A comparison of airborne and ground-based radar observations with rain gages during the CaPE experiment

The vicinity of KSC, where the primary ground truth site of the Tropical Rainfall Measuring Mission (TRMM) program is located, was the focal point of the Convection and Precipitation/Electrification (CaPE) experiment in Jul. and Aug. 1991. In addition to several specialized radars, local coverage was provided by the C-band (5 cm) radar at Patrick AFB. Point measurements of rain rate were provided by tipping bucket rain gage networks. Besides these ground-based activities, airborne radar measurements with X- and Ka-band nadir-looking radars on board an aircraft were also recorded. A unique combination data set of airborne radar observations with ground-based observations was obtained in the summer convective rain regime of central Florida. We present a comparison of these data intending a preliminary validation. A convective rain event was observed simultaneously by all three instrument types on the evening of 27 Jul. 1991. The high resolution aircraft radar was flown over convective cells with tops exceeding 10 km and observed reflectivities of 40 to 50 dBZ at 4 to 5 km altitude, while the low resolution surface radar observed 35 to 55 dBZ echoes and a rain gage indicated maximum surface rain rates exceeding 100 mm/hr. The height profile of reflectivity measured with the airborne radar show an attenuation of 6.5 dB/km (two way) for X-band, corresponding to a rainfall rate of 95 mm/hr

Improvements in the Scalability of the NASA Goddard Multiscale Modeling Framework for Hurricane Climate Studies

Improving our understanding of hurricane inter-annual variability and the impact of climate change (e.g., doubling CO2 and/or global warming) on hurricanes brings both scientific and computational challenges to researchers. As hurricane dynamics involves multiscale interactions among synoptic-scale flows, mesoscale vortices, and small-scale cloud motions, an ideal numerical model suitable for hurricane studies should demonstrate its capabilities in simulating these interactions. The newly-developed multiscale modeling framework (MMF, Tao et al., 2007) and the substantial computing power by the NASA Columbia supercomputer show promise in pursuing the related studies, as the MMF inherits the advantages of two NASA state-of-the-art modeling components: the GEOS4/fvGCM and 2D GCEs. This article focuses on the computational issues and proposes a revised methodology to improve the MMF's performance and scalability. It is shown that this prototype implementation enables 12-fold performance improvements with 364 CPUs, thereby making it more feasible to study hurricane climate

A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin

Numerical weather prediction (NWP) is in a period of transition. As resolutions increase, global models are moving towards fully nonhydrostatic dynamical cores, with the local and global models using the same governing equations; therefore we have reached a point where it will be necessary to use a single model for both applications. The new dynamical cores at the heart of these unified models are designed to scale efficiently on clusters with hundreds of thousands or even millions of CPU cores and GPUs. Operational and research NWP codes currently use a wide range of numerical methods: finite differences, spectral transform, finite volumes and, increasingly, finite/spectral elements and discontinuous Galerkin, which constitute element-based Galerkin (EBG) methods.Due to their important role in this transition, will EBGs be the dominant power behind NWP in the next 10 years, or will they just be one of many methods to choose from? One decade after the review of numerical methods for atmospheric modeling by Steppeler et al. (Meteorol Atmos Phys 82:287–301, 2003), this review discusses EBG methods as a viable numerical approach for the next-generation NWP models. One well-known weakness of EBG methods is the generation of unphysical oscillations in advection-dominated flows; special attention is hence devoted to dissipation-based stabilization methods. Since EBGs are geometrically flexible and allow both conforming and non-conforming meshes, as well as grid adaptivity, this review is concluded with a short overview of how mesh generation and dynamic mesh refinement are becoming as important for atmospheric modeling as they have been for engineering applications for many years.The authors would like to thank Prof. Eugenio Oñate (U. Politècnica de Catalunya) for his invitation to submit this review article. They are also thankful to Prof. Dale Durran (U. Washington), Dr. Tommaso Benacchio (Met Office), and Dr. Matias Avila (BSC-CNS) for their comments and corrections, as well as insightful discussion with Sam Watson, Consulting Software Engineer (Exa Corp.) Most of the contribution to this article by the first author stems from his Ph.D. thesis carried out at the Barcelona Supercomputing Center (BSCCNS) and Universitat Politècnica de Catalunya, Spain, supported by a BSC-CNS student grant, by Iberdrola Energías Renovables, and by grant N62909-09-1-4083 of the Office of Naval Research Global. At NPS, SM, AM, MK, and FXG were supported by the Office of Naval Research through program element PE-0602435N, the Air Force Office of Scientific Research through the Computational Mathematics program, and the National Science Foundation (Division of Mathematical Sciences) through program element 121670. The scalability studies of the atmospheric model NUMA that are presented in this paper used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357. SM, MK, and AM are grateful to the National Research Council of the National Academies.Peer ReviewedPostprint (author's final draft

Variational multiscale stabilization of finite and spectral elements for dry and moist atmospheric problems

In this thesis the finite and spectral element methods (FEM and SEM, respectively) applied to problems in atmospheric simulations are explored through the common thread of Variational Multiscale Stabilization (VMS). This effort is justified by three main reasons. (i) the recognized need for new solvers that can efficiently execute on massively parallel architectures ¿a spreading framework in most fields of computational physics in which numerical weather prediction (NWP) occupies a prominent position. Element-based methods (e.g. FEM, SEM, discontinuous Galerkin) have important advantages in parallel code development; (ii) the inherent flexibility of these methods with respect to the geometry of the grid makes them a great candidate for dynamically adaptive atmospheric codes; and (iii) the localized diffusion provided by VMS represents an improvement in the accurate solution of multi-physics problems where artificial diffusion may fail. Its application to atmospheric simulations is a novel approach within a field of research that is still open. First, FEM and VMS are described and derived for the solution of stratified low Mach number flows in the context of dry atmospheric dynamics. The validity of the method to simulate stratified flows is assessed using standard two- and three-dimensional benchmarks accepted by NWP practitioners. The problems include thermal and gravity driven simulations. It will be shown that stability is retained in the regimes of interest and a numerical comparison against results from the the literature will be discussed. Second, the ability of VMS to stabilize the FEM solution of advection-dominated problems (i.e. Euler and transport equations) is taken further by the implementation of VMS as a stabilizing tool for high-order spectral elements with advection-diffusion problems. To the author¿s knowledge, this is an original contribution to the literature of high order spectral elements involved with transport in the atmosphere. The problem of monotonicity-preserving high order methods is addressed by combining VMS-stabilized SEM with a discontinuity capturing technique. This is an alternative to classical filters to treat the Gibbs oscillations that characterize high-order schemes. To conclude, a microphysics scheme is implemented within the finite element Euler solver, as a first step toward realistic atmospheric simulations. Kessler microphysics is used to simulate the formation of warm, precipitating clouds. This last part combines the solution of the Euler equations for stratified flows with the solution of a system of transport equations for three classes of water: water vapor, cloud water, and rain. The method is verified using idealized two- and three-dimensional storm simulations.En esta tesis los métodos de elementos finitos y espectrales (FEM - finite element method y SEM- spectral element method, respectivamente), aplicados a los problemas de simulaciones atmosféricas, se exploran a través del método de estabilización conocidocomo Variational Multiscale Stabilization (VMS). Tres razones fundamentales justifican este esfuerzo: (i) la necesidad de tener nuevos métodos de solución de las ecuaciones diferenciales a las derivadas parciales usando máquinas paralelas de gran escala –un entorno en expansión en muchos campos de la mecánica computacional, dentro de la cual la predicción numérica de la dinámica atmosférica (NWP-numerical weather prediction)representa una aplicación importante. Métodos del tipo basado en elementos(por ejemplo, FEM, SEM, Galerkin discontinuo) presentan grandes ventajas en el desarrollo de códigos paralelos; (ii) la flexibilidad intrínseca de tales métodos respecto a lageometría de la malla computacional hace que esos métodos sean los candidatos ideales para códigos atmosféricos con mallas adaptativas; y (iii) la difusión localizada que VMSintroduce representa una mejora en las soluciones de problemas con física compleja en los cuales la difusión artificial clásica no funcionaría. La aplicación de FEM o SEM con VMS a problemas de simulaciones atmosféricas es una estrategia innovadora en un campo de investigación abierto. En primera instancia, FEM y VMS vienen descritos y derivados para la solución de flujos estratificados a bajo número de Mach en el contexto de la dinámica atmosférica. La validez del método para simular flujos estratificados es verificada por medio de test estándar aceptado por la comunidad dentro del campo deNWP. Los test incluyen simulaciones de flujos térmicos con efectos de gravedad. Se demostrará que la estabilidad del método numérico se preserva dentro de los regímenesde interés y se discutirá una comparación numérica de los resultados frente a aquellos hallados en la literatura. En segunda instancia, la capacidad de VMS para estabilizarmétodos FEM en problemas de advección dominante (i.e. ecuaciones de Euler y ecuaciones de transporte) se implementa además en la solución a elementos espectrales de alto orden en problemas de advección-difusión. Hasta donde el autor sabe, esta es una contribución original a la literatura de métodos basados en elementos espectrales en problemas de transporte atmosférico. El problema de monotonicidad con métodos de alto orden es tratado mediante la combinación de SEM+VMS con una técnica de shockcapturing para un mejor tratamiento de las discontinuidades. Esta es una alternativa a los filtros que normalmente se aplican a SEM para eilminar las oscilaciones de Gibbsque caracterizan las soluciones de alto orden. Como último punto, se implementa un esquema de humedad acoplado con el núcleo en elementos finitos; este es un primer paso hacia simulaciones atmosféricas más realistas. La microfísica de Kessler se emplea para simular la formación de nubes y tormentas cálidas (warm clouds: no permite la formación de hielo). Esta última parte combina la solución de las ecuaciones de Eulerpara atmósferas estratificadas con la solución de un sistema de ecuaciones de transporte de tres estados de agua: vapor, nubes y lluvia. La calidad del método es verificadautilizando simulaciones de tormenta en dos y tres dimensiones

Simulation of all-scale atmospheric dynamics on unstructured meshes

The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed

Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs

Many problems in geophysical and atmospheric modelling require the fast solution of elliptic partial differential equations (PDEs) in "flat" three dimensional geometries. In particular, an anisotropic elliptic PDE for the pressure correction has to be solved at every time step in the dynamical core of many numerical weather prediction models, and equations of a very similar structure arise in global ocean models, subsurface flow simulations and gas and oil reservoir modelling. The elliptic solve is often the bottleneck of the forecast, and an algorithmically optimal method has to be used and implemented efficiently. Graphics Processing Units have been shown to be highly efficient for a wide range of applications in scientific computing, and recently iterative solvers have been parallelised on these architectures. We describe the GPU implementation and optimisation of a Preconditioned Conjugate Gradient (PCG) algorithm for the solution of a three dimensional anisotropic elliptic PDE for the pressure correction in NWP. Our implementation exploits the strong vertical anisotropy of the elliptic operator in the construction of a suitable preconditioner. As the algorithm is memory bound, performance can be improved significantly by reducing the amount of global memory access. We achieve this by using a matrix-free implementation which does not require explicit storage of the matrix and instead recalculates the local stencil. Global memory access can also be reduced by rewriting the algorithm using loop fusion and we show that this further reduces the runtime on the GPU. We demonstrate the performance of our matrix-free GPU code by comparing it to a sequential CPU implementation and to a matrix-explicit GPU code which uses existing libraries. The absolute performance of the algorithm for different problem sizes is quantified in terms of floating point throughput and global memory bandwidth.Comment: 18 pages, 7 figure