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Ross Heikes and David A. Randall

Abstract

The finite-difference scheme for the Laplace and flux-divergence operators described in the companion paper (Part I) is consistent when applied on a grid consisting of perfect hexagons. The authors describe a necessary and sufficient condition for this finite-difference scheme to be consistent when applied on a grid consisting of imperfect hexagons and pentagons, and present an algorithm for generating a spherical geodesic grid on a sphere that guarantees that this condition is satisfied. Also, the authors qualitatively describe the error associated with the operators and estimate their order of accuracy when applied on the new grid.

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Ross Heikes and David A. Randall

Abstract

The streamfunction-velocity potential form of shallow-water equations, implemented on a spherical geodesic grid, offers an attractive solution to many of the problems associated with fluid-flow simulations in a spherical geometry. Here construction of a new type of spherical geodesic grid is outlined, and discretization of the equations is explained. The model is subjected to the NCAR suite of seven test cases for shallow-water models.

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Ross Gunn and Paul A. Allee
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A. N. Ross, A. M. Tompkins, and D. J. Parker

Abstract

Gravity-current models have been used for many years to describe the cold pools of low-level air that are generated by cumulonimbus precipitation. More recently, it has been realized that surface fluxes of heat and water vapor can be important in modifying these flows, through turbulent mixing of buoyancy by convection, and through direct modification of the cold pool buoyancy. In this paper, simple models describing the role of surface fluxes in depleting the negative buoyancy of a gravity current and the consequences of this for the flow dynamics are discussed.

It is pointed out that the depletion of cold pool buoyancy by surface fluxes is analogous to the depletion of buoyancy in a turbidity current through particle sedimentation, and in one regime of parameter values the analogy is exact. This analogy allows one to use simple flow models that have been tested extensively against laboratory experiments on turbidity currents. A simple “box model” and a more sophisticated shallow water model are each developed. It is shown how these models can give relatively simple expressions for cold pool “runout length” and buoyancy distributions. These runout lengths compare well with maximum cold pool sizes previously observed in cloud-resolving model simulations of unorganized tropical deep convection.

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Allan Frei, Ross Brown, James A. Miller, and David A. Robinson

Abstract

Eighteen global atmospheric general circulation models (AGCMs) participating in the second phase of the Atmospheric Model Intercomparison Project (AMIP-2) are evaluated for their ability to simulate the observed spatial and temporal variability in snow mass, or water equivalent (SWE), over North America during the AMIP-2 period (1979–95). The evaluation is based on a new gridded SWE dataset developed from objective analysis of daily snow depth observations from Canada and the United States with snow density estimated from a simple snowpack model. Most AMIP-2 models simulate the seasonal timing and the relative spatial patterns of continental-scale SWE fairly well. However, there is a tendency to overestimate the rate of ablation during spring, and significant between-model variability is found in every aspect of the simulations, and at every spatial scale analyzed. For example, on the continental scale, the peak monthly SWE integrated over the North American continent in AMIP-2 models varies between ±50% of the observed value of ∼1500 km3. The volume of water in the snowpack, and the magnitudes of model errors, are significant in comparison to major fluxes in the continental water balance. It also appears that the median result from the suite of models tends to do a better job of estimating climatological mean features than any individual model. Year-to-year variations in large-scale SWE are only weakly correlated to observed variations, indicating that sea surface temperatures (specified from observations as boundary conditions) do not drive interannual variations of SWE in these models. These results have implications for simulations of the large-scale hydrologic cycle and for climate change impact assessments.

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Ross P. Heikes, David A. Randall, and Celal S. Konor

Abstract

This paper discusses the generation of icosahedral hexagonal–pentagonal grids, optimization of the grids, how optimization affects the accuracy of finite-difference Laplacian, Jacobian, and divergence operators, and a parallel multigrid solver that can be used to solve Poisson equations on the grids. Three different grid optimization methods are compared through an error convergence analysis. The optimization process increases the accuracy of the operators. Optimized grids up to 1-km grid spacing over the earth have been created. The accuracy, performance, and scalability of the multigrid solver are demonstrated.

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Robert S. Ross, T. N. Krishnamurti, S. Pattnaik, and A. Simon

Abstract

This paper provides an understanding of essential differences between developing and nondeveloping African easterly waves, which was a major goal of NAMMA, NASA’s field program in the eastern Atlantic, which functioned as an extension of the African Monsoon Multidisciplinary Analysis (AMMA) program during 2006.

Three NAMMA waves are studied in detail using FNL analysis: NAMMA wave 2, which developed into Tropical Storm Debby; NAMMA wave 7, which developed into Hurricane Helene; and NAMMA wave 4, which did not develop within the NAMMA domain. Diagnostic calculations are performed on the analyzed fields using energy transformation equations and the isentropic potential vorticity equation.

The results show that the two developing waves possess clear and robust positive barotropic energy conversion in conjunction with positive diabatic heating that includes a singular burst of heating at a particular time in the wave’s history. This positive barotropic energy conversion is facilitated in waves that have a northeast–southwest tilt to the trough axis and a wind maximum to the west of this axis. The nondeveloping wave is found to have the same singular burst of diabatic heating at one point in its history, but development of the wave does not occur due to negative barotropic energy conversion. Such conversion is facilitated by a northwest–southeast tilt to the trough axis and a wind maximum to the east of this axis.

The conclusions about wave development and nondevelopment formulated in this research are viewed as important and significant, but they require additional testing with detailed observational- and numerical-based studies.

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Todd D. Ringler, Ross P. Heikes, and David A. Randall

Abstract

This paper documents the development and testing of a new type of atmospheric dynamical core. The model solves the vorticity and divergence equations in place of the momentum equation. The model is discretized in the horizontal using a geodesic grid that is nearly uniform over the entire globe. The geodesic grid is formed by recursively bisecting the triangular faces of a regular icosahedron and projecting those new vertices onto the surface of the sphere. All of the analytic horizontal operators are reduced to line integrals, which are numerically evaluated with second-order accuracy. In the vertical direction the model can use a variety of coordinate systems, including a generalized sigma coordinate that is attached to the top of the boundary layer. Terms related to gravity wave propagation are isolated and an efficient semi-implicit time-stepping scheme is implemented. Since this model combines many of the positive attributes of both spectral models and conventional finite-difference models into a single dynamical core, it represents a distinctively new approach to modeling the atmosphere’s general circulation.

The model is tested using the idealized forcing proposed by Held and Suarez. Results are presented for simulations using 2562 polygons (approximately 4.5° × 4.5°) and using 10 242 polygons (approximately 2.25° × 2.25°). The results are compared to those obtained with spectral model simulations truncated at T30 and T63. In terms of first and second moments of state variables such as the zonal wind, meridional wind, and temperature, the geodesic grid model results using 2562 polygons are comparable to those of a spectral model truncated at slightly less than T30, while a simulation with 10 242 polygons is comparable to a spectral model simulation truncated at slightly less than T63.

In order to further demonstrate the viability of this modeling approach, preliminary results obtained from a full-physics general circulation model that uses this dynamical core are presented. The dominant features of the DJF climate are captured in the full-physics simulation.

In terms of computational efficiency, the geodesic grid model is somewhat slower than the spectral model used for comparison. Model timings completed on an SGI Origin 2000 indicate that the geodesic grid model with 10 242 polygons is 20% slower than the spectral model truncated at T63. The geodesic grid model is more competitive at higher resolution than at lower resolution, so further optimization and future trends toward higher resolution should benefit the geodesic grid model.

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Mary McRae, Ross A. Lee, Scott Steinschneider, and Frank Galgano
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Mary McRae, Ross A. Lee, Scott Steinschneider, and Frank Galgano

Abstract

Increases in maximum and minimum air temperatures resulting from anthropogenic climate change will present challenges to aircraft performance. Elevated density altitude (DA) reduces aircraft and engine performance and has a direct impact on operational capabilities. The frequency of higher DA will increase with the combination of higher air temperatures and higher dewpoint temperatures. The inclusion of dewpoint temperature in DA projections will become increasingly critical as minimum air temperatures rise. High DA impacts aircraft performance in the following ways: reduction in power because the engine takes in less air; reduction in thrust because a propeller is less efficient in less dense air; reduction in lift because less dense air exerts less force on the airfoils. For fixed-wing aircraft, the performance impacts include decreased maximum takeoff weight and increased true airspeed, which results in longer takeoff and landing distance. For rotary-wing aircraft, the performance impacts include reduced power margin, reduced maximum gross weight, reduced hover ceiling, and reduced rate of climb. In this research, downscaled and bias-corrected maximum and minimum air temperatures for future time periods are collected and analyzed for a selected site: Little Rock Air Force Base, Arkansas. Impacts corresponding to DA thresholds are identified and integrated into risk probability matrices enabling quantifiable comparisons. As the magnitude and frequency of high DA occurrences are projected to increase as a result of climate change, it is imperative for military mission planners and acquisition officers to comprehend and utilize these projections in their decision-making processes.

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