Akio Arakawa

Interaction of a Cumulus Cloud Ensemble with the Large-Scale Environment, Part I

Abstract A theory of the interaction of a cumulus cloud ensemble with the large-scale environment is developed. In this theory, the large-scale environment is divided into the subcloud mixed layer and the region above. The time changes of the environment are governed by the heat and moisture budget equations for the subcloud mixed layer and for the region above, and by a prognostic equation for the depth of the mixed layer. In the environment above the mixed layer, the cumulus convection affects the temperature and moisture fields through cumulus-induced subsidence and detrainment of saturated air containing liquid water which evaporates in the environment. In the subcloud mixed layer, the cumulus convection does not act directly on the temperature and moisture fields, but it affects the depth of the mixed layer through cumulus-induced subsidence. Under these conditions the problem of parameterization of cumulus convection reduces to the determination of the vertical distributions of the total vertical ma...

Breaking the Cloud Parameterization Deadlock

A key factor limiting the reliability of simulations of anthropogenic climate change is the inability to accurately represent the various effects of clouds on climate. Despite the best efforts of t...

A Potential Enstrophy and Energy Conserving Scheme for the Shallow Water Equations

Abstract To improve the simulation of nonlinear aspects of the flow over steep topography, a potential enstrophy and energy conserving scheme for the shallow water equations is derived. It is pointed out that a family of schemes can conserve total energy for general flow and potential enstrophy for flow with no mass flux divergence. The newly derived scheme is a unique member of this family, that conserves both potential enstrophy and energy for general flow. Comparison by means of numerical experiment with a scheme that conserves (potential) enstrophy for purely horizontal nondivergent flow demonstrated the considerable superiority of the newly derived potential enstrophy and energy conserving scheme, not only in suppressing a spurious energy cascade but also in determining the overall flow regime. The potential enstrophy and energy conserving scheme for a spherical grid is also presented.

Peruvian Stratus Clouds and the Tropical Pacific Circulation: A Coupled Ocean-Atmosphere GCM Study

Abstract Extensive and persistent stratus cloud decks are prominent climatic features off the Peruvian coast. They are believed to play a key role in the coupled atmosphere-ocean processes that determine the sea surface temperature (SST) throughout the eastern tropical Pacific. This notion is examined and further developed using a coupled ocean-atmosphere general circulation model (GCM): a control simulation, in which the simulated amount of Peruvian stratus clouds is unrealistically low, is compared with an experiment in which a stratus cloud deck is prescribed to persistently cover the ocean off the Peruvian coast. Beneath the prescribed cloud deck SSTs are reduced by up to 5 K, as expected from decreased solar radiation reaching the surface. In addition, there is significant cooling over much of the eastern tropical Pacific south of the equator, and even along the equator well into the central Pacific. The prescribed stratus deck largely alleviates the coupled GCMs warm bias in SST in the southeastern...

INTEGRATION OF THE NONDIVERGENT BAROTROPIC VORTICITY EQUATION WITH AN ICOSAHEDRAL-HEXAGONAL GRID FOR THE SPHERE1

Abstract A finite difference scheme is developed for numerical integration of the nondivergent barotropic vorticity equation with an icosahedral-hexagonal grid covering the sphere. The grid is made by dividing the 20 triangular faces of an icosahedron into smaller triangles, the vertices of which are the grid points. Each grid point is surrounded by six neighboring points, except the 12 vertices of the icosahedron which are surrounded by five points. The difference scheme for the advection of vorticity exactly conserves total vorticity, total square vorticity, and total kinetic energy. A numerical test is made, with a stationary Neamtan wave as the initial condition, by integrating over 8 days with 1-hr. time steps and a grid of 1002 points for the sphere. There is practically no distortion of the waves over the 8 days, but there is a phase displacement error of about 1° of long. per day toward the west.

Vertical differencing of the primitive equations in sigma coordinates

Abstract A vertical finite-difference scheme for the primitive equations in sigma coordinates is obtained by requiring that the discrete equations retain some important properties of the continuous equations. A family of schemes is derived whose members conserve total energy, maintain an integral constraint on the vertically integrated pressure gradient force, have a local differencing of the hydrostatic equation, and give exact forms of the hydrostatic equation and the pressure gradient force for particular atmospheres. The proposed scheme is a member of this family that in addition conserves the global mass integral of the potential temperature under abiabatic processes.

Improvement of Orographic Gravity Wave Parameterization Using a Mesoscale Gravity Wave Model

Abstract Parameterization of gravity waves due to subgrid-scale orography is now included in most existing large-scale models of the atmosphere. Parameterization schemes, however, have so far been evaluated mainly in view of the overall performance of the large-scale models. This may lead to an inappropriate assessment of the schemes since errors from various sources may interact with one another. To avoid this situation, an approach is taken in which a numerical model that explicitly resolves gravity waves is used to evaluate the performance of the schemes. For this purpose, a mesoscale two-dimensional nonlinear anelastic nonhydrostatic model is developed and used to numerically simulate gravity waves for a variety of orographic conditions. Regarding a subdomain of the mesoseale model as the horizontal grid interval of a large-scale model, two vertical profiles of gravity wave drag are compared–one for the subdomain-averaged values of the drag simulated by the mesoseale model and the other for the drag c...

The Parameterization Of the Planetary Boundary Layer in the UCLA General Circulation Model: Formulation and Results

Abstract A planetary boundary layer (PBL) parameterization for general circulation models (GCMs) is presented. It uses a mixed-layer approach in which the PBL is assumed to be capped by discontinuities in the mean profiles. Both clear and cloud-topped boundary layers are parameterized. Particular emphasis is placed on the formulation of the coupling between the PBL and both the free atmosphere and cumulus convection. For this purpose a modified σ-coordinate is introduced in which the PBL top and the lower boundary are both coordinate surfaces. The use of a bulk PBL formulation with this coordinate is extensively discussed. Results are presented from a July simulation produced by the UCLA GCM. PBL-related variables are shown, to illustrate the various regimes the parameterization is capable of simulating.

Numerical Modeling of the Atmosphere with an Isentropic Vertical Coordinate

Abstract In constructing a numerical model of the atmosphere, we must choose an appropriate vertical coordinate. Among the various possibilities, isentropic vertical coordinates such as the θ-coordinate seem to have the greatest potential, in spite of the technical difficulties in treating the intersections of coordinate surfaces with the lower boundary. The purpose of this paper is to describe the θ-coordinate model we have developed and to demonstrate its potential through simulating the nonlinear evolution of a baroclinic wave. In the model we have developed, vertical discretization maintains important integral constraints, such as conservation of the angular momentum and total energy. In treating the intersections of coordinate surfaces with the lower boundary, we have followed the massless-layer approach in which the intersecting coordinate surfaces are extended along the boundary by introducing massless layers. Although this approach formally eliminates the intersection problem, it raises other comp...

Interaction of a Cumulus Cloud Ensemble with the Large-Scale Environment. Part II

Abstract The closure assumption of the Arakawa-Schubert (1974) cumulus parameterization takes the form of a balance between the generation of moist convective instability by large-scale processes and its destruction by clouds. This assumption can be justified by consideration of the kinetic energy budget of a cumulus subensemble. First, the kinetic energy generation and dissipation per unit cloud-base mass flux should approximately balance over time scales of the order of the large-scale processes. Second, the dissipation per unit cloud-base mass flux and, therefore, the kinetic energy generation per unit cloud-base mass flux (the cloud-work function) for a given subensemble should not depend substantially on the large-scale conditions. The cloud-work function quasi-equilibrium follows consequently and the unknown cloud-base mass flux is determined by an integral equation. Observational evidence for the cloud-work function quasi-equilibrium is presented. Cloud-work functions are calculated from a variety ...