Claude Girard

A New Terrain-Following Vertical Coordinate Formulation for Atmospheric Prediction Models

Most numerical weather prediction models rely on a terrain-following coordinate framework. The computational mesh is thus characterized by inhomogeneities with scales determined by the underlying topography. Such inhomogeneities may affect the truncation error of numerical schemes. In this study, a new class of terrainfollowing coordinate systems for use in atmospheric prediction models is proposed. Unlike conventional systems, the new smooth level vertical (SLEVE) coordinate yields smooth coordinates at mid- and upper levels. The basic concept of the new coordinate is to employ a scale-dependent vertical decay of underlying terrain features. The decay rate is selected such that small-scale topographic variations decay much faster with height than their large-scale counterparts. This generalization implies a nonlocal coordinate transformation. The new coordinate is tested and compared against standard sigma and hybrid coordinate systems using an idealized advection test. It is demonstrated that the presence of coordinate transformations induces substantial truncation errors. These are critical for grid inhomogeneities with wavelengths smaller than approximately eight grid increments, and may overpower the regular-grid truncation error of the underlying finite-difference approximation. These results are confirmed by a theoretical analysis of the truncation error. In addition, the new coordinate is tested in idealized and real-case numerical experiments using a nonhydrostatic model. The simulations using the new coordinate yield a substantial reduction of small-scale noise in dynamical and thermodynamical model fields.

Boundary Layer and Shallow Cumulus Clouds in a Medium-Range Forecast of a Large-Scale Weather System

Abstract The role and impact that boundary layer and shallow cumulus clouds have on the medium-range forecast of a large-scale weather system is discussed in this study. A mesoscale version of the Global Environmental Multiscale (GEM) atmospheric model is used to produce a 5-day numerical forecast of a midlatitude large-scale weather system that occurred over the Pacific Ocean during February 2003. In this version of GEM, four different schemes are used to represent (i) boundary layer clouds (including stratus, stratocumulus, and small cumulus clouds), (ii) shallow cumulus clouds (overshooting cumulus), (iii) deep convection, and (iv) nonconvective clouds. Two of these schemes, that is, the so-called MoisTKE and Kuo Transient schemes for boundary layer and overshooting cumulus clouds, respectively, have been recently introduced in GEM and are described in more detail. The results show that GEM, with this new cloud package, is able to represent the wide variety of clouds observed in association with the la...

Stability functions correct at the free convection limit and consistent for for both the surface and Ekman layers

For the thermal stability function Φh used to calculate heat and moisture fluxes in the surface layer, we choose a formulation which has the theoretically correct free convection limit % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeikaiabgk% HiTGqaciaa-PhacaqGVaGaamitaiaabMcadaahaaWcbeqaaiabgkHi% TiaaigdacaGGVaGaaG4maaaaaaa!3DFE!\[{\rm{(}} - z{\rm{/}}L{\rm{)}}^{ - 1/3} \]. We then use the experimental result that z/L ≈ Ri to deduce a formulation with an exponent -1/6 for the momentum stability function Φm. This formulation also resolves the matching problem at the interface between the surface and Ekman layers. The proposed functions are found to remain reasonably close to another formulation that is well supported by observations and has exponents -1/2 for Φh and -1/4 for Φm. The intent of the proposals is mainly to clarify and simplify the parameterization of the convective boundary layer in present day atmospheric models, without significantly altering the results.

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...

Wind Energy Simulation Toolkit (WEST): a wind mapping system for use by the wind-energy industry

A state-of-art wind mapping system, the Wind Energy Simulation Toolkit (WEST), was developed in the Meteorological Service of Canada (MSC) for use by the wind energy industry. WEST is based on a statistical-dynamical downscaling approach, i.e. (i) a statistical analysis of climate data to determine the basic atmospheric states, and (ii) a dynamic adaptation of each basic state to high-resolution terrain and surface roughness by using mesoscale and microscale models. The approach has already been used by Frank and Landberg (1997), in their KAMM/WAsP method, to create a numerical wind atlas. The novel part of WEST is the fixed wind-speed interval in classification scheme and the integration of different modules (meso-/micro-scale models and statistical module) into a single toolkit in a more portable form. WEST was built for use by industries not having sophisticated computer facilities. WEST is applied to the Gaspé region of Canada. The mesoscale model MC2 (operated within WEST) is run at 5 km resolution, while the microscale model within WEST is at 200 m resolution. The simulation results are evaluated in comparison with tower observations at a height of 40 m above ground level. The mean of the 29 observed sets of wind data is 6.6 m/s. The mean absolute difference between the observed and simulated sets of wind data is 0.83 m/s with MC2 (meso-component of WEST) and 0.69 with ‘full WEST’ (with both meso- and micro- components). The correlation coefficient of the mean wind-speeds between the simulations and observations for the 29 stations is improved from 0.5 with MC2 to 0.7 with WEST.

A new adiabatic kernel for the MC2 model

Abstract Traditional semi‐implicit formulations of nonhydrostatic compressible models may not be stable in the presence of steep terrain when pressure gradient terms are split and lagged in time. If all pressure gradient terms and the divergence are treated implicitly, the resulting wave equation for the pressure contains off‐diagonal cross‐derivative terms leading to a highly nonsymmetric linear system of equations. In this paper we present a more implicit formulation of the Mesoscale Compressible Community (MC2) model employing a Generalized Minimal Residual (GMRES) Krylov iterative solver and a more efficient semi‐Lagrangian advection scheme. Open boundaries now permit exact upwind interpolation and the ability to reproduce simulations to machine precision is illustrated for one‐way nesting at equivalent resolution. Numerical simulations of hydrostatic and nonhydrostatic mountain waves demonstrate the stability and accuracy of the new adiabatic kernel. The computational efficiency of the model is repor...

Stable Schemes for Nonlinear Vertical Diffusion in Atmospheric Circulation Models

Abstract The intensity of vertical mixing in atmospheric models generally depends on wind shear and static stability, making the diffusion process nonlinear. Traditional implicit numerical schemes, which treat the variables to be diffused implicitly but the diffusion coefficients explicitly, are shown to be only conditionally stable. Instability arises in statically stable conditions with an increase of the vertical resolution or of the time step. Stable schemes are derived whose principal characteristic is to take into account the variation of the diffusion coefficient with respect to the basic variables. One scheme looks like a traditional scheme in which the parameter that determines how implicit the calculations are done is made to vary locally instead of being a constant. This insures stability and at the same time provides optimum accuracy. This scheme did remove spurious oscillations found in the Canadian spectral weather forecasting model.

A second-order accurate in time IMplicit-EXplicit (IMEX) integration scheme for sea ice dynamics

Current sea ice models use numerical schemes based on a splitting in time between the momentum and continuity equations. Because the ice strength is explicit when solving the momentum equation, this can create unrealistic ice stress gradients when using a large time step. As a consequence, noise develops in the numerical solution and these models can even become numerically unstable at high resolution. To resolve this issue, we have implemented an iterated IMplicit-EXplicit (IMEX) time integration method. This IMEX method was developed in the framework of an already implemented Jacobian-free Newton-Krylov solver. The basic idea of this IMEX approach is to move the explicit calculation of the sea ice thickness and concentration inside the Newton loop such that these tracers evolve during the implicit integration. To obtain second-order accuracy in time, we have also modified the explicit time integration to a second-order Runge-Kutta approach and by introducing a second-order backward difference method for the implicit integration of the momentum equation. These modifications to the code are minor and straightforward. By comparing results with a reference solution obtained with a very small time step, it is shown that the approximate solution is second-order accurate in time. The new method permits to obtain the same accuracy as the splitting in time but by using a time step that is 10 times larger. Results show that the second-order scheme is more than five times more computationally efficient than the splitting in time approach for an equivalent level of error.

Wintertime Subkilometer Numerical Forecasts of Near-Surface Variables in the Canadian Rocky Mountains

AbstractNumerical weather prediction (NWP) systems operational at many national centers are nowadays used at the kilometer scale. The next generation of NWP models will provide forecasts at the subkilometer scale. Large impacts are expected in mountainous terrain characterized by highly variable orography. This study investigates the ability of the Canadian NWP system to provide an accurate forecast of near-surface variables at the subkilometer scale in the Canadian Rocky Mountains in wintertime when the region is fully covered by snow. Observations collected at valley and high-altitude stations are used to evaluate forecast accuracy at three different grid spacing (2.5, 1, and 0.25 km) over a period of 15 days. Decreasing grid spacing was found to improve temperature forecasts at high-altitude stations because of better orography representation. In contrast, no improvement is obtained at valley stations due to an inability of the model to fully capture at all resolutions the intensity of valley cold pool...

The Utility of Upper-Boundary Nesting in NWP

AbstractThe importance of stratospheric influences for medium-range numerical weather prediction (NWP) of the troposphere has led to increases in the heights of global model domains at operational centers around the world. Grids now routinely extend to 0.1 hPa (approximately 65 km) in these systems, thereby covering the full depth of the stratosphere and the lower portion of the mesosphere. Increasing the vertical extent of higher-resolution limited-area models (LAMs) nested within the global forecasts is problematic because of the computational cost of additional levels and the possibility of inaccuracy or instability in the high-speed stratospheric jets. An upper-boundary nesting (UBN) technique is developed that allows information from high-topped driving grids to influence the evolution of a lower-topped (~10 hPa) LAM integration in a manner analogous to the treatment of lateral boundary conditions.A stratospheric vortex displacement event in the winter of 2007 is used to study the effectiveness of th...