturbances are only a minor factor in the maintenance of this 200mb jet stream. Along any given latitude, 500mb winter mean temperatures are warmer over the Tibetan Plateau. Consequently, the north-south temperature gradient over the Tibetan Plateau is weaker than it is to the north or south, which is congruent with the splitting of the westerly flow at this level. There is no indication of a northward sensible heat flux due to transient eddies directed from the tropics (India-Bay of Bengal), across the Tibetan Plateau, to the Mongolia-Siberia region. In contrast, sensible heat fluxes due to transient eddies are northward and substantial over central and northern China where low-level northerly surges bursting out of Siberia are associated with cold temperatures. Fairly strong northward sensible heat fluxes due to transient eddies are also noted over the Kazakh region as the prevailing southwesterlies transport large amounts of moisture and heat from the Mediterranean-Caspian Seas region.
Some of the characteristic features of diurnal variations over and around the Tibetan Plateau were investigated by using twice-daily wind, temperature and geopotential height data at eight standard pressure levels for the period from 1 December 1978 through 28 February 1979. These standard pressure level data were then used to compute twice-daily pressure, temperature and wind data over the smoothed topographic surface determined by Berkofsky and Bertoni (1955). At the surface, winter mean 12-hr difference, (12-00 GMT) wind vectors are directed northward and flow up the southeastern slope of the Himalayan massif. The higher elevations of the Tibetan Plateau are characterized by convergent surface wind differences, and positive (negative) 12-hr difference surface temperatures (pressures). Equatorward of about 25°N over the Arabian Sea, Bay of Bengal and the South China Sea, (1) vertical profiles of winter mean 12-hr temperature differences exhibit wavelike fluctuations with amplitudes (wavelengths) on the order of 0.5°(5-10km), and (2) hodographs of wind difference vectors clearly display clockwise rotation with height. These features resemble the structures of planetary-scale "vertically propagating" tidal oscillations. Over the Tibetan Plateau, (1) winter mean temperature differences decrease gradually with increasing height which is an indication of deep penetration of the diabatic processes (eddy sensible heat fluxes and longwave emission) operating within the planetary boundary layer, and (2) 12-hr difference wind holographs vary markedly from one geographical location to another, implying large local orographic influence. Near Assam, a pronounced meridionally-oriented, diurnal vertical circulation is induced with terrain slope and high-low land contrasts as a controlling influence. Here, diurnal upward motions forced by up-slope southerly winds are associated with positive 12-hr difference temperatures throughout the troposphere, indicating diurnal variations of local kinetic energy generation. These conversion processes are far more pronounced at 12 GMT (early evening) than at 00 GMT (early morning). In the lower (upper) troposphere equatorward of about 30°N, horizontal sensible heat fluxes due to winter mean diurnal oscillations are down (up) the gradient of the winter mean temperature fields. At 300mb over central India, the magnitude of sensible heat flux convergence associated with winter mean diurnal variations corresponds to a rate of tempera ture change of about 2°C per 10 days.
The extended correction method of the University of Hawaii at Manoa (UHM), National Meteorological Center (NMC) Hough analysis, and subjective streamline analysis (SUB), were employed to provide grid-point winds by using the Data Systems Test (DST) data during the period from 30 August to 4 September 1975. These wind data were used for the computation of barotropic energetics over six limited regions in the Pacific and Indian Oceans. No significant difference was encountered between UHM and NMC stream-function analyses. This is due to the fact that NMC analyzed data was used as a first guess in the UHM objective analyses. NMC velocity potential fields were extremely weak, while UHM analysis provided weak to moderate divergent winds with a major outflow center located over the summer monsoon region. This is attributed to an enhancement of the divergence fields by incorporating satellite observed outgoing longwave radiation data in the UHM analysis scheme. SUB analyses exhibited an extremely strong easterly jet over the equatorial Indian Ocean, and strong upper divergence over the Bay of Bengal. This is obviously due to no data smoothing and the introduction of climatological information in SUB over datasparse regions. Over data-rich regions, the three analysis schemes show good resemblance in both sign and magnitude for energy exchanges between area-averaged zonal mean flows and disturbances. However, substantial differences between objective and subjective analyses were noted over data-sparse regions. For example, over the equatorial Indian Ocean, area-averaged zonal mean flow was barotropically unstable (stable) in UHM and NMC (SUB).
In order to investigate the variety of the sea breeze pattern, surface wind data in three areas in Japan were analysed statistically. In the criteria for the occurrence of the sea breeze, the direction of the synoptic-scale pressure gradient is an important factor as well as its intensity and the strength of land heating. Furthermore, the sea breeze patterns, which vary from day to day even at the same point, are shown to be influenced systematically by the geostrophic wind direction.
A three-dimensional mesoscale atmospheric model, previously used to simulate airflow over cooling ponds and hypothetical, simplified mountains, has been modified to simulate development of nocturnal drainage flow in realistic terrain, part of the California Geysers area. Turbulent fluxes appearing in the governing equations for mean variables are computed from simplified second-moment turbulence-closure equations where only a turbulence energy equation and a master-length scale equation are solved prognostically. Qualitative simulation of drainage flow, horizontal covergence in the valley, and resulting vertical motions are satisfactory. Simulated wind speeds near the surface are greater than observed values, possibly due to inadequate resolution of observations or to a lack of consideration of the drag associated with canopy flow.
A limited area model has been developed to study mainly the influence of the large scale field on a mesoscale disturbance. It has seven levels for height and horizontal velocity and six levels for vertical velocity, temperature and humidity. The interval between levels is smaller in lower atmosphere so that a low level disturbance can be effectively simulated. The data of 00GMT 23 May 1968 is chosen as the initial data of the simulation. A typical case of squall line generation was observed in the NSSL network a few hours later than that time. According to the preliminary experiment, the lateral boundary conditions proposed do not give rise to any artificial change in the total mass field and seem to be applicable to the initial field of our case. The simulated field in the main experiment, where the horizontal grid size is 47.7km at 60°N, is essentially of large scale. The position of the maximum value of the upward motion corresponds well to line storms observed and the upward motion seems to be an important factor in the generation and maintenance of the local line storms in this case.
Economical time integration schemes, which preserve important meteorological waves fairly well, while damp effectively high-frequency noises, are proposed. In order to reduce computation times, low-frequency terms in the primitive equations, which need expensive times for computation, are assumed to be constant within a several time steps. Furthermore, the forward-backward scheme is applied to the integration of high-frequency terms. The integration is carried periodically with the combination of one calculation of obtaining a constant value of low-frequency terms and several forward-backward integrations of high-frequency terms. The constant value used for low-frequency terms is calculated from the weighted mean of the actual value at a certain time level of integration and the temporarily integrated value from that time with a relatively long time step. Two different schemes are proposed to evaluate the temporarily integrated value. One, in which both the low-frequency and the high-frequency terms in the primitive equations are used in the temporary integration, is called Scheme 1 in this report, and the other, in which only the low-frequency terms are used, is called Scheme 2. Moreover, at the backward step of the forward-backward technique a certain weight parameter is multiplied to high-frequency terms pre-predicted at the forward step. This technique is also introduced into the adjustment stage of the so-called Gadd's split explicit scheme. This revised Gadd scheme is called Scheme 3 in this report. These three scheme are applied to the one-dimensional linearized shallow water equations and their stability properties are described as a function of a wave-frequency and a weight parameter. It is shown that all schemes are stable over a certain range of wavefrequency, if a weight parameter used at the backward step is larger than unity. It is alsoshown that a wave-amplitude suffers more damping for a larger value of a weight para meter, while the maximum allowable time increment decreases. In order to demonstrate the usefulness of these schemes, they are applied to a 5-daysprediction of one dimensional linearized primitive equations, and the predicted results are compared with the analytic solution. The followings are concluded. First of all, all schemes reduce the computation time to about 1/5 of the time required by the iterative time integration scheme. Secondly, the meteorological waves are preserved almost perfectly, while the high-frequency gravity waves are damped effectively. Although all schemes give almost the same results, it seems that Scheme 1 gives the best agreement to the analytic solution of a meteorological wave. In order to achieve more economy of computation, the hybrid method is proposed. In this method, the scheme using a large weight parameter with a short time increment and the scheme using a small weight parameter with a relatively long time increment are applied aternately. By applying this method, the computation time is reduced to about 1/10 of the original iterative time integration scheme.
The stability of parallel shear flows of a shallow fluid is investigated by linear analysis. Following Blumen (1970), a necessary condition for instability and the Howard semi-circle theorem are rederived for a shallow water, and energy equations are also derived. Then we examine the stability of two types of basic flows: plane Couette flow bounded in both sides (case I), and the same flow but unbounded in one side to connect with a rest fluid (case II). By obtaining solutions expressed as power series, eigenvalues and eigenfunctions are determined to high accuracy. In the case I, it is shown that normal modes of gravity waves in a channel are modified by the basic shear flow to become unstable in some discrete ranges of the wavenumber, if Froude number, Fr, is greater than 2. In the case II, it is shown that two types of unstable waves are found for Fr>1: One is similar to the unstable waves in the case I but modified by the presence of the rest fluid. The wave is trapped near the boundary. The other is a wave destabilized by the shear too, . but radiates its energy to the unbounded rest fluid. The unstable regions of the waves of this type are continuous in wave number space. The structure of all unstable waves found in this paper are similar to that of gravity waves. It is shown that the unstable waves extract their energy not from the "ordinary" mean kinetic energy, but from an additional term of the mean kinetic energy arising from the correlation between perturbation zonal velocity and perturbation depth, and thus reduce the "depth-weighted" mean kinetic energy. Variation of the basic flow with time and some possibilities of redistribution of momentum by these unstable gravity waves are discussed. Relation between our results and Blumen et al. (1975) is also commented.