Search Results

You are looking at 1 - 10 of 26 items for :

  • Author or Editor: Terry L. Clark x
  • Journal of the Atmospheric Sciences x
  • Refine by Access: All Content x
Clear All Modify Search
Terry L. Clark

Abstract

Lagragian parcel calculations of condensation and coalescence theory are presented where both a distribution function approach as well as a conventional finite-difference approach are compared. The comparisons suggest that the use of series of log-normal distributions to represent the water droplet spectra may be a practical approach to treating cloud physical process in multi-dimensioned cloud models.

Full access
Terry L. Clark

Abstract

Two cumulus cloud models in two space dimensions are presented; one is a bulk physical model without microphysics and the other includes the microphysical processes such as nucleation, diffusional growth of cloud droplets, stochastic coalescence, and fallout of raindrops. Some numerical aspects of the models are discussed; in particular, a method is described which allows long time steps to be used for the calculation of condensation in regions of relatively old droplet populations. The bulk-physical and microphysical models are compared for a non-precipitation case. The numerical results revealed that the inclusion of microphysics had little effect on the whole cloud dynamics, a result which considerably differs from that of Árnason and Greenfield.

The microphysical model produced hi-modal spectra of droplets through the interaction of a mid-level nucleation region, which corresponds to the base of an upper intense thermal, and the vertical advection and diffusion of existing droplets from a lower thermal. Supersaturations calculated ranged from approximately 0.4 to 1% in non-nucleation regions to slightly over 2% in nucleation regions for a non-coalescence run in which Warner's nuclei distribution was assumed. Some calculations with coalescence included resulted in unrealistically high values of supersaturation, which were caused by the model's inability to replenish scavenged droplets fast enough. The results indicate not only that breakup will have to be included (as is physically clear), but that the nuclei resolution may have to be extended to relatively high values of critical supersaturation to account for droplet replenishment in the presence of scavenging raindrops.

Full access
Terry L. Clark

Abstract

One-dimensional, kinematical microphysical cloud models are used to study two numerical aspects associated with modelling the initial microphysical stages of cloud growth in Eulerian spatial domain. First, the high-frequency oscillations in the spatially integrated nucleation rate and maximum supersaturation which became apparent in Clark’s model calculations are reproduced in the present paper and their cause and effect studied. Second, the spatial and radius resolution requirements for calculations of the initial phases of cloud development are studied. It is found that rather high spatial as well as radius resolution are required to obtain a reasonable degree of convergence for the solution of the droplet spectrum coefficient of dispersion for a case where an eddy mixing coefficient K=2 m2 sec−1 was used.

The effect of eddy mixing on droplet spectral broadening is investigated where adequate spatial and radius resolution are used. The results indicate that mixing has a rather strong effect on the coefficient of dispersion for the droplet spectrum. Arbitrary values of K=0, 1, 2 and 4 m2 sec−1 were Used where it was found that results similar to those of Warner were obtained for the K=0 case only.

The gamma distribution parameterization of Clark has been generalized to include condensation coefficient effects. The original parameterization scheme has been given a far more thorough comparison with a finite-difference model in one spatial dimension.

Full access
Terry L. Clark

Abstract

Simulations with a three-dimensional numerical cloud model are presented for airflow over a bell-shaped mountain and for a multicellular severe storm.

A comparison of results using the Orlanski (1976) and Klemp and Wilhelmson (1978) treatments for the normal velocities shows that physical modes can be computationally excited using the latter's treatment with the result of very large horizontally averaged vertical velocities.

Cell splitting occurs for the model calculations and the analysis indicates the splitting is caused by an entrainment effect which may be an artifact of the experimental design.

An analysis of subgrid/resolved scale kinetic energy shows that this ratio is much smaller for the current severe storm simulations than that found by Lipps (1977) for his trade wind cumuli simulations.

A comparison of some general features of the multicellular severe storm with observational data is presented.

Full access
Terry L. Clark

Abstract

A relatively sophisticated cloud phase parameterization scheme based on the gamma distribution is presented which, it is hoped, will eventually make it possible for cloud modellers to include the effects of microphysics more realistically than has been so far possible.

Cloud phase calculations are presented using Lagrangian parcel theory, one-dimensional Eulerian formulation in the vertical, and two-dimensional Eulerian formulation in the horizontal and vertical directions. The solutions obtained using the parameterized scheme were compared with the more conventional finite-difference microphysical calculations of Clark and there was found to be very good agreement for all cases treated.

The efficiency of the scheme allowed a one-dimensional study on the effect of vertical spatial resolution on the prediction of microphysical parameters such as droplet number concentration, mean droplet radius and supersaturation. It was found that poor spatial resolution results in a rather slight under-estimation of the droplet number concentration.

Full access
Terry L. Clark and Roland List

Abstract

A numerical experiment on falling particles arranged in zones, with slab symmetry, constant air density, and initially still air is performed whereby single-shed particles are treated by a Lagrangian method and the air motion by an Eulerian method.

The results of this study of the zone's dynamics indicate that the zones fall considerably faster than their respective terminal velocity. This additional or convective velocity depends on loading and terminal speed. The spreading velocities, away from the axis of symmetry, appear to be dependent on terminal velocity such that a maximum occurs near the terminal velocity of 4 m sec−1.

In all cases considered, the magnitude of the perturbation nonhydrostatic pressure gradient in the vertical is found to be an order of magnitude smaller than the perturbation hydrostatic pressure gradient.

Full access
V. Balaji and Terry L. Clark

Abstract

Deep cumulus dynamics has often been treated as an initial value problem where the long time effect of surface energy fluxes are neglected. Initiation is often assumed to follow from a strong localized deformation of the flow field, which is elsewhere quiescent. In nature, however, the atmosphere is rarely found in an undisturbed condition just prior to the inception of deep growth. One likely cause of widespread motions is the natural modal response of the environment to surface energy fluxes which results in a field of disturbances. Evidence is presented in this paper for the possible existence of a class of solutions when deep convection is allowed to evolve in the context of a thermally forced field of shallow convection. This class of solutions is neglected when one visualizes the growth of severe local storms in term of buoyant bubbles in an otherwise tranquil atmosphere. Considering deep cumulus initiation as a field problem severely limits the concept of an isolated cloud. Individual clouds may owe much of their structure to the existence of, and interaction with, the field of thermally forced deep normal modes. The importance of the local forcing terms is demonstrated here through a numerical simulation of the evolution of deep and severe convection out of a locally forced shallow cloud field in the absence of large scale forcing.

When convection is initiated over the entire domain locally through thermal forcing at the ground, the modal solution first observed corresponds to the Rayleigh solution which consist of modes confined to the boundary-layer. However, solutions in the deep linear equations show that a second modal solution also exists. The dominance of this solution, which consists of deep modes of longer horizontal wavelength, is shown here to lead to deep convection.

While the contribution of local forcing terms to the overall energy budget may be negligible at the severe convective stage, the mechanism of initiation appears to influence the pattern of evolution even into the mature stage. At the stage of shallow cumulus, the well-known phenomenon of upshear cumulus development is observed. As clouds grow deeper, an interesting phenomenon of phase-decoupled modal solutions is observed:. the growth of clouds appears to decouple the boundary-layer horizontal motions in phase from the stable layer motions, an effect that cyclically enhances and suppresses cloud growth. A characteristic time may be computed, and average cloud longevity inferred. Finally; the interaction of a moving storm system in its severe stage with the boundary-layer modes appears to provide one explanation for the spatial and temporal distribution of new convective cells in a multicellular storm system.

Full access
Terry L. Clark and W. D. Hall

Abstract

Numerical simulations of stochastic coalescence in a parcel framework are presented using a series of distribution functions. The equations governing the distribution parameter tendencies are derived using a variational approach with constraints. Solutions with two and three log-normal distribution functions are compared with a conventional benchmark model and the distribution model is shown to produce accurate solutions. Although only coalescence is considered within this paper, the procedures for including further physical processes is discussed. All of the simulations presented use the log-normal distribution although the method is general enough that it could be adapted to use other distributions such as the gamma distribution.

A decrease in the number of dependent variables by as much as by a factor of 10 as well as an equivalent reduction in computation time required for the treatment of the coalescence equation makes the distribution model attractive for multi-dimensional cloud model simulations. Further research in the direction of extending the distribution model for such purposes is currently in progress.

Full access
Piotr K. Smolarkiewicz and Terry L. Clark

Abstract

A surface boundary layer model was developed which utilizes the single-level surface mesonet data and the results of a surface energy and moisture budget calculation. The heat and moisture fluxes calculated using this model were employed in the three-dimensional simulation of a cumulus cloud field. The analytical treatment of the surface layer represents a significant computational advantage.

The cloud field simulation represents seven hours of the 20 June 1981 case of the Cooperative Convective Precipitation Experiment (CCOPE) conducted in Montana. The model results are compared .with the available radar and aircraft data, with the record of hourly surface observations and with the available cloud photographs.

The results of the numerical experiments suggest that dynamical inhomogeneities imposed on the flow by the terrain plays a leading role in the rate of development of the convective cloud field. The thermodynamical inhomogeneities generated by such things as the type of soil and vegetation coverage are equally important in the early stage of the cloud field formation, while later they primarily affect the local properties of the cloud field, i.e., temporal and spatial location of single clouds For this case the global characteristics of the cloud field, i.e., geometrical structure of the field, cloud size distribution, and cloud sky coverage are mostly determined by the surface orography rather than by the thermodynamics of the surface layer.

Full access
Jean-Luc Redelsperger and Terry L. Clark

Abstract

Two- and three-dimensional numerical simulations were performed to investigate the scale selection and initiation of both moist and dry convection over gentle western and gentle eastern slopes where the latter represents an idealization of the eastern Colorado region of the Great Plains of North America. This work extends earlier studies of thermally forced convection by considering a model framework that is large enough to resolve both the convective scale dynamics as well as the larger scale dynamics within which the convection is embedded. As a result, the scale interaction problem leading to the selection of the dominant deep modes of the troposphere and consequent convection initiation is more realistically treated. The main physical mechanisms involved in the initiation of convection in these studies are the usual boundary-layer instabilities leading to the development of eddies and/or shear-aligned rolls, the excitation of gravity waves by the boundary-layer motions interacting with the free atmosphere, and the eventual development of coherent vertical structures that link the boundary layer motions and the overlying gravity waves into larger horizontally spaced modes than typically obtained from an isolated boundary layer.

It has previously been shown that the mean wind shear spanning the region between the top of the boundary layer and the overlying stable layer plays an important role in producing energetic deep modes in the presence of thermal forcing. In the present simulation this shear results from a combination of initial baroclinicity associated with the westerlies and production by the differential thermal gradients formed by heating gently sloping terrain. Westerly geostrophic shears of either 3 or 5 m s−1 km−1 over the first 5.5 km above sea level were used as initial conditions. A balance is maintained between shear production through large-scale forcing and shear destruction through boundary-layer mixing that results in significant shear. The experiments showed a broad range of responses as a consequence of the horizontal variability of the shear structures. The preferred region of both dry and moist convection was found to be the eastern slope where the terrain effects result in an enhancement of the low-level shear. In response to the directional structure of the shear spanning the boundary layer and free atmosphere both a banded and a less coherent scattered organization were obtained for the waves and clouds.

Dominant deep modes were found to organize and initiate moist convection. West–east horizontal scales of the deep modes in the dry experiments were found to range from about 11 to 28 km with either a banded or a cellular structure with scales between 4 to 6 km in the south–north direction. The timing of the onset of the moist convection appeared to affect the final horizontal-scale selection in the moist experiments. The moist convection appears to lock onto the scales of the dry modes that initiate the convection for these particular experiments. The largest horizontal scales of dominant modes in the dry experiments were about 28 km and developed rather slowly as compared with the 11 km scale dominant modes. These largest horizontal scales did not develop in the moist experiments where clouds appeared early but did develop in those moist experiments where moist convection took longer to develop.

Full access