Christiane Jablonowski

The effect of horizontal resolution on simulation quality in the Community Atmospheric Model, CAM5.1

We present an analysis of version 5.1 of the Community Atmospheric Model (CAM5.1) at a high horizontal resolution. Intercomparison of this global model at approximately 0.25°, 1°, and 2° is presented for extreme daily precipitation as well as for a suite of seasonal mean fields. In general, extreme precipitation amounts are larger in high resolution than in lower-resolution configurations. In many but not all locations and/or seasons, extreme daily precipitation rates in the high-resolution configuration are higher and more realistic. The high-resolution configuration produces tropical cyclones up to category 5 on the Saffir-Simpson scale and a comparison to observations reveals both realistic and unrealistic model behavior. In the absence of extensive model tuning at high resolution, simulation of many of the mean fields analyzed in this study is degraded compared to the tuned lower-resolution public released version of the model.

A Comparison of Two Shallow-Water Models with Nonconforming Adaptive Grids

Abstract In an effort to study the applicability of adaptive mesh refinement (AMR) techniques to atmospheric models, an interpolation-based spectral element shallow-water model on a cubed-sphere grid is compared to a block-structured finite-volume method in latitude–longitude geometry. Both models utilize a nonconforming adaptation approach that doubles the resolution at fine–coarse mesh interfaces. The underlying AMR libraries are quad-tree based and ensure that neighboring regions can only differ by one refinement level. The models are compared via selected test cases from a standard test suite for the shallow-water equations, and via a barotropic instability test. These tests comprise the passive advection of a cosine bell and slotted cylinder, a steady-state geostrophic flow, a flow over an idealized mountain, a Rossby–Haurwitz wave, and the evolution of a growing barotropic wave. Both static and dynamics adaptations are evaluated, which reveal the strengths and weaknesses of the AMR techniques. Overa...

Hurricanes and Climate: The U.S. CLIVAR Working Group on Hurricanes

AbstractWhile a quantitative climate theory of tropical cyclone formation remains elusive, considerable progress has been made recently in our ability to simulate tropical cyclone climatologies and to understand the relationship between climate and tropical cyclone formation. Climate models are now able to simulate a realistic rate of global tropical cyclone formation, although simulation of the Atlantic tropical cyclone climatology remains challenging unless horizontal resolutions finer than 50 km are employed. This article summarizes published research from the idealized experiments of the Hurricane Working Group of U.S. Climate and Ocean: Variability, Predictability and Change (CLIVAR). This work, combined with results from other model simulations, has strengthened relationships between tropical cyclone formation rates and climate variables such as midtropospheric vertical velocity, with decreased climatological vertical velocities leading to decreased tropical cyclone formation. Systematic differences...

The Pros and Cons of Diffusion, Filters and Fixers in Atmospheric General Circulation Models

All atmospheric General Circulation Models (GCMs) need some form of dissipation, either explicitly specified or inherent in the chosen numerical schemes for the spatial and temporal discretizations. This dissipation may serve many purposes, including cleaning up numerical noise generated by dispersion errors or computational modes, and the Gibbs ringing in spectral models. Damping processes might also be used to crudely represent subgrid Reynolds stresses, eliminate undesirable noise due to poor initialization or grid-scale forcing from the physics parameterizations, cover up weak computational stability, damp tracer variance, and prevent the accumulation of potential enstrophy or energy at the smallest grid scales. This chapter critically reviews the wide selection of dissipative processes in GCMs. They are the explicitly added diffusion and hyper-diffusion mechanisms, divergence damping, vorticity damping, external mode damping, sponge layers, spatial and temporal filters, inherent diffusion properties of the numerical schemes, and a posteriori fixers used to restore lost conservation properties. All theoretical considerations are supported by many practical examples from a wide selection of GCMs. The examples utilize idealized test cases to isolate causes and effects, and thereby highlight the pros and cons of the diffusion, filters and fixers in GCMs.

Moving Vortices on the Sphere: A Test Case for Horizontal Advection Problems

A new two-dimensional advection test on the surface of the sphere is proposed. The test combines a solid-body rotation and a deformational flow field to form moving vortices over the surface of the sphere. The resulting time-dependent deforming vortex centers are located on diametrically opposite sides of the sphere and move along a predetermined great circle trajectory. The horizontal wind field is deformational and nondivergent, and the analytic solution is known at any time. During one revolution around the sphere the initially smooth transported scalar develops strong gradients. Such an approach is therefore more challenging than existing advection test cases on the sphere. To demonstrate the effectiveness and versatility of the proposed test, three different advection schemes are employed, such as a discontinuous Galerkin method on a cubed-sphere mesh, a classical semi-Lagrangian method, and a finite-volume algorithm with adaptive mesh refinement (AMR) on a regular latitude–longitude grid. The numerical results are compared with the analytic solution for different flow orientation angles on the sphere.

Block-Structured Adaptive Grids on the Sphere: Advection Experiments

Abstract A spherical 2D adaptive mesh refinement (AMR) technique is applied to the so-called Lin–Rood advection algorithm, which is built upon a conservative and oscillation-free finite-volume discretization in flux form. The AMR design is based on two modules: a block-structured data layout and a spherical AMR grid library for parallel computer architectures. The latter defines and manages the adaptive blocks in spherical geometry, provides user interfaces for interpolation routines, and supports the communication and load-balancing aspects for parallel applications. The adaptive grid simulations are guided by user-defined adaptation criteria. Both statically and dynamically adaptive setups that start from a regular block-structured latitude–longitude grid are supported. All blocks are logically rectangular, self-similar, and independent data units that are split into four in the event of refinement requests, thereby doubling the horizontal resolution. Grid coarsenings reverse this refinement principle. ...

High-order finite-volume methods for the shallow-water equations on the sphere

This paper presents a third-order and fourth-order finite-volume method for solving the shallow-water equations on a non-orthogonal equiangular cubed-sphere grid. Such a grid is built upon an inflated cube placed inside a sphere and provides an almost uniform grid point distribution. The numerical schemes are based on a high-order variant of the Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) pioneered by van Leer. In each cell the reconstructed left and right states are either obtained via a dimension-split piecewise-parabolic method or a piecewise-cubic reconstruction. The reconstructed states then serve as input to an approximate Riemann solver that determines the numerical fluxes at two Gaussian quadrature points along the cell boundary. The use of multiple quadrature points renders the resulting flux high-order. Three types of approximate Riemann solvers are compared, including the widely used solver of Rusanov, the solver of Roe and the new AUSM^+-up solver of Liou that has been designed for low-Mach number flows. Spatial discretizations are paired with either a third-order or fourth-order total-variation-diminishing Runge-Kutta timestepping scheme to match the order of the spatial discretization. The numerical schemes are evaluated with several standard shallow-water test cases that emphasize accuracy and conservation properties. These tests show that the AUSM^+-up flux provides the best overall accuracy, followed closely by the Roe solver. The Rusanov flux, with its simplicity, provides significantly larger errors by comparison. A brief discussion on extending the method to arbitrary order-of-accuracy is included.

Aquaplanet Experiments Using CAM’s Variable-Resolution Dynamical Core

AbstractA variable-resolution option has been added within the spectral element (SE) dynamical core of the U.S. Department of Energy (DOE)–NCAR Community Atmosphere Model (CAM). CAM-SE allows for static refinement via conforming quadrilateral meshes on the cubed sphere. This paper investigates the effect of mesh refinement in a climate model by running variable-resolution (var-res) simulations on an aquaplanet. The variable-resolution grid is a 2° (~222 km) grid with a refined patch of 0.25° (~28 km) resolution centered at the equator. Climatology statistics from these simulations are compared to globally uniform runs of 2° and 0.25°.A significant resolution dependence exists when using the CAM version 4 (CAM4) subgrid physical parameterization package across scales. Global cloud fraction decreases and equatorial precipitation increases with finer horizontal resolution, resulting in drastically different climates between the uniform grid runs and a physics-induced grid imprinting in the var-res simulation...

Operator-Split Runge–Kutta–Rosenbrock Methods for Nonhydrostatic Atmospheric Models

This paper presents a new approach for discretizing the nonhydrostatic Euler equations in Cartesian geometry using an operator-split time-stepping strategy and unstaggered upwind finite-volume model formulation. Following the method of lines, a spatial discretization of the governing equations leads to a set of coupled nonlinear ordinary differential equations. In general, explicit time-stepping methods cannot be applied directly to these equations because the large aspect ratio between the horizontal and vertical grid spacing leads to a stringent restriction on the time step to maintain numerical stability. Instead, an A-stable linearly implicit Rosenbrock method for evolving the vertical components of the equations coupled to atraditionalexplicitRunge‐Kutta formulainthehorizontalisproposed.Uptothird-ordertemporalaccuracy is achieved by carefully interleaving the explicit and linearly implicit steps. The time step for the resulting Runge‐Kutta‐Rosenbrock‐type semi-implicit method is then restricted only by the grid spacing and wave speed in the horizontal. The high-order finite-volume model is tested against a series of atmospheric flow problems to verify accuracy and consistency. The results of these tests reveal that this method is accurate, stable, and applicable to a wide range of atmospheric flows and scales.

A multidecadal simulation of Atlantic tropical cyclones using a variable‐resolution global atmospheric general circulation model

Using a variable-resolution option within the National Center for Atmospheric Research/Department of Energy Community Atmosphere Model (CAM) Spectral Element (SE) global model, a refined nest at 0.25° (∼28 km) horizontal resolution located over the North Atlantic is embedded within a global 1° (∼111 km) grid. The grid is designed such that fine grid cells are located where tropical cyclones (TCs) are observed to occur during the Atlantic TC season (June–November). Two simulations are compared, one with refinement and one control case with no refinement (globally uniform 1° grid). Both simulations are integrated for 23 years using Atmospheric Model Intercomparison Protocols. TCs are tracked using an objective detection algorithm. The variable-resolution simulation produces significantly more TCs than the unrefined simulation. Storms that do form in the refined nest are much more intense, with multiple storms strengthening to Saffir-Simpson category 3 intensity or higher. Both count and spatial distribution of TC genesis and tracks in the variable-resolution simulation are well matched to observations and represent significant improvements over the unrefined simulation. Some degree of interannual skill is noted, with the variable-resolution grid able to reproduce the observed connection between Atlantic TCs and the El Nino-Southern Oscillation (ENSO). It is shown that Genesis Potential Index (GPI) is well matched between the refined and unrefined simulations, implying that the introduction of variable-resolution does not affect the synoptic environment. Potential “upscale” effects are noted in the variable-resolution simulation, suggesting stronger TCs in refined nests may play a role in meridional transport of momentum, heat, and moisture.