Aim: WP1 will identify and define Weather & Climate Dwarfs, a prerequisite for other work-packages and an important facilitator for co-design and future code development. Moreover, WP1 in collaboration with other work packages will provide prototypical implementations, delivering a toolbox with NWP specific algorithms that can be classified by their data flow and data locality, their parallel communication pattern, their energy efficiency, their need for numerical precision and accuracy, and their floating point rate on various HPC architectures. WP1 will make available and further develop new data structures, mathematical algorithms and numerical methods including time-stepping strategies that allow global and regional forecast models to employ structured and unstructured meshes as well as multi-scale numerical techniques for enhancing parallelism and scientific flexibility.

Approach and methodology: A significant contribution to this work package will be drawn from the research supported by the frontier research project PantaRhei as well as the ECMWF scalability programme. As part of these projects, substantial advances have been made and software developed at ECMWF that implements alternative options and generalized formulations for geophysical fluid dynamics in support of future operational NWP. Through ESCAPE, these developments will be shared with the European NWP community, and rigorously tested and optimized for future HPC architectures. Specific developments will focus on the topic of horizontal and vertical discretization and on scalable solvers, with both topics using hierarchical meshes and multi-level themes.

A key focus area of this work package will be an adaptation of the “Berkeley Dwarfs” (Asanovic et al. 2006) and the “mini-apps” (Heroux et al., 2009) themes. Their translation to NWP modelling (Weather & Climate Dwarfs) necessitates work on the following topics leading to Weather & Climate Dwarfs:

• Spectral transforms, involving the Fast Fourier Transform (FFT) and the (Fast) Legendre Transform (FLT) kernels. The spectral transforms constitute a substantial part of the compute-intensive part, and thus the energy consumption in global, high-resolution simulations with IFS. But despite their cost, their application provides the tool for a very fast direct solver, which in combination with large time steps still gives the shortest time-to-solution in operational NWP today. This dwarf thus serves both as an important part of the reference solution as well as a tool for exploring the acceleration and energy-efficiency of this technique on emerging hardware architectures, e.g. optical processors which promise to substantially accelerate FFTs and matrix-matrix multiplications (with the latter being the most costly part of the Legendre transform computations).
• Structured grids, or block-structured grids, the former oriented along latitudes and longitudes of the spherical Earth still forming the basis of most operational NWP model computations today. Supporting grids with some structure can have advantages in both scalability as well as accuracy. The vertical column level structure of essentially all NWP models today is not least a reflection of the dominant hydrostatic balance of the atmosphere, and the columnar structure is an essential part of all physical parameterization and observation operator packages that substantially contribute to the accuracy of NWP models.
• Unstructured meshes, facilitating locally compact stencils (thus global communication avoiding) and facilitating refinement. The use of unstructured meshes is new in operational NWP (with the exception of the semi-structured icosahedral grid models) and there are numerous developments in this area to exploit the flexibility of different meshes for future NWP and climate simulations.
• Advective transport strategies, important for both the evolution of the moist-dynamic atmosphere as well as for chemical tracer advection, as needed for ECMWF’s atmospheric composition services (Copernicus). Semi-Lagrangian transport techniques have been used so far with great success due to the robustness and the large time steps that can be afforded. On the other hand, Eulerian flux-form schemes have been successfully applied in cloud-resolving simulations, where monotone, sign-preserving transport is important. The implications for energy-aware metrics has yet to be established when these different techniques are applied in the context of NWP on emerging hardware architectures.
• Time-stepping strategies, important for achieving minimal time-to-solution in the “critical path” for operational NWP applications. Typically, the best possible solution that can be afforded must be completed within less than one hour, or equivalently, 200-300 times faster than real time. The time-stepping strategy is not necessarily independent from the transport choices. Semi-implicit time stepping is the standard reference solution applied in IFS, but several horizontally-explicit and vertically implicit solution procedures emerge for applications in NWP.
• Bespoke scalable, preconditioned, non-symmetric Krylov solvers, arising in large time-step, semi-implicit problems in compressible or sound-proof atmospheric models. These solvers can be self-adaptive, and may provide robust solution procedures for NWP applications, but their scalability and competitiveness must be explored in the context of NWP. An important aspect is successful pre-conditioning of the global NWP problem.
• Hierarchies, including multi-scale, multi-level and multi-grid techniques for use in process-dependent and scale-selective algorithms and data layouts. There is also substantial scope for extracting parallelism and energy-efficiency in using multiple grid options for specific processes, e.g. radiation, physical and chemical parameterizations, dynamic or static mesh adaptation, and employing spatial and temporal filtering. Some of these options will be encapsulated in Weather & Climate Dwarfs.