Welcome to CGD

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Summary of achievements

My science work is centered around numerical methods for dynamical cores, that is (roughly speaking), algorithms that approximate the solution to the adiabatic frictionless equations of motion for the atmosphere on resolved scales. For climate models and chemical transport models it is important that local and global balances dictated by physical principles are maintained in the numerical discretizations, for example, in the absence of sources and sinks mass should be conserved both locally and globally. At the same time the algorithm should be efficient on massively parallel supercomputers. Achieving a good balance between accuracy and efficiency is the overall goal of my research.

In an attempt to gather the global dynamical core research community I lead the 2008 NCAR ASP summer colloquium (http://www.cgd.ucar.edu/cms/pel/colloquium.html). The co-organizers were Dr. Christiane Jablonowski (University of Michigan), Dr. Mark Taylor (Sandia National Laboratories) and Dr. Ramachandran D. Nair (IMAGe, NCAR). The colloquium surveyed the latest developments in numerical methods for Atmospheric General Circulation Models and included an unprecedented student-run dynamical core inter-comparison project. The test case suite used for the inter-comparison was formulated by the colloquium organizers and 12 modeling groups (both US-based and international) participated in the colloquium by porting their model to NCAR computers, setting them up for the idealized test case suite formulated by the organizers and providing expert mentors to help the students run their models during the colloquium. The data produced by the students is currently being analyzed by the organizers. To facilitate the inter-comparison of the many models and test case data, meta-data describing the models and test case settings was put together and made available through the Earth System Grid portal by the Curator project (http://dycore.ucar.edu/browse/viewProject.htm?projectId=6ab23d33-b8c0-4317-b1ee-84ce236739b0). Also, the organizers are editing a book based on contributions from the colloquium lecturers that is going to be published in the Springer series Lecture Notes in Computational Science and Engineering.

Land, ocean and atmosphere components of coupled climate system models are often implemented on different spherical grids, individually designed to enhance the accuracy or capture features unique to their respective settings. Historically, the regular latitude-longitude (RLL) grid has been the predominant choice for global atmospheric models, but problems associated with the polar singularity persist, and hence this grid is not well-suited for highly scalable atmospheric models. Much interest in recent years has been instead directed towards the development of atmospheric solvers on more isotropic spherical grids. For example, the so-called cubed sphere grid, which divides the polar singularities among eight weaker singularities located at the corners of a cube, and is otherwise highly scalable on parallel architectures. For the land component, however, the RLL grid does not pose polar singularity problems as is the case for the atmosphere (with the current complexity of land models). Neither does the land model seem to be susceptible to scalability problems since most of the computation is in vertical columns rather than in the horizontal. Hence for the foreseeable future the RLL grid seems to be a viable and convenient grid for land model components. An intricate problem introduced by defining the model components on different spherical grids is that the exchange of information between the grids is non-trivial and requires a regridding algorithm. In a coupled climate system model it is paramount that the regridding process is not a spurious source or sink for first-order moment variables such as mass. Also, to prevent the generation of unphysical negative and/or large values, the regridding must also be shape-preserving/monotone for mixing-ratio related variables. Regridding with these constraints, conservation and monotonicity, is a non-trivial problem if higher than first order accuracy is desired. During the summer of 2008 I supervised the SIParCS (Summer Internships in Parallel Computational Science) student Paul Ullrich with whom I developed a new remapping algorithm to conservatively regrid scalars between the cubed-sphere and regular RLL grids.

Publications

Paul A. Ullrich, Peter H. Lauritzen and Christiane Jablonowski, 2009: Geometrically Exact Conservative Remapping (GECoRe): Regular latitude-longitude and cubed-sphere grids. Mon. Wea. Rev., doi:10.1175/2008MWR2817.1

Figure 1: High resolution figure

Abstract: 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 monotone (to prevent unphysical values).

For global applications the cubed-sphere grids are gaining popularity in the atmospheric community whereas, for example, the land modeling groups are mostly using the regular latitude-longitude grid. Most existing regridding schemes fail to take advantage of geometrical symmetries between these grids and hence accuracy of the calculations can be lost. Hence, a new geometrically exact conservative remapping scheme (GECoRe) with a monotone option is proposed for remapping between regular latitude-longitude and gnomonic cubed sphere grids. GECoRe is compared against existing remapping schemes published in the meteorological literature. We conclude that the geometrically exact scheme significantly improves the accuracy of the resulting remapping in idealized test cases.

Figure caption: Spatial distribution of the error (×10^-2) for the remapping of Y ¹⁶ ₃₂ from a coarse-resolution ABP grid (N_c = 40) to a RLL grid (N_λ = 128, N_θ = 64) using (a) GECoRe, (b) SCRIP and (c) CaRS with piecewise parabolic (third-order) reconstructions.p>

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Gettelman, A., P.H. Lauritzen, M. Park and J.E. Kay. 2009: Processes Regulating Short Lived Species in the Tropical Tropopause Layer. Journal of Geophysical Research, doi:10.1029/2009JD011785.

Figure 2: High resolution figure

Abstract: 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 (VSLS) in the TTL. The model simulates evanescent profiles of short lived hydrocarbon species observed by satellite, and is also used to simulate short lived bromine species. Tracers with chemical lifetimes of 25 days or longer have significant concentrations in the stratosphere and vertical advection is critical. Convection is important up to its peak altitude, nearly 19km. Convection dominates the distribution of species with lifetimes less than 25 days. The annual cycle of species with lifetimes longer than 25 days is governed primarily by the variations of vertical velocity, not convection. This is particularly true for carbon monoxide, where a seasonal cycle in the lower stratosphere of the right phase is produced without variations in tropospheric emissions. An analysis of critical short lived bromine species (CH2Br2 and CHBr3) indicates that substantial amounts of these tracers may get advected into the lower stratosphere as source gases at 18km, and are estimated to contribute 2.8 pptv (1.1{4.1) to stratospheric bromine.

Figure caption: ACE tropical (20°S-20°N) average mixing ratios for 2004-2006 by season for (A) CO, (B) C₂H₆, (C) C₂H₂.

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Machenhauer, B., E. Kaas and P.H. Lauritzen. 2009: Finite-Volume Methods in Meteorology. Journal of Geophysical Research, doi:10.1016/S1570-8659(08)00201-9.

Figure 3: High resolution figure

Abstract: 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.

Figure caption: Squared modulus of the amplification factor as a function of α for the (a) 2Δx, (b) 3Δx, (c) 4Δx, and (d) 5Δ!x waves. Red and green lines are for the DCISL scheme using PPM2 and piecewise constant subgrid-cell representation, respectively. For comparison, the squared modulus of the amplification factor for the traditional semi-Lagrangian scheme based on cubic Lagrange interpolation (blue line) is shown as well.