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Clive Temperton
and
David L. Williamson

Abstract

In Part I of this paper we review initialization methods for numerical weather prediction models, leading up to the development of schemes based on the normal modes of the forecast model. We present the derivation of the normal modes of ECMWF's multilevel global grid-point model, and compare the horizontal normal modes with those obtained using alternative finite-difference schemes. The impact of stability-enhancing Fourier filtering procedures on the normal modes is also discussed. Finally in Part I we apply linear normal mode initialization to a nine-level version of the model with 3.75° horizontal resolution. The application of nonlinear normal mode initialization to this model is presented in Part II.

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David L. Williamson
and
Clive Temperton

Abstract

In Part II of this paper, we describe the nonlinear normal mode initialization applied to the ECMWF multilevel global grid-point model and show that the procedure is highly successful in eliminating spurious high-frequency oscillations from forecasts made by the model. We determine the number of vertical modes that can be included in the procedure and demonstrate insensitivity to minor changes in the definitions of the modes. Attempts to include physical parameterizations within the initialization procedure are described as are the problems which arise with such attempts. It is shown that adiabatic nonlinear initialization is adequate to eliminate high-frequency gravity mode oscillations from a forecast by a model which includes non-adiabatic processes.

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David L. Williamson
and
Robert E. Dickinson

Abstract

A procedure is developed for expanding grid-point data into the normal modes of the linearized NCAR GCM. The approach assumes small-amplitude perturbations about a state of rest and involves separation of variables to give vertical and latitudinal structure equations for each longitudinal wavenumber. As an example of the procedure, 30 days of GCM model simulation data are expanded into the normal modes. It is concluded that the time and space computational modes regarded as noise have amplitudes at least an order of magnitude smaller than the dominant Rossby waves. Except for the Kelvin modes, the model gravity waves have magnitudes no larger than the noise level. The largeness of the Kelvin modes suggests that they may be an important part of the model tropical climatology.

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Roger Daley
,
Joseph Tribbia
, and
David L. Williamson

Abstract

Recent experimental results indicate that there are serious problems in forecasting planetary scales of motion. In contrast with predictability theory which suggests that the planetary scales are the most predictable, forecast experiments indicate that the long waves are predicted less accurately than the synoptic scales.

The present work suggests that one of the causes of model long wave error is the spurious excitation of transient external large-scale Rossby modes. It was found that these modes can be excited by the imposition of an equatorial wall, or by the use of unsuitable data in the tropics. Paradoxically, the imposition of a wall north of the equator may tend to suppress these spurious Rossby modes. The excited external Rossby modes are relatively fast-moving and can have a substantial negative impact on midlatitude forecast skill after only 24 h of integration.

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David L. Williamson
,
Jerry G. Olson
, and
Christiane Jablonowski

Abstract

Two flaws in the semi-Lagrangian algorithm originally implemented as an optional dynamical core in the NCAR Community Atmosphere Model (CAM3.1) are exposed by steady-state and baroclinic instability test cases. Remedies are demonstrated and have been incorporated in the dynamical core. One consequence of the first flaw is an erroneous damping of the speed of a zonally uniform zonal wind undergoing advection by a zonally uniform zonal flow field. It results from projecting the transported vector wind expressed in unit vectors at the arrival point to the surface of the sphere and is eliminated by rotating the vector to be parallel to the surface. The second flaw is the formulation of an a posteriori energy fixer that, although small, systematically affects the temperature field and leads to an incorrect evolution of the growing baroclinic wave. That fixer restores the total energy at each time step by changing the provisional forecast temperature proportionally to the magnitude of the temperature change at that time step. Two other fixers are introduced that do not exhibit the flaw. One changes the provisional temperature everywhere by an additive constant, and the other changes it proportionally by a multiplicative constant.

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David L. Williamson
,
Jerry G. Olson
, and
Byron A. Boville

Abstract

At the modest vertical resolutions typical of climate models, simulations produced by models based on semi-Lagrangian approximations tend to develop a colder tropical tropopause than matching simulations from models with Eulerian approximations, all other components of the model being the same. The authors examine the source of this relative cold bias in the context of the NCAR CCM3 and show that it is primarily due to insufficient vertical resolution in the standard 18-level model, which has 3-km spacing near the tropopause. The difference is first diagnosed with the Held and Suarez idealized forcing to eliminate the complex radiative–convective feedback that affects the tropopause formation in the complete model. In the Held and Suarez case, the tropical simulations converge as the vertical grid layers are halved to produce 36 layers and halved again to produce 72 layers. The semi-Lagrangian approximations require extra resolution above the original 18 to capture the converged tropical tropopause. The Eulerian approximations also need the increased resolution to capture the single-level tropopause implied by the 36- and 72-level simulations, although with 18 layers it does not produce a colder tropopause, just a thicker multilevel tropopause. The authors establish a minimal grid of around 25 levels needed to capture the structure of the converged simulation with the Held and Suarez forcing. The additional resolution is added between 200 and 50 mb, giving a grid spacing of about 1.3 km near the tropopause. With this grid the semi-Lagrangian and Eulerian approximations also create the same tropical structure in the complete model. With both approximations the convective parameterization is better behaved with the extra upper-tropospheric resolution. A benefit to both approximations of the additional vertical resolution is a reduction of the tropical temperature bias compared to the NCEP reanalysis. The authors also show that the Eulerian approximations are prone to stationary grid-scale noise if the vertical grid is not carefully defined. The semi-Lagrangian shows no indication of stationary vertical-grid-scale noise. In addition, the Eulerian simulation exhibits significantly greater transient vertical-grid-scale noise than the semi-Lagrangian.

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David L. Williamson
,
Ronald M. Errico
, and
Roger Daley

Abstract

We illustrate systematic oscillations of the global average temperature in forecasts produced by the NCAR Community Climate Model (CCM). These oscillations are not simple linear oscillations associated with normal modes calculated about a state of rest Rather they result from an interaction between zonal-average gravity modes and zonal-average Rossby modes. Their amplitudes are related to the difference between the initial conditions and the model's average climate.

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David L. Williamson
,
Roger Daley
, and
Thomas W. Schlatter

Abstract

The relative importance of various sources of imbalance in analyses produced by multivariate optimal interpolation is determined. The experimental design uses the shallow-water equations and nonlinear normal mode initialization to define the correct balanced reference atmospheric state and thus restricts this study to horizontal aspects of the problem. The experiments show that the analysis procedure itself introduces systematic imbalances in lows due to the use of the geostrophic relationship to determine the height–wind covariances from the height–height covariances. Random observational errors introduce imbalances but not out of proportion to the observational errors themselves. Data-void areas are responsible for a region of imbalance with width approximately equal to the maximum radius of influence of the analysis on the data-void side of the data-void/data-rich boundary. Model errors in the form of equivalent depth errors do not introduce large imbalances.

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Markus Gross
,
Hui Wan
,
Philip J. Rasch
,
Peter M. Caldwell
,
David L. Williamson
,
Daniel Klocke
,
Christiane Jablonowski
,
Diana R. Thatcher
,
Nigel Wood
,
Mike Cullen
,
Bob Beare
,
Martin Willett
,
Florian Lemarié
,
Eric Blayo
,
Sylvie Malardel
,
Piet Termonia
,
Almut Gassmann
,
Peter H. Lauritzen
,
Hans Johansen
,
Colin M. Zarzycki
,
Koichi Sakaguchi
, and
Ruby Leung

Abstract

Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and microphysical processes. Typically, each component is developed, at least initially, independently. Once development is mature, the components are coupled to deliver a model of the required complexity. The implementation of the coupling can have a significant impact on the model. As the error associated with each component decreases, the errors introduced by the coupling will eventually dominate. Hence, any improvement in one of the components is unlikely to improve the performance of the overall system. The challenges associated with combining the components to create a coherent model are here termed physics–dynamics coupling. The issue goes beyond the coupling between the parameterizations and the resolved fluid dynamics. This paper highlights recent progress and some of the current challenges. It focuses on three objectives: to illustrate the phenomenology of the coupling problem with references to examples in the literature, to show how the problem can be analyzed, and to create awareness of the issue across the disciplines and specializations. The topics addressed are different ways of advancing full models in time, approaches to understanding the role of the coupling and evaluation of approaches, coupling ocean and atmosphere models, thermodynamic compatibility between model components, and emerging issues such as those that arise as model resolutions increase and/or models use variable resolutions.

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