Scale Analysis of Deep and Shallow Convection in the Atmosphere

Evolution of Raindrops in an Axisymmetric Cumulus Model

“…The physical treatment of these processes is basically due to Ogura and Takahashi (1973 This spectrum was used by Golovin (1963) and Berry (1967). With use of (1) the actual number of cloud droplets with mass x formed per unit time by condensation is written as where *(*, z, t) is the number concentration of condensation nuclei.…”

“…For droplets with radius less than 40*, the regime of Stokes flow is applied following Ogura and Takahashi (1973), by which the terminal velocity is given as 5) Evaporation of water drops The rate of change of mass * of a droplet due to evaporation is given exactly by the same form as (3) except for the sign. In the present model, any droplet whose radius became smaller by evaporation than the smallest radius considered in the model is again treated as condensation nucleus.…”

“…Ever since the role of condensed water in the life cycle of a convective cloud was clarified by Das (1964), Takeda (1966), andSrivastava (1967), the importance of interaction of dynamical and microphysical processes in the evolution of clouds has been definitely recognized through many studies (Liu and Orville, 1969;Ogura and Takahashi, 1971;Takeda, 1971;Wilhelmson and Ogura, 1972;Murray and Koenig, 1972;Soong and Ogura, 1973;Lopetz, 1973;Shiino, 1978;etc. ) although microphysical processes are in most cases are parameterized in these models.…”

“…Because of these difficulties, microphysical processes are always treated rather simply or in parameterized forms if the main purpose of their researches is to investigate any dynamical aspect of the cloud. However, if their major concerns are the effect on the dynamics of microphysical processes, or the mechanism of precipitation in clouds, microphysical processes are treated in detail with discrete size-distributions of water drops (Danielsen et al, 1972;Ogura and Takahashi, 1973;Takahashi, 1973Takahashi, , 1974Takahashi, , 1975Takahashi, , 1976Takahashi, , 1981Silverman and Glass, 1973;Soong, 1974;Takeda, 1975;Yau, 1980;Hall, 1980).…”

“…He stressed in the study the importance of the stochastic coalescence and the vertical water transport on the initiation of warm rain. Since then, stimulated by Nelson's successful result, Berry's algorithm was widely used, particularly in one-dimensional modeling of warm clouds (Ogura and Takahashi, 1973;Takahashi, 1973;Silverman and Glass, 1973;etc.). The attempts in multi-dimensional models have also been performed by Takahashi (1974Takahashi ( , 1975Takahashi ( , 1981 and Soong (1974).…”