Celal S. Konor

Design of an Atmospheric Model Based on a Generalized Vertical Coordinate

Abstract Although there are important advantages in the use of an isentropic vertical coordinate in atmospheric models, it requires overcoming computational difficulties associated with intersections of coordinate surfaces with the earth’s surface. In this paper, the authors present a model based on the generalized vertical coordinate, ζ = F(θ, p, pS), in which an isentropic coordinate can be combined with a terrain-following σ coordinate near the surface with a smooth transition between the two. One of the key issues in developing such a model is to satisfy consistency between the predictions of the pressure and the potential temperature. In the model presented in this paper, consistency is maintained by the use of an equation that determines the vertical mass flux. A procedure to properly choose ζ = F(θ, p, pS) is also presented, which guarantees that ζ is a monotonic function of height even when unstable stratification occurs. In the vertical discretization, the Charney–Phillips grid is used since, wit...

Unification of the Anelastic and Quasi-Hydrostatic Systems of Equations

Abstract A system of equations is presented that unifies the nonhydrostatic anelastic system and the quasi-hydrostatic compressible system for use in global cloud-resolving models. By using a properly defined quasi-hydrostatic density in the continuity equation, the system is fully compressible for quasi-hydrostatic motion and anelastic for purely nonhydrostatic motion. In this way, the system can cover a wide range of horizontal scales from turbulence to planetary waves while filtering vertically propagating sound waves of all scales. The continuity equation is primarily diagnostic because the time derivative of density is calculated from the thermodynamic (and surface pressure tendency) equations as a correction to the anelastic continuity equation. No reference state is used and no approximations are made in the momentum and thermodynamic equations. An equation that governs the time change of total energy is also derived. Normal-mode analysis on an f plane without the quasigeostrophic approximation and...

Parameterization of PBL Processes in an Atmospheric General Circulation Model: Description and Preliminary Assessment

Abstract This paper presents the basic features of a newly developed planetary boundary layer (PBL) parameterization, and the performance assessment of a version of the University of California, Los Angeles (UCLA), Atmospheric General Circulation Model (AGCM) to which the parameterization is incorporated. The UCLA AGCM traditionally uses a framework in which a sigma-type vertical coordinate for the PBL shares a coordinate surface with the free atmosphere at the PBL top. This framework facilitates an explicit representation of processes concentrated near the PBL top, which is crucially important especially for predicting PBL clouds. In the new framework, multiple layers are introduced between the PBL top and earth’s surface, allowing for predictions of the vertical profiles of potential temperature, total water mixing ratio, and horizontal winds within the PBL. The vertically integrated “bulk” turbulent kinetic energy (TKE) is also predicted for the PBL. The PBL-top mass entrainment is determined through a...

Optimized Icosahedral Grids: Performance of Finite-Difference Operators and Multigrid Solver

AbstractThis paper discusses the generation of icosahedral hexagonal–pentagonal grids, optimization of the grids, how optimization affects the accuracy of finite-difference Laplacian, Jacobian, and divergence operators, and a parallel multigrid solver that can be used to solve Poisson equations on the grids. Three different grid optimization methods are compared through an error convergence analysis. The optimization process increases the accuracy of the operators. Optimized grids up to 1-km grid spacing over the earth have been created. The accuracy, performance, and scalability of the multigrid solver are demonstrated.

A Study of the Stratospheric Major Warming and Subsequent Flow Recovery during the Winter of 1979 with an Isentropic Vertical Coordinate Model

Abstract The principal goal of this paper is to gain further insight into the dynamical processes during the stratospheric major warming of February and early March 1979, with a special emphasis on the recovery stage. To achieve this goal, first the entire evolution of the warming event is numerically simulated using an isentropic vertical coordinate model. Then the results from the following complementary points of view are quantitatively analyzed: wave effects on the mean flow, potential enstrophy conversion and transport, and potential vorticity redistribution on a synoptic chart. There is an indication that wavenumber 1 during the recovery stage amplifies through a mechanism within the stratosphere and propagates downward. The simulated Eliassen–Palm flux field shows that the amplified wave 1 is responsible for the mean flow acceleration in the recovery stage. It is therefore concluded that the in situ amplification mechanism for wave 1 plays a crucial role in the dynamics of the flow recovery. In ord...

Design of a Dynamical Core Based on the Nonhydrostatic “Unified System” of Equations*

AbstractThis paper presents the design of a dry dynamical core based on the nonhydrostatic “unified system” of equations. The unified system filters vertically propagating acoustic waves. The dynamical core predicts the potential temperature and horizontal momentum. It uses the predicted potential temperature to determine the quasi-hydrostatic components of the Exner pressure and density. The continuity equation is diagnostic (and used to determine the vertical mass flux) because the time derivative of the quasi-hydrostatic density is obtained from the predicted potential temperature. The nonhydrostatic component of the Exner pressure is obtained from an elliptic equation. The main focus of this paper is on the integration procedure used with this unique dynamical core. In the implementation described in this paper, height is used as the vertical coordinate, and the equations are vertically discretized on a Lorenz-type grid. Cartesian horizontal coordinates are used along with an Arakawa C grid. A detaile...

Modeling Rossby Wave Breaking in the Southern Spring Stratosphere

AbstractRossby wave breaking (RWB) plays a central role in the evolution of stratospheric flows. The generation and evolution of RWB is examined in the simple dynamical framework of a one-layer shallow-water system on a sphere. The initial condition represents a realistic, zonally symmetric velocity profile corresponding to the springtime southern stratosphere. Single zonal wavenumber Rossby waves, which are either stationary or traveling zonally with realistic speeds, are superimposed on the initial velocity profile. Particular attention is placed on the Lagrangian structures associated with RWB. The Lagrangian analysis is based on the calculation of trajectories and the application of a diagnostic tool known as the “M” function. Hyperbolic trajectories (HTs), produced by the transverse intersections of stable and unstable invariant manifolds, may yield chaotic saddles in M. Previous studies associated HTs with “cat’s eyes” generated by planetary wave breaking at the critical levels. HTs, and hence RWB, ...

Choice of a Vertical Grid in Incorporating Condensation Heating into an Isentropic Vertical Coordinate Model

Abstract Advantages of using an isentropic vertical coordinate in atmospheric models are well recognized. In particular, the use of an isentropic coordinate virtually eliminates discretization errors for vertical advection since isentropic surfaces are material surfaces under dry-adiabatic processes. This is also advantageous for predicting moist-adiabatic condensation processes because their occurrence and maintenance largely depend on the converging moisture transport through the surrounding unsaturated regions. In this paper, a basic problem in incorporating condensation heating into an isentropic coordinate model is discussed: that is, the problem of choosing a proper vertical grid for predicting moisture and computing condensation amount and condensation heating. Two different vertical grids are described, one of which predicts moisture for each model layer (M grid) and the other predicts it at each interface separating the model layers (N grid). The models based on these two vertical grids become id...

Multipoint Explicit Differencing (MED) for Time Integrations of the Wave Equation

Abstract For time integrations of the wave equation, it is desirable to use a scheme that is stable over a wide range of the Courant number. Implicit schemes are examples of such schemes, but they do that job at the expense of global calculation, which becomes an increasingly serious burden as the horizontal resolution becomes higher while covering a large horizontal domain. If what an implicit scheme does from the point of view of explicit differencing is looked at, it is a multipoint scheme that requires information at all grid points in space. Physically this is an overly demanding requirement because wave propagation in the real atmosphere has a finite speed. The purpose of this study is to seek the feasibility of constructing an explicit scheme that does essentially the same job as an implicit scheme with a finite number of grid points in space. In this paper, a space-centered trapezoidal implicit scheme is used as the target scheme as an example. It is shown that an explicit space-centered scheme wi...

A Flexible Atmospheric Modeling Framework for the CESM

We have created two global dynamical cores based on the unified system of equations and Z-grid staggering on an icosahedral grid, which are collectively called UZIM (Unified Z-grid Icosahedral Model). The z-coordinate version (UZIM-height) can be run in hydrostatic and nonhydrostatic modes. The sigma-coordinate version (UZIM-sigma) runs in only hydrostatic mode. The super-parameterization has been included as a physics option in both models. The UZIM versions with the super-parameterization are called SUZI. With SUZI-height, we have completed aquaplanet runs. With SUZI-sigma, we are making aquaplanet runs and realistic climate simulations. SUZI-sigma includes realistic topography and a SiB3 model to parameterize the land-surface processes.