Sylvie Gravel

The Operational CMC–MRB Global Environmental Multiscale (GEM) Model. Part I: Design Considerations and Formulation

Abstract An integrated forecasting and data assimilation system has been and is continuing to be developed by the Meteorological Research Branch (MRB) in partnership with the Canadian Meteorological Centre (CMC) of Environment Canada. Part I of this two-part paper motivates the development of the new system, summarizes various considerations taken into its design, and describes its main characteristics.

The Operational CMC–MRB Global Environmental Multiscale (GEM) Model. Part II: Results

Abstract An integrated forecasting and data assimilation system has been and is continuing to be developed by the Meteorological Research Branch (MRB) in partnership with the Canadian Meteorological Centre (CMC) of Environment Canada. Part II of this two-part paper presents the objective and subjective evaluations of the intercomparison process that led to the operational implementation of the new Global Environmental Multiscale model. The results of a “proof of concept” experiment and those of a meso-γ-scale simulation further demonstrate the validity and versatility of this model.

The CMC–MRB Global Environmental Multiscale (GEM) Model. Part III: Nonhydrostatic Formulation

Abstract An integrated forecasting and data assimilation system has been and is continuing to be developed by the Meteorological Research Branch (MRB) in partnership with the Canadian Meteorological Centre (CMC) of Environment Canada. Part III of this series of papers presents the nonhydrostatic formulation and some sample results. The nonhydrostatic formulation uses Laprises hydrostatic pressure as the basis for its vertical coordinate. This allows the departure from the hydrostatic formulation to be incorporated in an efficient switch-controlled perturbative manner. The time discretization of the model dynamics is (almost) fully implicit semi-Lagrangian, where all terms including the nonlinear terms are (quasi-) centered in time. The spatial discretization for the adjustment step employs a staggered Arakawa C grid that is spatially offset by half a mesh length in the meridional direction with respect to that employed in previous model formulations. It is accurate to second order, whereas the interpolat...

Staggered Vertical Discretization of the Canadian Environmental Multiscale (GEM) Model Using a Coordinate of the Log-Hydrostatic-Pressure Type

AbstractThe Global Environmental Multiscale (GEM) model is the Canadian atmospheric model used for meteorological forecasting at all scales. A limited-area version now also exists. It is a gridpoint model with an implicit semi-Lagrangian iterative space–time integration scheme. In the “horizontal,” the equations are written in spherical coordinates with the traditional shallow atmosphere approximations and are discretized on an Arakawa C grid. In the “vertical,” the equations were originally defined using a hydrostatic-pressure coordinate and discretized on a regular (unstaggered) grid, a configuration found to be particularly susceptible to noise. Among the possible alternatives, the Charney–Phillips grid, with its unique characteristics, and, as the vertical coordinate, log-hydrostatic pressure are adopted. In this paper, an attempt is made to justify these two choices on theoretical grounds. The resulting equations and their vertical discretization are described and the solution method of what is formi...

A Mass-Conserving Semi-Lagrangian Scheme for the Shallow-Water Equations

Abstract By generalizing the algorithm of Priestley for passively advected fields, a mass-conserving scheme for the coupled shallow-water equations is obtained. It is argued that the interpolation step of semi-Lagrangian schemes is the principal reason for their lack of formal conservation. The corrections introduced by the proposed algorithm to achieve conservation appropriately reflect the localized nature of the interpolation errors that induce its violation.

A Stability Analysis of a Family of Baroclinic Semi-Lagrangian Forecast Models

Abstract The computational stability of a family of recently introduced semi-Lagrangian schemes for baroclinic models is analyzed to better explain their observed behavior and to provide additional theoretical justification. The linear stability analysis is a generalization of that presented in Bates et al. that includes the important impact of evaluating certain (nonlinear) terms using extrapolated quantities. There are three sets of physical modes, namely, the usual gravity and slow (“Rossby”) modes, corresponding to the three solutions of a third-order (in time) normal-mode differential equation. For one-, two-, and three- term extrapolation of quantities, there are also zero, one, and two computational modes, respectively, since the normal-mode difference equation is then of higher order than third. The following conclusions hold equally well for both the Bates et al. and McDonald and Haugen model formulations, which although different in detail behave very similarly. The slow mode is stable and sligh...

A Generalized Family of Schemes that Eliminate the Spurious Resonant Response of Semi-Lagrangian Schemes to Orographic Forcing

Abstract The one-parameter three-time-level family of O(Δt2)-accurate schemes, introduced in Rivest et al. to address the problem of the spurious resonant response of semi-implicit semi-Lagrangian schemes at large Courant number, has been generalized to a two-parameter family by introducing the possibility of evaluating total derivatives using an additional time level. The merits of different members of this family based on both theory and results are assessed. The additional degree of freedom might be expected a priori to permit a reduction of the time truncation errors while still maintaining stability and avoiding spurious resonance. Resonance, stability, and truncation error analyses for the proposed generalized family of schemes are given. The subfamily that is formally O(Δt3)-accurate is unfortunately unstable for gravity modes. Sample integrations for various members of the generalized family are shown. Results are consistent with theory, and stable nonresonant forecasts at large Courant number are...

Variable Resolution and Robustness

Abstract Within the context of a semi-Lagrangian shallow-water model, the dependence of forecast accuracy on the distribution of variable resolution and its robustness with respect to rapid variations in resolution is examined. This study also touches on the broader problem of designing a variable-resolution nested grid for regional modeling. It is demonstrated that the widely held belief that variable resolution induces severe noise problems at resolution interfaces—even for simple models—is not of universal applicability. In particular, no evidence of noise is found in the forecasts even when the resolution is changed abruptly by a factor of 3.5 across an internal boundary, thereby demonstrating the robustness of this particular variable-resolution technique. This result is achieved without any numerical smoothing technique other than that implicitly associated with the interpolation of a semi-Lagrangian scheme. The forecast produced on a uniform high-resolution mesh can be accurately reproduced for a l...

Preliminary Results from a Dry Global Variable-Resolution Primitive Equations Model

ABSTRACT The viability of a proposed global variable-grid strategy was previously tested (Cote et al., 1993) using a shallow-water-equations prototype. It was demonstrated that by using a global variable-resolution mesh, a high-resolution short-term forecast can be obtained for a region of interest at a fraction of the cost of using uniformly-high resolution everywhere. The prototype is generalized here to use the hydrostatic primitive equations. Preliminary results obtained with an adiabatic version of this baroclinic model are presented. They confirm the potential of the proposed strategy: differences between the 48-h forecasts for the 500 hPa geopotential height and mean-sea-level pressure fields obtained from a uniform 1.2° model, and those obtained from a variable-mesh model with equivalent resolution on a 81.6° × 60° sub-domain, are small.

Recent Advances in Canada’s National Operational AQ Forecasting System

Environment Canada routinely issues twice-daily, 48-h public forecasts of (a) gridded surface and near-surface O3, PM2.5, and NO2 concentration fields made by the GEM-MACH15 on-line chemical weather forecast model on a 15-km North American grid plus (b) point-specific forecasts for Canadian cities of the national Air Quality Health Index (AQHI) prepared by a statistical post-processing package called UMOS-AQ. The AQHI is a health-based, additive, no-threshold, hourly AQ index that ranges from 0 to 10+ and is based on a weighted sum of local O3, PM2.5, and NO2 concentrations. An objective analysis scheme for surface O3, PM2.5, and NO2, which will provide model-measurement data fusion and model error diagnostics, is now being tested. These recent advances as well as plans for further improvements to the AQ forecasting system are described.