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- Author or Editor: René Laprise x
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Abstract
A procedure for identifying the resolved scales in nested limited-area models (LAMs) and for computing the nonlinear interactions between these scales is sketched in this paper. The spectral perspective is adopted and implemented semiempirically by analogy with global and r-periodic sectorial models. The analysis indicates that resolved scales are limited in LAMs and sectorial models compared to global models of similar resolution, and that nonlinear interactions may be treated less accurately in LAMs than in global models. A further result of the analysis is the evidence of the paramount importance of nesting, which acts as a type of closure scheme required by LAMs due to their limited computational domain. The assignment of lateral boundary values (LBVs) is responsible for making LAMs nonperiodic; these LBVs include scales exceeding the size of the LAM's domain and several other shorter scales that are nonperiodic on the limited computational domain.
Abstract
A procedure for identifying the resolved scales in nested limited-area models (LAMs) and for computing the nonlinear interactions between these scales is sketched in this paper. The spectral perspective is adopted and implemented semiempirically by analogy with global and r-periodic sectorial models. The analysis indicates that resolved scales are limited in LAMs and sectorial models compared to global models of similar resolution, and that nonlinear interactions may be treated less accurately in LAMs than in global models. A further result of the analysis is the evidence of the paramount importance of nesting, which acts as a type of closure scheme required by LAMs due to their limited computational domain. The assignment of lateral boundary values (LBVs) is responsible for making LAMs nonperiodic; these LBVs include scales exceeding the size of the LAM's domain and several other shorter scales that are nonperiodic on the limited computational domain.
Abstract
A novel form of the Euler equations is developed through the use of a different vertical coordinate system. It is shown that the use of hydrostatic pressure as an independent variable has the advantage that the Euler equations then take a form that parallels very closely the form of the hydrostatic equations cast in isobaric coordinates. This similarity holds even when topography is incorporated through a further transformation into terrain-following coordinates. This leads us to suggest that hydrostatic-pressure coordinates could be used advantageously in nonhydrostatic atmospheric models based on the fully compressible equations.
Abstract
A novel form of the Euler equations is developed through the use of a different vertical coordinate system. It is shown that the use of hydrostatic pressure as an independent variable has the advantage that the Euler equations then take a form that parallels very closely the form of the hydrostatic equations cast in isobaric coordinates. This similarity holds even when topography is incorporated through a further transformation into terrain-following coordinates. This leads us to suggest that hydrostatic-pressure coordinates could be used advantageously in nonhydrostatic atmospheric models based on the fully compressible equations.
Abstract
The combination of semi-implicit and semi-Lagrangian marching algorithms leads to stable integration of the meteorological equations with long time steps even for large advecting velocities and fast-moving free waves. In recent years, however, attention has been drawn to the fact that forced stationary waves may not be handled properly when the time step exceeds some limit dictated by the advecting velocity and the mesh size. The MC2 (Mesoscale Compressible Community) model is used to investigate numerically the behavior of internal gravity waves forced by stable flow over topography as a function of time step. Although the semi-implicit semi-Lagrangian scheme employed in the MC2 model allows larger time steps than classic Eulerian schemes, it leads to an inaccurate solution when the time step is increased beyond some limit. A stability analysis of the numerical response is conducted in order to explain model results. The response of two off-centered semi-implicit schemes proposed by Rivest et al. and Tanguay et al. to solve this problem for large-scale models is studied. The analysis of the response of forced mesoscale disturbances shows that these alternative schemes may allow the time step limit of forced mesoscale models to extend somewhat but that solutions still diverge for sufficiently large Courant number.
Abstract
The combination of semi-implicit and semi-Lagrangian marching algorithms leads to stable integration of the meteorological equations with long time steps even for large advecting velocities and fast-moving free waves. In recent years, however, attention has been drawn to the fact that forced stationary waves may not be handled properly when the time step exceeds some limit dictated by the advecting velocity and the mesh size. The MC2 (Mesoscale Compressible Community) model is used to investigate numerically the behavior of internal gravity waves forced by stable flow over topography as a function of time step. Although the semi-implicit semi-Lagrangian scheme employed in the MC2 model allows larger time steps than classic Eulerian schemes, it leads to an inaccurate solution when the time step is increased beyond some limit. A stability analysis of the numerical response is conducted in order to explain model results. The response of two off-centered semi-implicit schemes proposed by Rivest et al. and Tanguay et al. to solve this problem for large-scale models is studied. The analysis of the response of forced mesoscale disturbances shows that these alternative schemes may allow the time step limit of forced mesoscale models to extend somewhat but that solutions still diverge for sufficiently large Courant number.
Abstract
A new regional climate model (RCM) is presented in this paper and its performance is investigated through a pair of 60-day simulations. This new model is based on the dynamical formulation of the Cooperative Centre for Research in Mesometeorology (CCRM) mesoscale nonhydrostatic community model and on the complete subgrid-scale physical parameterization package of the second-generation Canadian Centre for Climate modeling and analysis General Circulation Model (CCCma GCMII). The main feature of the Canadian RCM (CRCM) comes from the very efficient semi-implicit and semi-Lagrangian (SISL) numerical scheme used for the integration of the fully elastic nonhydrostatic Euler equations. The efficiency of the SISL scheme allows the use of longer time steps (at least by a factor of 5) for the integration of this model (e.g., the 45-km resolution version of the model uses a 15-min time step). A complete description of the numerical formulation of the model is presented with a review of the principal characteristics of the physical package. A pair of two-month-long winter simulations is also analyzed to investigate the behavior of the model and to evaluate the potential of the SISL integration scheme in the context of regional climate simulation. The two integrations, produced with a 45-km resolution version of the model, developed realistic small-scale details from the low-resolution GCMII fields used to initialize and drive the RCM.
Abstract
A new regional climate model (RCM) is presented in this paper and its performance is investigated through a pair of 60-day simulations. This new model is based on the dynamical formulation of the Cooperative Centre for Research in Mesometeorology (CCRM) mesoscale nonhydrostatic community model and on the complete subgrid-scale physical parameterization package of the second-generation Canadian Centre for Climate modeling and analysis General Circulation Model (CCCma GCMII). The main feature of the Canadian RCM (CRCM) comes from the very efficient semi-implicit and semi-Lagrangian (SISL) numerical scheme used for the integration of the fully elastic nonhydrostatic Euler equations. The efficiency of the SISL scheme allows the use of longer time steps (at least by a factor of 5) for the integration of this model (e.g., the 45-km resolution version of the model uses a 15-min time step). A complete description of the numerical formulation of the model is presented with a review of the principal characteristics of the physical package. A pair of two-month-long winter simulations is also analyzed to investigate the behavior of the model and to evaluate the potential of the SISL integration scheme in the context of regional climate simulation. The two integrations, produced with a 45-km resolution version of the model, developed realistic small-scale details from the low-resolution GCMII fields used to initialize and drive the RCM.
Abstract
Variable-resolution grids are used in global atmospheric models to improve the representation of regional scales over an area of interest: they have reduced computational cost compared to uniform high-resolution grids, and avoid the nesting issues of limited-area models. To address some concerns associated with the stretching and anisotropy of the variable-resolution computational grid, a general convolution filter operator was developed.
The convolution filter that was initially applied in Cartesian geometry in a companion paper is here adapted to cylindrical polar coordinates as an intermediate step toward spherical polar latitude–longitude grids. Both polar grids face the so-called “pole problem” because of the convergence of meridians at the poles.
In this work the authors will present some details related to the adaptation of the filter to cylindrical polar coordinates for both uniform as well as stretched grids. The results show that the developed operator is skillful in removing the extraneous fine scales around the pole, with a computational cost smaller than that of common polar filters. The results on a stretched grid for vector and scalar test functions are satisfactory and the filter’s response can be optimized for different types of test function and noise one wishes to remove.
Abstract
Variable-resolution grids are used in global atmospheric models to improve the representation of regional scales over an area of interest: they have reduced computational cost compared to uniform high-resolution grids, and avoid the nesting issues of limited-area models. To address some concerns associated with the stretching and anisotropy of the variable-resolution computational grid, a general convolution filter operator was developed.
The convolution filter that was initially applied in Cartesian geometry in a companion paper is here adapted to cylindrical polar coordinates as an intermediate step toward spherical polar latitude–longitude grids. Both polar grids face the so-called “pole problem” because of the convergence of meridians at the poles.
In this work the authors will present some details related to the adaptation of the filter to cylindrical polar coordinates for both uniform as well as stretched grids. The results show that the developed operator is skillful in removing the extraneous fine scales around the pole, with a computational cost smaller than that of common polar filters. The results on a stretched grid for vector and scalar test functions are satisfactory and the filter’s response can be optimized for different types of test function and noise one wishes to remove.
Abstract
The purpose of this work is to study the added value of a regional climate model with respect to the global analyses used to drive the regional simulation, with a special emphasis on the nonlinear interactions between different spatial scales, focusing on the moisture flux divergence. The atmospheric water budget is used to apply the spatial-scale decomposition approach, as it is a key factor in the energetics of the climate. A Fourier analysis is performed individually for each field on pressure levels. Each field involved in the computation of moisture flux divergence is separated into three components that represent selected scale bands, using the discrete cosine transform. The divergence of the moisture flux is computed from the filtered fields. Instantaneous and monthly mean fields from a simulation performed with the Canadian Regional Climate Model are decomposed and allowed to separate the added value of the model to the total fields.
Results show that the added value resides in the nonlinear interactions between large (greater than 1000 km) and small (smaller than 600 km) scales. The main small-scale forcing of the wind is topographic, whereas the humidity tends to show more small scales over the ocean. The time-mean divergence of moisture flux is also decomposed into contributions from stationary eddies and transient eddies. Both stationary and transient eddies are decomposed into different spatial scales and show very different patterns. The time-mean divergence due to transient eddies is dominated by large-scale (synoptic scale) features with little small scales. The divergence due to stationary eddies is a combination of small- and large-scale terms, and the main small-scale contribution occurs over the topography.
The same decomposition has been applied to the NCEP–NCAR reanalyses used to drive the regional simulation; the results show that the model best reproduces the time-fluctuation component of the moisture flux divergence, with a correlation between the model simulation and the NCEP–NCAR reanalyses above 0.90.
Abstract
The purpose of this work is to study the added value of a regional climate model with respect to the global analyses used to drive the regional simulation, with a special emphasis on the nonlinear interactions between different spatial scales, focusing on the moisture flux divergence. The atmospheric water budget is used to apply the spatial-scale decomposition approach, as it is a key factor in the energetics of the climate. A Fourier analysis is performed individually for each field on pressure levels. Each field involved in the computation of moisture flux divergence is separated into three components that represent selected scale bands, using the discrete cosine transform. The divergence of the moisture flux is computed from the filtered fields. Instantaneous and monthly mean fields from a simulation performed with the Canadian Regional Climate Model are decomposed and allowed to separate the added value of the model to the total fields.
Results show that the added value resides in the nonlinear interactions between large (greater than 1000 km) and small (smaller than 600 km) scales. The main small-scale forcing of the wind is topographic, whereas the humidity tends to show more small scales over the ocean. The time-mean divergence of moisture flux is also decomposed into contributions from stationary eddies and transient eddies. Both stationary and transient eddies are decomposed into different spatial scales and show very different patterns. The time-mean divergence due to transient eddies is dominated by large-scale (synoptic scale) features with little small scales. The divergence due to stationary eddies is a combination of small- and large-scale terms, and the main small-scale contribution occurs over the topography.
The same decomposition has been applied to the NCEP–NCAR reanalyses used to drive the regional simulation; the results show that the model best reproduces the time-fluctuation component of the moisture flux divergence, with a correlation between the model simulation and the NCEP–NCAR reanalyses above 0.90.
Abstract
Global climate models with variable resolution are effective means to represent regional scales over an area of interest while avoiding the nesting issues of limited-area models. The stretched-grid approach provides a dynamical downscaling approach that naturally allows two-way interactions between the regional and global scales of motion. Concentrating the resolution over a subset of the earth’s surface increases computational efficiency and reduces the computational costs compared to global uniform high-resolution models; however, it does not come free of some problems related to the variation of resolution.
To address the issues associated with the stretching and anisotropy of the computational grid, a general convolution filter with a flexible response function is developed. The main feature of this filter is to locally remove scales shorter than a user-prescribed spatially varying length scale. The filtering effectiveness and computational efficiency of the filter can be custom tailored by an appropriate compromise between the filtering response and the width of the convolution stencil. This approach has been tested in one- and two-dimensional Cartesian geometry. It is shown that an effective filter can be obtained using a limited spatial stencil for the convolution to reduce computational cost, and that an adjustable spatially variable and nearly isotropic response can be obtained for application on variable grids.
Abstract
Global climate models with variable resolution are effective means to represent regional scales over an area of interest while avoiding the nesting issues of limited-area models. The stretched-grid approach provides a dynamical downscaling approach that naturally allows two-way interactions between the regional and global scales of motion. Concentrating the resolution over a subset of the earth’s surface increases computational efficiency and reduces the computational costs compared to global uniform high-resolution models; however, it does not come free of some problems related to the variation of resolution.
To address the issues associated with the stretching and anisotropy of the computational grid, a general convolution filter with a flexible response function is developed. The main feature of this filter is to locally remove scales shorter than a user-prescribed spatially varying length scale. The filtering effectiveness and computational efficiency of the filter can be custom tailored by an appropriate compromise between the filtering response and the width of the convolution stencil. This approach has been tested in one- and two-dimensional Cartesian geometry. It is shown that an effective filter can be obtained using a limited spatial stencil for the convolution to reduce computational cost, and that an adjustable spatially variable and nearly isotropic response can be obtained for application on variable grids.
Abstract
A numerical scheme for the vertical discretization of primitive equations in a generalized pressure-type coordinate is developed through application of the Galerkin formalism with piecewise-constant finite elements: this methodology affords an elegant—and direct—mean of formulating conservative discretization schemes without the arbitrariness that usually characterizes the development of finite differences. The form of the resulting semidiscrete equations is equivalent to some second-order accurate finite-difference approximation to the continuous equations. Flexibility of this scheme in the choice of different layers for projecting the thermodynamic and momentum variables effectively allows for staggering of these variables in the vertical.
Numerical integrations performed with this scheme at various vertical resolutions have revealed the sensitivity of the simulated circulation to resolution in the lower stratosphere. We found that application of the “lid” upper boundary condition at a finite height alleviates a documented bias in the estimation by this scheme of the thermal wind relationship at upper level with coarse resolution, and this is accomplished here without sacrificing the conservation properties of the scheme.
Abstract
A numerical scheme for the vertical discretization of primitive equations in a generalized pressure-type coordinate is developed through application of the Galerkin formalism with piecewise-constant finite elements: this methodology affords an elegant—and direct—mean of formulating conservative discretization schemes without the arbitrariness that usually characterizes the development of finite differences. The form of the resulting semidiscrete equations is equivalent to some second-order accurate finite-difference approximation to the continuous equations. Flexibility of this scheme in the choice of different layers for projecting the thermodynamic and momentum variables effectively allows for staggering of these variables in the vertical.
Numerical integrations performed with this scheme at various vertical resolutions have revealed the sensitivity of the simulated circulation to resolution in the lower stratosphere. We found that application of the “lid” upper boundary condition at a finite height alleviates a documented bias in the estimation by this scheme of the thermal wind relationship at upper level with coarse resolution, and this is accomplished here without sacrificing the conservation properties of the scheme.
Abstract
Over the last years, probability weather forecasts have become increasingly popular due in part to the development of ensemble forecast systems. Despite its widespread use in atmospheric sciences, probability forecasting remains a subtle and ambiguous way of representing the uncertainty related to a future meteorological situation. There are several schools of thought regarding the interpretation of probabilities, none of them without flaws, internal contradictions, or paradoxes. Usually, researchers tend to have personal views that are mostly based on intuition and follow a pragmatic approach.
These conceptual differences may not matter when accuracy of a probabilistic forecast is measured over a long period (e.g., through the use of Brier score), which may be useful for particular objectives such as cost/benefit decision making. However, when scientists wonder about the exact meaning of the probabilistic forecast in a single case (e.g., rare and extreme event), the differences of interpretation become important.
This work intends to describe this problem by first drawing attention to the more commonly accepted interpretations of probability, and then, the consequences of these assumptions are studied. Results suggest that without agreement on the interpretation, the usefulness of the probability forecast as a tool for single events—which include record-breaking events—remains unknown. An open discussion of this topic within the community would be useful to clarify the communication among researchers, with the public and with decision makers.
Abstract
Over the last years, probability weather forecasts have become increasingly popular due in part to the development of ensemble forecast systems. Despite its widespread use in atmospheric sciences, probability forecasting remains a subtle and ambiguous way of representing the uncertainty related to a future meteorological situation. There are several schools of thought regarding the interpretation of probabilities, none of them without flaws, internal contradictions, or paradoxes. Usually, researchers tend to have personal views that are mostly based on intuition and follow a pragmatic approach.
These conceptual differences may not matter when accuracy of a probabilistic forecast is measured over a long period (e.g., through the use of Brier score), which may be useful for particular objectives such as cost/benefit decision making. However, when scientists wonder about the exact meaning of the probabilistic forecast in a single case (e.g., rare and extreme event), the differences of interpretation become important.
This work intends to describe this problem by first drawing attention to the more commonly accepted interpretations of probability, and then, the consequences of these assumptions are studied. Results suggest that without agreement on the interpretation, the usefulness of the probability forecast as a tool for single events—which include record-breaking events—remains unknown. An open discussion of this topic within the community would be useful to clarify the communication among researchers, with the public and with decision makers.
