Peter Lauritzen

National Center for Atmospheric Research

The non‐hydrostatic Model for Prediction Across Scales‐Atmosphere (MPAS‐A) dynamical core has recently been adapted for the Specified Chemistry Whole Atmosphere Community Climate Model (SC‐WACCM). In this study, the mean zonal wind and temperature climatology from SC‐WACCM/MPAS‐A is compared with the results from SC‐WACCM using the finite volume an...

This paper describes and analyzes the Reed–Jablonowski (RJ) tropical cyclone (TC) test case used in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016). This intermediate-complexity test case analyzes the evolution of a weak vortex into a TC in an idealized tropical environment. Reference solutions from nine general circulation models...

Motivated by reducing errors in the energy budget related to enthalpy fluxes within the Energy Exascale Earth System Model (E3SM), we study several physics–dynamics coupling approaches. Using idealized physics, a moist rising bubble test case, and the E3SM's nonhydrostatic dynamical core, we consider unapproximated and approximated thermodynamics a...

Plain Language Summary Small‐scale waves originate from the lower atmosphere have been shown to propagate into the thermosphere. To study their effects a high‐resolution whole atmosphere model has been employed. Using this high‐resolution model, which can partially resolve the small‐scale waves, we can directly quantify the force exerted by these w...

Motivated by reducing errors in the energy budget related to enthalpy fluxes with E3SM, we study several physics-dynamics coupling approaches. Using idealized physics, a moist rising bubble test case, and E3SM's nonhydrostatic dynamical core, we consider unapproximated and approximated thermodynamics applied at constant pressure or constant volume....

High‐resolution Whole Atmosphere Community Climate Model with thermosphere/ionosphere extension is used to simulate the responses to the Hunga‐Tonga volcano eruption on 15 January 2022. Global propagation of the Lamb wave L’0 and L’1 pseudomodes are reproduced in the simulation, with the exponential growth of wave amplitudes with altitudes. The wav...

This paper describes and analyzes the Reed-Jablonowski (RJ) tropical cyclone (TC) test case used in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016). The intermediate complexity test case analyzes the evolution of a weak vortex into a TC in an idealized tropical environment. Simulations from 9 general circulation models (GCMs) that...

Six different configurations, a mixture of grids and atmospheric dynamical cores available in the Community Earth System Model, version 2.2 (CESM2.2), are evaluated for their skill in representing the climate of the Arctic and the surface mass balance of the Greenland Ice Sheet (GrIS). The finite‐volume dynamical core uses structured, latitude‐long...

This paper provides a comprehensive derivation of the total energy equations for the atmospheric components of Earth System Models (ESMs). The assumptions and approximations made in this derivation are motivated and discussed. In particular, it is emphasized that closing the energy budget is conceptually challenging and hard to achieve in practice...

A new configuration of the Community Earth System Model (CESM)/Community Atmosphere Model with full chemistry (CAM‐chem) supporting the capability of horizontal mesh refinement through the use of the spectral element (SE) dynamical core is developed and called CESM/CAM‐chem‐SE. Horizontal mesh refinement in CESM/CAM‐chem‐SE is unique and novel in t...

For the Community Atmosphere Model version 6 (CAM6), an adjustment is needed to conserve dry air mass. This adjustment exposes an inconsistency in how CAM6’s energy budget incorporates water—in CAM6 water in the vapor phase has energy, but condensed phases of water do not. When water vapor condenses, only its latent energy is retained in the model,...

Accurate representation of stratospheric trace gas transport is important for ozone modeling and climate projection. Intermodel spread can arise from differences in the representation of transport by the diabatic (overturning) circulation vs. comparatively faster adiabatic mixing by breaking waves, or through numerical errors, primarily diffusion....

The transport of trace gases by the atmospheric circulation plays an important role in the climate system and its response to external forcing. Transport presents a challenge for Atmospheric General Circulation Models (AGCMs), as errors in both the resolved circulation and the numerical representation of transport processes can bias their abundance...

The Community Earth System Model 2 (CESM2) is the latest Earth System Model developed by the National Center for Atmospheric Research in collaboration with the university community and is significantly advanced in most components compared to its predecessor (CESM1). Here, CESM2's representation of the large‐scale atmospheric circulation and its var...

Numerical general circulation models of the atmosphere are generally required to conserve mass and energy for their application to climate studies. Here we draw attention to another conserved global integral, viz. the component of angular momentum (AM) along the Earth's axis of rotation, which tends to receive less consideration. We demonstrate the...

An overview of the Community Earth System Model Version 2 (CESM2) is provided, including a discussion of the challenges encountered during its development and how they were addressed. In addition, an evaluation of a pair of CESM2 long preindustrial control and historical ensemble simulations is presented. These simulations were performed using the...

Two high‐resolution versions of a Coupled Earth System Model (CESM1.3: 0.25° atmosphere, 1° ocean; CESM1.1: 0.25° atmosphere, 0.1° ocean) are compared to the standard resolution CESM1.1 and CESM1.3 (1° atmosphere, 1° ocean). The CESM1.3 versions are documented, and the consequences of model resolution, air‐sea coupling, and physics in the atmospher...

Abstract. We present a numerical method to enforce global conservation of atmospheric axial angular momentum (AM) in the Community Atmosphere Model (CAM). We discuss the results in a hierarchy of numerical simulations of the atmosphere of increasing complexity, and we demonstrate the importance of global AM conservation in climate simulations.

Abstract This paper describes the implementation of a coarser‐resolution physics grid into the Community Atmosphere Model (CAM), containing 59 fewer grid columns than the dynamics grid. The dry dynamics is represented by the spectral element dynamical core, and tracer transport is computed using the Conservative Semi‐Lagrangian Finite Volume Method...

A closed total energy (TE) budget is of utmost importance in coupled climate system modeling; in particular, the dynamical core or physics-dynamics coupling should ideally not lead to spurious TE sources/sinks. To assess this in a global climate model, a detailed analysis of the spurious sources/sinks of TE in National Center for Atmospheric Resear...

This paper describes the splitting supercell idealized test case used in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016). These storms are useful test beds for global atmospheric models because the horizontal scale of convective plumes is O(1 km), emphasizing non-hydrostatic dynamics. The test case simulates a supercell on a reduc...

Atmospheric modeling with element-based high-order Galerkin methods presents a unique challenge to the conventional physics-dynamics coupling paradigm, due to the highly irregular distribution of nodes within an element and the distinct numerical characteristics of the Galerkin method. The conventional coupling procedure is to evaluate the physical...

Numerical models of the climate system have typically been restricted to grid resolutions from a few hundred down to a few tens of kilometers due to computational constraints, and a representation of sub-grid physical processes by parameterization is required. The continuing advances of science and technology are allowing larger computations and th...

The 2nd World Climate Research Programme (WCRP) Summer School on Climate Model Development was held in Cachoeira Paulista, São Paulo, Brazil, from January 22nd to January 31st, hosted by the National Institute for Space Research, Center for Weather Forecasting and Climate Studies (INPE/CPTEC) to bring together expert scientists to share knowledge w...

Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and micr...

This paper describes the splitting supercell idealized test case used in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016). These storms are useful testbeds for global atmospheric models because the horizontal scale of convective plumes is O(1km), emphasizing non-hydrostatic dynamics. The test case simulates a supercell on a reduced...

It is the purpose of this paper to provide a comprehensive documentation of the new NCAR (National Center for Atmospheric Research) version of the spectral element (SE) dynamical core as part of the Community Earth System Model (CESM2.0) release. This version differs from previous releases of the SE dynamical core in several ways. Most notably the...

The spectral element (SE) variable-resolution (VR) mesh dynamical core is tested in developmental versions of the Community Earth System Model version 2 (CESM2). The SE dynamical core is tested in baroclinic wave, aquaplanet and full physics configurations to evaluate variable-resolution simulations against uniform high and uniform low-resolution s...

Key developments have been made to the NCAR Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension (WACCM-X). Among them, the most important are the self-consistent solution of global electrodynamics, and transport of O⁺ in the F-region. Other ionosphere developments include time-dependent solution of electron/ion tempe...

Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems and are responsible for capturing the dynamical behavior of the Earth's atmosphere via numerical integration of the Navier–Stokes equations. These systems have existed in one form or another for over half of a century, with the earliest discretizations ha...

Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems, and are responsible for capturing the dynamical behavior of the Earth's atmosphere via numerical integration of the Naviér–Stokes equations. These systems have existed in one form or another for over half of a century, with the earliest discretizations h...

An algorithm to consistently couple a conservative semi-Lagrangian finite-volume transport scheme with a spectral element (SE) dynamical core is presented. The semi-Lagrangian finite-volume scheme is the Conservative Semi-Lagrangian Multitracer (CSLAM), the SE dynamical core is the National Center for Atmospheric Research (NCAR)'s Community Atmosph...

Geophysical models of the atmosphere and ocean invariably involve parameterizations. These represent two distinct areas: a) Subgrid processes which the model cannot (yet) resolve, due to its discrete resolution, and b) sources in the equation, due to radiation for example. Hence coupling between these physics parameterizations and the resolved flui...

It is the purpose of this paper to document the NCAR global model topography generation software for unstructured grids (NCAR_Topo (v1.0)). Given a model grid, the software computes the fraction of the grid box covered by land, the grid-box mean elevation (deviation from a geoid that defines nominal sea level surface), and associated sub-grid-scale...

It is the purpose of this paper to document the NCAR global model topography generation software for unstructured grids. Given a model grid, the software computes the fraction of the grid box covered by land, the gridbox mean elevation, and associated sub-grid scale variances commonly used for gravity wave and turbulent mountain stress parameteriza...

This test extends the evaluation of transport schemes from prescribed advection of inert scalars to reactive species. The test consists of transporting two interacting chemical species in the Nair and Lauritzen 2-D idealized flow field. The sources and sinks for these two species are given by a simple, but non-linear, "toy" chemistry that represent...

This study presents a diagnosis of a multiresolution approach using the Model for Prediction Across Scales-Atmosphere (MPAS-A) for simulating regional climate. Four Atmospheric Model Intercomparison Project (AMIP) experiments were conducted for 1999-2009. In the first two experiments, MPAS-A was configured using global quasi-uniform grids at 120- a...

This paper examines the impact of the dynamical core on the simulation of tropical cyclone (TC) frequency, distribution, and intensity. The dynamical core, the central fluid flow component of any general circulation model (GCM), is often overlooked in the analysis of a model's ability to simulate TCs compared to the impact of more commonly document...

A recently developed cell-integrated semi-Lagrangian (CISL) semi-implicit nonhydrostatic atmospheric solver that uses the conservative semi-Lagrangian multitracer (CSLAM) transport scheme is extended to include orographic influences. With the introduction of a new semi-implicit CISL discretization of the continuity equation, the nonhydrostatic solv...

In the continued effort to understand the climate system and improve its representation in atmospheric general circulation models (AGCMs), it is crucial to develop reduced-complexity frameworks to evaluate these models. This is especially true as the AGCM community advances toward high horizontal resolutions (i.e., grid spacing less than 50 km), wh...

Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a "minimal" set of idealized model configurations/runs/ diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volu...

For the first time a mesoscale-resolving whole atmosphere general circulation model (GCM) has been developed, using the NCAR Whole Atmosphere Community Climate Model (WACCM) with ~0.25° horizontal resolution and 0.1 scale height vertical resolution above the middle stratosphere (higher resolution below). This is made possible by the high accuracy a...

This test extends the evaluation of transport schemes from prescribed advection of inert scalars to reactive species. The test consists of transporting two reacting chlorine-like species (Cl and Cl2) in the Nair and Lauritzen 2-D idealized flow field. The sources and sinks for the two species are given by a simple, but non-linear, "toy" chemistry....

A high-order incremental 'remap-type' transport scheme is presented (FF-CSLAM). The scheme utilizes bi-quadratic polynomial sub-grid-cell reconstruction functions based on the weighted least-squares method. The integration of the reconstruction functions over flux-areas, which is inherent in remap schemes, makes use of CSLAM approach of line integr...

SUMMARYA new approach is proposed for constructing a fully explicit third-order mass-conservative semi-Lagrangian scheme for simulating the shallow-water equations on an equiangular cubed-sphere grid. State variables are staggered with velocity components stored pointwise at nodal points and mass variables stored as element averages. In order to ad...

Extended, high-resolution (0.23° latitude × 0.31° longitude) simulations with Community Atmosphere Model versions 4 and 5 (CAM4 and CAM5) are examined and compared with results from climate simulations conducted at a more typical resolution of 0.9° latitude × 1.25° longitude. Overall, the simulated climate of the high-resolution experiments is not...

A cell-integrated semi-Lagrangian (CISL) semi-implicit nonhydrostatic solver for the fully compressible moist Euler equations in two-dimensional Cartesian (x-z) geometry is presented. The semi-implicit CISL solver uses the inherently conservative semi-Lagrangian multitracer transport scheme (CSLAM) and a new flux-form semi-implicit formulation of t...

In this paper an analysis of the global AAM conservation properties of NCAR's Community Atmosphere Model Spectral Element (CAM-SE) dynamical core under Held-Suarez forcing is presented. It is shown that the spurious sources/sinks of AAM in CAM-SE are three orders of magnitude smaller than the parameterized (physical) sources/sinks. The effect on AA...

A new hybrid Eulerian Lagrangian numerical scheme (HEL) for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstrea...

Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a "minimal" set of idealized model configurations/runs/diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volum...

The Community Atmosphere Model, version 4 (CAM4), was released as part of the Community Climate System Model, version 4 (CCSM4). The finite volume (FV) dynamical core is now the default because of its superior transport and conservation properties. Deep convection parameterization changes include a dilute plume calculation of convective available p...

A Cartesian semi-implicit solver using the Conservative Semi-Lagrangian Multitracer (CSLAM) transport scheme is constructed and tested for shallow-water (SW) flows. The SW equations solver (CSLAM-SW) uses a discrete semi-implicit continuity equation specifically designed to ensure a conservative and consistent transport of constituents by avoiding...

A new hybrid Eulerian Lagrangian numerical scheme (HEL) for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstrea...

It is the purpose of this short article to analyze mass conservation in high-order rigorous remapping schemes, which contrary to flux-based methods, relies on elaborate integral constraints over overlap areas and reconstruction functions. For applications on the sphere these integral constraints may be violated primarily as a result of inexact or i...

The problem of two-dimensional tracer advection on the sphere is extremely important in modeling of geophysical fluids and has been tackled using a variety of approaches. A class of popular approaches for tracer advection include ‘incremental remap’ or cell-integrated semi-Lagrangian-type schemes. These schemes achieve high-order accuracy without t...

The authors evaluate the climate produced by the Community Climate SystemModel, version 4, runningwith the new spectral element atmospheric dynamical core option. The spectral element method is configured to use a cubed-sphere grid, providing quasi-uniform resolution over the sphere and increased parallel scalability and removing the need for polar...

With the inclusion of a scalable spectral-element-based version of the High-Order Method Modeling Environment (HOMME) in NCAR's Community Atmosphere Model (CAM) and the need for on the order of 100 prognostic tracers in next generation climate modeling efforts, there is an urgent need for a scalable, monotonic, and conservative multitracer advectio...

To help understand the large disparity in the results of circulation modeling for the atmospheres of Titan and Venus, where the whole atmosphere rotates faster than the surface (superrotation), the atmospheric angular momentum budget is detailed for two General Circulation Models (GCMs). The LMD GCM is tested for both Venus (with simplified and wit...

The Community Atmosphere Model (CAM) has been interfaced to the Data Assimilation Research Testbed (DART), a community facility for ensemble data assimilation. This provides a large set of data assimilation tools for climate model research and development. Aspects of the interface to the Community Earth System Model (CESM) software are discussed an...

It is the purpose of this paper to propose a standard test case suite for two-dimensional transport schemes on the sphere intended to be used for model development and facilitating scheme intercomparison. The test cases are designed to assess important aspects of accuracy in geophysical fluid dynamics such as numerical order of convergence, "minima...

Atmospheric tracers are often observed to be functionally related, and these relations can be physically or chemically significant. It is therefore highly desirable that the transport schemes used in chemistry and chemistry-climate models should not disrupt such functional relations in unphysical ways through numerical mixing or, indeed, unmixing....

In numerical modeling of atmospheric dynamical and chemical processes a considerable number of desired properties have been formulated in the literature over the last 3 to 4 decades. These include conservation of mass, monotonicity, positive definiteness, elimination of the wind-mass inconsistency problem, computational efficiency etc. Simple examp...

The number of prognostic tracers in climate and weather models is constantly increasing to accommodate modern microphysics parameterizations, more prognostic chemical species, etc. From a computational point of view the cost of the resolved-scale dynamics can easily be dominated by the cost of tracer transport hence efficient multi-tracer transport...

Numerical weather and climate modelling is under constant development. Semi-implicit semi-Lagrangian (SISL) models have proven to be numerically efficient in both short-range weather forecasts and climate models, due to the ability to use long time steps. Chemical/aerosol feedback mechanism are becoming more and more relevant in NWP as well as clim...

We discuss and evaluate the representation of at-mospheric chemistry in the global Community Atmosphere Model (CAM) version 4, the atmospheric component of the Community Earth System Model (CESM). We present a va-riety of configurations for the representation of tropospheric and stratospheric chemistry, wet removal, and online and of-fline meteorol...

Two new filtering/diffusion operators have been implemented in the Community Atmosphere Model finite-volume dynamical core (CAM-FV). First, a fourth-order divergence damping operator has been added to optionally replace the second-order version that has traditionally been used. This provides more scale selective dissipation of divergent modes that...

The Community Atmosphere Model (CAM) version 5 includes a spectral element dynamical core option from NCAR’s High-Order Method Modeling Environment. It is a continuous Galerkin spectral finite-element method designed for fully unstructured quadrilateral meshes. The current configurations in CAM are based on the cubed-sphere grid. The main motivatio...

In areas of heavy precipitation, condensed water species can add significant mass to an atmospheric column. This mass can create positive pressure anomalies of up to several hPa at the surface. This pressure is expected to force a divergent component in the low-level flow that may have an impact on the evolution of the precipitating system. In this...

It is the purpose of this paper to propose a standard test case suite for two-dimensional transport schemes on the sphere intended to be used for model development and facilitating scheme intercomparison. The test cases are designed to assess important aspects of accuracy in geophysical fluid dynamics such as numerical order of convergence, "minima...

We discuss and evaluate the representation of atmospheric chemistry in the global Community Atmosphere Model (CAM) version 4, the atmospheric component of the Community Earth System Model (CESM). We present a variety of configurations for the representation of tropospheric and stratospheric chemistry, wet removal, and online and offline meteorology...

The dynamical core of an atmospheric general circulation model is engineered to satisfy a delicate balance between numerical stability, computational cost, and an accurate representation of the equations of motion. It generally contains either explicitly added or inherent numerical diffusion mechanisms to control the buildup of energy or enstrophy...

The NCAR Community Climate System Model, version 4 (CCSM4), includes a new dynamical core option based on NCAR’s High-Order Method Modeling Environment (HOMME). HOMME is a petascale-capable high-order element-based conservative dynamical core developed on the cubed-sphere grid. Initial simulations have been completed in an aquaplanet configuration...

The flux-form incremental remapping transport scheme introduced by Dukowicz and Baumgardner [1] converts the transport problem into a remapping problem. This involves identifying overlap areas between quadrilateral flux-areas and regular square grid cells which is non-trivial and leads to some algorithm complexity. In the simpler swept area approac...

This chapter has twofold purpose. After a short introduction to the mass continuity equations in atmospheric models, desirable properties for mass transport schemes intended for meteorological applications are discussed in some detail. This includes a discussion on the complications caused by the non-linearity of most problems of interest that make...

This chapter discusses the development of discontinuous Galerkin (DG) schemes for the hyperbolic conservation laws relevant to atmospheric modeling. Two variants of the DG spatial discretization, the modal and nodal form, are considered for the one- and two-dimensional cases. The time integration relies on a second- or third-order explicit strong s...

A conservative semi-Lagrangian cell-integrated transport scheme (CSLAM) was recently introduced, which ensures global mass conservation and allows long timesteps, multi-tracer efficiency, and shape preservation through the use of reconstruction filtering. This method is fully two-dimensional so that it may be easily implemented on non-cartesian gri...

Part I: Equations of motion and some basic ideas on discretizations.- Pat II. Conservation laws, finite-volume methods, remapping techniques and spherical grids.- Part III. Some aspects of atmospheric dynamical cores

The Jablonowski test case is widely used for debugging and evaluating the numerical characteristics of global dynamical cores that describe the fluid dynamics component of Atmospheric General Circulation Models. The test is defined in terms of a steady-state solution to the equations of motion and an overlaid perturbation that triggers a baroclinic...

DART (www.image.ucar.edu/DAReS/DART) is a general purpose, freely available, ensemble Kalman filter, data assimilation system, which is being used to generate state-of-the-art, partially coupled, ocean-atmosphere re-analyses in support of the decadal predictions planned for the next IPCC report. The resulting gridded product is directly comparable...

A class of new benchmark deformational flow test cases for the two-dimensional horizontal linear transport problems on the sphere is proposed. The scalar field follows complex trajectories and undergoes severe deformation during the simulation; however, the flow reverses its course at half-time and the scalar field returns to its initial position a...

The Technical Note series provides an outlet for a variety of NCAR manuscripts that contribute in specialized ways to the body of scientific knowledge but which are not suitable for journal, monograph, or book publication. Reports in this series are issued by the NCAR Scientific Divisions; copies may be obtained on request from the Publications Off...

A conservative multi-tracer transport algorithm on the cubed-sphere based on the semi-Lagrangian approach (CSLAM) has been developed. The scheme relies on backward trajectories and the resulting upstream cells (polygons) are approximated with great-circle arcs. Biquadratic polynomial functions are used for approximating the density distribution in...

Recent developments in finite-volume methods provide the basis for new dynamical cores that conserve exactly integral invariants, globally as well as locally, and, especially, for the design of exact mass conserving tracer transport models. The new technologies are reviewed and the perspectives for the future are discussed.

A one-dimensional model of vertical transport in the tropical tropopause layer (TTL) is developed. The model uses vertical advection, a convective source, and a chemical sink to simulate the profiles of very short lived substances in the TTL. The model simulates evanescent profiles of short-lived hydrocarbon species observed by satellite and is als...

Land, ocean, and atmospheric models are often implemented on different spherical grids. As a conseqence coupling these model components requires state variables and fluxes to be regridded. For some variables, such as fluxes, it is paramount that the regridding algorithm is conservative (so that energy and water budget balances are maintained) and m...

The Data Assimilation Research Testbed (DART) is a community facility for ensemble data assimilation available from the Data Assimilation Research Section at the National Center for Atmospheric Research (NCAR). DART can assimilate a variety of in situ and remote sensing observations using several atmospheric general circulation models including bot...

We will describe recent high resolution Aqua planet simulation results from CAM/HOMME, a highly scalable cubed-sphere based atmospheric model that has been integrated into the Community Climate System Model (CCSM). Aqua planet simulations have no known "correct" answer, so we evaluate the simulations using the Williamson equivalent resolution model...

The Jablonowski-Williamson test case is a widely used test case for debugging and evaluating the accuracy of global dynamical cores. It is defined in terms of a steady state solution to the equations of motion and an overlaid perturbation that triggers a baroclinically unstable wave. The steady state initial condition is zonally symmetric that to s...