scholarly journals A New Dynamical Core of the Global Environmental Multiscale (GEM) Model with a Height-Based Terrain-Following Vertical Coordinate

2019 ◽  
Vol 147 (7) ◽  
pp. 2555-2578 ◽  
Author(s):  
Syed Zahid Husain ◽  
Claude Girard ◽  
Abdessamad Qaddouri ◽  
André Plante
Keyword(s):  
Numerical Experiments ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dynamical Core ◽  
Vertical Coordinate ◽  
Solution Approach ◽  
Global Environmental ◽  
Wide Range ◽  
Terrain Following ◽  
Global Environmental Multiscale

Abstract A new dynamical core of Environment and Climate Change Canada’s Global Environmental Multiscale (GEM) atmospheric model is presented. Unlike the existing log-hydrostatic-pressure-type terrain-following vertical coordinate, the proposed core adopts a height-based approach. The move to a height-based vertical coordinate is motivated by its potential for improving model stability over steep terrain, which is expected to become more prevalent with the increasing demand for very high-resolution forecasting systems. A dynamical core with height-based vertical coordinate generally requires an iterative solution approach. In addition to a three-dimensional iterative solver, a simplified approach has been devised allowing the use of a direct solver for the new dynamical core that separates a three-dimensional elliptic boundary value problem into a set of two-dimensional independent Helmholtz problems. The issue of dynamics–physics coupling has also been studied, and incorporating the physics tendencies within the discretized dynamical equations is found to be the most acceptable approach for the height-based vertical coordinate. The new dynamical core is evaluated using numerical experiments that include two-dimensional nonhydrostatic theoretical cases as well as 25-km resolution global forecasts. For a wide range of horizontal grid resolutions—from a few meters to up to 25 km—the results from the direct solution approach are found to be equivalent to the iterative approach for the new dynamical core. Furthermore, results from the different numerical experiments confirm that the new height-based dynamical core is equivalent to the existing pressure-based core in terms of solution accuracy.

scholarly journals On the Progressive Attenuation of Finescale Orography Contributions to the Vertical Coordinate Surfaces within a Terrain-Following Coordinate System

2020 ◽  
Vol 148 (10) ◽  
pp. 4143-4158
Author(s):  
Syed Zahid Husain ◽  
Claude Girard ◽  
Leo Separovic ◽  
André Plante ◽  
Shawn Corvec
Keyword(s):  
Complex Terrain ◽  
Large Scale ◽  
Computational Cost ◽  
Vertical Motion ◽  
Atmospheric Model ◽  
Vertical Coordinate ◽  
Global Environmental ◽  
Terrain Following ◽  
Prediction Systems ◽  
Global Environmental Multiscale

AbstractA modified hybrid terrain-following vertical coordinate has recently been implemented within the Global Environmental Multiscale atmospheric model that introduces separately controlled height-dependent progressive decaying of the small- and large-scale orography contributions on the vertical coordinate surfaces. The new vertical coordinate allows for a faster decay of the finescale orography imprints on the coordinate surfaces with increasing height while relaxing the compression of the lowest model levels over complex terrain. A number of tests carried out—including experiments involving Environment and Climate Change Canada’s operational regional and global deterministic prediction systems—demonstrate that the new vertical coordinate effectively eliminates terrain-induced spurious generation and amplification of upper-air vertical motion and kinetic energy without increasing the computational cost. Results also show potential improvements in precipitation over complex terrain.

scholarly journals The magnetorotational instability prefers three dimensions

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190622
Author(s):  
Jeffrey S. Oishi ◽  
Geoffrey M. Vasil ◽  
Morgan Baxter ◽  
Andrew Swan ◽  
Keaton J. Burns ◽  
...  
Keyword(s):  
Shear Rate ◽  
Angular Velocity ◽  
Laboratory Experiments ◽  
Three Dimensional ◽  
Linear Instability ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Magnetorotational Instability ◽  
Dynamo Action ◽  
Wide Range

The magnetorotational instability (MRI) occurs when a weak magnetic field destabilizes a rotating, electrically conducting fluid with inwardly increasing angular velocity. The MRI is essential to astrophysical disc theory where the shear is typically Keplerian. Internal shear layers in stars may also be MRI-unstable, and they take a wide range of profiles, including near-critical. We show that the fastest growing modes of an ideal magnetofluid are three-dimensional provided the shear rate, S , is near the two-dimensional onset value, S c . For a Keplerian shear, three-dimensional modes are unstable above S  ≈ 0.10 S c , and dominate the two-dimensional modes until S  ≈ 2.05 S c . These three-dimensional modes dominate for shear profiles relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal laboratory experiments. Significant numbers of rapidly growing three-dimensional modes remainy well past 2.05 S c . These finding are significant in three ways. First, weakly nonlinear theory suggests that the MRI saturates by pushing the shear rate to its critical value. This can happen for systems, such as stars and laboratory experiments, that can rearrange their angular velocity profiles. Second, the non-normal character and large transient growth of MRI modes should be important whenever three-dimensionality exists. Finally, three-dimensional growth suggests direct dynamo action driven from the linear instability.

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

2014 ◽  
Vol 142 (3) ◽  
pp. 1183-1196 ◽  
Author(s):  
Claude Girard ◽  
André Plante ◽  
Michel Desgagné ◽  
Ron McTaggart-Cowan ◽  
Jean Côté ◽  
...  
Keyword(s):  
Hydrostatic Pressure ◽  
Solution Method ◽  
Time Integration ◽  
Atmospheric Model ◽  
Integration Scheme ◽  
Limited Area ◽  
Vertical Coordinate ◽  
Global Environmental ◽  
Time Integration Scheme ◽  
Global Environmental Multiscale

Abstract The 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 forming the new dynamical core of GEM is presented, focusing on these two aspects.

scholarly journals 314 Automated left atrial volume measurement by two-dimensional speckle-tracking echocardiograpy. Feasibility, accuracy, and reproducibility

2021 ◽  
Vol 23 (Supplement_G) ◽  
Author(s):  
Diana Ruxandra Florescu ◽  
Luigi Paolo Badano ◽  
Michele Tomaselli ◽  
Camilla Torlasco ◽  
Georgica Tartea ◽  
...  
Keyword(s):  
Left Atrial ◽  
Speckle Tracking ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Left Atrial Volume ◽  
Volume Measurement ◽  
Two Dimensional ◽  
Automated Measurement ◽  
Maximal Volume ◽  
Wide Range

Abstract Aims A by-product of left atrial (LA) strain analysis is the automated measurement of LA maximal volume (LAVmax), which may decrease the time of echocardiography reporting, and increase the reproducibility of the LAVmax measurement. However, the automated measurement of LAVmax by two-dimensional speckle-tracking analysis (2DSTE) has never been validated. Accordingly, we sought to: (i) assess the feasibility of automated LAVmax measurement by 2DSTE; (ii) compare the automated LAVmax by 2DSTE with conventional two-dimensional (2DE) biplane and three-dimensional echocardiography (3DE) measurements; and (iii) evaluate the accuracy and reproducibility of the three echocardiography techniques. Methods and results LAVmax (34–197 ml) were obtained from 198/210 (feasibility 94%) consecutive patients with various cardiac diseases (median age 67 years, 126 men) by 2DSTE, 2DE, and 3DE. 2DE and 2DSTE measurements resulted in similar LAVmax values (bias = 1.5 ml, limits of agreement, LOA ± 7.5 ml), and slightly underestimated 3DE LAVmax (biases = −5 ml, LOA ± 17 ml, and −6 ml, LOA ± 16 ml, respectively). LAVmax by 2DSTE and 2DE were strongly correlated to those obtained by cardiac magnetic resonance (CMR) (r = 0.946, and r = 0.935, respectively; P < 0.001). However, LAVmax obtained by 2DSTE (bias = −9.5 ml, LOA ± 16 ml) and 2DE (bias = −8 ml, LOA ± 17 ml) were significantly smaller than those measured by CMR. Conversely, 3DE LAVmax were similar to CMR (bias = −2 ml, LOA ± 10 ml). Excellent intra- and inter-observer intraclass correlations were found for 3DE (0.995 and 0.995), 2DE (0.990 and 0.988), and 2DSTE (0.990 and 0.989). Conclusions Automated LAVmax measurement by 2DSTE is highly feasible, highly reproducible, and provided similar values to conventional 2DE calculations in consecutive patients with a wide range of LAVmax.

scholarly journals WAVETRISK-1.0: an adaptive wavelet hydrostatic dynamical core

2019 ◽  
Author(s):  
Nicholas K.-R. Kevlahan ◽  
Thomas Dubos
Keyword(s):  
Shallow Water ◽  
General Circulation ◽  
Wave Train ◽  
Shallow Water Equation ◽  
Three Dimensional ◽  
Circulation Model ◽  
Time Step ◽  
Adaptive Wavelet ◽  
Dynamical Core ◽  
Vertical Coordinate

Abstract. This paper presents the new adaptive dynamical core wavetrisk. The fundamental features of the wavelet-based adaptivity were developed for the shallow water equation on the β-plane in Dubos and Kevlahan (2013) and extended to the icosahedral grid on the sphere in Aechtner et al. (2015). The three-dimensional dynamical core solves the compressible hydrostatic multilayer rotating shallow water equations on a multiscale dynamically adapted grid. The equations are discretized using a Lagrangian vertical coordinate version of dynamico introduced in Dubos et al. (2015). The horizontal computational grid is adapted at each time step to ensure a user-specified relative error in either the tendencies or the solution. The Lagrangian vertical grid is remapped using an adaptive Lagrangian-Eulerian (ALE) algorithm onto the initial hybrid σ pressure-based coordinates as necessary. The resulting grid is adapted horizontally, but uniform over all vertical layers. Thus, the three-dimensional grid is a set of columns of varying sizes. The code is parallelized by domain decomposition using mpi and the variables are stored in a hybrid data structure of dyadic quad trees and patches. A low storage explicit fourth order Runge-Kutta scheme is used for time integration. Validation results are presented for three standard dynamical core test cases: mountain-induced Rossby wave train, baroclinic instability of a jet stream and the Held and Suarez simplified general circulation model. The results confirm good strong parallel scaling and demonstrate that wavetrisk can achieve grid compression ratios of several hundred times compared with an equivalent static grid model.

Numerical experiments with a salt dome

Geophysics ◽  
1989 ◽  
Vol 54 (8) ◽  
pp. 1042-1045 ◽  
Author(s):  
Irshad R. Mufti
Keyword(s):  
Numerical Experiments ◽  
Three Dimensional ◽  
Salt Dome ◽  
Model Structure ◽  
Two Dimensional ◽  
Geologic Structure ◽  
Cross Sectional ◽  
Salt Domes ◽  
D Model

A salt dome is a familiar example of a three‐dimensional (3-D) geologic structure. Surprisingly, most of the literature devoted to the investigation of salt domes deals only with cross‐sectional views of the domes. This is particularly true for seismic work. A notable exception is the work of French (1974) which discusses inaccuracies in focusing introduced by performing two‐dimensional (2-D) migration of data obtained over a 3-D model structure.

scholarly journals Use of a Two-Dimensional Simulation Model in the Thermal Analysis of a Multi-Board Electronic Module

1994 ◽  
Vol 116 (2) ◽  
pp. 126-133 ◽  
Author(s):  
C. Beckermann ◽  
T. F. Smith ◽  
B. Pospichal
Keyword(s):  
Heat Transfer ◽  
Simulation Model ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Circuit Boards ◽  
Depth Direction ◽  
Wide Range ◽  
Local Board ◽  
Dimensional Simulation ◽  
Effective Component

A study is reported of heat transfer and air flow in an electronic module consisting of an array of narrowly spaced vertical circuit boards with highly-protruding components contained in a naturally vented chassis. A two-dimensional simulation model is developed that accounts for heat transfer by conduction, convection, and radiation, and sensitivity studies are performed. Experiments are conducted using a specially constructed test module. Comparisons with the experiments reveal the need to calibrate the model by selecting an effective component height that represents the drag properties of the actual three-dimensional component geometry. The need to account in the model for heat losses in the depth direction is also discussed. The importance of accurate thermophysical properties and of multi-dimensional radiation is shown. Good agreement with measured velocities and local board temperatures is obtained over a wide range of power levels, and it is concluded that the calibrated model is capable of representing the thermal behavior of the present module.

The Modeling of a Three-Dimensional Reservoir with a Two-Dimensional Reservoir Simulator-The Use of Dynamic Pseudo Functions

1973 ◽  
Vol 13 (03) ◽  
pp. 175-185 ◽  
Author(s):  
Hugh H. Jacks ◽  
Owen J.E. Smith ◽  
C.C. Mattax
Keyword(s):  
Capillary Pressure ◽  
Cross Section ◽  
Relative Permeability ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Relative Permeabilities ◽  
Large Reservoir ◽  
Model Simulations ◽  
Wide Range ◽  
Section Model

Abstract Dynamic pseudo-relative permeabilities derived from cross-section models can be used to simulate three-dimensional flow accurately in a two-dimensional areal model of a reservoir Techniques are presented for deriving and using dynamic pseudos that are applicable over a wide range of rates and initial fluid saturations. Their validity is demonstrated by showing calculated results from comparable runs in a vertical cross-section model and in a one-dimensional areal model using the dynamic pseudo-relative permeabilities and vertical equilibrium (VE) pseudo-capillary pressures. Further substantiation is provided by showing the close agreement in calculated performance for a three-dimensional model and corresponding two-dimensional areal model representing a typical pattern on the flanks of a large reservoir. The areal pattern on the flanks of a large reservoir. The areal model gave comparable accuracy with a substantial savings in computing and manpower costs. Introduction Meaningful studies can be made for almost all reservoirs now that relatively efficient three-dimensional reservoir simulators are available. In many instances, however, less expensive two-dimensional areal (x-y) models can be used to solve the engineering problem adequately, provided the nonuniform distribution and flow of fluids in the implied third, or vertical, dimension of the areal model is properly described. This is accomplished through the use of special saturation-dependent functions that have been labeled pseudo-relative permeability (k ) and pseudo-capillary pressure permeability (k ) and pseudo-capillary pressure (P ) or, for simplicity "pseudo functions", to distinguish them from the conventional laboratory measured values that are used in their derivation. Two types of reservoir models have been suggested in the past to derive pseudo functions: the vertical equilibrium (VE) model of Coats et al., which is based on gravity-capillary equilibrium in the vertical direction; and the stratified model of Hearn, which assumes that viscous forces dominate vertical fluid distribution. Neither of these models accounts for the effects of large changes in flow rate that take place as a field is developed, approaches and place as a field is developed, approaches and maintains its peak rate, and then falls into decline. This paper presents an alternative method for developing pseudo functions that are applicable over a wide range of flow rates and over the complete range of initial fluid saturations. The functions may be both space and time dependent and, again for clarity and convenience in nomenclature, we have labeled them "dynamic pseudo functions". DESCRIPTION OF PSEUDO-RELATIVE PERMEABILITY FUNCTIONS PERMEABILITY FUNCTIONS Methods for developing pseudo functions have been presented in the literature. The distinction between our method and those used by others lies in the technique for deriving the vertical saturation distribution upon which the pseudo-relative permeabilities are based. In our approach, the permeabilities are based. In our approach, the vertical saturation distribution is developed through detailed simulation of the fluid displacement in a vertical cross-section (x-z) model of the reservoir. The simulation is run under conditions that are representative of those to be expected during the period to be covered in the areal model simulations. period to be covered in the areal model simulations. Results of the cross-section simulation are then processed to give depth-averaged fluid saturations processed to give depth-averaged fluid saturations (S ) and "dynamic" pseudo-relative permeability values (k ) for each column of blocks in the cross-section model at each output time. The above approach can result in a different set of dynamic pseudo functions for each column of blocks due to differences in initial saturation, rate of displacement, reservoir stratification, and location. However, differences between columns are frequently minor or they can be accounted for by correlation of the data. In this and several other reservoir studies, it was possible to reduce the complexity of the pseudo function sets through correlations with initial fluid saturations and fluid velocities. SPEJ P. 175

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

scholarly journals Beyond the Rigid Lid: Baroclinic Modes in a Structured Atmosphere

2017 ◽  
Vol 74 (11) ◽  
pp. 3551-3566 ◽  
Author(s):  
Jacob P. Edman ◽  
David M. Romps
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Mode Decomposition ◽  
Wide Range ◽  
Tropospheric Heating ◽  
Baroclinic Modes

Abstract The baroclinic-mode decomposition is a fixture of the tropical-dynamics literature because of its simplicity and apparent usefulness in understanding a wide range of atmospheric phenomena. However, its derivation relies on the assumption that the tropopause is a rigid lid that artificially restricts the vertical propagation of wave energy. This causes tropospheric buoyancy anomalies of a single vertical mode to remain coherent for all time in the absence of dissipation. Here, the authors derive the Green’s functions for these baroclinic modes in a two-dimensional troposphere (or, equivalently, a three-dimensional troposphere with one translational symmetry) that is overlain by a stratosphere. These Green’s functions quantify the propagation and spreading of gravity waves generated by a horizontally localized heating, and they can be used to reconstruct the evolution of any tropospheric heating. For a first-baroclinic two-dimensional right-moving or left-moving gravity wave with a characteristic width of 100 km, its initial horizontal shape becomes unrecognizable after 4 h, at which point its initial amplitude has also been reduced by a factor of 1/π. After this time, the gravity wave assumes a universal shape that widens linearly in time. For gravity waves on a periodic domain the length of Earth’s circumference, it takes only 10 days for the gravity waves to spread their buoyancy throughout the entire domain.

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