(1) An Eulerian solver based on a flux formulation of the fully compressible nonhydrostatic equations with a mass (hydrostatic pressure) vertical coordinate has been constructed and is being tested within the WRF coding framework. Prognostic variables for this solver are the mass in the column (hydrostatic surface pressure), and coupled with the column mass - potential temperature, horizontal velocities u and v the vertical velocity w, and the geopotential. This core is available in the current WRF release, and will be the basis for the research release due out in early 2004.
For further information:
Contact: Bill Skamarock (skamaroc@ucar.edu,
303-497-8161)
Available papers and presentations:
Equations
and Discretization for the Eulerian mass-coordinate model
Time-splitting Integration Techniques: 2nd-order
Runge-Kutta and 3rd
Order Runge-Kutta
Presentations showing some of the results from
this model: 2D
prototype, 3D prototype
(2) A semi-Lagrangian solver based on the fully compressible nonhydrostatic equations with a generalized vertical coordinate is being constructed.
The motivating philosophy behind the development of the semi-Lagrangian WRF dynamical core is that, for some atmospheric simulations, especially real-time forecasting (where faithful treatment of phase information becomes vital), it is advantageous to use numerical operators possessing a high degree of formal accuracy. In the spatial dimensions, the best differencing schemes for a given order are the so-called "compact" (spatially implicit) methods. Experience, and the corroborating evidence from the formal analysis of truncation errors, suggests that any advantages of staggering the variables of a model (such as the wind components relative to mass and tracers) is greatly diminished once high-order spatial operators are adopted. Having all variables collocated obviates the need to interpolate among grids when access to one variable is required at the point where another is stored. But it also simplifies the implementation of semi-Lagrangian schemes, since only one family of grid-associated trajectories is ever required.
The Lagrangian framework is very often the one in which the state evolves in the slowest and smoothest way and, in combination with a semi-implicit treatment of acoustic and deep gravity modes, it provides the most practical escape from the costly Courant-Friedrichs- Lewy time step restrictions that Eulerian models must obey. By dimensionally splitting the grid-to-grid interpolations in a "cascade" of one-dimensional sweeps, the semi-Lagrangian algorithm is able to accommodate both high-order interpolation operators and first-order conservation at a reasonable cost. Moreover, by facilitating the use of forward trajectories, the method does not hinder the adoption of various high-order temporal discretizations for the explicitly treated modes. Then, consistent with the philosophy expressed above, the truncation errors can be kept low even in the time dimension, despite the relatively long time steps which the semi-Lagrangian approach encourages.
For further information:
Contact: Jim Purser (wd23jp@sun1.wwb.noaa.gov,
301-763-8000, ext 7267)
Available papers:
Radiative Upper Boundary
Conditions for a Nonhydrostatic Atmosphere. R. J. Purser and S. K. Kar,
May 2001
Parallel
Implementation of Compact Numerical Schemes. T. Fujita and R. J.
Purser, July 2001.
Proposed
Semi-Implicit Adaptations of Two Low-Storage Runge-Kutta Schemes.
Part I: Theoretical Formulation and Stability Analysis. R. J.
Purser,
August 2001
Prototypes for the WRF (Weather and Research Forecasting) model; Skamarock, Klemp, and Dudhia
A manuscript examining the choice of parameters for use in the turbulence parameterizations found in the mass and height coordinate cores: The effects of subgrid model mixing and numerical filtering in simulations of mesoscale cloud systems; Takemi and Rotunno
The semi-Lagrangian prototype will be evaluated in the near future as the prototype becomes available.
Statement and plans for initial implementation of nesting in WRF