Stabilization of Nonlinear Vertical Diffusion Schemes in the Context of NWP Models

Self Cite

127

154

† The contribution of C. Smith was written in the course of his employment at the Met Office, UK and is published with the permission of the controller of HMSO and the Queen's Printer for Scottland.Drawing from the results of theoretical studies about the behaviour of constantcoefficients semi-implicit schemes, the dynamical kernel of the Aladin-NH spectral limited-area numerical weather prediction (NWP) model has been modified in order to allow for a stable and efficient integration of the fully elastic Euler equations. The resulting dynamical kernel offers the possibility to use semi-Lagrangian transport schemes together with two-time-level discretizations at kilometric scales for NWP purposes. The main characteristics of the adiabatic part of the model formulation and the space and time discretization are described in this article. In order to illustrate the dependence of the results on adjustable parameters of the dynamical kernel, some real-case dynamical-adaptation forecasts performed with a basic physical parameterization package are presented. The results obtained with this model in real-case experiments fully confirm the conclusions drawn in previous numerical analysis studies. The good quality of the results is found to be compatible with a routine exploitation in a NWP framework. The Aladin-NH dynamical kernel has been used in the operational NWP 'AROME' model since December 2008 at the kilometric scale, with an appropriate physical parameterization package and data assimilation system.

Section: Physical Parameterizations and Interface To Dynamicsmentioning

confidence: 99%

Dynamical kernel of the Aladin–NH spectral limited‐area model: Revised formulation and sensitivity experiments

Bénard

Vivoda

Mašek

et al. 2010

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127

154

“…A further consequence of the stiffness of the problem (Kalnay and Kanamitsu, 1988;Girard and Delage, 1990;Bénard et al, 2000) arises when the diffusion coefficient is a function of the variables on which the diffusion operator is itself acting -as is the case for planetaryboundary-layer schemes. The resulting nonlinearity can then lead to numerical instability.…”

Section: Introductionmentioning

confidence: 99%

A monotonically‐damping second‐order‐accurate unconditionally‐stable numerical scheme for diffusion

Wood

Diamantakis

Staniforth

2007

ABSTRACT:We present a new two-step temporal discretization of the diffusion equation, which is formally secondorder-accurate and unconditionally stable. A novel aspect of the scheme is that it is monotonically damping: the damping rate is a monotonically-increasing function of the diffusion coefficient, independent of the size of the time step, when the diffusion coefficient is independent of the variable being diffused. Furthermore, the damping rate increases without bound as the diffusion coefficient similarly increases. We discuss the nonlinear behaviour of the scheme when the diffusion coefficient is a function of the diffused variable. The scheme is designed to maintain any steady-state solution. We present examples of the performance of the scheme.  Crown

“…It should be noted that in the realistic models vertical diffusion is most often treated in an over-implicit way to avoid nonlinear instabilities (Bénard et al, 2000). This kills the second-order accuracy in both the AAA models and in IFS which in practice runs with (ξ, ν, µ I , µ I I ) = (1/2, 0, 3/2, 3/2) not satisfying the accuracy condition in (23).…”

Section: Discussionmentioning

confidence: 99%

Stability and accuracy of the physics—dynamics coupling in spectral models

Termonia

Hamdi

2007

This article first reviews the existing spectral time-step organizations of the Integrated Forecast System (IFS) of the ECMWF and the ARPEGE/ALADIN/AROME models of Météo-France and the ALADIN partners. They are characterized according to four choices concerning the physics -dynamics coupling: (1) the order in which the physics parametrization and the dynamics are called and coupled inside the time-step computation, (2) the space-time location of the physics coupling on the semi-Lagrangian trajectory, (3) parallel or sequential time stepping of the different physics parametrizations and (4) parallel or sequential physics -dynamics coupling. It is found that according to this classification, IFS on the one hand and the ARPEGE/ALADIN/AROME models on the other hand exhibit two distinct structures.In the models, the dynamical cores of the semi-implicit semi-Lagrangian two-time-level schemes are linearized around a stationary reference state. This state differs from the real atmospheric state (i.e. the exact solution of the equations). This article generalizes the framework introduced by Staniforth, Wood and Côté to study the relation between the coupled physics parametrization and such reference and atmospheric states. Subsequently, the two above-mentioned time-step organizations are translated into this simplified frame. Extra degrees of freedom are added to allow for obvious improvements of the existing spectral time-step organizations. In order to deal with the complexity of the emerging structures and to avoid tedious algebraic manipulations, a numerical methodology is proposed to characterize their properties. This framework is then used to make a comparative study of the numerical stability and the accuracy of the physics -dynamics coupling within the two above-mentioned time-step organizations. Potential improvements are briefly discussed.