# Seminars (AMM)

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Event When Speaker Title Presentation Material
AMMW01 22nd August 2012
13:30 to 14:30
M Piggott Modelling geophysical fluid dynamics with anisotropic adaptive mesh methods
Many geophysical fluid dynamics problems include large variations in spatial scales that are important to resolve in a numerical simulation. An important example being the global ocean where dynamics at spatial scales of thousands of kms has strong two-way coupling with processes occurring at the km, and sub-km, scale, e.g. boundary layers, eddies and buoyancy driven flows interacting with bathymetry. Adaptive and unstructured mesh methods represent a possible means to simulate these multi-scale systems efficiently. In addition, smaller scale processes often have high aspect ratios and hence anisotropic mesh methods should be considered. In this talk our work applying anisotropic adaptive methods to geophysical fluid dynamics problems will be reviewed. A series of recent applications will also be presented.
AMMW01 22nd August 2012
14:30 to 15:00
J Steppeler Variable resolution and uniform second and third Order approximation order
Approximations on polygonal grids, such as cube sphere or icosahedral require a slightly irregular grid, as for high resolution no uniform polygonal cover by cells is possible. For variable resolution sudden refinement is considered not possible by some authors and a gradual change of resolution is preferred,such as with the new MPAS model of NCAR. It will be shown that such problems can be traced back to a decrease of approximation order to 1 in points where the resolution is irregular. Examples will be given to show that a jump of resolution is possible without problems when care is taken that in such points an approximation order 2 or 3 is maintained.
AMMW01 22nd August 2012
15:30 to 16:30
Development of the Nonhydrostatic Unified Model of the Atmosphere (NUMA): a unified model for both local-area modeling and global modeling
In this talk I will give an overview of the Nonhydrostatic Unified Model of the Atmosphere (NUMA). NUMA solves the fully compressible nonhydrostatic equations with the goal to have it unified across various fronts including: applications (local-area and global modeling); numerics (using both continuous and discontinuous Galerkin methods); time-integration (explicit and implicit-explicit methods); iterative solvers and preconditioners (using a suite of these); grid generation (using both conforming and non-conforming grids); and finally, parallelization (using both CPU and GPU based parallelization). In this talk, we will describe what we mean by each of these components and will report on the status of each of these components. The work that we shall describe will set the stage for the work we wish to carry out during the stay of my group at the Newton Institute.
AMMW01 22nd August 2012
16:30 to 17:00
M Taylor Variable resolution experiments using CAM's spectral finite element dynamical core
Much recent work in the Community Earth System Model (CESM) and its atmosphere component (CAM) has been devoted to developing higher resolution configurations, motivating new dynamical cores which can use unstructured quasi-isotropic grids. These dynamical cores also allow for variable resolution configurations in CAM, but making use of variable resolution (adaptive or statically refined grids) is difficult due to the strong resolution sensitivity of CAM's many subgrid physical parameterizations.

Here we will describe our work with statically refined grids in CAM, using CAM's spectral finite element dynamical core. This work is supporting the development of a model/observation "test bed". Test-beds combine models, observations and uncertainty quantification methodologies in order to evaluate existing models, quickly develop and test new parameterizations and constrain parameters with observations. It is hoped that variable resolution can provide a 10-100 times more efficient way to calibrate and evaluate high-resolution configurations of CAM. Our initial focus is on central U.S. precipitation, using a global 14km grid and a variable resolution grid with 14km resolution over the central U.S., transitioning to 110km over most of the globe. For both configurations, we will present computational performance and compare precipitation related diagnostics.
AMMW01 23rd August 2012
09:00 to 10:00
In my 2006 monograph on Adaptive Atmospheric Modeling the last section titled "Roadmap for the next five years" outlines several aspects of numerical methods for multi-scale phenomena in the atmosphere. Now, more than five years later, it is time to review a few of the issues raised in 2006. As one would expect, the grand solution to adaptive multi-scale modeling has not been found so far, and some solutions have generated new questions. But a lot has been achieved since 2006 and it is interesting to see, which directions have been taken. I will cover the aspects of consistent numerical methods, refinement criteria and strategies, applications and efficiency of adaptive methods in atmosphere and ocean applications.
AMMW01 23rd August 2012
10:00 to 10:30
A highly adaptive three dimensional hybrid vortex method for inviscid flows
Motivated by outstanding problems surrounding vortex stretching, a new numerical method to solve the inviscid Euler equations for a three-dimensional, incompressible fluid is presented. Special emphasis on spatial adaptivity is given to resolve as broad a range of scales as possible in a completely self-similar fashion. We present a hybrid vortex method whereby we discretise the vorticity in Lagrangian filaments and perform an inversion to compute velocity on an adapted finite-volume grid. This allows for a two-fold adaptivity strategy. First, although naturally spatially adaptive by definition, the vorticity filaments undergo renoding'. We redistribute nodes along the filament to concentrate their density in regions of high curvature. Secondly the Eulerian mesh is adapted to follow high strain by increasing resolution based on local filament dimensions. These features allow vortex stretching and folding to be resolved in a completely automatic and self-similar way. The method is validated via well known vortex rings and newly discovered helical vortex equilibria are also used to test the method.
AMMW01 23rd August 2012
11:00 to 11:30
Adaptive mesh method in the Met Office variational data assimilation system
A frequent problem in forecasting fog or icy roads in a numerical weather prediction system is attributed to the misinterpretation of the boundary layer structure in the assimilation procedure. Case studies showed that much of the misinterpretation of temperature inversions and stratocumulus layers in the assimilation is due to inappropriate background error covariances. This paper looks at the application of adaptive mesh methods in the Met Office variational assimilation system to modify the background error correlations in the boundary layer when temperature inversions or stratocumulus layers are present in the background state.
AMMW01 23rd August 2012
11:30 to 12:30
Adaptive Numerical Simulation of Idealized Cyclones
The processes causing a cyclone's formation, its intensification, its motion and finally its terminating all proceed at multiple and interacting temporal and spatial scales. Therefore the forecasting of a cyclone's dynamic can make great benefits of adaptive techniques such as local mesh refinement. Mesh adaptation strategies are often based on problem-dependent indicators that need to be determined and which have different properties with respect to the associated computational effort and the quality of the resulting meshes. For example, the computation of goal-oriented error indicators requires sensitivity information provided by the solution of an additional linear problem which leads to a remarkable overhead in computation time and additional storage requirements. In that context, we address the question whether the complexity of different criteria for refinement is justifiable. To this end, we investigate idealized cyclone scenarios and systematically analyze the efficiency of adaptive numerical methods employing a selection of different indicators based on physical criteria, heuristic criteria, a posteriori error estimators, and goal-oriented approaches. We compare these approaches with regard to the related computational costs, storage requirements, implementation complexity, and the accuracy of the resulting solution.
AMMW01 23rd August 2012
13:30 to 14:00
A Müller Are adaptive simulations more accurate than uniform simulations?
Adaptive mesh refinement generally serves to increase computational efficiency without compromising the accuracy of the numerical solution significantly. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result significantly. Another open question is the following: does an adaptive computation simulate large scale features of the flow more accurately than a uniform simulation when both use the same CPU time? These questions are investigated in the case of a 2D dry warm air bubble with the help of a recently developed adaptive discontinuous Galerkin model.

A method is introduced which allows one to compare the accuracy between different choices of refinement regions even in a case when the exact solution is not known. Essentially this is done by comparing features of the solution that are strongly sensitive to spatial resolution. The additional error by using adaptivity is smaller than 1% of the total numerical error if the average number of elements used for the adaptive simulation is about 50% smaller than the number used for the simulation with the uniform fine-resolution grid. Correspondingly the adaptive simulation is almost two times faster than the uniform simulation. Furthermore the adaptive simulation is more accurate than a uniform simulation when both use the same CPU time.
AMMW01 23rd August 2012
15:30 to 16:30
D Holm Parameterizing interaction of disparate scales: selective decay by Casimir dissipation in fluids
The problem of parameterizing the interactions of disparate scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a Casimir of the ideal formulation (enstrophy in 2D flows) decays in time, while the energy stays essentially constant. This paper introduces a mechanism that produces selective decay by enforcing Casimir dissipation in fluid dynamics. This mechanism turns out to be related in certain cases to the numerical method of anticipated vorticity discussed in \cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of selective decay is developed that uses the Lie-Poisson structure of the ideal theory. A scale-selection operator allows the resulting modifications of the fluid motion equations to be interpreted in several examples as parameterizing the nonlinear, dynamical interactions between disparate scales. The type of modified fluid equation systems derived here may be useful in turbulent geophysical flows where it is computationally prohibitive to rely on the slower, indirect effects of a realistic viscosity, such as in large-scale, coherent, oceanic flows interacting with much smaller eddies.
AMMW01 23rd August 2012
16:30 to 17:00
Adaptive multiscale discontinuous Galerkin methods for multiphase morphodynamics
We present a strongly coupled, eigendecomposition problem for an extension of the Saint–Venant shallow water equations in two dimensions strongly coupled to a completely generalized Exner form of the sediment discharge equation. This formulation is used to implement an adaptive discontinuous Galerkin (DG) finite element method, using a Roe Flux for the advective components and the unified form for the dissipative components. We discuss important mathematical and numerical nuances that arise due to the emergence of nonconservative product formalisms in the presence of sharp gradients, and present some large scale candidate application models with examples
AMMW01 24th August 2012
09:00 to 10:00
A Framework for the Development of Computable Error Bounds for Finite Element Approximations
We present an overview of our recent work on the development of fully computable upper bounds for the discretisation error measured in the natural (energy) norm for a variety of problems including linear elasticity, convection-diffusion-reaction and Stokes flow in three space dimensions. The upper bounds are genuine upper bounds in the sense that the actual numerical value of the estimated error exceeds the actual numerical value of the true error regardless of the coarseness of the mesh or the nature of the data for the problem, and are applicable to a variety of discretisation schemes including conforming, non-conforming and discontinuous Galerkin finite element schemes. All constants appearing in the bounds are fully specified. Numerical examples show the estimators are reliable and accurate even in the case of complicated three dimensional problems, and are suitable for driving adaptive finite element solution algorithms.
AMMW01 24th August 2012
10:00 to 10:30
Adapting to life: Ocean ecosystem modelling using an unstructured and adaptive mesh ocean model
Primary production in the world ocean is significantly controlled by meso- and sub-mesocale process. Thus existing general circulation models applied at the basin and global scale are limited by two opposing requirements: to have high enough spatial resolution to resolve fully the processes involved (down to order 1km) and the need to realistically simulate the basin scale. No model can currently satisfy both of these constraints. Adaptive unstructured mesh techniques offer a fundamental advantage over standard fixed structured mesh models by automatically generating very high resolution at locations only where and when it is required. Mesh adaptivity automatically resolves fine-scale physical or biological features as they develop, optimising computational cost by reducing resolution where it is not required.

Here, we describe Fluidity-ICOM, a non-hydrostatic, finite-element, unstructured mesh ocean model, into which we have embedded a six-component ecosystem model, that has been validated at a number of ocean locations. We show the different meshes that arise from using different metrics to create the adaptive mesh and from the underlying physical and biological processes that occur at each station. We then apply the model to a three-dimensional restratification problem and examine the effect of mesh resolution on simulated biological productivity on both fixed and adaptive meshes.
AMMW01 24th August 2012
11:00 to 11:30
Y Li A new approach to implement sigma coordinate in a numerical model
This study shows a new way to implement terrain-following σ-coordinate in a numerical model, which does not lead to the well-known “pressure gradient force (PGF)” problem. First, the causes of the PGF problem are analyzed with existing methods that are categorized into two different types based on the causes. Then, the new method that bypasses the PGF problem all together is proposed. By comparing these three methods and analyzing the expression of the scalar gradient in a curvilinear coordinate system, this study finds out that only when using the covariant scalar equations of σ-coordinate will the PGF computational form have one term in each momentum component equation, thereby avoiding the PGF problem completely.

A convenient way of implementing the covariant scalar equations of σ-coordinate in a numerical atmospheric model is illustrated, which is to set corresponding parameters in the scalar equations of the Cartesian coordinate. Finally, two idealized experiments manifest that the PGF calculated with the new method is more accurate than using the classic one. Specifically, the relative error of PGF in the new method is reduced by orders of magnitude compared with the result obtained by the classic method; and the pattern of PGF in the new method is more consistent with the analytical PGF pattern than using the classic method. This new method can be used for oceanic models as well, and needs to be tested in both the atmospheric and oceanic models.
AMMW01 24th August 2012
11:30 to 12:30
Discontinuous Galerkin Methods for Adaptive Atmospheric Flow
In this talk we present higher order discontinuous Galerkin methods for convection dominated problems (using a limiter based stabilization [3]) or diusion dominated problems (see [4]). A comparison of these methods with COSMO, a well established dynamical core for weather forecast, for standard test cases for atmospheric ow [5] is presented. This talk also highlights software techniques as well as recent development of the software package Dune [1] and the discretization module Dune-Fem [2]. In particular we comment on implemented techniques to allows for local grid adaptivity even in parallel environments. In this case dynamic load-balancing is applied to maintain scalability of the simulation code.

References [1] P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klofkorn, R. Kornhuber, M. Ohlberger, and O. Sander. A generic grid interface for parallel and adaptive scientic computing. II: Implementation and tests in Dune. Computing, 82(2-3):121{138, 2008.

[2] A. Dedner, R. Klofkorn, M. Nolte, and M. Ohlberger. A Generic Interface for Parallel and Adaptive Scientic Computing: Abstraction Principles and the Dune- Fem Module. Computing, 90(3{4):165{196, 2010.

[3] A. Dedner and R. Klofkorn. A Generic Stabilization Approach for Higher Order Discontinuous Galerkin Methods for Convection Dominated Problems. J. Sci. Comput., 47(3):365{388, 2011.

[4] S. Brdar, A. Dedner, and R. Klofkorn. Compact and stable Discontinuous Galerkin methods for convection-diusion problems. Preprint no. 2/2010, Mathematisches Institut, Universitat Freiburg, 2010. accepted for publication in SIAM J. Sci. Comput.

[5] S. Brdar, M. Baldauf, A. Dedner, and R. Klofkorn. Comparison of dynamical cores for NWP models. Theor. Comput. Fluid Dyn., 2012.
AMMW01 24th August 2012
13:30 to 14:30
Monge ampere based moving mesh methods with applications to numerical weather prediction
Moving mesh methods can be very effective for problems with many scales such as those which arise in numerical weather prediction and data assimilation. However traditional moving mesh methods can have problems with implementation and mesh tangling which have made them less effective than other adaptive methods for problems in meteorology. In this talk I will describe a moving mesh method based on ideas in the theory of optimal transport which derives a mesh by solving a Monge-Ampere equation. This can then be coupled to a CFD solver to provide an effective method for solving multiscale incompressible flows. I will describe the method and apply it to several meteorological problems.

Joint work with mike Cullen , chiara piccolo , Emily Walsh and Phil Browne
AMMW01 24th August 2012
14:30 to 15:00
Parallelization and Software Concepts for Tsunami Simulation on Dynamically Adaptive Triangular Grids
We present a memory- and cache-efficient approach for simulations on recursively refined dynamically adaptive triangular grids. Grid cells are stored and processed in an order defined by the Sierpinski curve; the resulting locality properties are exploited for optimised serial implementation and parallelisation. The approach is particularly designed for Finite Volume and discontinuous Galerkin solvers, with Tsunami simulation as the main target application. In the talk, we will discuss approaches for parallelisation in shared and distributed memory. We will present a classical partitioning-based strategy, as well as a novel shared-memory approach based on the dynamical scheduling of many small sub-partitions. Here, the intention is to allow for strongly varying computational load per element (as required for inundation modelling, or for local time-stepping methods).

In addition, we would like to discuss some ideas on how to provide bathymetry data and (time-dependent) displacements for a simulation with dynamically adaptive refinement. We'll present some first results of adaptive simulations using the augmented Riemann solvers provided with GeoClaw.
AMMW01 24th August 2012
15:30 to 16:00
Unified Multiscale Operational Weather Forecasting at the Canadian Meteorological Centre
The genesis of the unified Global Environmental Multiscale model and forecasting system that was gradually deployed since 1997 will be presented. It was originally designed for both forecasting and data assimilation at uniform resolution global scale and variable resolution continental scale. It could also be run for mesoscale forecasting over smaller areas by increasing the stretching of the grid. The formulation of the model allowed it to be run either in hydrostatic or non-hydrostatic mode. Tangent linear and adjoint models were developed for variational data assimilation, and data assimilation was performed first using 3D Var and later 4D Var. More recently a global ensemble system was developed based on the GEM model for both ensemble forecasting and data assimilation. The modelling system has been generalised in different directions to become a complete environmental prediction system: emergency response, volcanic ashes, air quality, stratospheric ozone, wave modelling, coupling to rivers and oceans etc.

The development of a nested version of the model is having a profound impact on the forecasting system. After thorough testing, it was used successfully for operational forecasting at 1 km during the Vancouver Olympics in 2010 and it will become operational at 2.5 km over several windows in Canada. A large uniform resolution nested model has been shown to be equivalent to the variable resolution version for continental forecast and was implemented operationally. The nested version has allowed the development of a regional ensemble system. A replacement of the uniform resolution global grid by the composite Yin-Yang grid based on two uniform resolution limited-area grids is under study. Preliminary testing is showing this version to be equivalent in accuracy, but free of the “pole problem” affecting the grid point latitude-longitude models and much more suitable for future supercomputer architectures.
AMMW01 24th August 2012
16:00 to 16:30
Finite element exterior calculus framework for geophysical fluid dynamics
Finite element exterior calculus provides an extension of the mimetic differencing approach that underlies the C-grid schemes used in the ICON and MPAS projects. This talk will lay out an extension of this approach, in particular of the approach of Ringler, Thuburn, Skamarock and Klemp (2010), to a finite element framework. The required properties of (a) stationary geostrophic linear modes on the f-plane, (b) local conservation of mass, and (c) conservative, consistent advection of potential vorticity are retaining in this framework, whilst allowing higher-order accuracy and increased flexibility which can be used to alter the balance of vorticity and mass degrees of freedom to minimise the potential for spurious modes.
AMM 28th August 2012
10:30 to 11:00
Discussion on Adaptive DG Methods for Flow Problems
AMM 29th August 2012
10:00 to 10:30
Nonhydrostatic atmospheric cut cell model on a block-structured Cartesian mesh
One of the most pressing concerns of next-generation atmospheric modeling is the handling of highly-resolved complex topography. Since an increase in horizontal resolution introduces steep slopes over mountainous areas, this leads to the conventional terrain-following models suffering from large truncation errors, hence they are no longer considered accurate enough for future high resolution models. In this study, a cut cell method for representing topography on a Cartesian grid is applied to a two-dimensional nonhydrostatic atmospheric model to achieve high resolution and highly-precise simulations over steep topography. Small cells cut by topography are combined with neighboring cells either vertically or horizontally to avoid severe restrictions on time steps due to the CFL condition. In addition, a block-structured mesh approach is introduced to achieve computationally efficient Cartesian grid simulations with both high vertical resolution near the ground and reasonable conservation characteristics.

This model successfully reproduces flows over not only a gently sloping bell-shaped mountain but also a semicircular mountain where significant errors are observed in a terrain-following model. It also reproduces a smooth and accurate mountain wave on a locally refined mesh around the semicircular mountain. This result agrees well with that using a uniformly fine mesh despite of its substantially low computational cost, thereby demonstrating the advantage of the model to simulate flows over steep topography.

AMM 29th August 2012
10:30 to 11:00
Resolution-dependent self-scaling physical parameterizations and numerical closures
AMM 30th August 2012
10:00 to 11:00
Resolution independent topography: from cut cells to thin walls and porous barriers
AMM 31st August 2012
10:00 to 11:00
J Steppeler High Order Polygonal Grids and Cut Cells (Polynomial degree 2 or 3)
The method will be of uniform representation order 2 or 3, which implies the convergence order. Any Polygonal grid, consisting of triangles or quadrilaterals may be used. As an example the icosahedral grid will be presented. Inside each cell the serendipity representation will be used. The dynamic equations are derived from the L-Galerkin method. This method differs from classical Galerkin by being strictly local. Examples for smooth solutions in the presence of irregular points will be given.
AMM 3rd September 2012
14:00 to 14:30
Non-linear trajectories with simultaneous space integration and auto-regressive predictors in Semi-Lagrangian integration: a discussion session
AMM 4th September 2012
14:00 to 15:00
WC Skamarock & A Adcroft Transport Schemes: a discussion session
AMM 5th September 2012
10:00 to 11:00
Some remarks about new computing architectures and a proposed alternative way to address time splitting for ocean models
AMM 5th September 2012
13:00 to 14:00
Mixed Finite Elements: a discussion session
AMM 6th September 2012
13:30 to 14:30
H Weller Accuracy and efficiency comparisons at the Newton Institute and beyond: a discussion session
AMM 7th September 2012
09:30 to 10:00
Non-linear trajectories with simultaneous space integration and auto-regressive predictors in Semi-Lagrangian integration
AMM 7th September 2012
10:00 to 11:00
Cauchy-Riemann differential equations of the spherical geometry
A system of PDEs relating to the transformation of the latitude- longitude parameterisation of the sphere was described in the work of F. Schmidt[Sch77]. This system of PDEs is known in the Meteorological literature as Cauchy-Riemann equations of the sphere. However the connection between this form of PDEs and the complex analytic function theory is not known to be reported. This talk will describe the connection between complex analytic function theory and the differential geometry of the sphere. A class of variable separable solutions of the C-R equations are useful in creating variable mesh configurations. One such solution had been applied to create a variable resolution global spectral method on the sphere[JNM12]. Complex function theory provides some useful insights on the types of variable resolution mesh configurations that can be generated on the sphere.

References

[JNM12] S. Janakiraman, Ravi S. Nanjundiah, and A.S. Vasudeva Murthy, A novel variable resolution global spectral method on the sphere, Journal of Computational Physics 231 (2012), no. 7, 2794 2810.

[Sch77] F. Schmidt, Variable ne mesh in spectral global models, Beiträge zur Physik der Atmosphäre 50 (1977), no. 12, 211 217.
AMM 10th September 2012
10:00 to 10:30
Part I: Iterative Solvers and Preconditioners for solving large sparse linear systems
In this talk, I will outline the role of iterative solvers in building scalable methods and describe the bottleneck in such solvers. In particular, I will review GMRES and BiCGStab. After, this we will review preconditioning and describe the preconditioners that we have tried and those that we have been developing. The preconditioners that we describe fall under the general category of Sparse Approximate Inverse (SPAI) Preconditioner.
AMM 10th September 2012
10:30 to 11:00
Part II: Iterative Solvers and Preconditioners for solving large sparse linear systems
AMM 10th September 2012
14:00 to 15:00
Scalable multilevel iterative solvers for elliptic problems: a discussion session
AMM 11th September 2012
10:00 to 11:00
AMM 11th September 2012
13:30 to 14:30
Logarithmic reconstruction on unstructured grids
AMM 12th September 2012
10:00 to 11:00
The reversibly-staggered CCAM and VCAM models
AMM 13th September 2012
10:00 to 11:00
Multilayer abstractions for PDEs
AMM 13th September 2012
14:00 to 15:00
J Steppeler To what extent can order of accuracy improve forecast skill? A discussion session
AMM 17th September 2012
10:30 to 11:00
Numerical analyses of Runge-Kutta IMEX schemes for use in atmospheric models
AMM 17th September 2012
13:30 to 14:00
The leapfrog is dead. Long live the leapfrog!
The centred-difference time-stepping scheme, known affectionately as the leapfrog scheme, has been used widely in atmosphere and ocean models for over 40 years. However, the numerical dissipation and loss of accuracy associated with the Robert-Asselin filter (which is used to control the computational mode) are becoming unacceptable to some modellers, who are starting to turn to schemes that are less dissipative and more accurate.

This talk will argue that there is still plenty of life left in the leapfrog. I will describe some simple and computationally inexpensive strategies to improve it, including the replacement of the Robert-Asselin filter with the RAW filter. The methods reduce the numerical dissipation and increase the accuracy, whilst retaining the stability of the physical mode and effectively controlling the computational mode. Examples will be shown of recent implementations of these methods in several models, leading to improvements in the simulation skill.
AMM 18th September 2012
10:00 to 10:30
IMEX methods for fast-wave slow-wave problems
AMM 18th September 2012
10:30 to 11:00
Which type of time-integrators will make dynamic grid adaptivity feasible?
AMM 18th September 2012
13:30 to 14:00
H Weller Runge-Kutta IMEX schemes for HEVI and semi-implicit simulations
AMM 18th September 2012
14:00 to 15:00
D Durran & F Giraldo & H Weller IMEX: a discussion session
AMM 19th September 2012
10:00 to 10:30
Time-Parallel Algorithms for Weather Prediction and Climate Simulation
AMM 20th September 2012
10:00 to 10:30
A High-Order Unstaggered Finite-Volume Approach for Atmospheric Numerical Modeling
AMM 21st September 2012
10:00 to 11:00
Suggestions for adaptive test cases: a discussion session
AMM 21st September 2012
13:30 to 14:00
Does the energy that drives hurricanes also heat your beer?
AMMW02 24th September 2012
10:30 to 10:55
John Thuburn Mimetic Semi-implicit Solution of the Shallow Water Equations on Hexagonal-Icosahedral and Cubed-Sphere Grids
A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic spatial discretization with a Crank-Nicolson time scheme for fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity. The algorithm is tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cube-sphere grids. For the cubed-sphere case, a key ingredient is the development of a suitable discrete Hodge star operator for the non-orthogonal grid.

Results of several test cases will be presented. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, vanishing curl of grad, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and for advective Courant numbers up to about one.

The accuracy of the scheme appears to be limited by the accuracy of the various mimetic spatial operators. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.
AMMW02 24th September 2012
10:55 to 11:20
Variational derivation of energy-conserving finite-difference schemes for geophysical fluid equations
At the continuous level, the so-called vector-invariant form of the equations of fluid motion can be obtained from Hamilton's principle of least action, using the Euler-Poincaré formalism. In this form of the equations, the mass flux and Bernoulli function appear as functional derivatives of the Hamiltonian. The integral conservation of energy and the Lagrangian conservation of potential vorticity then follow straightforwardly.

This setting can be imitated at the discrete level to yield energy-conserving schemes. Key ingredients include an energy-conserving vector product, a discrete rule of integration by parts, a discrete approximation of total energy, and the definition of the discrete mass flux and Bernoulli function from partial derivatives of the discrete energy. For the rotating shallow-water equations, it turns out that schemes by Sadourny (1975) on Cartesian meshes and by Bonaventura & Ringler (2005) on Delaunay-Voronoi meshes fit in the above framework.

Furthermore new schemes can be obtained. For instance it is possible to modify the discrete mass flux to match a modification of the discrete energy, as Renner (1981) and Skamarock et al. (2012) did to suppress a numerical instability. Finally, a so-called discrete Hodge star operator is obtained on a non-orthogonal pair of primal and dual meshes. This operator is part of a potential-vorticity conserving scheme of the shallow-water equations on meshes for which an orthogonal dual does not exist, like the equiangular cubed sphere. Potential application to sets of three-dimensional equations will be discussed.
AMMW02 24th September 2012
11:20 to 11:45
Finite element exterior calculus framework for geophysical fluid dynamics
We present a finite element framework that extends the mimetic approach of Ringler, Thuburn, Skamarock and Klemp (2010) to finite element methods. The framework preserves the following benefits of the mimetic approach: local mass conservation, steady geostrophic linear modes on the f-plane, consistent conservative potential vorticity advection, but allows for selection of higher-order finite element discretisations and adjustment of the balance of vorticity and mass degrees of freedom. We will explain the foundations of the framework and present some preliminary numerical results which form part of the UK Met Office/NERC/STFC GungHo dynamical core project.
AMMW02 24th September 2012
11:45 to 12:10
A multilevel time integrator for computing longwave shallow water flows at low Froude numbers
A new multilevel semi-implicit scheme for the computation of low Froude number shallow water flows is presented. Motivated by the needs of atmospheric flow applications, it aims to minimize dispersion and amplitude errors in the computation of long wave gravity waves. While it correctly balances "slaved" dynamics of short-wave solution components induced by slow forcing, the method eliminates freely propagating compressible short-wave modes, which are under- resolved in time. This is achieved through the multilevel approach borrowing ideas from multigrid schemes for elliptic equations. The scheme is second order accurate and admits time steps depending only on the flow velocity. It incorporates a predictor step using a Godunov-type method for hyperbolic conservation laws and two elliptic corrections. The multilevel method is initially derived for the one-dimensional linearized shallow water equations. Scale-wise decomposition of the data enables a scale- dependent blending of time integrators with different principal features. To guide the selection of these integrators, the discrete-dispersion relations of some standard second-order schemes are analyzed, and their response to high wave number low frequency source terms is discussed. The resulting method essentially consists of the solution of a Helmholtz problem on the original fine grid, where the operator and the right hand side incorporate the multiscale information of the discretization. The performance of the method in the linear case is illustrated on a test case with "multiscale" initial data and a problem with a slowly varying high wave number source term. For the computation of fully nonlinear shallow water flows, a projection method for zero Froude number flows is generalized by incorporating the local time derivatives of the height. This semi-implicit method is combined with the multilevel method for the linearized equations to obtain the above mentioned properties of the scheme. Numerical tests address the scheme's ability to correctly cover the asymptotic flow regime of long-wave gravity waves passing over short-range topography and its balancing properties for the lake at rest.
AMMW02 24th September 2012
14:00 to 14:25
Sergey Danilov Multiscale ocean simulations with FESOM
Finite-Element Sea-ice Ocean circulation Model (FESOM) uses unstructured triangular meshes and is employed either as standing-alone global ocean model or as part of FESOM-ECHAM5/6 coupled setup. Several examples pertaining to studies focused on polar oceans will be given to characterize the potential of FESOM and also to indicate typical difficulties related to the strongly variable resolution.

Brief intercomparison of FESOM to a global cell-vertex finite-volume setup is presented. While it is more numerically efficient than the finite-element setup of FESOM, it requires special measures to maintain stable performance because of its too large velocity space. Most effective stabilization is provided by either computing the momentum advection on scalar (median-dual) control volumes, or making use of the vector-invariant form. Both approaches effectively trim the nonlinear term in the momentum equation to the size of scalar space.
AMMW02 24th September 2012
14:25 to 14:50
Uniformly third Order conserving Schems on Polygonal Grids
Uniformly third Order conserving Schems on Polygonal Grids. The interest in polygonal grids is increasing. They are an alternative to the more commonly used spectral and latitude longitude grids. Among other advantages they offer the possibility of a rather uniform cover of the sphere with grid cells. Other advantages concern the ease of using multiprocessing computers and using special vertical treatments, such as shaved cells. Well known examples of polygonal grids are the cube sphere and the icosahedral grid. After initial research by Sadourny and Williamsson the practicability of this approach was shown by Baumgardner and Steppeler. In particular Baumgardner showed that problems with some approaches can be traced back to the fact that for slightly irregular resolution methods are not uniformly second order. After correcting this problem Baumgardner was able to show that problems arising from irregular grids do not occur. Steppeler generalized this approach to third order. Both Baumgardners and Steppelers approaches were non conser ving. A generalization to conserving schemes will be presented and computational examples given. Another high order approach is the pecral element method, which currently is available for orders 4 an higher only. The approach presented can be considered as a version of third order spectral elements. The advantages of third order schemes over even higher order approaches will be discussed.
AMMW02 24th September 2012
14:50 to 15:15
A Semi-Lagrangian Discontinuous Galerkin (SLDG) Conservative Transport Scheme on the Cubed-Sphere
The discontinuous Galerkin (DG) method combines fine features of high-order accurate finite-element and finite-volume methods. Because of its geometric flexibility and high parallel efficiency, DG method is becoming increasingly popular in atmospheric and ocean modeling. However, a major drawback of DG method is its stringent CFL stability restriction associated with explicit time-stepping. A way to get around this issue is to combine DG method with a Lagrangian approach based on the characteristic Lagrange-Galerkin philosophy. Unfortunately, a fully 2D approach combining DG and Lagrangian methods is algorithmically complex and computationally expensive for practical application, particularly for non-orthogonal curvilinear geometry such as the cubed-sphere grid system. We adopt a dimension-splitting approach where a regular semi-Lagrangian (SL) scheme is combined with the DG method. The resulting SLDG scheme employs a sequence of 1D operations for solving transport equation on the cubed-sphere. The SLDG scheme is inherently conservative and has the option to incorporate a local positivity-preserving filter for tracers. A novel feature of the SLDG algorithm is that it can be used for multi-tracer transport for global models employing spectral-element (structured or unstructured) grids. The SLDG scheme is tested for various benchmark advection test-suites on the sphere and results will be presented in the seminar.
AMMW02 24th September 2012
15:45 to 16:10
Compact finite difference schemes on the Cubed-Sphere
The Cubed-Sphere is a spherical grid made of six quasi-cartesian square like patches. It was originally introduced by Sadourny some forty years ago. We extend to this grid the design of high-order finite difference compact operators. Such discrete operators are used in Computational Fluid Dynamics on structured grids for applications such as Direct Numerical Simulation of turbulent flows, or aeroacoustics problems. We consider in this work the design of a uniformly fourth-order accurate spherical gradient. The main approximation principle consists in defining a network of great circles covering the Cubed-Sphere along which a high-order hermitian gradient can be calculated. This procedure allows a natural treatment at the interface of the six patches. The main interest of the approach is a fully symmetric approximation system on the Cubed-Sphere. We numerically demonstrate the accuracy of the approximate gradient on several test problems, in particular the cosine-bell test-case of Williamson et al. for climatology.
AMMW02 24th September 2012
16:10 to 16:35
A conservative adaptive wavelet method for the shallow water equations on staggered grids
This paper presents the first dynamically adaptive wavelet method for the shallow water equations on a staggered hexagonal C-grid. Pressure is located at the centres of the primal grid (hexagons) and velocity is located at the edges of the dual grid (triangles). Distinct biorthogonal second generation wavelet transforms are developed for the pressure and the velocity. These wavelet transforms are based on second-order accurate interpolation and restriction operators. Together with compatible restriction operators for the mass flux and Bernoulli function, they ensure that mass is conserved and that there is no numerical generation of vorticity when solving the shallow water equations. Grid refinement relies on appropriate thresholding of the wavelet coefficients, allowing error control in both the quasi-geostrophic and inertia-gravity wave regimes. The shallow water equations are discretized on the dynamically adapted multiscale grid using a mass and potential-enstrophy conserving finite-difference scheme. The conservation and error control properties of the method are verified by applying it to a propagating inertia-gravity wave packet and to rotating shallow water turbulence. Significant savings in the number of degrees of freedom are achieved even in the case of rotating shallow-water turbulence. The numerical dissipation introduced by the grid adaptation is quantified. The method has been designed so it can be extended easily to the icosahedral subdivision of the sphere. This work provides important building blocks for the development of fully adaptive general circulation models.
AMMW02 24th September 2012
16:35 to 17:00
Tae-Jin Oh Dynamical Core Developments at KIAPS
Korea Institute of Atmospheric Prediction Systems (KIAPS) is a new organization founded to develop the next generation operational numerical weather prediction (NWP) model for Korea Meteorological Administration (KMA). With the increasing demand for global high-resolution simulation, scalability becomes an important issue and highly scalable numerical methods such as spectral element (continuous Galerkin, CG) or discontinuous Galerkin (DG) methods are gaining interest. Although conventional finite difference (FD) or finite volume (FV) methods offer excellent efficiency, it is difficult to formulate high order schemes on nonorthogonal grid structures which is needed to avoid grid singularities. On the other hand, CG/DG methods are not constrained to lower order on unstructured, nonorthogonal grids. We present high order convergence properties of CG/DG methods for advection, shallow water equations on structured and/or unstructured grids in one and/or two dimensions. In order t o match the high order spatial truncation error, an explicit general order m-stage m–1 order strong stability preserving (SSP) Runge-Kutta time integrator is used. With this setup, we can obtain arbitrary order convergence rates.
AMMW02 25th September 2012
09:00 to 09:25
Slope-limited transport schemes using icosahedral hexagonal grid
In this work two simple advection schemes for unstructured meshes are proposed and implemented over spherical icosahedral-hexagonal grids. One of them is fully discrete in space and time while the other one is a semi discrete scheme with third order RungeKutta time integration. Both schemes use cell-wise linear reconstruction. We therefore also present two possible candidates for consistent gradient discretization over general grids. These gradients are designed in a finite volume sense with an adequate modification to guarantee convergence in the absence of a special grid optimization. Monotonicity of the advection schemes is enforced by a slope limiter, at contrast with the widely used of posterior approach of flux-corrected transport (FCT). Convergence of the proposed gradient reconstruction operators is verified numerically. It is found that the proposed modification is indeed necessary for convergence on non-optimized grids. Recently proposed advection test cases are used to evaluate the performance of the slope-limited advection schemes. It is verified that they are convergent and positive. We also compare these schemes to a variant where positivity is enforced by the FCT approach. FCT produces slightly less diffusion but it seems to be at the price of some nonphysical anti-diffusion. These results suggest that the proposed slope limited advection schemes are a viable option for icosahedral-hexagonal grids over sphere.
AMMW02 25th September 2012
09:25 to 09:50
Numerical Solution of the Advection Equation on Unstructured Spherical Grids with Logarithmic Reconstruction
There are numerous approaches for solving hyperbolic differential equations in the context of finite volume methods. One popular approach is the limiter free Local-Double-Logarithmic-Reconstruction (LDLR) of Artebrant and Schroll. The aim of this work is to construct a three-dimensional reconstructing function based on the LDLR for solving the advection equation on unstructured spherical grids. The new method should preserve the characteristics of the LDLR. That means in particular a reconstruction without use of limiters and with a small stencil of only the nearest neighbors of a particular cell. Also local extrema should be conserved while the local variation of the reconstruction within one cell should be under control.

We propose an ansatz which works on unstructured polyhedral grids. To come up to this, an ansatz function with one logarithmic expression for each face of the polyghedron is constructed. Required gradients at cell face midpoints are determined by use of the Multi-Point-Flux-Approximation (MPFA) method. Further derivative information are obtained with the help of special barycentric coordinates. All necessary integrals of the ansatz functions can be computed exactly. The spatially discretized equations are combined with explicit Runge-Kutta methods to advance the solution in time.

The new advection procedure is numerically evaluated with standard test cases from the literature on different unstructured spherical grids.
AMMW02 25th September 2012
09:50 to 10:15
Janakiraman Subburathnam Linear advection characteristics of a variable resolution global spectral method on the sphere
Advection experiments are conducted with a variable resolution global spectral method on the sphere. The variable resolution grid has finer resolution over the tropics and the resolution decreases smoothly as we move towards the poles [Janakiraman et al (2012) ]. An Eulerian formulation of the linear advection is used to for the spectral discretization. Near dispersion-free advection is achieved on the high resolution tropical belt. The transport across homogeneous resolution regions produce very less dispersion errors. Transport over the poles result in severe grid representation errors. It is shown that increasing the resolution over the reatly reduces this error. Transport of a feature from apoint close to poles but not over it does not produce such representation errors. A comparison of time-schemes such as 4-th order Runge-Kutta method, Magazenkov scheme and Leap-frog scheme for the advection experiment is also presented.

Reference(s) : S. Janakiraman, Ravi S Nanjundiah and A.S. Vasudeva Murthy, A novel variable resolution global spectral method on the sphere, Vol. 231, No. 7, pp 2794--2810, 2012.
AMMW02 25th September 2012
10:15 to 10:40
Optimization-based Conservative Transport on the Sphere
We present a new optimization-based conservative transport algorithm for scalar quantities (i.e. mass) that preserves monotonicity without the use of flux limiters. The method is formulated as a singly linearly constrained quadratic program with simple bounds where the net mass updates to the cell are the optimization variables. The objective is to minimize the discrepancy between a target or high-order mass update and a mass update that satisfies physical bounds. In this way, we separate accuracy considerations, handled by the objective functional from the enforcement of physical bounds, handled by the contraints. With this structure mass conservation is incorporated as a constraint and a simple, efficient, and easily parallelizable optimization algorithm is obtained. This algorithm has been extended to a latitude-longitude grid for two-dimensional remapping and transport on the sphere. Results for several standard test problems on the sphere will be shown to illustrate the accuracy and robustness of the method.
AMMW02 25th September 2012
11:10 to 11:35
Colin Zarzycki Improving tropical cyclone representation in general circulation models through the use of variable resolution
Modeling of tropical cyclones in General Circulation Models (GCMs) has been a historically difficult task due to issues such as relatively small storm sizes and intense convective processes. However, recent advances in GCM model design coupled with improvements in computing ability now allow for GCM simulations with grid spacings as small as 15-30 km. This presentation evaluates the potential of GCMs at these high horizontal resolutions to simulate tropical cyclones. In particular, we explore a novel variable-resolution mesh approach that allows for high spatial resolutions in areas of interest, such as low-latitude ocean basins where tropical cyclones are prevalent. Such GCM designs with variable-resolution meshes have the potential to become a future tool in weather forecasting as well as for regional climate assessments.

A statically-nested, variable-resolution mesh option has recently been introduced into the National Center for Atmospheric Research (NCAR) Community Atmosphere Model's (CAM) Spectral Element (SE) dynamical core. We present preliminary CAM-SE model simulations using an idealized tropical cyclone test case with a variety of grid sizes and refinement scales. We evaluate the evolution of tropical cyclones initialized at various locations in or near grid scale transition regions. Specific focus is centered on factors crucial to storm cyclogenesis and maintenance such as air-sea interaction and vertical development. In addition to short-term, deterministic tests, we also investigate the performance of multi-resolution meshes in longer-term climate simulations, including attention paid to the dependance of non-seeded tropical cyclone genesis on spatial resolution and the subsequent implications for regional climate modeling within a global modeling framework. We also discuss pot ential computational consequences of using such a setup in either process or climate studies.
AMMW02 25th September 2012
11:35 to 12:00
Adaptive High-order Finite Volume Discretizations on Spherical Thin Shells
We present an adaptive, conservative finite volume approach applicable to solving hyperbolic PDE's on both 2D surface and 3D thin shells on the sphere. The starting point for this method is the equiangular cubed-sphere mapping, which maps six rectangular coordinate patches (blocks) onto the sphere. The images of these blocks form a disjoint union covering the sphere, with the mappings of adjacent blocks being continuous, but not differentiable, at block boundaries. Our method uses a fourth-order accurate discretization to compute flux averages on faces, with a higher-order least squares-based interpolation to compute stencil operations near block boundaries. To suppress oscillations at discontinuities and underresolved gradients, we use a limiter that preserves fourth-order accuracy at smooth extrema, and a redistribution scheme to preserve positivity where appropriate for advected scalars. By using both space- and time-adaptive mesh refinement, the solver allocates comp utational effort only where greater accuracy is needed. The resulting method is demonstrated to be fourth-order accurate for advection and shallow water equation model problems, and robust at solution discontinuities. We will also present an approach for the compressible Euler equations on a 3D thin spherical shell. Refinement is performed only in the horizontal directions, The radial direction is treated implicitly (using a fourth-order RK IMEX scheme) to eliminate time step constraints from vertical acoustic waves.
AMMW02 25th September 2012
12:00 to 12:25
Generation of Provably Correct Curvilinear Meshes
The development of high-order numerical technologies for CFD is underway for many years now. For example, Discontinuous Galerkin methods (DGM) have been largely studied in the literature, initially in a quite theoretical context, and now in the application point of view. In many contributions, it is shown that the accuracy of the method strongly depends of the accuracy of the geometrical discretization. In other words, the following question is raised:we have the high order methods, but how do we get the meshes?

This talk focus on the generation of highly curved ocean meshes of polynomial order 2 to 4.

In the first part, we propose a robust procedure that allows to build a curvilinear mesh for which every element is guaranteed to be valid. The technique builds on standard optimization method (BICG) combined with a log-barrier objective function to guarantee the positivity of the elements Jacobian and thus the validity of the elements.

To be valid is not the only requirement for a good-quality mesh. If the temporal discretization is explicit, even a valid element can lead to a very stringent constraint on the stable time step. The second part of the talk is devoted to the optimization of the curvilinear ocean meshes to obtain large stable time steps.
AMMW02 25th September 2012
14:00 to 14:25
Donna Calhoun A logically Cartesian, adaptively refined two-patch sphere grid for modeling transport in the atmosphere
Recently, we demonstrated results using a second order finite volume scheme on a novel, logically Cartesian, two-patch 2d sphere grid. The numerical scheme, based on the wave-propagation algorithms in Clawpack ( R. J. LeVeque, Univ. of Washington), was easily adapted to the single grid Cartesian layout of our two-patch sphere grid mapping. Furthermore, we were able to use an existing adaptive mesh refinement patch-based (AMR) code (Berger, Oliger et al.) to run computational efficient simulations.

In our current work, we are developing a new AMR code which uses wave propagation algorithms on non-overlapping AMR grids stored as leaves in a forest of quad- or oct-trees. The underlying tree-based code, p4est (Carsten Burstedde, Univ. of Bonn) manages the multi-block connectivity in a multi-processor environment and has been shown to be highly scalable in applications of interest to geophysicists. This new AMR code, which we call ForestClaw, will easily handle the adaptivity for our two-patch sphere grid, as well as the cubed-sphere, and more generally, any multi-block geometry.

We will present preliminary results from our efforts to use ForestClaw for modeling volcanic ash dispersal in the atmosphere. This is joint work with Carsten Burstedde (Univ. of Bonn) and researchers at the Cascade Volcanic Observatory (Vancouver, Washington).
AMMW02 25th September 2012
14:25 to 14:50
Accuracy of adaptive discontinuous Galerkin simulations
Adaptive mesh refinement generally serves to increase computational efficiency without compromising the accuracy of the numerical solution significantly. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result significantly. This question is investigated for a specific example of dry atmospheric convection, namely the simulation of warm air bubbles. For this purpose a novel numerical model is developed that is tailored towards this specific meteorological problem. The compressible Euler equations are solved with a Discontinuous Galerkin method. Time integration is done with a semi-implicit approach and the dynamic grid adaptivity uses space filling curves via the AMATOS function library. The numerical model is validated with a convergence study and five standard test cases.

A method is introduced which allows one to compare the accuracy between different choices of refinement regions even in a case when the exact solution is not known. Essentially this is done by comparing features of the solution that are strongly sensitive to spatial resolution. For a rising warm air bubble the additional error by using adaptivity is smaller than 1% of the total numerical error if the average number of elements used for the adaptive simulation is about 50% smaller than the number used for the simulation with the uniform fine-resolution grid. Correspondingly the adaptive simulation is almost two times faster than the uniform simulation.
AMMW02 25th September 2012
14:50 to 15:15
Giovanni Tumolo A semi-implicit, semi-Lagrangian, p-adaptive Discontinuous Galerkin method for the rotating shallow water equations
As a first step towards construction and analysis of a DG based dynamical core for high resolution atmospheric modeling, a semi-implicit and semi-Lagrangian Discontinuous Galerkin method for the shallow water equations with rotation is proposed and analyzed.

The method is equipped with a simple p-adaptivity criterion, that allows to adjust dynamically the number of local degrees of freedom employed to the local structure of the solution.

Numerical results in the framework of two dimensional test cases prove that the method captures accurately and effectively the main features of linear gravity and inertial gravity waves. Also the solution of nonlinear Stommel problem is correctly simulated. The effectiveness of the method is also demonstrated by numerical results obtained at high Courant numbers and with automatic choice of the local approximation degree.

The present research has been carried out during the PhD of the autor (supervisors F. Giorgi and L. Bonaventura) with financial support from the {\it Abdus Salam International Center for Theoretical Physics} and in collaboration with L.Bonaventura and M. Restelli {\it MOX - Politecnico di Milano}.

See MOX-Report 04/2012 Tumolo, G.; Bonaventura, L.; Restelli, M. A semi-implicit, semi-Lagrangian, p-adaptive Discontinuous Galerkin method for the shallow water equations.
AMMW02 25th September 2012
15:45 to 16:10
Particle methods for geophysical flow on the sphere
We develop a fluid dynamics solver for spherical domains based on the Lagrangian form of the equations of motion and a tree-structured mesh of fluid particles. Initial discretizations are based on the cubed sphere or icosahedral triangles, but these arrangements distort as the particles move with the fluid velocity. A remeshing scheme based on interpolation of the Lagrangian parameter is applied at regular intervals to maintain computational accuracy as the flow evolves. Ongoing work with adaptive mesh refinement is introduced. We present solutions of the advection equation with prescribed velocities from recent test cases (Nair and Lauritzen, 2010), and solutions of the barotropic vorticity equation where velocity is given by an approximate Biot-Savart integral and midpoint rule quadrature for test cases including Rossby-Haurwitz waves and Gaussian vortices . The discrete equations in the barotropic vorticity equation are those of point vortices on the sphere (e.g. Bogo molov, 1977). For the shallow water equations, we must also include the effects of point sources upon the fluid particles; we discuss the challenges posed by divergent flows in this Lagrangian context and strategies for evaluating nonlinear forcing terms on irregular meshes.
AMMW02 25th September 2012
16:10 to 16:35
John Boyd Progress in Radial Basis Function Methods: Adaptive Vortex-RBF Methods for the Sphere and Other Advances
Vortex methods, in which flow is modelled by overlapping Lagrangian vortex blobs, and radial basis function pseudospectral methods, which have proven their worth for irregular, adaptive grids, are combined into a single algorithm to compute flows on a sphere. The strengths and limitations of vortex-RBF methods for vortex-dominated flows with and without rotation will be illustrated by case studies including finite amplitude Rossby waves, vortex merger and deformation, and roll-up and instability. Other pertinent advances will be described as time permits.
AMMW02 25th September 2012
16:35 to 17:00
Michal Kopera Adaptive mesh refinement for discontinuous Galerkin method on quadrilateral non-conforming grid
In recent years there has been a significant interest in using the discontinuous Galerkin method (DG) for solving fluid dynamics problems. Studies in [1], [2], and [3] have shown that the DG method is indeed a good choice for the construction of future non-hydrostatic numerical weather prediction models. It combines high-order accuracy of the solution with geometric flexibility of unstructured grids and exhibits excellent scaling properties.

In order to increase the scale resolution capabilities of DG, as well as to take better advantage of available computing power, the use of adaptive mesh refinement (AMR) for a quadrilateral non-conforming grid is being investigated. The results of AMR implementation to a 2D version of the Non-hydrostatic Unified Model of the Atmosphere (NUMA) will be presented during the talk. Both static and dynamic h-adaptivity (element grid adaptivity) will be considered. Since increased local grid resolution has to impose severe constraints on the time-step of an explicit method, implicit-explicit (IMEX) and multi rate time integration will be discussed as well.

As the latest trend in scientific computing is to employ clusters of GPUs for high-performance computations, the implementation of CUDA kernels into AMR NUMA will be examined.

[1] Giraldo, F. & Restelli, M. (2008). A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in non-hydrostatic mesoscale atmospheric modelling: Equation sets and test cases. Journal of Computational Physics, 227, 3849-3877

[2] Restelli, M. & Giraldo, F.X. (2009). A conservative discontinuous Galerkin semi-implicit formulation for the Navier-Stokes equations in nonhydrostatic mesoscale modelling. SIAM J. Sci. Comp., 31, 2231-2257

[3] Kelly, J.F. & Giraldo, F.X. (2012). Continuous and discontinuous Galerkin methods for scalable nonhydrostatic atmospheric models: limited-area mode. Journal of Computational Physics, in review (2012).
AMMW02 25th September 2012
17:00 to 17:25
Second-order conservative remapping between unstructured spherical meshes
Remapping from one finite-dimensional description of a function to another is a common problem in numerical modelling. In particular, information transit between meshes is required for, e.g., model coupling or mesh adaptation. In order to preserve the properties of a numerical scheme such as conservativity, accuracy, positivity, etc., the remapping algorithm must itself possess these properties. A second-order, conservative remapping between unstructured spherical meshes is presented. Areas are computed exactly by the defect formula and gradients estimated by the Gauss formula. Data is tree-structured, so that neighbour search is done in logarithmic time. In addition, the algorithm lends itself well to parallelisation. Numerical tests on various unstructured grids are given.
AMMW02 26th September 2012
09:00 to 09:25
The orthogonal curvilinear terrain-following coordinate for atmospheric models
This study designs a novel terrain-following coordinate, called the “Orthogonal curvilinear terrain-following coordinate” (Orthogonal sigma coordinate, OS-coordinate), which has the ability to handle both the well-known “high level errors” and the “pressure gradient force (PGF) errors” above the steep terrain in the classic terrain-following coordinate (sigma-coordinate).

The OS-coordinate is proposed through a way quite different from and against the sigma-coordinate. The basis vectors of OS-coordinate which is unit and terrain-following are firstly designed, and then the corresponding definitions of every coordinates are solved, so that the scalar equations of OS-coordinate are solved. The PGF computational form has only one term in each momentum equation of OS-coordinate, thereby avoiding the PGF problem completely.

Finally, a unified framework is proposed to combine the equations of the Cartesian coordinate, sigma-coordinate and OS-coordinate together via an “on-off”, and is used to implement idealized advection experiments for testing the OS-coordinate. The evaluation on the experimental results show the vertical coordinate surfaces in the OS-coordinate can be much smoother than those in the sigma-coordinate, and therefore the OS-coordinate outperforms all along the sigma-coordinate. This new coordinate can be used for oceanic models as well, and needs to be tested in both the idealized and real-case experiments.
AMMW02 26th September 2012
09:25 to 09:50
Takeshi Enomoto Reexamination of non-hydrostatic formulations using the hydrostatic-pressure based co-ordinates
The rapid increase of computing power is making global non-hydrostatic simulations affordable. A natural approach is to extend the formulation to include the non-hydrostatic effect. The advantage of this approach is that the existing data assimilation and tools require minimal changes. ECMWF and JMA seem to pursue this approach. ECMWF has achieved TL7999 (corresponding to approximately 2.5 km) with a fast Lendre transform using the butterfly algorithm (Nils Wedi, pers. comm.). Hiromasa Yoshimura (MRI/JMA) has built a non-hydrostatic version of JMA GSM using double Fourier series. Their formulations are based on Laprise (1992) that proposes the vertical co-ordinates based on hydrostatic pressure. Juang (1992, 2000) also adopts hydrostatic sigma–co-ordinates in the vertical but there are subtle differences. The latter introduces the hydrostatic temperature. In a limited-area model, such as MSM, the hydrostatic temperature may be given externally. In a GCM, however, the hyd rostatic temperature must be determined internally if is not time-independent. We investigated the two formations and found the assumption of the hydrostatic state of Laprise (1992) may be used to diagnose the hydrostatic temperature within MSM. Similarly the hydrostatic assumption of Arakawa and Konor (2009) can be used. MSM is found to run stably with any of these diagnosed hydrostatic states. The diagnosed hydrostatic temperature would enable the application of the formulation of MSM to the global domain.
AMMW02 26th September 2012
09:50 to 10:15
A Variational Multiscale Stabilized Finite Element Method to solve the Euler Equations for Nonhydrostatic Stratified Benchmarks
In this talk we present a Variational Multiscale Stabilization (VMS) for Compressible Euler Equations applied to the Finite Element (FE) solution of nonhydrostatic stratified flows. The VMS method was firstly presented by Hughes and co-workers [1] in the context of incompressible flows. In the present work, recentely presented in [3], we extend these concepts to Compressible Flows. In the framework of nonhydrostatic atmospheric dynamics, we test the algorithm for problems at low Mach numbers. A general version of the current compressible VMS technique was originally devised for Computational Fluid Dynamics (CFD) of compressible flows without stratification [2]. The present work is justified by the previously observed good performance of VMS and by the advantages that an element-based Galerkin formulation offers on massively parallel architectures, a challange for both CFD and Numerical Weather Prediction (NWP). Unphysical vertical oscillations that may appear for not well-balanced approximations are a relevant problem in NWP, especially in the proximity of steep topography. In that respect, to properly discretize the dominant hydrostatics, a particular interpolation technique is proposed. To evaluate the performance of the method in this context, some standard test cases of stratified environments are presented.

References [1] T. Hughes, Multiscale Phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, CMAME 127 (1995) 387–401.

[2] M. Moragues, M. V´azquez, G. Houzeaux, R. Aubry, Variational Multiscale Stabilization of Compressible flows in Parallel Architectures, Parallel CFD 2010, Taiwan, May 2010.

[3] S. Marras, M. Moragues, M. V´azquez, O. Jorba, G. Houzeaux, A Variational Multiscale Stabilized Finite Element Method for the Solution of the Euler Equations of Nonhydrostatic Stratified Flows, J. Comput. Phys. (submitted 2012)
AMMW02 26th September 2012
10:15 to 10:40
2D and 3D simulations of a nonhydrostatic atmospheric model on a block-structured Cartesian mesh
Under the rapid development of computing power, this study aims at developing a next-generation atmospheric model for ultra-high resolution simulations at horizontal grid intervals of less than 100 meters. Recently, Cartesian grids are drawing attention as an attractive choice for high-resolution atmospheric models that need to handle steep slopes in mountainous areas. They have the advantage of avoiding errors because of the slantwise orientation of grid lines in models using conventional terrain-following grids. In our model, a cut cell method is used for representing topography on a Cartesian grid. Also, a block-structured mesh approach is introduced to achieve computationally efficient Cartesian grid simulations with both high vertical resolution near the ground and reasonable conservation characteristics.

The result of a 2D numerical simulation shows the model successfully reproduces a flow over a semi-circular mountain on a locally refined mesh around the mountain. The result agrees well with that using a uniformly fine mesh. Some recent 3D results of our model will also be discussed.
AMMW02 26th September 2012
11:10 to 11:35
Colm Clancy Semi-implicit predictor-corrector methods for atmospheric models
A class of semi-implicit time integration schemes is proposed for use in atmospheric modelling. Various explicit predictor-corrector methods can be combined with an implicit treatment of the linear terms responsible for fast modes in order to improve computational stability. Linear analysis is used to identify promising algorithms. These are then tested in a finite volume shallow water model on an icosahedral grid. This framework has been developed at Environment Canada and will be extended to a more complete, three-dimensional atmospheric model in the future. Experiments with standard test cases show that the proposed time schemes allow for stable integrations with relatively long time-steps, while maintaining a sufficient level of accuracy. In particular, they are more robust than the traditional, single-stage semi-implicit method using the leapfrog discretisation and do not require a time filter to control the computational mode.
AMMW02 26th September 2012
11:35 to 12:00
Laplace transform integration and the slow equations
We consider the Laplace transform (LT) filtering integration scheme applied to the shallow water equations, and demonstrate how it can be formulated as a finite difference scheme in the time domain by analytical inversion of the transform.

Both Eulerian and semi-Lagrangian versions of the scheme are analyzed. We show the relationship between the LT scheme and the slow equations. We demonstrate the advantages of the LT scheme by means of numerical integrations.
AMMW02 26th September 2012
12:00 to 12:25
A stable treatment of conservative thermodynamic variables for semi-implicit semi-Lagrangian dynamical cores
Atmospheric motions span a wide array of frequencies, the slowest of which provide us with our day to day weather. In numerical weather prediction it is necessary to narrow the focus to these lower frequencies for efficiency. The way this is typically done in global modeling is to apply an implicit time-differencing method to terms linked to high frequency motions while applying an explicit method to terms linked to low frequency motions like advection, thereby allowing a larger stable time step. While semi-Lagrangian schemes further increase efficiency by removing the stability restrictions of the standard CFL condition concerning velocity, they are still held to a slightly different deformation CFL condition concerning the local variation in velocity. As such, it is still necessary to slow these fast wave modes in the semi-Lagrangian framework to maintain a stable system.

Semi-Lagrangian systems employing a conservative thermodynamic variable such as potential temperature as a prognostic variable face a unique dilemma in applying this standard method because the term responsible for gravity wave generation is also a vertical advection term which is absorbed into the total derivative. Application of the scheme in the absence of an explicit gravity wave term results in an unstable system since the fast gravity mode frequencies are not properly reduced. Stability can be maintained at the expense of both accuracy and efficiency by way of artificial damping and reduced time steps.

The modification discussed here defines a basic state potential temperature field which is advected in an Eulerian fashion while the semi-Lagrangian method is applied to the perturbation potential temperature. As the gravity-wave term in question is now expressed explicitly through the total derivative of the basic state potential temperature, gravity mode stability is returned to the system; the semi-implicit treatment of the new term manages stability with respect to the associated CFL condition. Tests of the new scheme in the Navy Global Environmental Model (NAVGEM) show that the method allows stable integration at typical semi-Lagrangian time steps in the absence of artificial damping.
AMMW02 26th September 2012
12:25 to 12:50
Multi-Moment ADER-Taylor Methods for Systems of Conservation Laws with Source Terms in One Dimension
A new integration method combining the ADER time discretization with a multi-moment finite-volume framework is introduced. ADER runtime is reduced by performing only one Cauchy-Kowalewski (C-K) procedure per cell per time step, and by using the Differential Transform Method for high-order derivatives. Three methods are implemented: (1) single-moment WENO [WENO], (2) two-moment Hermite WENO [HWENO], and (3) entirely local multi-moment [MM-Loc]. MM-Loc evolves all moments, sharing the locality of Galerkin methods yet with a constant time step during p -refinement.

Five experiments validate the methods: (1) linear advection, (2) Burger's equation shock, (3) transient shallow-water (SW) , (4) steady-state SW simulation, and (5) SW shock. WENO and HWENO methods showed expected polynomial h -refinement convergence and successfully limited oscillations for shock experiments. MM-Loc showed expected polynomial h -refinement and exponential p -refinement convergence for linear advection and showed sub-exponential (yet super-polynomial) convergence with p -refinement in the SW case.

HWENO accuracy was generally equal to or better than a five-moment MM-Loc scheme. MM-Loc was less accurate than RKDG at lower refinements, but with greater h - and p -convergence, RKDG accuracy is eventually surpassed. The ADER time integrator of MM-Loc also proved more accurate with p -refinement at a CFL of unity than a semi-discrete RK analog of MM-Loc. Being faster in serial and requiring less frequent inter-node communication than Galerkin methods, the ADER-based MM-Loc and HWENO schemes can be spatially refined and have the same runtime, making them a competitive option for further investigation.
AMMW02 27th September 2012
09:00 to 09:25
Todd Ringler A Multi-Resolution Modeling Approach for Global Ocean Modeling
AMMW02 27th September 2012
09:25 to 09:50
Jared Whitehead Potential Vorticity: A Diagnostic Tool for General Circulation Models
Maintaining correlation between tracers and the dynamical wind and temperature fields with which they interact is a desirable trait of climate and weather models. A systematic, explicit test is developed to measure the consistency between a dynamical core's integration of the momentum equation, and its tracer transport algorithm. Potential vorticity is used as a diagnostic tool allowing direct comparison between the treatment of the dynamics and the integration of passive tracers. Several quantitative and qualitative metrics are suggested to measure this consistency including grid-independent probability density functions. Comparisons between the four primary dynamical cores of the National Center for Atmospheric Research's (NCAR) Community Earth System Model 1.0 (CESM) are presented. It is found that the finite volume (CAM-FV) and spectral-element (CAM-SE) dynamical cores perform better than the spectral-transform based Eulerian (CAM-EUL) and semi-Lagrangian (CA M-SLD) dynamical cores in the presence of a breaking wave.
AMMW02 27th September 2012
09:50 to 10:15
Peter Lauritzen A standard test case suite for two-dimensional linear transport on the sphere
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, “minimal” resolution, the ability of the transport scheme to preserve filaments, transport “rough” distributions, and to preserve pre-existing functional relations between species/tracers under challenging flow conditions.

The experiments are designed to be easy to set up. They are specified in terms of two analytical wind fields (one non-divergent and one divergent) and four analytical initial con- ditions (varying from smooth to discontinuous). Both conventional error norms as well as novel mixing and filament preservation diagnostics are used that are easy to implement. The experiments pose different challenges for the range of transport approaches from Lagrangian to Eulerian. The mixing and filament preservation diagnostics do not require an analytical/reference solution, which is in contrast to standard error norms where a “true” solution is needed. Results using a dozen state-of-the-art transport schemes that participated in the 2011 NCAR workshop on transport are presented.
AMMW02 27th September 2012
10:15 to 10:40
Evaluating numerical methods by using asymptotic limit solutions
Numerical models of the atmosphere and ocean 'solve' the governing Navier-Stokes equations, but because of the complexity of the true solutions, can only do so in a grossly averaged sense. Standard numerical analysis theory is then of limited use, because it expects solutions to be close to the truth. The Navier-Stokes equations are known to have solutions close to computable asymptotic limits in many cases of practical interest. This talk gives examples, including dynamics/boundary-layer interaction, frontal solutions where the asymptotic limit is singular, and long-term behaviour of baroclinic systems, together with numerical demonstrations. The technique should help to validate the new integration schemes being proposed.
AMMW02 27th September 2012
11:10 to 11:35
Paul Ullrich MCore: Towards a Multi-Resolution Non-Hydrostatic Finite-Volume Dynamical Core
This talk will focus on recent efforts towards developing a true multi-resolution framework for modeling regional climate in a global domain. In particular, I will present ongoing work on the high-order non-hydrostatic finite-volume MCore atmospheric general circulation model, which has been designed for massively parallel systems and with a focus on using mesh refinement to seamlessly tie together regional and global scales. Further, efforts to develop test cases of intermediate complexity, which include moisture and simplified physics parameterizations, have been undertaken and simulated within MCore. These efforts will be presented, along with a look at some upcoming approaches to numerical modeling using finite-volume methods on the sphere.
AMMW02 27th September 2012
11:35 to 12:00
A Three-Dimensional Finite-Volume Nonhydrostatic Icosahedral Modle (NIM)
The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM’s modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM uses innovations in model formulation similar to its hydrostatic version of the Flow-following Icosahedral Model (FIM) developed by Earth System Research Laboratory (ESRL) which has been tested and accepted for future use by the National Weather Service as part of their operational global prediction ensemble. Innovations from the FIM used in the NIM include:

* A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), * All differentials evaluated as finite-volume integrals around the cells, *Icosahedral grid optimization (Wang and Lee, 2011)

NIM extends the two-dimensional finite-volume operators used in FIM into the three-dimensional finite-volume solvers designed to improve pressure gradient calculation and orographic precipitation over complex terrain. The NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as warm bubble, density current, internal gravity wave, and mountain waves. Physical parameterizations have been incorporated into the NIM dynamic core and successfully tested with multimonth aqua-planet simulations.
AMMW02 27th September 2012
12:00 to 12:25
Xingliang Li A multi-moment constrained finite volume model for non-hydrostatic atmospheric dynamics
Two dimensional non‐hydrostatic compressible dynamic cores for atmosphere are developed by using a new nodal type high order conservative method, so called multi‐moment constrained finite volume (MCV) method. Different from conventional finite volume method, the predicted variables (unknowns) in an MCV scheme are the values at the solution points distributed within each mesh cell. The time evolution equations to update the unknown point values are derived from a set of constraint conditions based on multi‐moment concept, where the constraint on the volume integrated average (VIA) for each mesh cell is cast into a flux form and thus guarantees rigorously the numerical conservation. Two important features makes MCV method particularly attractive as an accurate and practical numerical framework for atmospheric and oceanic modelling. 1) Using nodal values at uniformly located solution points as the predicted variables provides great convenience in de aling with complex geometry and source terms, and 2) High order schemes can be built by using constraints in terms of different moments, which makes the numerical schemes more flexible and efficient. We present in this paper the dynamic cores that use the third and the fourth order MCV schemes. We have verified the numerical outputs of both schemes by widely used standard benchmark tests and obtained competitive results. The present numerical cores provide a promising and practical framework for further development of non‐hydrostatic compressible atmospheric models.
AMMW02 27th September 2012
13:35 to 14:00
DCMIP 2012: Tracer Transport Tests in Dynamical Cores
We investigate the accuracy of tracer transport algorithms in dynamical cores of weather and climate models using prescribed velocity test cases. The tests make use of three-dimensional flow, with the focus on extreme deformation, horizontal-vertical coupling, and flow in the presence of orography. These tests highlight common problems associated with advection in dynamical cores. Standard error measures allow us to assess convergence rates, monotonicity, and the effects of the diffusion mechanisms in tracer transport algorithms. We will present results form the 2012 Dynamical Core Model Intercomparison Project (DCMIP) workshop.
AMMW02 27th September 2012
14:00 to 14:25
Sasa Gabersek Numerical Simulations with a Three-Dimensional Spectral Element Model
Highly accurate numerical methods for solving partial differential equations that have been traditionally used in the computational fluid dynamics have yet to be fully exploited for geophysical fluid dynamics applications, such as weather prediction. We will present results obtained with a fully compressible, non-hydrostatic spectral element (SE) model in three dimensions. All of our results are obtained using an eighth order polynomial (p=8), which provides the best compromise between accuracy and computational cost. The number of elements (h), into which the computational domain is decomposed, is varied among experiments to achieve different effective spatial resolutions.

Introducing physical parameterizations into an SE model is challenging due to a number of aspects including the varying nodal spacing within each element. We highlight some of these challenges and our approaches to address them. The model is applied in a series of idealized experiments that include physical process parameterizations such as: i) flow over complex terrain with sub-grid scale mixing, and ii) a sea breeze that includes an evolving planetary boundary layer with surface fluxes.

We discuss the issues that arise when physical parameterizations are introduced into SE models. Also, scalability results over many computational cores will be addressed. In addition, we will compare the efficiency and accuracy of the results with a finite difference model (FD).
AMMW02 27th September 2012
14:25 to 14:50
Design of a dynamical core based on the nonhydrostatic unified system of equations
In this talk, we present the design of a dry dynamical core based on the nonhydrostatic “unified system” of equations. The unified system filters vertically propagating acoustic waves. The dynamical core predicts the potential temperature and horizontal momentum. It uses the predicted potential temperature to determine the quasi-hydrostatic components of the Exner pressure and density. The continuity equation is diagnostic (and used to determine vertical mass flux) because the time derivative of the quasi-hydrostatic density is obtained from the predicted potential temperature. The nonhydrostatic component of the Exner pressure is obtained from an elliptic equation. The main focus of this paper is on the integration procedure of this unique dynamical core. Height is used as the vertical coordinate, and the equations are vertically discretized on a Lorenz-type grid. Cartesian horizontal coordinates are used along with an Arakawa C-grid in the planar version of the dynamical core. The global version of the dynamical core is based on the vorticity and divergence predicting Z-grid formulation. The performance of the model in simulating a wide range of dynamical scales in the planar and global domains is demonstrated through idealized extratropical cyclogenesis simulations, and warm and cold bubble test cases.
AMMW02 27th September 2012
14:50 to 15:15
ICON-IAP: A non-hydrostatic global model designed for energetic consistency
The talk describes a new global non-hydrostatic dynamical core (ICON-IAP: Icosahedral Nonhydrostatic model at the Institute for Atmospheric Physics) on a hexagonal C-grid which is designed to conserve mass and energy. Energy conservation is achieved by discretising the antisymmetric Poisson bracket which mimics correct energy conversions between the different kinds of energy (kinetic, potential, internal). Because of the bracket structure this is even possible in a complicated numerical environment with (i) the occurrence of terrain-following coordinates with all the metric terms in it, (ii) the horizontal C-grid staggering on the Voronoi-mesh and the complications induced by the need for an acceptable stationary geostrophic mode, and (iii) the necessity for avoiding the Hollingsworth-instability. The model is equipped with a Smagorinsky-type nonlinear horizontal diffusion. The associated dissipative heating is accounted for by the application of the discrete product rule for derivatives. The time integration scheme is explicit in the horizontal and implicit in the vertical. In order to ensure energy conservation, the Exner pressure has to be off-centered in the vertical velocity equation and extrapolated in the horizontal velocity equation.

Test simulations are performed for small scale and global scale flows. A test simulation of linear nonhydrostatic flow over a rough mountain range shows the theoretically expected gravity wave propagation. The baroclinic wave test is extended to 40 days in order to check the Lorenz energy cycle. The model exhibits excellent energy conservation properties even in this strongly nonlinear and dissipative case. The Held-Suarez test confirms the reliability of the model over even longer timescales.
AMMW02 27th September 2012
15:45 to 16:10
Global, non-hydrostatic, cloud-permitting, medium-range forecasts using the spectral transform method: progress and challenges
Numerical weather prediction (NWP) requires an answer in real time with a window of approximately one hour to run a medium-range global forecast such that it can be delivered in time to its customers worldwide. While computational efficiency remains one of the most pressing needs of NWP, it is an open question how to most efficiently use the computer power available over the next twenty years, while seeking the most accurate and cost-effective solution. At the same time, there are significant scientific challenges to increase resolution further, changes to the governing equations, and how sub-gridscale (SGS) processes are represented. ECMWF plans to implement a global horizontal resolution of approximately 10km by 2015 for its assimilation and deterministic forecast system, and approximately 20km for the ensemble prediction system (EPS). The scales resolved at these resolutions are still hydrostatic and the efficiency of the contemporary hydrostatic, semi-Lagrangian, semi-imp licit solution procedure using the spectral transform method is likely to remain a relevant benchmark. However, due to the relative cost increase of the Legendre transforms compared to the gridpoint computations, very high resolution spectral models may become prohibitively expensive. Moreover, spectral-to-gridpoint transformations require data-rich global communications at every timestep that may become too expensive on massively parallel computers. Recent progress in the development of fast spherical harmonics transforms (Tygert, 2008,2010) based on the butterfly scheme (O’Neil et al, 2010) mitigate the computational expense of the spectral transforms. Results are presented that demonstrate the cost-effectiveness of the fast Legendre transforms (FLT) on the ibm_power7 architecture. The FLTs save both memory and computing time enabling the "world's first" successful T7999 (or equivalently ~2.5km horizontal resolution) global weather forecast with a spectral transform model.

Tygert, M., Fast algorithms for spherical harmonic expansions, II, J. of Comput. Physics, Vol. 227 (8), 2008, 4260-4279.

Tygert, M., Fast algorithms for spherical harmonic expansions, III, J. of Comput. Physics, Vol. 229 (18), 2010, 6181-6192.

O’Neil, M., F. Woolfe, V. Rohklin, An algorithm for the rapid evaluation of special function transforms, Appl. Comput. Harmon. Anal., Vol. 28(2), 2010, 203-226.
AMMW02 27th September 2012
16:10 to 16:35
Evaluation of mass fixing schemes for the ECMWF Integrated Forecasting System (IFS)
The purpose of this talk is to summarize the conservation properties of the ECMWF spectral semi-Lagrangian, semi-implicit IFS model and present results from some recently implemented algorithms for correcting global mass imbalances due to advection.

Several established algorithms of different complexity, such as the ones described in [1,2,3,4], will be summarized and assessed in the context of NWP forecasts. Results from water species advection and passive tracer advection will be presented. Strengths and limitations of these schemes will be analyzed as well as their ability to preserve monotonicity and the impact they have on forecast skill.

References

Bermejo R., Conde J., 2002: A conservative Quasi-Monotone Semi-Lagrangian Scheme. MWR, 130, 423-430.

A. Priestley, 1993: A Quasi-Conservative Version of the Semi-Lagrangian Advection Scheme, MWR, 121, 621-629.

Zerroukat M., 2010, A simple mass conserving semi-Lagrangian scheme for transport problems, JCP, 229, 9011-9019.

Williamson D.L., Rasch P.J., 1994, Water vapor transport in the NCAR CCM2, Tellus, 46A, 34-51.
AMMW02 27th September 2012
16:35 to 17:00
Michael Baldauf An exact analytical solution for gravity wave expansion of the compressible, non-hydrostatic Euler equations on the sphere
For the development and assessment of dynamical cores for atmospheric simulation models, suitable idealized test setups with known solutions are very useful. But only in rare cases exact analytical solutions exist for the underlying equation systems. In this work a slightly modified version of the original idea of Skamarock, Klemp (1994) is proposed: the quasi linear expansion of sound and gravity waves on a sphere induced by a weak warm bubble. For this case an exact analytical solution for the compressible, non-hydrostatic Euler equations was found for a shallow atmosphere and optionally with inclusion of Coriolis effects for a 'spherical f-plane-approximation'.

This solution can be used as reference for convergence studies of global models. 'Small earth' convergence tests with the ICON model of the Deutscher Wetterdienst (DWD) and the Max-Planck Institut of Meteorology (MPI) are shown.
AMMW02 27th September 2012
17:00 to 17:25
Christiane Jablonowski Highlights of the Dynamical Core Model Intercomparison Project (DCMIP)
The talk presents highlights of the Dynamical Core Model Intercomparison Project (DCMIP) and its associated 2-week summer school that has been held at NCAR in August 2012. DCMIP paid special attention to non-hydrostatic global models that are an emerging trend, especially in the climate modeling community. These allow high-resolution simulations and provide a pathway for embedded variable-resolution meshes in regions of interest. The primary goals of DCMIP were to assess the scientific designs of over 16 current and forthcoming dynamical cores, to establish new non-hydrostatic and moist dynamical core test cases in the dynamical core community, and to introduce innovative cyberinfrastructure tools. The talk surveys the DCMIP dynamical core test suite. This test hierarchy with increasing complexity (1) assesses the accuracy of 3D advection schemes via 3D deformational flows, (2) evaluates the evolution of gravity waves in non-rotating model configurations, (3) sheds light on the impact of orography, especially in the presence of orography-following vertical coordinates, (4) assesses dry baroclinic waves with dynamic tracers, and (5) suggests test cases of intermediate complexity that incorporate moisture and very simplified physical parameterizations. The latter include a new moist variant of the baroclinic wave test case, and idealized tropical cyclones. The test suite makes extensive use of small-planet experiments that are suggested as a computationally-efficient tool for high-resolution non-hydrostatic model evaluations. Highlights of the DCMIP model results are shown.
AMMW02 28th September 2012
09:00 to 09:25
Günther Zängl The Icosahedral Nonhydrostatic (ICON) model: formulation of the dynamical core and physics-dynamics coupling
The nonhydrostatic dynamical core of the ICON model is formulated on an icosahedral-triangular C-grid and uses the edge-normal wind component, the vertical wind speed, density and virtual potential temperature as prognostic variables. In the vertical, a generalized terrain-following coordinate based on height is used that allows for a rapid decay with height of topographic structures, thereby reducing the numerical discretization errors over steep mountains. Moreover, a truly horizontal formulation of the horizontal pressure gradient term is used that greatly improves numerical stability over steep mountains. The spatial discretizations are second-order, with some slight degradation near the pentagon points of the basic icosahedron, and are primarily optimized for computational efficiency, ensuring strict mass conservation and consistent tracer transport but no exact conservation of energy or vorticity-related quantities. Time integration is based on a second-order predictor-corrector scheme that is fully explicit in the horizontal and implicit for the terms entering into vertical sound wave propagation. The dynamics time step is therefore limited by the CFL stability condition for horizontal sound wave propagation, but a longer time step (typically 4x or 5x) is used for tracer transport and fast-physics parameterizations. A important aspect of physics-dynamics coupling is that all terms related to latent heat release have to be converted into temperature changes at constant volume because density is used as a prognostic variable and is kept fixed during the physics call.
AMMW02 28th September 2012
09:25 to 09:50
Mark Taylor CAM high-resolution AMIP simulations using a spectral finite element dynamical core
We will present results from high-resolution AMIP simulations using CAM-SE: The Community Atmosphere Model (CAM), running with the Spectral finite Element dynamical core from NCAR's High-Order Method Modeling Environment. CAM-SE is now supported within the Community Earth System Model. It uses fully unstructured conforming quadrilateral grids, and thus supports global high resolution through quasi-uniform grids and localized regions of high resolution with unstructured grids. For global 1/4 and 1/8 degree resolutions, CAM-SE runs efficiently on hundreds of thousands of processors on modern Cray and IBM supercomputers and obtains excellent simulation throughput. For variable resolution grids, our simulations benefit from a new mixed-formulation tensor-based hyper-viscosity operator. The mixed-formulation allows for efficient implementation in finite element methods, and a tensor form is used to provide the correct scale-aware dissipation, especially in the distorted elements which appear in resolution transition regions.
AMMW02 28th September 2012
09:50 to 10:15
John McGregor Comparing the formulations of CCAM and VCAM and their performance as atmospheric GCMs
Two cube-based atmospheric GCMs have been developed at CSIRO, the Conformal-Cubic Atmospheric Model (CCAM) and, more recently, the Variable Cubic Atmospheric Model (VCAM). The formulations of the dynamical cores of both models will be described and compared. CCAM is formulated on the conformal-cubic grid, whereas VCAM is cast on the equiangular gnomonic-cubic grid. CCAM is a 2-time-level semi-Lagrangian semi-implicit Eulerian model, whereas VCAM employs a split-explicit flux-conserving approach. Both models use reversible staggering for the wind components (McGregor, MWR, 2005) to produce good wave dispersion behavior. CCAM employs several orographic treatments that are not available for use in the VCAM dynamical core, with the interesting consequence that only VCAM requires hybrid vertical coordinates.

Both models include the same efficient message-passing framework. Although VCAM avoids the message-passing overheads necessitated by the Helmholtz solver of CCAM, if does have some overheads from more frequent calls to the wind staggering/unstaggering routines.

Aspects of the climatologies of both models will be compared and their overall advantages and disadvantages discussed. VCAM is presently being coupled to the Parallel Cubic Ocean Model (PCOM) from JAMSTEC; both the atmosphere and ocean model employ identical grids, and progress on this activity will be briefly presented.
AMMW02 28th September 2012
10:15 to 10:40
Thomas Melvin & Nigel Wood The dynamical core of the Met Office's Unified Model
The Met Office's Unified Model (MetUM) is used across a wide range of spatial and temporal scales, from very high resolution nowcasting to centennial climate predictions. Key to the accuracy and efficiency of its predictions is the dynamical core. The scalability of the dynamical core is becoming increasingly critical to the efficiency of the model as a whole.

An update on the progress, benefits and plans for the replacement dynamical core of the Met Office's Unified Model (ENDGame) will be given together with an overview of the project to design the next generation dynamical core for the the Unified Model (GungHo).
AMMW02 28th September 2012
11:10 to 11:35
The CMC 15-Km operational deterministic global forecast system with Yin-Yang grid
At Canadian meteorological center (CMC), we are currently implementing the future 15-km operational deterministic global forecast system. In the horizontal we use spherical coordinates on the overset Yin-Yang grid while in the vertical, we use a log-hydrostatic-pressure coordinate on the Charney-Phillips grid. The global forecast on the Yin-Yang grid is performed by considering a domain decomposition (a two-way coupling method) between two limited-area models (LAM), discretized on the two panels of Yin-Yang grid and using the same time step. Each panel of the Yin-Yang grid system is extended by a static halo region that plays the same role as the piloting region in limited-area modeling. Since the two sub-grids of the Yin-Yang grid do not match, the update of the variables in the pilot region is done by interpolation.

Each limited-area model uses the same fully implicit semi-Lagrangian method as in the GEM operational model to solve its own dynamic core. Geophysical fields are produced separately for each LAM grid however, The two LAM models use the same parametrization schemes for the physics configuration. For data assimilation, we use the Ensemble-Var (En-Var) approach where the 4D ensemble covariances are used to produce 4D analysis without TL/AD models.

In this presentation we will present some preliminary results of this work.
AMMW02 28th September 2012
11:35 to 12:00
The global nonhydrostatic atmospheric model MPAS: Preliminary results from variable-resolution mesh tests
The Model for Prediction Across Scales (MPAS) is comprised of geophysical fluid flow solvers using horizontally-unstructured spherical centriodal Voronoi meshes and a C-grid staggering of the prognostic variables. We have constructed a global atmospheric model for these meshes that solves the fully compressible nonhydrostatic equations using a finite-volume formulation coupled with a split-explicit time integration technique to handle acoustic modes. The Voronoi meshes are unstructured grids that permit variable horizontal resolution, and we plan to make use of variable-resolution meshes in our weather and regional climate applications. Towards this end, we have begun testing the robustness of variable-resolution global mesh simulations using both idealized test cases (baroclinic waves) and full NWP forecasts. Preliminary results for hydrostatic-scale tests (dx > 10 km) indicate that flow features are appropriately resolved relative to the local resolution if the mesh t ransition zones provide a smooth transition from coarser to finer resolution regions and if model filters are appropriately scaled by the local mesh spacing. We will present these results and discuss their implications for variable-resolution mesh configurations and for the end applications.
AMMW02 28th September 2012
12:00 to 12:25
The Icosahedral Nonhydrostatic (ICON) model: Scalability on Massively Parallel Computer Architectures
Simulation in numerical weather prediction and climate forecasting has a fast-growing demand for memory capacity and processing speed. For the last decade, however, computer technology has shifted towards multi-core chip designs while at the same time on-chip clock rates have increased only moderately. The parallel implementation of the ICON model's nonhydrostatic dynamical core therefore follows a hybrid distributed/shared memory approach, based on the Message Passing Interface (MPI) and the OpenMP API.

The ICON code couples the different encapsulated components of the earth system model, e.g. dynamics, soil, radiation, and ocean, with high-level language constructs. Its communication characteristics and programming patterns are designed to meet the main challenges in high performance computing, i.e. load balancing, cache efficiency, and low-latency networking, and take the unstructured triangular C-grid into account, which implies indirect addressing. Besides basic optimization strategies such as loop tiling and grid point reordering, the implementation employs special domain decomposition heuristics, parallel range-searching algorithms with logarithmic complexity, and makes use of asynchronous I/O servers to deal with the potentially prohibitive amount of data generated by earth system models. This facilitates the ICON code to extract an adequate level of performance on a wide range of HPC platforms, targeting large scalar cluster systems with thousands of cores as well as vector computers.
AMMW02 28th September 2012
13:30 to 13:55
SCALE-LES: Strategic development of large eddy simulation suitable to the future HPC
The Large Eddy Simulation is a vital dynamical framework to investigate the cloud-aerosol-chemistry-radiation interaction from the viewpoint of climate problem. So far, the LES using in the meteorological filed are having several problems. One problem was that it is large grid-size used, compromising to the suitability of LES. In addition, the aspect ratio of horizontal and vertical grids was much larger than unity. The grid-size must be reduced to several 10m and it is desirable that the aspect ratio is near unity for the atmospheric LES. The target domain was also narrow for less of computer resources. The large-scale computing using the recent powerful super-computer may enable us to conduct the LES with reasonable grid-size and wide domain. Ultimately, the global LES is one of milestones in near future. Another problem in LES applied on meteorological field is that the heat source owing to water condensation is injected in a grid box. Strictly considering, the grid-box heating collapse the theory of LES that the grid size is in the energy cascade domain. Nevertheless, we have used the dry theory of LES. Beside the above problem that should be resolved in the future, we are now confronting with computational problems for such large-scale calculations. The numerical method of fluid dynamical part in the atmospheric model has been shifted from the spectral transform method to the grid-point method. The former is no longer acceptable on the massively parallel platforms form the limitation of inner-connect communication. On the other hand, the latter also contains a new problem, which is so-called memory bandwidth problem. For example, even on K Computer, the B/F ratio is just 0.5. The key to get high computational performance is the reduction of load/store from and to the main memory and efficient use of cash memory. Similar problem occurs in the communication between computer nodes. The multidisciplinary team (Team SCALE) in RIKE/AICS is now tackling to such problems.
AMMW02 28th September 2012
13:55 to 14:20
An Inter-Comparison of Icosahedral Climate Models on the G8 Call: ICOMEX Project
The ICOsahedral-grid Models for EXascale Earth system simulations (ICOMEX) is the consortium for the climate models development toward the exascale computing. It started since October 2011 as one of the G8 call projects. Participated are NICAM (Japan), ICON (Germany), MPAS (UK and US), and DYNAMICO (France) model teams. On the road to the exascale computing, we would find many road blocks, such as file I/O speed, lower byte/flops rate, outer/inner node communication. In order to examine these problems, six working groups are seated together. The Japan team works on the model inter-comparison to be synergistic among working groups. Although all the participated models use the icosahedral-grid, the discretization methods are different. For example, the hexagonal shape of a control volume is used in NICAM, while the triangular shape is used in ICON. Through intercomparison of both computational and physical performances between models, we will find which aspects of the model configuration are advantagous toward exascale computing. Two types of experiments were performed until now using NICAM and ICON: the baroclinic wave test (Jablonowski and Williamson, 2006) and the statistical climatology test (Held and Suarez, 1994). The horizontal resolution is from 240km (glevel-5) to 14km (glevel-9), and higher resolution runs will be tested in future. For the Held and Suarez test case, NICAM and ICON simulated climatology similar to that shown in the original paper. The baroclinic wave test is also compared between the two models. To investigate computational aspects, we examined strong scaling of parallel computing. Tests were performed on the Westmere and Bulldozer machine by using 5 through 40 MPI processes. We found that the two models have a good scaling: the measured scaling efficiency is 0.8-0.9. We plan to perform the intercomparison experiments using K computer using a larger number of processes O(10^5) to examine detail profiles of very massive parallel cores.
AMMW02 28th September 2012
14:20 to 14:45
Time-parallel algorithms for weather prediction and climate simulation
The forecast of weather relies on computer models that need to be executed in real-time, meaning that a forecast needs to be disseminated to users well before the time period for which it is made. A challenge in the future will be to succeed in using the computing power available in massively parallel high-performance computers and meet the real-time requirement. Until now weather forecast and related climate simulation models have taken advantage of the parallelism of the computers by dividing the task to be performed in the horizontal space dimensions.

The purpose of this work is to develop algorithms that allow also parallelism in the time dimension. This increased parallelism should allow an acceleration of the execution time of weather and climate models. This acceleration in turn permits an increase in the space accuracy of models while still meeting the real-time requirement. The talk will present our preliminary work on the "Parareal" algorithm that has been developed for that purpose (Lions et al., 2001) and whose applications to date have included among others air quality, but ignored weather forecasting.

Weather forecasting presents a challenge for the method because of the presence of waves and advection. An important question is to examine how the traditional way to accelerate models with the semi-implicit semi-Lagrangian methodology can be advantageously blended with the “Parareal” approach.
AMM 1st October 2012
10:00 to 10:30
N Beisiegel Adaptive Discontinuous Galerkin Inundation Modelling
AMM 1st October 2012
10:30 to 11:00
D Holm Multiscale Fluid Models with Convected Microstructure
We will propose a multi-scale model of fluid dynamics which is loosely based on LF Richardson’s turbulence rhyme.

Big whirls have little whirls . . . and little whirls have lesser whirls . . .

The model will propose answers to the questions, “How do larger whirls affect the circulations of smaller whirls?” “How do the smaller scales participate in the interactions among the larger scales”.

The two key ideas are: (1) A WKB-like Fourier series decomposition of fluid velocity (2) Convection of microstructure
AMM 1st October 2012
13:30 to 14:00
T Ringler A Way Point on the Road to Dynamic Adaptivity: Early Results from Multi-Resolution Atmosphere and Ocean Models
AMM 1st October 2012
14:00 to 15:00
T Ringler What are the remaining outstanding issues with respect to multi-resolution models? A discussion session
AMM 1st October 2012
17:00 to 18:00
The Science of Ice Sheets: the Mathematical Modeling and Computational Simulation of Ice Flows
As a complement to the ongoing Newton Institute program "Multiscale Numerics for the Atmosphere and Ocean", we consider another component of climate systems, namely land ice. The melting of ice in Greenland and Antarctica would, of course, be by far the major contributor to sea level rise. Thus, to make science-based predictions about sea- level rise, it is crucial that the ice sheets covering those land masses be accurately mathematically modeled and computationally simulated. In fact, the 2007 IPCC report on the state of the climate did not include predictions about sea level rise because it was concluded there that the science of ice sheets was not developed to a sufficient degree so that such predictions could not be rationally and confidently made. In recent years, there has been much activity in trying to improve the state-of-the-art of ice sheet modeling and simulation. In this lecture, we review a hierarchy of mathematical models for the flow of ice, pointing out the relative merits and demerits of each, showing how they are coupled to other climate system components, and discussing where further modeling work is needed. We then discuss algorithmic approaches for the approximate solution of ice sheet flow models and present and compare results obtained from simulations using the different mathematical models.
AMM 2nd October 2012
10:00 to 10:30
Sound-proof global modeling for NWP and Climte
AMM 2nd October 2012
10:30 to 11:00
Sound-proof modeling on unstructured meshes
AMM 2nd October 2012
13:30 to 14:00
Quasi-anelastic vs. elastic modeling with ECMWF's IFS model
AMM 2nd October 2012
14:00 to 15:00
Sound-proof global models for atmospheres and oceans: a discussion session
AMM 3rd October 2012
10:00 to 10:30
J Klemp Experiences with a smoothed terrain-following vertical coordinate in MPAS
AMM 3rd October 2012
13:30 to 14:30
Weakly compressible flows: regime of validity of sound-proof approximations
The design regime of established sound-proof flow models (anelastic, pseudo-incompressible) involves tropospheric flows at length scales of 10-100 km and associated advective time scales. Most derivations of such models require "weak background stratification" in some sense. In this lecture I demonstrate through arguments of multiple scales asymptotics that this constraint can be quantified: The anelastic and pseudo-incompressible approximations should be valid up to dimensionless potential temperature stratifications of the order of the Mach number to the power 2/3.

Building on the morning lecture "Weakly compressible flows I: regime of validity of sound-proof appoximaitons", I will discuss regimes of length scales different from the orginal design regime of sound-proof models, which involves tropospheric flows at horizontal scales of 10-100 km and associated advective scales. In particular, I will show that short wave internal wave packets in the stratosphere can be described by the pseudo-incompressible approximation, but that the anelastic model looses its formal validity in this case.

At very small scales the pseudo-incompressible model reduces to the zero Mach number variable density equations, whereas the anelastic model reduces to the more restrictive Boussinesq approximation.

Sound-proofing appoximations affect the thermodynamic relationships. I will introduce a definition for the notion of "thermodynamic consistency" of sound-proof approximations, show how complying anelastic and pseudo-incompressible models can be formulated, and discuss their regimes of validity.

References:

Klein R., Achatz U., Bresch D., Knio O.M., and Smolarkiewicz P.K., Regime of Validity of Sound-Proof Atmospheric Flow Models, JAS vol. 67, pp 3226--3237 (2010)

Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., 42, 249-274 (2010)

AMM 4th October 2012
10:00 to 10:30
Multilevel time integrators for large-scale atmospheric flows
The fluid dynamically most comprehensive mathematical model of the atmosphere, the Euler equations, admits solutions driven by compressibility, buoyancy, and inertia. In the low Mach number case there is a scale separation of the three effects, and reduced sets of equations have been developed from the fully compressible model to describe the different regimes. In a context of increasing computing resources, reliable discrete solvers have to be devised, which can resolve the different scales and conserve of physical quantities as mass and total energy. As for the time discretization, one faces the choice between the stability-constrained explicit methods and the unconditionally stable, but costly and overdispersive implicit methods. Semi- implicit methods aim at exploiting the advantages of the two approaches as well as reducing their weak points. The goal of the work we present is to obtain a second-order accurate method to reproduce multiscale features of solutions of the fully compressible equations, filtering unwanted small-scale disturbances but retaining the properties of significant waves. An anelastic code for small-scale flows discretised with a projection method is extended with the insertion of an implicit pressure term; as a result, an additional zero-order term is added to the Poisson equation for the pressure in the correction step. On one hand, the approach is in agreement with a standard discretisation of the wave equation for the pressure; on the other hand, the discretisation reduces to the anelastic one for vanishing Mach number. Preliminary runs on advection test cases confirm the feasibility of the approach; large-scale tests will be performed with the insertion of the Coriolis term and the adoption of a suitable spherical grid. Then, a multilevel time discretisation based on multigrid techniques will enable to simulate multiscale test cases, thereby paving the way for an accurate and efficient all-speed solver.
AMM 4th October 2012
10:30 to 11:00
(non)-convergence properties of the Laplacian operator on the conformal cubed-sphere
AMM 4th October 2012
13:30 to 14:30
H Weller Planning meeting for new test cases and comparisons: a discussion session
AMM 8th October 2012
10:00 to 11:00
Automated parallel adjoints for model differentiation, optimisation and stability analysis
AMM 9th October 2012
10:00 to 11:00
M Gunzburger Multiscale spectral viscosity discretization methods for the Navier-Stokes equations or, another explicit filtering turbulence model, or another tweak of Smagor
AMM 10th October 2012
10:00 to 11:00
Designing numerical methods to respect asymptotic limit solutions
AMM 11th October 2012
10:00 to 11:00
B Seny A parallel multirate time-stepping strategy for ocean modelling
AMM 11th October 2012
13:30 to 14:30
The importance and examples of asymptotic limit solutions in the atmosphere and ocean: a discussion session
AMM 16th October 2012
10:00 to 10:30
Finite-volume transport schemes for Voronoi (hexagonal) meshes
AMM 16th October 2012
10:30 to 11:00
Can we make high-order spectral elements (quasi) monotonic?
AMM 17th October 2012
10:00 to 10:30
Comparison of finite element and finite volume in ocean modelling
AMM 17th October 2012
13:30 to 14:30
Transport modeling: How much accuracy do we need for atmospheric simulation and how should we achieve high order? A discussion session
AMMW03 22nd October 2012
13:30 to 14:15
Nigel Wood The Dynamical Core of the Met Office Unified Model: the challenge of future supercomputer architectures
This decade is set to be an interesting one for operational weather and climate modelling. The accuracy of weather forecasts has reached unprecedented and probably unexpected levels: large-scale measures of accuracy continue to improve at the rate of 1 day every 10 years so that today's 3 day forecast is as accurate as the 1 day forecast was 20 years ago.

In order to maintain this level of improvement operational centres need to continue to increase the resolutions of their models. Increasingly this means running models at resolutions of the order of a kilometre. This leads to many challenges. One is how to handle processes that are only barely resolved at those scales. Another is how to present, and also verify, forecasts that are inherently uncertain due to the chaotic nature of the atmosphere.

A more practical issue though is simply how to run the models at these increased resolutions! To do so requires harnessing the power of some of the world's largest supercomputers which are entering a period of radical change in their architecture.

That challenge is made more difficult by the fact that the UK Met Office's model (the MetUM) is unified in that the same dynamical core (and increasingly also the same physics packages and settings) is used for all our operational weather and climate predictions. The model therefore has to perform well across a wide range of both spatial scales [O(10^0)-O(10^4)km] and temporal scales [O(10^0)-O(10^4) as well as a wide range of platforms.

This talk will start by outlining the current status of the MetUM, then discuss planned developments (focussing on numerical aspects) before going on to highlight recent progress within GungHo! - the project that is redesigning the dynamical core of the model.
AMMW03 22nd October 2012
14:15 to 14:40
Mikhail Tolstykh Development of the next generation SLAV global atmospheric model
SLAV is the global finite-difference semi-Lagrangian numerical weather prediction model used operationally at Hydrometcentre of Russia. Its features are the use of vorticity-divergence formulation (in horizontal plane) on the unstaggered grid and 4th-order finite differences. The current version in work has the resolution of (0.18-0.22) degrees in latitude, 0.225 degrees in longitude, 51 levels. The presentation covers two topics: 1. Further development of the existing hydrostatic version. This includes: - Implementation of the mass-conserving semi-Lagrangian advection on the reduced lat-lon grid. This is a 3D extension of (Tolstykh, Shashkin, JCP 2012). Some preliminary results will be shown. - Recent increase of code scalability from 160 to more than 800 cores. - Work on further increase of scalability. 2. Plans for development of the global nonhydrostatic model. We plan to test a parallel elliptic solver (the code developed at INM) on different massively parallel platforms with a matrix arising in the semi-implicit discretization of MC2-type nonhydrostatic model formulation. Depending on the results, we will choose between the semi-implicit and horizontally explicit-vertically implicit (HE-VI) time integration schemes. The potential choice of HE-VI would imply the radical changes in the next generation of our dynamical core. These changes will be also discussed in the presentation.
AMMW03 22nd October 2012
15:10 to 15:55
Nils Wedi ECMWF's roadmap for non-hydrostatic modelling, existing and future challenges and recent progress in solving these
AMMW03 22nd October 2012
16:00 to 16:25
A cell-integrated SLSI shallow-water model with conservative and consistent mass and scalar mass transport
AMMW03 22nd October 2012
16:45 to 17:20
Richard Loft G8 ECS: Enabling climate simulation at extreme scale
AMMW03 23rd October 2012
09:30 to 10:05
Günther Zängl The ICON model and its relationship to the ICOMEX project
The ICON (ICOsahedral Nonhydrostatic) model is formulated on an unstructured icosahedral-triangular C-grid and applies several levels of optimization for efficient use on future computer architectures. The time-stepping scheme of the dynamical core is a horizontally fully explicit predictor-corrector scheme with implicit treatment of vertically propagating sound waves only. This way, only nearest-neighbour communication is required at runtime if the optional global diagnostics are turned off. The decision for a fully explicit dynamical core in favour of a split-explicit one is based on the fact that a global model extending into the mesosphere needs to be numerically stable up to wind speeds well in excess of 200 m/s because such high extrema can be reached in breaking gravity waves in the mesosphere. The ratio between maximum wind speed and sound speed is thus too small to benefit from a split-explicit approach. Time splitting is applied instead between the dynamical core and tracer transport and the physics parameterizations, the time step ratio being usually 4 or 5. Further optimizations include a dedicated radiation grid for which at most 60% of the grid points belonging to a given processor are sunlit at once, and an option to turn off moist physics and the transport of cloud an precipitation variables from the lower stratosphere upwards. Lower-level optimizations include a variable inner loop length for cache blocking or, alternatively, efficient use of vector architectures, a directive-based option to optimize the loop order for indirectly addressed operations, placement the halo grid points at the index vector with an ordering according to their halo level. Substantial improvements are still needed in the field of memory scaling, particularly regarding the setup phase of the domain decomposition, and for I/O, which so far is asynchronous but not yet parallelized. ICON is one of the models participating in the ICOMEX (ICOsahedral-grid Models for EXascale earth-system simulations) project, which is dedicated at optimizing several key components of our modelling systems for future computer architectures. The sub-projects include a domain-specific language approach to optimize the memory order of the array variables for a variety of platforms, parallel internal postprocessing, parallelization concepts for I/O and optimized data formats, usage of GPUs and optimization of Helmholtz equation solvers needed for implicit time-stepping schemes. In addition, a continuous model intercomparison effort is made in order to systematically analyze the strengths and weaknesses of the participating models with respect to computational efficiency and scientific aspects (accuracy, conservation properties etc.), with the goals to learn from each other and to iteratively improve the identified weaknesses in each participating model.
AMMW03 23rd October 2012
10:05 to 10:40
Jones and Jacobsen "Can Models Built upon Unstructured Grids be Computationally Competitive on Emerging High-Performace Architectures?
AMMW03 23rd October 2012
11:00 to 11:45
Limited area model weather prediction using COSMO with emphasis on the numerics of dynamical cores (including some remarks on the NEC vector supercomputer)
The current developments of the dynamical core of the COSMO model will be described. These are mainly a consolidated version of the fast waves solver in the split-explicit (horizontally explicit – vertically implicit, HE-VI) time-integration framework. The new formulation contains the use of an improved vertical discretisation. A discretisation error analysis shows the need for weighted averages in strongly stretched staggered (Lorenz) grids, in particular for the divergence operator. The use of the strong conservation form for the divergence operator potentially increases again the accuracy of metric correction terms. Further use of a Mahrer (1984) discretisation of horizontal pressure gradients allows the stable integration of steeper slopes compared to the traditional terrain following formulation. The experiences during this development with our NEC vector computer will be discussed, too. A new test case for models using the compressible non-hydrostatic Euler equations was defined, which allows the derivation of an analytic solution. This solution is exact in the sense that it can be used for convergence studies of compressible models. The new fast waves solver is tested against this test case. Another development branch in COSMO concerns the improvement of both the conservation properties of the dynamical core and the ability to handle steep slopes. For this purpose the usability of the anelastic Lipps, Hemler (1982) equation set and the discretisation of the EULAG model are considered. In the framework of the ‘Metström’ priority program of the German Research Community (DFG) the ‘Discontinous Galerkin’ method is inspected as another possible option of a future dynamical core for COSMO.
AMMW03 23rd October 2012
11:45 to 12:10
A primal-dual mixed finite element method for accurate and efficient atmospheric modelling on massively parallel computers
Efficient modelling of the atmosphere using massively parallel computers will require a quasi-uniform grid to avoid the communication bottleneck associated with the poles of the traditional latitude-longitude grid. However, achieving an accurate solution on a quasi-uniform grid is non-trivial. A mixed finite element method can provide the following desirable properties: mass conservation; a C-grid-like placement of variables for accurate wave dispersion and adjustment; vanishing curl of gradient; linear energy conservation; and steady geostrophic modes in the linear f-plane case. A further desirable property is that the potential vorticity (PV) should evolve as if advected by some chosen (accurate) advection scheme. This can be achieved by inserting the PV fluxes into the nonlinear Coriolis term that appears in the vector invariant' form of the momentum equation, provided the PV fluxes themselves can be constructed. Introducing a dual family of function spaces, in which the PV lives in a piecewise constant function space, along with suitable maps between primal and dual spaces, provides a convenient framework in which the PV fluxes can be computed by a finite volume advection scheme in the dual space.

The scheme can be implemented in terms of a small number of sparse matrices that can be precomputed off-line, avoiding the need for numerical quadrature at run time. A mass matrix and two dual-primal mapping operators need to be inverted at each time step, but these are well conditioned and the inversion can be absorbed into the iterative solver used for implicit time stepping at only a modest increase in cost. Some sample shallow water model results on a hexagonal icosahedral grid and a cubed sphere grid will be presented.
AMMW03 23rd October 2012
12:10 to 12:35
Time-parallel algorithms for weather prediction and climate simulation
The forecast of weather relies on computer models that need to be executed in real-time, meaning that a forecast needs to be disseminated to users well before the time period for which it is made. A challenge in the future will be to succeed in using the computing power available in massively parallel high-performance computers and meet the real-time requirement. Until now weather forecast and related climate simulation models have taken advantage of the parallelism of the computers by dividing the task to be performed in the horizontal space dimensions.

The purpose of this work is to develop algorithms that allow also parallelism in the time dimension. This increased parallelism should allow an acceleration of the execution time of weather and climate models. This acceleration in turn permits an increase in the space accuracy of models while still meeting the real-time requirement. The talk will present our preliminary work on the "Parareal" algorithm that has been developed for that purpose (Lions et al., 2001) and whose applications to date have included among others air quality, but ignored weather forecasting.

Weather forecasting presents a challenge for the method because of the presence of waves and advection. An important question is to examine how the traditional way to accelerate models with the semi-implicit semi-Lagrangian methodology can be advantageously blended with the “Parareal” approach.
AMMW03 23rd October 2012
13:30 to 14:15
Henry Weller Addressing unstructuredness and hardware and software divergence
AMMW03 23rd October 2012
14:15 to 14:40
Development of a Nonhydrostatic Unified Atmospheric Model (NUMA) on Multi-Core and Many-core Computer Architectures
We have been developing a nonhydrostatic atmospheric model based on the fully compressible Euler equations for applications in both local and global atmospheric modeling. This new model, NUMA, has been designed to be unified in terms of: the class of problems that it can solve (i.e., local and global modeling); the class of numerical methods that it uses in space (i.e., continuous AND discontinuous Galerkin methods); the class of time-integrators that it can use (i.e., Implicit-Explicit methods using multi-step and multi-stage methods); the types of iterative solvers and preconditioners that it contains (an entire suite of methods such as GMRES, BiCGStab, Chebyshev, etc.); and the types of computer architectures that it is targeted for (e.g., multi-core and many-core/heterogeneous computing). In this presentation, we shall touch on all the highlights listed above and describe the current status of the model especially focusing on the performance of this new model.
AMMW03 23rd October 2012
15:10 to 15:55
tba
AMMW03 23rd October 2012
16:00 to 16:25
Fully automatic adjoints: a robust and efficient mechanism for generating adjoint dynamical cores
AMMW03 23rd October 2012
16:45 to 17:20
Peter Jimack On the Development of Implicit Solvers for Time-Dependent Systems
This presentation will describe some of our recent experiences in the development of efficient implicit solvers for systems of nonlinear time-dependent partial differential equations. These experiences are for different applications to weather and climate prediction, so the primary aim of the presentation is to stimulate discussion on some of the challenges and opportunities associated with the development of efficient implicit solvers. The main issues that will be addressed centre around the fast solution of the discrete algebraic systems arising at each time step: with a focus on multilevel solution methods and their parallel implementation. If time permits the further issues of adaptivity in time and space will also be considered.
AMMW03 24th October 2012
09:30 to 10:05
Cube-based atmospheric GCMs at CSIRO
Two cube-based atmospheric GCMs have been developed at CSIRO, the Conformal-Cubic Atmospheric Model (CCAM) and, more recently, the Variable Cubic Atmospheric Model (VCAM). The design of the dynamical cores of both models will be described and compared. CCAM is formulated on the conformal-cubic grid, and employs 2-time-level semi-Lagrangian semi-implicit numerics. On the other hand, VCAM is cast on the highly-uniform equiangular gnomonic-cubic grid and employs a split-explicit flux-conserving approach, which provides benefits for modelling trace gases. Both models use reversible staggering for the wind components (McGregor, MWR, 2005) to produce good wave dispersion behaviour. The models use the same physics package. CCAM includes the Miller-White nonhydrostatic treatment, whereas VCAM is presently an hydrostatic model.

Both models use an efficient MPI message-passing strategy. Although VCAM avoids the message-passing overheads necessitated by the Helmholtz solver of CCAM, it instead has some minor overheads related to more frequent calls to the wind staggering/unstaggering routines. Timings will be shown for simulations utilising up to 288 processors.

Comparative model performance will be shown for idealized advection tests, the Held-Suarez test case, aquaplanet simulations, and for AMIP simulations.
AMMW03 24th October 2012
10:05 to 10:40
I will present initial results for a three-dimensional, hydrostatic, global atmospheric model combining quadtree, horizontal adaptivity on a cubed sphere grid with a standard, layered vertical discretisation. This model is implemented within the Gerris framework (http://gfs.sf.net) and thus automatically inherits attributes such as data parallelism and load-balancing. For large-scale atmospheric simulations, I will show that quadtree-adaptivity leads to a large gain in the scaling exponent relating computational cost to the resolution of sharp frontal structures.
AMMW03 24th October 2012
11:00 to 11:45
High resolution and variable resolution capabilities of the Community Atmosphere Model (CAM) with a spectral finite element dynamical core
I will describe our work developing CAM-SE, a highly scalable version of the Community Atmosphere Model (CAM) running with the spectral element dynamical core from NCAR's High-Order Method Modeling Environment. For global 1/4 and 1/8 degree resolutions CAM-SE runs efficiently on hundreds of thousands of processors on modern supercomputers and obtains excellent simulation throughput. CAM-SE also supports fully unstructured conforming quadrilateral grids. I will show results using a variable resolution grid with 1/8 degree resolution over the central U.S., transitioning to 1 degree over most of the globe. We hope that the variable resolution can provide a 10-100 times more efficient way to calibrate and evaluate the CAM 1/8 degree configuration.

CAM-SE uses quadrilateral elements and tensor-product Gauss-Lobatto quadrature. Its fundamental computational kernels look like dense matrix-vector products which map well to upcoming computer architectures. It solves the hydrostatic equations with a spectral element horizontal descritization and the hybrid coordinate Simmons & Burridge (1981) vertical discretization. It uses a mimetic formulation of spectral elements which preserves the adjoint and annihilator properties of the divergence, gradient and curl operations. These mimetic properties result in local conservation (to machine precision) of mass, tracer mass and (2D) potential vorticity, and semi-discrete conservation (exact with exact time-discretization) of total energy. Hyper-viscsoity is used for all numerical dissipation.
AMMW03 24th October 2012
11:45 to 12:10
Evaluating Variable-Resolution CAM-SE as a Numerical Weather Prediction Tool
The global modeling community has traditionally struggled simulating meso-alpha and meso-beta scale (25-500 km) systems in the atmosphere such as tropical cyclones, strong fronts, and squall lines. With traditional General Circulation Model (GCM) resolutions of 50-300 km, these features have been under-resolved and require significant parameterization at the sub-grid scale. In an effort to help alleviate these issues, the use of limited area models (LAMs) with high resolution has become popular, although, by definition, these models typically lack two-way communication with the exterior domain. Variable-resolution global dynamical models can serve as the bridge between traditional global forecast models and high-resolution LAMs by applying fine grid spacing in areas of interest. These models can utilize existing computing platforms to model high resolutions on a regional basis while maintaining global continuity, therefore eliminating the need for externally-forced and possib ly numerically and physically inconsistent boundary conditions required by LAMs.

A statically-nested, variable-mesh option has recently been introduced into the National Center for Atmospheric Research (NCAR) Community Atmosphere Model's (CAM) Spectral Element (SE) dynamical core. We present short-term CAM-SE model simulations of historical tropical cyclones and compare the model's prediction of storm track and intensity to other global and regional models used operationally by hurricane forecast centers. Additionally, we explore the model's ability to simulate other weather phenomenon traditionally unavailable to global modelers such as mesoscale convective systems and precipitation lines associated with frontal passages. We also discuss the performance of existing parameterizations in CAM with respect to high-resolution modeling as well as consider the potential computational benefits in using a variable-resolution setup as an operational tool for both weather and climate prediction.
AMMW03 24th October 2012
12:10 to 12:35
A prototype model for coupled simulations of regional climate suitable for massively parallel architectures
The formulation of regional climate models has been undergoing major changes, including advances in variable-resolution models and attempts to simulate regionally the coupled atmosphere-ocean system. This talk outlines the design of a prototype global variable-resolution, coupled atmosphere-ocean model. Although the grid can be smoothly deformed into a global simulation, the climate model has been optimised for regional simulations where the grid can be focused over a specified location using a Schmidt transformation. Both atmosphere and ocean dynamical cores employ a reversible staggerring between Arakawa A and C grids. Theoretically this approach can produce very good dispersion characteristics for both atmosphere and ocean models. The performance of the model scales well for 300+ processors and is expected to be suitable for massively parallel architectures, as the approach avoids latency problems associated with mismatched atmosphere and ocean grids. Furthermore, th e approach could be appropriate for global climate models if computing resources are increased by a factor of 10 with the next generation of supercomputers. We can suppress error growth on the coarser regions of the variable-resolution grid by downscaling with a system of scale-selective filters, where the filters use an efficient convolution-based approach that can operate with non-periodic boundary conditions and irregular coastlines, in the case of the ocean model. Some preliminary results are presented for practical applications of the model simulating regional climate, as well as a discussion of the algorithms used for the reversible staggering and the scale-selective filters.
AMMW03 24th October 2012
13:30 to 14:15
Tom Edwards Earth system modeling strategies on extreme scale architectures
Achieving the highest possible performance capability is a key requirement for earth system modeling community. Extreme scale architectures, including those currently available, provide opportunities for the advancement of simulation capabilities and present challenges for the HPC community as a whole. A number of significant factors have been identified in the development and deployment of Exascale systems. Approaches to address these challenges will strongly influence modeling strategies. As we enter into the Exascale era, a determinant for success will be greater levels of cooperation between model developers and the broader HPC community. Several modeling groups have already engaged in co-development approaches to identify and address factors limiting performance, scalability and efficiency. A further consideration moving forward will be the impact on HPC architectures and workflows as the science community becomes increasingly engaged with data intensive approaches.
AMMW03 24th October 2012
14:15 to 14:40
Scalability of Elliptic Solvers in Numerical Weather and Climate Prediction
Numerical weather- and climate- prediction requires the solution of elliptic partial differential equations with a large number of unknowns on a spherical grid. In particular, if implicit time stepping is used in the dynamical core of the forecast model, an elliptic PDE has to be solved at each time step. This often amounts to a significant proportion of the model runtime. The goal of the Next Generation Weather and Climate Prediction (NGWCP) project is the development of a new dynamical core for the UK Met Office Unified Model with a significantly increased global model resolution, resulting in more than $10^{10}$ degrees of freedom for each atmospheric variable. To run the model operationally, the solver has to scale to hundreds of thousands of processor cores on modern computer architectures.

To investigate the scalability of the implicit time stepping algorithm we have tested and optimised existing solvers in the Distributed and Unified Numerics Environment (DUNE) and the Hypre library. In addition we also implemented a matrix-free parallel geometric multigrid code with a vertical line smoother. We demonstrate the scalability of the solvers on up to 65536 cores of the Hector supercomputer for a system with $10^{10}$ degrees of freedom for the elliptic PDE arising from semi-implicit semi-Lagrangian time stepping.

To identify the most promising solver we investigated the robustness of simple and widely used preconditioners, such as vertical line relaxation, and more advanced multigrid methods. We compared algebraic- and matrix-free geometric multigrid algorithms to quantify the matrix- and coarse-grid- setup costs and studied the performance of various solvers on different computer architectures.
AMMW03 24th October 2012
15:10 to 15:55
Max Gunzberger Parallel Algorithm for Spherical Delaunay Triangulations and Spherical Centroidal Voronoi Tessellations
AMMW03 24th October 2012
16:00 to 16:25
Multilevel Markov-Chain Monte Carlo Methods for Large Scale Problems
Monte Carlo methods play a central role in stochastic uncertainty quantification and data assimilation. In particular Markov chain Monte Carlo methods are of great interest also in the atmospheric sciences. However, they are notorious for their slow convergence and high computational cost. In this talk I will present revolutionary recent developments to mitigate and overcome this serious problem using a novel multilevel strategy and deterministic sampling rules. The talk will focus on methodology. The applications are so far mainly coming from other fields.
AMMW03 24th October 2012
16:45 to 17:20
Richard Loft Meeting the Challenge of Many-core Architectures in Weather and Climate Models
Many-core processor systems such as GPU's and Intel's Xeon Phi achieve higher theoretical performance and improved power efficiency by a trading a decrease in clock speed for an increase in the number of compute threads. The questions relevant to this meeting are: 1) Do these architectures offer real benefits in performance over conventional multiprocessors for climate and weather applications? 2) If so, is it worth refactoring these large, complex applications to achieve these benefits? Over the past few years, many weather and a few climate groups around the world have been trying to answer these questions. This talk will survey the their progress and experiences, as presented by them at a series of many-core workshops held at NCAR over the past two years.

Specific topics will include: the right and wrong way to measure, report, and think about many-core performance; assessment of the various programming paradigms currently available for the processor + many-core accelerator architecture; experience with different compilers and tools; and the viability of the code refactoring strategies for many-core processors that have been tried.
AMMW03 25th October 2012
09:30 to 10:05
Porting and optimisation of the Met Office Unified Model on Petascale architectures
We present porting, optimisation and scaling results from our work with the United Kingdom's Unified Model on a number of massively parallel architectures: the UK MONSooN and HECToR systems, the German HERMIT and the French Curie supercomputer, part of the Partnership for Advanced Computing in Europe (PRACE). The model code used for this project is a configuration of the Met Office Unified Model (MetUM) called Global Atmosphere GA3.0, in its climate mode (HadGEM3, Walters et al., 2011, and Malcolm et al., 2010). The atmospheric dynamical core uses a semi-implicit, semi-Lagrangian scheme. The model grid is spherical (a lat/lon grid) and polar filtering is applied around the two singularities. For the configuration used on PRACE, with a horizontal grid spacing of 25km (N512) and 85 vertical levels up to 85km, we use a 10-minute time step. Initial conditions are derived from fully balanced coupled experiments at lower resolution and atmosphere/land surface perturbations are imposed using standard Met Office tools for ensemble initialisation. Initial development occurred on a NERC-MO joint facility, MONSooN, with 29 IBM-P6 nodes, using up to 12 nodes. In parallel with this activity, we have tested the model on the NERC/EPSRC supercomputer, HECToR (CRAY XE6), using 1'536 to 24'576 cores. The scaling breakthroughs came after implementing the use of hybrid parallelism: OpenMP and MPI. The N512 model scales effectively up to 12'244 cores and has now been successfully ported to PRACE TIER-0 systems (Curie and HERMIT), where it is operated in ensemble mode. Current developments include extensions to 17km and 12km grid spacing (N768 and N1024), which make use of up to 96 nodes on the new Met Office IBM-P7 system. The use of the next UM dynamical core, "EndGame", offers scaling improvements, with good performance on twice the current amount of cores, by altering the horizontal and vertical grid stagger, as well as eliminating the need for polar filtering.
AMMW03 25th October 2012
10:05 to 10:30
Chris Budd Adaptivity using moving meshes
AMMW03 25th October 2012
10:30 to 10:55
Michal A. Kopera & Frank X. Giraldo Adaptive mesh refinement for a 2D unified continuous/discontinuous Galerkin Non-hydrostatic Atmospheric Model
The adaptive mesh refinement techniques for element-based Galerkin methods are becoming a strong candidate for future numerical weather prediction models. Particular attention has been paid to the discontinuous Galerkin method [1], [2], [3] as it avoids global assembly of data and makes the implementation of the algorithm easier. In this presentation we will focus on the extension of the 2D discontinuous Galerkin, quad-based non-conforming adaptive mesh refinement algorithm to a continuous Galerkin formulation. The novelty of this approach is that we propose to do this within a unified CG/DG nonhydrostatic atmospheric model that we call NUMA (Nonhydrostatic Unified Model of the Atmosphere). NUMA is equipped to handle AMR at various levels: IMEX time-integrators are used to be able to use large time-steps and a new class of preconditioners [4] have been specifically designed to handle the IMEX methods with AMR.

[1] A. Muller, J. Behrens, F.X. Giraldo, V. Wirth (2011). An Adaptive Discontinuous Galerkin Method for Modelling Atmospheric Convection. Defense Technical Information Center Report, http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA546279

[2] S. Blaise, and A. St-Cyr (2011). A Dynamic hp-Adaptive Discontinuous Galerkin Method for Shallow-Water Flows on the Sphere with Application to a Global Tsunami Simulation, Monthly

[3] M. A. Kopera and F.X. Giraldo (2012). AMR for a 2d DG Nonhydrostatic atmospheric model, in preparation.

[4] L.E. Carr, C.F. Borges, and F.X. Giraldo (2012). An element-based spectrally-optimized approximate inverse preconditioner for the Euler equations, SIAM J. Sci. Comp. (in press).
AMMW03 25th October 2012
11:15 to 11:40
Linear analyses of RK IMEX schemes for atmospheric modelling
AMMW03 25th October 2012
11:40 to 12:05
tba
AMM 1st November 2012
10:00 to 10:30
Q Chen A co-volume scheme for the nonlinear shallow water equations on non-orthogonal grid
AMM 5th November 2012
10:00 to 11:00
S Vater On asymptotically adaptive numerical methods for long wave shallow water flows
AMM 6th November 2012
10:00 to 11:00
R LeVeque High-resolution finite volume methods and multidimensional wave-propagation algorithms
AMM 6th November 2012
13:30 to 14:30
J Behrens On the trial against Italian seismologists following the l'Aquila earthquake - facts, questions, consequences? A discussion session
Here is a link to the Prezi presentation, I prepared to introduce to today's discussion on the l'Aquila trial. Please note that the presentation stays online, and cannot be downloaded. http://prezi.com/1yuc8fkg0omj/background-and-discussion-material-to-laquila-trial/
AMM 7th November 2012
10:00 to 11:00
R LeVeque Cut-cell Cartesian grid finite volume methods for complex geometry
AMM 7th November 2012
13:30 to 14:30
R LeVeque Cut-cell approaches: a discussion session
AMM 8th November 2012
10:00 to 11:00
J Z Shi Mixing and stratification within the plume of the Changjiang River estuary, East China Sea: a numerical study
AMM 9th November 2012
10:00 to 11:00
P Peixoto Analysis of grid imprinting on geodesical spherical icosahedral grids
AMM 14th November 2012
13:30 to 14:30
T Dubos Wavelet building blocks for dynamic adaptivity : application to shallow-water equations on a hexagonal C-grid
AMM 15th November 2012
10:00 to 11:00
Discrete analyses and numerical simulation of the shallow-water system
The shallow-water system, obtained from the Navier-Stokes equations by vertical averaging, is extensively used in environmental studies (ocean, atmosphere, rivers) to simulate the propagation of inertia-gravity and Rossby waves. For most of the discretization schemes, the numerical approximation of shallow-water models is a delicate problem leading to the appearance of spurious (non physical) solutions in the representation of the fast (inertia-gravity) and slow (Rossby) waves. In order to understand these difficulties and to select appropriate spatial discretization schemes, Fourier / dispersion analyses and the study of the null space of the associated discretized problems have proven beneficial. The aim of this talk is to present such results and to propose a class of possible discretization schemes that is not affected by the spurious modes. Both discrete analyses and numerical simulations involving the eddy propagation in an oceanic context will be presented.
AMM 16th November 2012
10:00 to 11:00
High order finite volume methods using multi-moments or multi-moment constraints:basic idea, numerical formulations & applications to geophysical fluid dynamics
Discrete quantities, such as cell integrated average, point value and derivatives, which are appellatively called moments in our context, reveal different respects of a physical field. Using more than two kinds of these quantities simultaneously as the predicted variables or the constraints to derive the evolution equations for the predicted variables leads to a class of schemes that are different from the conventional finite difference or finite volume methods. Rather than the Galerkin inner product procedure, the moments in a high order multi-moment finite volume (MV) or multi-moment constrained finite volume (MCV) scheme can be chosen through a more intuitive and physically motivated way, which allows greater flexibility in defining the computational variables and in deriving the corresponding prognostic equations to update the unknowns. Different moments are connected by a local (cell-wise) reconstruction, and time marching is based on a set of equations which can be of different forms but consistent to the original governing equation(s). For example, a semi-Lagrangian scheme which maps the point values, can be combined with a finite volume formulation, which predicts the cell integrated values through a flux form, to devise a conservative scheme. The moments can be either used directly as the prognostic variables as in an MV scheme, which can be interpreted as a modal type method, or used as the constraints to generate the equations to update the unknowns. A representative formulation of the latter is the nodal type MCV method, in which the unknowns are the point values defined at the solution points, and the prognostic equations to predict these unknowns are derived from the constraint conditions in terms of different moments. Multi-moment constraint concept also applies to the flux reconstruction formulation for conservation laws, which gives a more general platform to accommodate many existing high order scheme, including discontinuous Galerkin method and spectral element method. Using multi-moment constraints when reconstructing the numerical flux function makes the present method distinguished from other high order schemes. High order multi-moment methods have attractive properties for practical applications, such as algorithmic simplicity, flexibility and computational efficiency, and have been applied to various problems in computational fluid dynamics, such as compressible and incompressible flows, interfacial multi-phase flows. Efforts have also been made to develop numerical models for geophysical flows. This talk will present the underlying idea of the methods, typical schemes and the major differences compared to other existing methods. Progress of using the multi-moment approach to develop high order numerical models for geophysical fluid dynamics will be reported as well.
AMM 19th November 2012
10:00 to 11:00
C Chen Development of high-order adaptive global models by multi-moment (constrained) finite volume method
The numerical schemes using multi-moment concepts were developed recently. More than one kinds of moments, which denote the discrete quantities of the physical fields from different aspects, such as point value (PV), volume-integrated average (VIA), derivative values (DVs) of different orders and so on, are adopted as model variables or constraints to build high-order schemes with local (usually single-cell based) reconstructions. The concise formulations are derived to update different moments. The numerical conservation is always preserved through updating VIA by flux-form formulation. Compared to other advanced methods with local reconstruction, the multi-moment schemes often allow the larger CFL numbers and are more flexible for different applications, and thus are very suited for developing global models for atmospheric and oceanic dynamics. This talk will mainly report the following progress we have recently made to develop global models using multi-moment method. 1) A global SWE model up to fifth-order accuracy has been developed on cubed sphere. Compact reconstruction stencil is beneficial to reducing the excessive errors due to the discontinuous coordinates on adjacent patches. Furthermore, the AMR technique has be extended to spherical geometry on cubed sphere using a multi-moment finite volume formulation. 2) Multi-moment schemes have been used to construct high-order numerical models on icosahedral grid, which is a kind of unstructured grid in nature. By defining 7 and 10 DOFs within each element, the third- and fourth-order global SWE models have been developed on triangular- and hexagonal-type tessellations. 3) Two-dimensional non-hydrostatic model has been developed using the third- and fourth-order multi-moment constrained schemes. Proposed models have been checked by benchmark tests and the results are competitive to most existing models. The multi-moment framework is very promising for developing the high-performance dynamic core for GCMs.
AMM 20th November 2012
10:00 to 11:00
J Yano Dynamical adaptive mesh-refinement with NAM-SCA model
AMM 20th November 2012
13:30 to 14:30
Gent McWilliams parametrisation
AMM 21st November 2012
10:00 to 11:00
Adaptive grid generation with application to data assimilation-with Chiara Piccolo
AMM 21st November 2012
11:30 to 12:30
H Weller Progress with test cases: a discussion session
AMM 22nd November 2012
10:00 to 10:30
3D simulations of convective storms using Finite Elements with Variational Multiscale Stabilization
AMM 22nd November 2012
13:30 to 16:30
Finding the perfect horizontal discretisation: a discussion session
AMM 23rd November 2012
10:00 to 11:00
J Behrens Efficiency of adaptive mesh algorithms
AMM 26th November 2012
10:00 to 11:00
Reimann problems for gas dynamics with moisture and droplets
AMM 27th November 2012
10:00 to 11:00
Scaling turbulence simulations to beyond a million processes
AMM 28th November 2012
11:30 to 12:30
H Weller Progress with test cases: a discussion session
AMM 29th November 2012
10:00 to 11:00
Comparing a DG dynamical core with the production code COSMO
AMM 30th November 2012
10:00 to 11:00
New finite volume based tracer transport schemes for the Community Atmospheric Model (CAM-SE)
AMM 4th December 2012
13:30 to 14:30
J Thuburn Computational modes: What are they and how bad are they for a weather/climate model dynamical core?
In this presentation we will take a broad definition of computational mode', namely any gross mis-representation of linear wavelike behaviour of the continuous system by the discrete system. Computational modes are potentially problematic for a dynamical core because they are likely to be excited by nonlinear processes, physical parameterizations, or data assimilation. Some well-known and less well-known examples of computational modes will be reviewed, including isolated computational modes and entire branches of computational modes. Spatial computational modes will be related to grid staggering and to degrees of freedom of prognostic variables. The triangular and hexagonal C-grid cases will be examined in detail. It will be argued that the extra branch of Rossby modes that occurs for the hexagonal C-grid is, in fact, well behaved in the presence of a background flow provided an adequate advection scheme is used. The relation of computational modes to parasitic' mo des and to trapped modes on non-uniform grids will be discussed.
AMM 5th December 2012
10:00 to 11:00
A non-hydrostatic three dimensional finite volume icosahedral model
AMM 5th December 2012
11:30 to 12:30
H Weller Progress with test cases: a discussion session
AMM 6th December 2012
10:00 to 11:00
J Peitrzak Horizontal discretisations suitable for coastal flooding studies with applications to mega-tsunamis
AMM 10th December 2012
15:00 to 16:00
Introduction to GungHo Computational Science week: a discussion session
What are the plans for the week etc and I think it might be worth trying to get everyone up to speed on what we mean when we use terms like infrastructure, framework, data model etc. Do we all mean the same thing by these terms? What impact does any of the options for GungHo currently on the table, have on the framework, data model etc (a theme that would run through sessions 1-3)?
AMM 10th December 2012
16:00 to 17:00
E Mueller Elliptic Solvers on GPUs
AMM 11th December 2012
10:00 to 12:00
Kernel or execution model: a discussion session
Interfaces to code generation.
AMM 11th December 2012
14:00 to 17:00
R Ford Data model + interface to kernel + coupling: a discussion session
Coupling to eg the physics, DA, other dynamical cores (ie coupling to legacy codes that do not use the same data model - do we really need to rewrite the physics?). Can we sensibly separate the dynamical core from the infrastructure by dening a clear interface. Is k innermost a panacea and if not what do we do?
AMM 12th December 2012
09:00 to 10:00
H Weller Progess with test cases: a discussion session
AMM 12th December 2012
10:00 to 11:00
Variational Multiscale Approaches to Turbulence Modeling in the framework High Order Discretizations of Fluid Flow
AMM 12th December 2012
11:00 to 13:00
Infrastructure/framework (ESMFvsMCT etc)+interface to the data model + coupling issues. Identify potential show-stoppers & major obstacles etc. A discussion.
AMM 12th December 2012
14:00 to 16:00
How to effectively engage with the non-GungHo Met O people. A discussion session
Met O lead developer. What are the issues from a Met O non-dycore point of view? Issues with the current UM infrastructure to give an idea of the problems ahead.
AMM 13th December 2012
10:00 to 12:00
How are we going to manage actual code and coding? Ie plansfor Phase 2 Code. Coding standards etc. A discussion session
AMM 13th December 2012
13:00 to 16:00
GungHo Computational Science week wrap up: A discussion session
AMM 18th December 2012
11:30 to 12:30
H Weller Progress with test cases: a discussion session
AMM 18th December 2012
13:30 to 14:30
The long and short of modelling ocean tides