Willson, Justin L., Kevin A Reed, Christiane Jablonowski, James Kent, Peter H Lauritzen, Ramachandran Nair, Mark A Taylor, Paul A Ullrich, Colin M Zarzycki, David M Hall, Don Dazlich, Ross Heikes, Celal Konor, David A Randall, Thomas Dubos, Yann Meurdesoif, Xi Chen, and Lucas Harris, et al., April 2024: DCMIP2016: The tropical cyclone test case. Geoscientific Model Development, 17(7), DOI:10.5194/gmd-17-2493-20242493-2507. Abstract
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 (GCMs) with identical simplified physics parameterization packages that participated in DCMIP2016 are analyzed in this study at 50 km horizontal grid spacing, with five of these models also providing solutions at 25 km grid spacing. Evolution of minimum surface pressure (MSP) and maximum 1 km azimuthally averaged wind speed (MWS), the wind–pressure relationship, radial profiles of wind speed and surface pressure, and wind composites are presented for all participating GCMs at both horizontal grid spacings. While all TCs undergo a similar evolution process, some reach significantly higher intensities than others, ultimately impacting their horizontal and vertical structures. TCs simulated at 25 km grid spacings retain these differences but reach higher intensities and are more compact than their 50 km counterparts. These results indicate that dynamical core choice is an essential factor in GCM development, and future work should be conducted to explore how specific differences within the dynamical core affect TC behavior in GCMs.
The gnomonic cubed-sphere grid has excellent accuracy and uniformity, but the “kink” in the coordinates at the cube edges in the halo region can leave an imprint of the cube in the solution, and requires special edge handling. To reduce grid imprinting, we implement the novel “Duo-Grid” within the Geophysical Fluid Dynamics Laboratory's (GFDL) Finite-Volume Cubed-Sphere Dynamical Core (FV3). The Duo-Grid remaps a cube face's data from neighboring face from kinked to natural locations along great circle lines using 1D piecewise linear interpolation. A 2D interpolation algorithm is used to fill correct data at the eight corners of the cubed-sphere needed for FV3's 2D advection scheme. The Duo-Grid was tested in idealized tests using the 2D shallow water solver and the 3D hydrostatic and non-hydrostatic solvers. We found that error norms are greatly reduced and grid imprinting is practically eliminated when employing the Duo-Grid. These results indicate that FV3's accuracy and robustness have improved.
Chen, Xi, January 2021: The LMARS based shallow-water dynamical core on generic gnomonic cubed-sphere geometry. Journal of Advances in Modeling Earth Systems, 13(1), DOI:10.1029/2020MS002280. Abstract
The rapidly increasing computing powers allow global atmospheric simulations with aggressively high resolutions, challenging traditional model design principles. This study presents a Low Mach number Approximate Riemann Solver (LMARS) based unstaggered finite-volume model for solving the shallow-water equations on arbitrary gnomonic cubed-sphere grids. Using a novel reference line-based grid-generation process, it unifies the representation of arbitrary gnomonic cubed-sphere grid projections and permits high-efficiency 1D reconstruction in the halo regions. The numerical discretization also extends a widely used pressure gradient algorithm with the LMARS viscous term, thus improves the model's stability for various numerical applications. The solver demonstrates a broad range of organic diffusion control without any explicit filters, validated by a comprehensive set of test cases. Lastly, a newly introduced splash on the sphere test verifies the solver's desirable dispersion properties and consistent performance among different grid types. This study paves a solid foundation for a new generation of global circulation models with kilometer horizontal scales.
Harris, Lucas, Xi Chen, William M Putman, Linjiong Zhou, and Jan-Huey Chen, June 2021: A Scientific Description of the GFDL Finite-Volume Cubed-Sphere Dynamical Core, Princeton, NJ: NOAA Technical Memorandum OAR GFDL, 2021-001, DOI:10.25923/6nhs-5897 109pp.
Judt, Falko, Daniel Klocke, Rosimar Rios-Berrios, Benoit Vanniere, Florian Ziemen, Ludovic Auger, Joachim Biercamp, Christopher S Bretherton, Xi Chen, Peter Düben, Cathy Hohenegger, Marat Khairoutdinov, Chihiro Kodama, Luis Kornblueh, Shian-Jiann Lin, Masuo Nakano, Philipp Neumann, William M Putman, Niklas Röber, Malcolm J Roberts, Masaki Satoh, Ryosuke Shibuya, Bjorn Stevens, Pier Luigi Vidale, Nils Wedi, and Linjiong Zhou, June 2021: Tropical cyclones in global storm-resolving models. Journal of the Meteorological Society of Japan. Ser. II, 99(3), DOI:10.2151/jmsj.2021-029579-602. Abstract
Recent progress in computing and model development has initiated the era of global storm-resolving modeling, and with it the potential to transform weather and climate prediction. Within the general theme of vetting this new class of models, the present study evaluates nine global-storm resolving models in their ability to simulate tropical cyclones (TCs). Results indicate that, broadly speaking, the models produce realistic TCs and remove longstanding issues known from global models such as the deficiency in accurately simulating TC intensity. However, TCs are strongly affected by model formulation, and all models suffer from unique biases regarding the number of TCs, intensity, size, and structure. Some models simulated TCs better than others, but no single model was superior in every way. The overall results indicate that global storm-resolving models can open a new chapter in TC prediction, but they need to be improved to unleash their full potential.
This technical note explains updates to the GFDL Finite-Volume Cubed-Sphere Dynamical Core, abbreviated FV3 or FV[superscript 3], and the Split GFDL Microphysics. It does not repeat the contents of earlier documentation, especially publications. A list of publications and prior technical notes describing FV3 is available on the GFDL website.
We present the System for High‐resolution prediction on Earth‐to‐Local Domains (SHiELD), an atmosphere model developed by the Geophysical Fluid Dynamics Laboratory (GFDL) coupling the nonhydrostatic FV3 Dynamical Core to a physics suite originally taken from the Global Forecast System. SHiELD is designed to demonstrate new capabilities within its components, explore new model applications, and to answer scientific questions through these new functionalities. A variety of configurations are presented, including short‐to‐medium‐range and subseasonal‐to‐seasonal prediction, global‐to‐regional convective‐scale hurricane and contiguous U.S. precipitation forecasts, and global cloud‐resolving modeling. Advances within SHiELD can be seamlessly transitioned into other Unified Forecast System or FV3‐based models, including operational implementations of the Unified Forecast System. Continued development of SHiELD has shown improvement upon existing models. The flagship 13‐km SHiELD demonstrates steadily improved large‐scale prediction skill and precipitation prediction skill. SHiELD and the coarser‐resolution S‐SHiELD demonstrate a superior diurnal cycle compared to existing climate models; the latter also demonstrates 28 days of useful prediction skill for the Madden‐Julian Oscillation. The global‐to‐regional nested configurations T‐SHiELD (tropical Atlantic) and C‐SHiELD (contiguous United States) show significant improvement in hurricane structure from a new tracer advection scheme and promise for medium‐range prediction of convective storms.
This document describes the nonhydrostatic solver of the GFDL Finite-Volume Cubed-Sphere Dynamical Core, FV3. The nonhydrostatic solver works identically to the hydrostatic solver except for the need to solve for two new prognostic variables, the vertical velocity and geometric layer depth; and to use the full nonhydrostatic pressure in computing the pressure gradient force. In particular the Lagrangian dynamics described within L04 remains valid and all vertical processes (advection, wave propagation) remain implicit while all horizontal processes are explicit. This document assumes working knowledge of the hydrostatic discretization of FV3 described in LR96, LR97, L97, L04, PL07, and HL13. It is strongly recommended that anyone who wishes to understand the nonhydrostatic FV3 solver read and understand these documents first. Additional relevant material may be found in LPH17 and LH18. All of these documents may be found at www. gfdl.noaa.gov/fv3/fv3-documentation-and-references/.
We describe the baseline model configuration and simulation characteristics of the Geophysical Fluid Dynamics Laboratory (GFDL)'s Atmosphere Model version 4.1 (AM4.1), which builds on developments at GFDL over 2013–2018 for coupled carbon‐chemistry‐climate simulation as part of the sixth phase of the Coupled Model Intercomparison Project. In contrast with GFDL's AM4.0 development effort, which focused on physical and aerosol interactions and which is used as the atmospheric component of CM4.0, AM4.1 focuses on comprehensiveness of Earth system interactions. Key features of this model include doubled horizontal resolution of the atmosphere (~200 to ~100 km) with revised dynamics and physics from GFDL's previous‐generation AM3 atmospheric chemistry‐climate model. AM4.1 features improved representation of atmospheric chemical composition, including aerosol and aerosol precursor emissions, key land‐atmosphere interactions, comprehensive land‐atmosphere‐ocean cycling of dust and iron, and interactive ocean‐atmosphere cycling of reactive nitrogen. AM4.1 provides vast improvements in fidelity over AM3, captures most of AM4.0's baseline simulations characteristics, and notably improves on AM4.0 in the representation of aerosols over the Southern Ocean, India, and China—even with its interactive chemistry representation—and in its manifestation of sudden stratospheric warmings in the coldest months. Distributions of reactive nitrogen and sulfur species, carbon monoxide, and ozone are all substantially improved over AM3. Fidelity concerns include degradation of upper atmosphere equatorial winds and of aerosols in some regions.
We use the fvGFS model developed at the Geophysical Fluid Dynamics Laboratory (GFDL) to demonstrate the potential of the upcoming United States Next Generation Global Prediction System for hurricane prediction. The fvGFS retrospective forecasts initialized with the European Centre for Medium‐Range Weather Forecasts (ECMWF) data showed much‐improved track forecasts for the 2017 Atlantic hurricane season compared to the best performing ECMWF operational model. The fvGFS greatly improved the ECMWF's poor track forecast for Hurricane Maria (2017). For Hurricane Irma (2017), a well‐predicted case by the ECMWF model, the fvGFS produced even lower 5‐day track forecast errors. The fvGFS also showed better intensity prediction than both the United States and the ECMWF operational models, indicating the robustness of its numerical algorithms.
A new global model using the GFDL nonhydrostatic Finite-Volume Cubed-Sphere Dynamical Core (FV3) coupled to physical parameterizations from the National Centers for Environmental Prediction's Global Forecast System (NCEP/GFS) was built at GFDL, named fvGFS. The modern dynamical core, FV3, has been selected for National Oceanic and Atmospheric Administration’s Next Generation Global Prediction System (NGGPS) due to its accuracy, adaptability, and computational efficiency, which brings a great opportunity for the unification of weather and climate prediction systems.
The performance of tropical cyclone (TC) forecasts in the 13-km fvGFS is evaluated globally based on 363 daily cases of 10-day forecasts in 2015. Track and intensity errors of TCs in fvGFS are compared to those in the operational GFS. The fvGFS outperforms the GFS in TC intensity prediction for all basins. For TC track prediction, the fvGFS forecasts are substantially better over the northern Atlantic basin and the northern Pacific Ocean than the GFS forecasts. An updated version of the fvGFS with the GFDL 6-category cloud microphysics scheme is also investigated based on the same 363 cases. With this upgraded microphysics scheme, fvGFS shows much improvement in TC intensity prediction over the operational GFS. Besides track and intensity forecasts, the performance of TC genesis forecast is also compared between the fvGFS and operational GFS. In addition to evaluating the hit/false alarm ratios, a novel method is developed to investigate the lengths of TC genesis lead times in the forecasts. Both versions of fvGFS show higher hit ratios, lower false alarm ratios and longer genesis lead times than those of the GFS model in most of the TC basins.
Li, Cheng, and Xi Chen, February 2019: Simulating Nonhydrostatic Atmospheres on Planets (SNAP): Formulation, Validation, and Application to the Jovian Atmosphere. Astrophysical Journal Supplement Series, 240(2), DOI:10.3847/1538-4365/aafdaa. Abstract
A new nonhydrostatic and cloud-resolving atmospheric model is developed for studying moist convection and cloud formation in planetary atmospheres. It is built on top of the Athena++ framework, utilizing its static/adaptive mesh-refinement, parallelization, curvilinear geometry, and dynamic task scheduling. We extend the original hydrodynamic solver to vapors, clouds, and precipitation. Microphysics is formulated generically so that it can be applied to both Earth and Jovian planets. We implemented the Low Mach number Approximate Riemann Solver for simulating low-speed atmospheric flows in addition to the usual Roe and Harten–Lax–van Leer-Contact (HLLC) Riemann solvers. Coupled with a fifth-order weighted essentially nonoscillatory subgrid-reconstruction method, the sharpness of critical fields such as clouds is well-preserved, and no extra hyperviscosity or spatial filter is needed to stabilize the model. Unlike many atmospheric models, total energy is used as the prognostic variable of the thermodynamic equation. One significant advantage of using total energy as a prognostic variable is that the entropy production due to irreversible mixing processes can be properly captured. The model is designed to provide a unified framework for exploring planetary atmospheres across various conditions, both terrestrial and Jovian. First, a series of standard numerical tests for Earth's atmosphere is performed to demonstrate the performance and robustness of the new model. Second, simulation of an idealized Jovian atmosphere in radiative-convective equilibrium shows that (1) the temperature gradient is superadiabatic near the water condensation level because of the changing of the mean molecular weight, and (2) the mean profile of ammonia gas shows a depletion in the subcloud layer down to nearly 10 bars. Relevance to the recent Juno observations is discussed.
Understanding the root causes of forecast errors and occasional very poor forecasts is essential but difficult. In this paper we investigate the relative importance of initial conditions and model formulation for medium‐range errors in 500‐hPa geopotential height. The question is addressed by comparing forecasts produced with ECMWF‐IFS and NCEP‐GFS forecasting systems, and with the GFDL‐fvGFS model initialised with ECMWF and NCEP initial conditions. This gives two pairs of configurations that use the same initial conditions but different models, and one pair with the same model but different initial conditions. The first conclusion is that the initial conditions play the major role for differences between the configurations in terms of the average root‐mean‐square error for both northern and southern hemispheres as well as Europe and the contiguous U.S (CONUS), while the model dominates the systematic errors. A similar conclusion is also found by verifying precipitation over low latitudes and the CONUS. The day‐to‐day variations of 500‐hPa geopotential height scores are exemplified by one case of a forecast bust over Europe, where the error is found to be dominated by initial errors. The results are generalised by calculating correlations between errors integrated over Europe, CONUS and a region in southeastern Pacific respectively from the different configurations. For Europe and southeast Pacific, the correlations in the medium‐range are highest between the pairs that use the same initial conditions, while over CONUS it is for the pair with the same model. This suggests different mechanisms behind the day‐to‐day variability of the score for these regions. Over CONUS the link is made to the propagation of troughs over the Rockies, and the result suggests that the large differences in parameterisations of orographic drag between the models plays a role.
Surface layer (SL) variables [e.g., 2‐m temperature (T2) and 10‐m wind (U10)] are diagnosed by applying the flux‐profile relationships based on Monin‐Obukhov similarity theory to the lowest model height (LMH). This assumes that the LMH is in the SL, which is approximately the bottom 10% of the boundary layer, but atmospheric general circulation models rarely satisfy this in stable boundary layers (SBLs). To assess errors in the diagnostic variables due to the LMH solely linked to the diagnostic algorithm, offline tests of the flux‐profile relationships are performed with LMH from a few meters to 60 m for three SBL regimes: weakly stable, very stable, and transition stability regimes. The results show that T2 and U10 are underestimated by O(0.1–1 °C) and O(0.1–1 m s−1), respectively, if the LMH is higher than the SL height. The stronger the SL stability is, the larger the temperature biases are. The negative wind biases increase with the surface stress. Based on these findings, we analyze the impacts of the LMH on the climatologies of the diagnostic parameters in the GFDL AM4.0/LM4.0. The results show reduced negative biases in T2 and U10 by lowering the LMH. The decrease of the overall bias over land is mainly due to the sensitivity of the diagnostic method to the LMH in SBLs, as shown in the offline tests. The overall increase in T2 and U10 over the oceans results from the increase in the actual near‐surface temperature and wind rather than from the diagnostic method.
Stevens, Bjorn, Masaki Satoh, Ludovic Auger, Joachim Biercamp, Christopher S Bretherton, Xi Chen, Peter Düben, Falko Judt, Marat Khairoutdinov, Daniel Klocke, Chihiro Kodama, Luis Kornblueh, Shian-Jiann Lin, Philipp Neumann, William M Putman, Niklas Röber, Ryosuke Shibuya, Benoit Vanniere, Pier Luigi Vidale, Nils Wedi, and Linjiong Zhou, September 2019: DYAMOND: the DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains. Progress in Earth and Planetary Science, 6, 61, DOI:10.1186/s40645-019-0304-z. Abstract
A review of the experimental protocol and motivation for DYAMOND, the first intercomparison project of global storm-resolving models, is presented. Nine models submitted simulation output for a 40-day (1 August–10 September 2016) intercomparison period. Eight of these employed a tiling of the sphere that was uniformly less than 5 km. By resolving the transient dynamics of convective storms in the tropics, global storm-resolving models remove the need to parameterize tropical deep convection, providing a fundamentally more sound representation of the climate system and a more natural link to commensurately high-resolution data from satellite-borne sensors. The models and some basic characteristics of their output are described in more detail, as is the availability and planned use of this output for future scientific study. Tropically and zonally averaged energy budgets, precipitable water distributions, and precipitation from the model ensemble are evaluated, as is their representation of tropical cyclones and the predictability of column water vapor, the latter being important for tropical weather.
Zarzycki, Colin M., Christiane Jablonowski, James Kent, Peter H Lauritzen, Ramachandran Nair, Kevin A Reed, Paul A Ullrich, David M Hall, Don Dazlich, Ross Heikes, Celal Konor, David A Randall, Xi Chen, and Lucas Harris, et al., March 2019: DCMIP2016: the splitting supercell test case. Geoscientific Model Development, 12(3), DOI:10.5194/gmd-12-879-2019. Abstract
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 radius sphere with nominal resolutions ranging from 4km to 0.5km and is based on the work of Klemp et al. (2015). Models are initialized with an atmospheric environment conducive to supercell formation and forced with a small thermal perturbation. A simplified Kessler microphysics scheme is coupled to the dynamical core to represent moist processes. Reference solutions for DCMIP2016 models are presented. Storm evolution is broadly similar between models, although differences in final solution exist. These differences are hypothesized to result from different numerical discretizations, physics-dynamics coupling, and numerical diffusion. Intramodel solutions generally converge as models approach 0.5km resolution. These results can be used as a reference for future dynamical core evaluation, particularly with the development of non-hydrostatic global models intended to be used in convective-permitting and convective-allowing regimes.
The variable-resolution version of a Finite-Volume Cubed-Sphere Dynamical Core (FV3)-based global model improves the prediction of convective-scale features while maintaining skillful global forecasts.
The Geophysical Fluid Dynamics Laboratory (GFDL) has developed a new variable-resolution global model with the ability to represent convective-scale features that serves as a prototype of the Next Generation Global Prediction System (NGGPS). The goal of this prediction system is to maintain the skill in large-scale features while simultaneously improving the prediction skill of convectively-driven mesoscale phenomena. This paper demonstrates the new capability of this model in convective-scale prediction relative to the current operational Global Forecast System (GFS). This model uses the stretched-grid functionality of the Finite-Volume Cubed-Sphere Dynamical Core (FV3) to refine the global 13-km uniform-resolution model down to 4-km convection-permitting resolution over the Contiguous United States (CONUS), and implements the GFDL single-moment six-category cloud microphysics to improve the representation of moist processes.
Statistics gathered from two years of simulations by the GFS and select configurations of the FV3-based model are carefully examined. The variable-resolution FV3-based model is shown to possess global forecast skill comparable with that of the operational GFS while quantitatively improving skill and better representing the diurnal cycle within the high-resolution area compared to the uniform mesh simulations. Forecasts of the occurrence of extreme precipitation rates over the Southern Great Plains are also shown to improve with the variable-resolution model. Case studies are provided of a squall line and a hurricane to demonstrate the effectiveness of the variable-resolution model to simulate convective-scale phenomena.
Chen, Xi, Shian-Jiann Lin, and Lucas Harris, September 2018: Towards an unstaggered finite‐volume dynamical core with a fast Riemann solver: 1D linearized analysis of dissipation, dispersion, and noise control. Journal of Advances in Modeling Earth Systems, 10(9), DOI:10.1029/2018MS001361. Abstract
Many computational fluid dynamics codes use Riemann solvers on an unstaggered grid for finite volume methods, but this approach is computationally expensive compared to existing atmospheric dynamical cores equipped with hyper‐diffusion or other similar relatively simple diffusion forms. We present a simplified Low Mach number Approximate Riemann Solver (LMARS), made computationally efficient through assumptions appropriate for atmospheric flows: low Mach number, weak discontinuities, and locally‐uniform sound speed. This work will examine the dissipative and dispersive properties of LMARS using Von Neumann linearized analysis to the one‐dimensional linearized shallow water equations. We extend these analyses to higher‐order methods by numerically solving the Fourier‐transformed equations. It is found that the pros and cons due to grid staggering choices diminish with high‐order schemes.
The linearized analysis is limited to modal, smooth solutions using simple numerical schemes, and cannot analyze solutions with discontinuities. To address this problem, this work presents a new idealized test of a discontinuous wave packet, a single Fourier mode modulated by a discontinuous square‐wave. The experiments include studies of well‐resolved and (near) grid‐scale wave profiles, as well as the representation of discontinuous features and the results are validated against the Von Neumann analysis. We find the higher‐order LMARS produces much less numerical noise than do inviscid unstaggered and especially staggered schemes while retaining accuracy for better‐resolved modes.
In this two-part paper, a description is provided of a version of the AM4.0/LM4.0 atmosphere/land model that will serve as a base for a new set of climate and Earth system models (CM4 and ESM4) under development at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL). This version, with roughly 100km horizontal resolution and 33 levels in the vertical, contains an aerosol model that generates aerosol fields from emissions and a “light” chemistry mechanism designed to support the aerosol model but with prescribed ozone. In Part I, the quality of the simulation in AMIP (Atmospheric Model Intercomparison Project) mode – with prescribed sea surface temperatures (SSTs) and sea ice distribution – is described and compared with previous GFDL models and with the CMIP5 archive of AMIP simulations. The model's Cess sensitivity (response in the top-of-atmosphere radiative flux to uniform warming of SSTs) and effective radiative forcing are also presented. In Part II, the model formulation is described more fully and key sensitivities to aspects of the model formulation are discussed, along with the approach to model tuning.
In Part II of this two-part paper, documentation is provided of key aspects of a version of the AM4.0/LM4.0 atmosphere/land model that will serve as a base for a new set of climate and Earth system models (CM4 and ESM4) under development at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL). The quality of the simulation in AMIP (Atmospheric Model Intercomparison Project) mode has been provided in Part I. Part II provides documentation of key components and some sensitivities to choices of model formulation and values of parameters, highlighting the convection parameterization and orographic gravity wave drag. The approach taken to tune the model's clouds to observations is a particular focal point. Care is taken to describe the extent to which aerosol effective forcing and Cess sensitivity have been tuned through the model development process, both of which are relevant to the ability of the model to simulate the evolution of temperatures over the last century when coupled to an ocean model.
The modon, a pair of counter-rotating vortices propelling one another along a straight line, is an idealization of some observed large- and small-scale atmospheric and oceanic processes (e.g., twin cyclones), providing a challenging nonlinear test for fluid-dynamics solvers (known as “dynamical cores”). We present an easy-to-setup test of colliding modons suitable for both shallow-water and three-dimensional dynamical cores on the sphere. Two pairs of idealized modons are configured to collide, exchange vortices, and depart in opposite directions, repeating indefinitely in the absence of ambient rotation. This test is applicable to both hydrostatic and nonhydrostatic dynamical cores and particularly challenging for refined grids on the sphere, regardless of solution methodology or vertical coordinate.
We applied this test to three popular dynamical cores, used by three different general circulation models: the spectral element core of the Community Atmosphere Model, the Geophysical Fluid Dynamics Laboratory (GFDL) spectral core, and the GFDL finite-volume cubed-sphere core, FV3. Tests with a locally-refined grid and nonhydrostatic dynamics were also performed with FV3. All cores tested were able to capture the propagation, collision, and exchange of the modons, albeit the rate at which the modon was diffused varied between the three cores and showed a strong dependence on the strength of hyper-diffusion.
Ullrich, Paul A., Christiane Jablonowski, James Kent, Peter H Lauritzen, Ramachandran Nair, Kevin A Reed, Colin M Zarzycki, David M Hall, Don Dazlich, Ross Heikes, Celal Konor, David A Randall, Thomas Dubos, Yann Meurdesoif, Xi Chen, and Lucas Harris, et al., December 2017: DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models. Geoscientific Model Development, 10(12), DOI:10.5194/gmd-10-4477-2017. Abstract
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 having now evolved into a complex ecosystem of algorithms and computational strategies. In essence, no two dynamical cores are alike, and their individual successes suggest that no perfect model exists. To better understand modern dynamical cores, this paper aims to provide a comprehensive review of 11 non-hydrostatic dynamical cores, drawn from modeling centers and groups that participated in the 2016 Dynamical Core Model Intercomparison Project (DCMIP) workshop and summer school. This review includes a choice of model grid, variable placement, vertical coordinate, prognostic equations, temporal discretization, and the diffusion, stabilization, filters, and fixers employed by each system.
Chen, Xi, N Andronova, B van Leer, Joyce Penner, J P Boyd, Christiane Jablonowski, and Shian-Jiann Lin, July 2013: A control-volume model of the compressible Euler equations with a vertical Lagrangian Coordinate. Monthly Weather Review, 141(7), DOI:10.1175/MWR-D-12-00129.1. Abstract
Accurate and stable numerical discretization of the equations for the non-hydrostatic atmosphere is required, for example, to resolve interactions between clouds and aerosols in the atmosphere. Here we present a modification of the hydrostatic control-volume approach for solving the non-hydrostatic Euler equations with a Lagrangian vertical coordinate. A scheme with low numerical diffusion is achieved by introducing a low Mach number approximate Riemann solver (LMARS) for atmospheric flows. LMARS is a flexible way to ensure stability for finite volume numerical schemes in both Eulerian and vertical Lagrangian configurations. This new approach is validated on test cases using a 2D (x-z) configuration.
