CHAPTER 6. NUMERICAL METHODS OF THE ATMOSPERE AND OCEAN
6.6 COMPUTATIONAL ASPECTS
Concerning computing, the key figure is the electric power consumption per floating point operation per second (Watts/FLOPS) or, eventually, the total power cost for producing a forecast. In order to reach “exascale” performance the need to include highly parallel computing concepts into GCMs and the data post-processing stream is paramount. Despite ambitious targets being set for model resolution, complexity and ensemble size, today the bulk of the calculations are not performed with configurations that utilize the maximum possible number of processors. Initially, substantial
efficiency gains can be obtained from a rigorous utilization of the Message Passing Interface (MPI) and the Open Multi-Processing (OpenMP) techniques which are distributed-memory and shared-memory programming paradigms, respectively. These can be further enhanced by Partitioned Global Address Space (PGAS) programming models that are either part of existing languages, such as Fortran, or higher-level standards, such as the Partitioned Global Address Space Programming Interface (GASPI).
A source of uncertainty at present is the inconsistent support of compiler directives for hardware accelerators (e.g. Open Accelerators (OpenACC), OpenMP4, Govett et al. 2003, 2014), Fortran language features such as Coarray Fortran (CAF), and vectorization constructs across compilers.
In addition, new programming language extensions like CUDA-C or CUDA-Fortran are now available for vendor-specific General-Purpose Graphical Processing Units (GPGPUs). This
“Compute Unified Device Architecture” (CUDA) programming framework is able to fully utilize the power of GPU hardware accelerators. However, CUDA codes become non-portable and will not work on hardware platforms of other vendors. Dynamic task parallelism represents an interesting feature but it could impose load imbalance on the calculations. At present, limited experience exists with this feature in our community. Compiler development is an important interface between science and industry, ultimately aiming for a lower level of hardware awareness in science codes.
However, these enhancements are applied to existing science codes and do not require fundamentally different scientific and numerical solutions.
Performing calculations in single precision presents obvious efficiency gains in runtime and memory allocation, and can be applied to selected code components where the loss of accuracy does not affect scientific performance or numerical stability. Efficiency enhancement at the expense of precision can be further exploited towards inexact hardware (Düben et al. 2013).
Given that modern computer architectures are heterogeneous and consist of shared- and distributed-memory CPUs as well as various types of accelerators like GPGPUs or the “Many Integrated Core” (MIC) architecture the best numerical algorithms are those that are easy to localize (domain decomposition with good load balance) and compute intensive but require little data communication. Examples are spectral element, finite element and discontinuous Galerkin methods, or even parallel-in-time algorithms. Several examples of the parallel scalability of the NCAR Community Earth System Model (CESM) model are depicted in Dennis et al. (2012) who coupled the CAM spectral element atmospheric component to land, ocean and ice models at high resolutions (between 11-28 km grid spacings). The coupled climate model scaled reasonably well up to about 100 000 processors and more. Note that the scaling of CESM was highly impacted by the choice of the computing architecture. Alternative parallel scaling curves for the spectral
transform NWP model IFS are provided in Mozdzynski et al. (2015). They show that the scaling of IFS greatly benefits from the use of Coarray Fortran constructs. With a 10 km global grid spacing reasonable scaling was achieved on up to 40 000 processors.
Error resilience becomes an issue with increasing relevance on future exascale systems. Fault tolerant algorithms and techniques to compensate for missing calculations and data need to be developed. Failure detection is an important component and has a strong dependence on hardware and compilers. Ensembles are less critically affected since ensemble statistics can be derived from fewer than nominal members.
It is recognized that bit-reproducibility for a fixed processor configuration is of crucial importance for code debugging and operational error tracing, and the only means for distinguishing between hardware differences and code issues. However, reduced or part bit-reproducibility may be crucial
for operating on future architectures with acceptable fault tolerance and, e.g. for running large ensembles stably over long time periods.
While scientific choices differ quite substantially between individual models a more coordinated effort to develop common tools, e.g. libraries or workflows, between GCM model developers and computational scientists is required in the future. This also implies an enhanced level of flexibility with respect to the choice of numerical methods through shared libraries containing calls to highly optimized kernels that serve different applications. Efficiency gains from refactored code run on accelerators can be substantial (Shimokawabe et al. 2010; Lapillonne and Fuhrer, 2014) but require a trade-off between gains and code refactoring and maintenance effort.
In general, code development and maintenance becomes a problem going towards extreme parallelism and heterogeneous machines. A solution could be offered by machine-generated code from a high-level language. This has already been exploited with the finite-element formalism for the solutions of partial differential equations on the sphere (Rognes et al. 2013).
6.7 CONCLUSION
This chapter has reviewed the current state of the research in global weather and climate
modelling. The emerging challenge is to take advantage of future computing resources via modern numerical and computational techniques in order to fully exploit the power of exascale-type
computer generations. The chapter highlighted the intersections between the physical, mathematical and computational viewpoints, and thereby provides pointers to future high-performance and high-resolution GCM research.
There are many opportunities for GCM modellers, applied mathematicians and computational scientists to come together and foster the progress in the numerical design of atmosphere and ocean models. Examples are the regular “Partial Differential Equations (PDEs) on the Sphere”
Workshops (e.g. see Lauritzen et al. 2014c), the bi-annual ECMWF Workshop on High
Performance Computing in Meteorology, dedicated workshops and long programs like the 2012
“Isaac Newton Institute Programme on Multiscale Numerics for the Atmosphere and Ocean” or the recent 2015 “Workshop on Galerkin methods with applications in weather and climate forecasting”, as well as special sessions at the American Geophysical Union (AGU) Fall meeting, the European Geosciences Union (EGU) General Assembly and many other conferences like the 2014 World Weather Open Science Conference.
6.8 ACKNOWLEDGEMENTS
Jean Côté acknowledges the financial support of Environment Canada. Christiane Jablonowski acknowledges the financial support through the US Department of Energy (DoE), Office of Science, grants DE-SC0006684 and DE-SC0003990.
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