Monique Tanguay

A Semi-implicit Send-Lagrangian Fully Compressible Regional Forecast Model

Abstract The semi-implicit algorithm, originally developed by Robert for an economical integration of the primitive equations in large-scale models of the atmospheric, is here generalized in order to integrate the fully compressible, nonhydrostatic equations. We show that there is little computational overhead associated with the integration of the full, and hence presumably more correct, set of equations that do not invoke the hydrostatic assumption to exclude the high frequency, vertically propagating acoustic modes.

Extension of 3DVAR to 4DVAR: Implementation of 4DVAR at the Meteorological Service of Canada

On 15 March 2005, the Meteorological Service of Canada (MSC) proceeded to the implementation of a four-dimensional variational data assimilation (4DVAR) system, which led to significant improvements in the quality of global forecasts. This paper describes the different elements of MSC’s 4DVAR assimilation system, discusses some issues encountered during the development, and reports on the overall results from the 4DVAR implementation tests. The 4DVAR system adopted an incremental approach with two outer iterations. The simplified model used in the minimization has a horizontal resolution of 170 km and its simplified physics includes vertical diffusion, surface drag, orographic blocking, stratiform condensation, and convection. One important element of the design is its modularity, which has permitted continued progress on the three-dimensional variational data assimilation (3DVAR) component (e.g., addition of new observation types) and the model (e.g., computational and numerical changes). This paper discusses some numerical problems that occur in the vicinity of the Poles where the semi-Lagrangian scheme becomes unstable when there is a simultaneous occurrence of converging meridians and strong wind gradients. These could be removed by filtering the winds in the zonal direction before they are used to estimate the upstream position in the semi-Lagrangian scheme. The results show improvements in all aspects of the forecasts over all regions. The impact is particularly significant in the Southern Hemisphere where 4DVAR is able to extract more information from satellite data. In the Northern Hemisphere, 4DVAR accepts more asynoptic data, in particular coming from profilers and aircrafts. The impact noted is also positive and the short-term forecasts are particularly improved over the west coast of North America. Finally, the dynamical consistency of the 4DVAR global analyses leads to a significant impact on regional forecasts. Experimentation has shown that regional forecasts initiated directly from a 4DVAR global analysis are improved with respect to the regional forecasts resulting from the regional 3DVAR analysis.

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...

Impact of the Different Components of 4DVAR on the Global Forecast System of the Meteorological Service of Canada

A four-dimensional variational data assimilation (4DVAR) scheme has recently been implemented in the medium-range weather forecast system of the Meteorological Service of Canada (MSC). The new scheme is now composed of several additional and improved features as compared with the three-dimensional variational data assimilation (3DVAR): the first guess at the appropriate time from the full-resolution model trajectory is used to calculate the misfit to the observations; the tangent linear of the forecast model and its adjoint are employed to propagate the analysis increment and the gradient of the cost function over the 6-h assimilation window; a comprehensive set of simplified physical parameterizations is used during the final minimization process; and the number of frequently reported data, in particular satellite data, has substantially increased. The impact of these 4DVAR components on the forecast skill is reported in this article. This is achieved by comparing data assimilation configurations that range in complexity from the former 3DVAR with the implemented 4DVAR over a 1-month period. It is shown that the implementation of the tangent-linear model and its adjoint as well as the increased number of observations are the two features of the new 4DVAR that contribute the most to the forecast improvement. All the other components provide marginal though positive impact. 4DVAR does not improve the medium-range forecast of tropical storms in general and tends to amplify the existing, too early extratropical transition often observed in the MSC global forecast system with 3DVAR. It is shown that this recurrent problem is, however, more sensitive to the forecast model than the data assimilation scheme employed in this system. Finally, the impact of using a shorter cutoff time for the reception of observations, as the one used in the operational context for the 0000 and 1200 UTC forecasts, is more detrimental with 4DVAR. This result indicates that 4DVAR is more sensitive to observations at the end of the assimilation window than 3DVAR.

Four-Dimensional Variational Data Assimilation with Digital Filter Initialization

A four-dimensional variational (4DVAR) data assimilation problem may be constrained so that the solution closely fits the observations but is balanced. In this way, the processes of data analysis and initialization are combined. The method of initialization considered here, digital filtering, is widely used in weather forecasting centers. The digital filter was found to control high-frequency noise when implemented as a strong or as a weak constraint in the context of a global shallow water model. Implementation of a strong constraint did not result in a recovery of small scales although some recovery of intermediate scales did occur. Implementation of a weak constraint as a penalty method with a single fixed value of the penalty parameter resulted in analyses that were smooth, but depended upon the choice of the parameter. With a parameter value that was too large, the divergent kinetic energy spectrum of the analysis was excessively damped in the large scales. The rotational kinetic energy spectrum was also affected by the choice of penalty parameter. Both types of constraint were found to adequately control gravity wave noise although caution is advised in choosing the penalty parameter for the simple penalty term method.

Advantages of Spatial Averaging in Semi-implicit Semi-Lagrangian Schemes

Abstract A modified semi-Lagrangian scheme is proposed in the context of semi-implicit forecast models to reduce the important distortion of topographically forced waves that is produced when the Courant–Friedrichs–Lewy (CFL) number is greater than 1. The improved semi-Lagrangian scheme combines the original semi-implicit formulation and the spatial averaging of all nonlinear terms. The impact of the spatial averaging is assessed in two baroclinic forecast models: a global spectral model and a regional gridpoint model. The modified semi-implicit semi-Lagrangian scheme is shown to improve short- and medium-range forecasts, and to increase the efficiency of the models by reducing the number of interpolations by 20%–40%.

The Canadian Regional Data Assimilation and Forecasting System

Abstract This paper describes the recent changes to the regional data assimilation and forecasting system at the Canadian Meteorological Center. A major aspect is the replacement of the currently operational global variable resolution forecasting approach by a limited-area nested approach. In addition, the variational analysis code has been upgraded to allow limited-area three- and four-dimensional variational data assimilation (3D- and 4DVAR) analysis approaches. As a first implementation step, the constraints were to impose similar background error correlation modeling assumptions, equal computer resources, and the use of the same assimilated data. Both bi-Fourier and spherical-harmonics spectral representations of background error correlations were extensively tested for the large horizontal domain considered for the Canadian regional system. Under such conditions, it is shown that the new regional data assimilation and forecasting system performs as well as the current operational system and it produc...

Linearization of a Simplified Planetary Boundary Layer Parameterization

Abstract This study examines the linearization properties of a simplified planetary boundary layer parameterization based on the vertical diffusion equations, in which the exchange coefficients are a function of the local Richardson number and wind shear. Spurious noise, associated with this parameterization, develops near the surface in the tangent linear integrations. The origin of this problem is investigated by examining the accuracy of the linearization and the numerical stability of the scheme used to discretize the vertical diffusion equations. The noise is primarily due to the linearization of the exchange coefficients when the atmospheric state is near neutral static stability and when a long time step is employed. A regularization procedure based on the linearization error and a criterion for the numerical stability is proposed and tested. This regularization is compared with those recently adopted by Mahfouf, who neglects the perturbations of the exchange coefficients, and by Janiskova et al., ...

Elimination of the Helmholtz equation associated with the semi-implicit scheme in a grid point model of the shallow water equations

Abstract A modification is introduced in a semi-implicit version of a grid point model of the shallow water equations. The new model is simpler, runs one-third, and after 5 days of integration, the forecasts differ by less than 1 m.

Use of adjoint sensitivity analysis to diagnose the CMC global analysis performance: A case study

Abstract The sensitivity of forecast errors to initial conditions obtained from the adjoint of a numerical weather prediction model provides new insights into the analysis errors responsible for poor short‐range to mediumrange forecasts. In recent years, we have developed a sensitivity analysis system based on the tangent linear and adjoint of the Global Environmental Multiscale model, in which an iterative procedure minimizing the shortrange forecast errors leads to the so‐called key analysis errors. These errors are dominated by a small number of atmospheric structures, those growing the most rapidly. The algorithm has proven very useful in understanding improvements to the three‐dimensional variational data assimilation (3D‐Var) system implemented in the Canadian Meteorological Centre operational suite in December 2001. The main difference between the old and the new 3D‐Var systems is the assimilation of temperature and surface pressure from surface and upper air stations as opposed to geopotential heights, additional Tiros Operational Vertical Sounder channels, new sources of observations such as temperature observations from aircraft, and wind and temperature from dropsondes. In this paper, we examine key analysis errors of the old 3D‐Var analysis, which led to a very poor 3‐day forecast of a severe winter storm that struck eastern Canada on 10 February 2001. In this case, the same 3‐day forecast from the new 3D‐Var analysis is much better. We compare the difference between the two 3D‐Var analyses and the key analysis errors. We find that the main key analysis errors, in terms of potential vorticity, is located along the west shore of southern California and is characterized by a strong baroclinic structure that has its maximum amplitude in the upper part of the troposphere. The difference between the two analyses is three times more energetic than the key analysis errors and its structure is much more barotropic in the troposphere. However, we show that the large improvement in the new 3D‐Var analysis stems mainly from the reduction of the analysis errors that project onto the key analysis structures.