TREND TOWARDS HIGH-RESOLUTION, VARIABLE-RESOLUTION AND ADAPTATIVE MESH REFINEMENT (AMR) GCMs

6.4.1 High-resolution

There is an increasing scientific demand for high-resolution, even cloud-resolving, GCM simulations that can accurately represent processes at regional and local scales. This places strong demands on the numerical designs of GCMs and their computational efficiency since the doubling of the horizontal resolution and the consequent halving of the model time step due to CFL stability constraints increases the computational workload by a factor of around 8. The latter

estimate assumes perfect parallel scalability and that the memory footprint of the higher-resolution model configuration can be accommodated by the computer hardware.

Uniform high-resolution GCM grid spacings, that are currently feasible for multi-year simulations, range from 3.5-14 km as e.g. documented by Miura et al. (2007), Putman and Suarez (2011), Satoh et al. (2012), Jung et al. (2012), Manganello et al. (2012) or Miyamoto et al. (2014). The finest “ultra-high” resolution to date was employed by Miyamoto et al. (2013) who utilized a sub-km global grid with 870 m grid spacing. Such a small grid spacing only allows very short model

calculations on the order of hours or days on current High Performance Computing (HPC)

hardware platforms. However, it is likely that such resolutions will become the new norm in future decades as called for by the 2008 “World Modelling Summit for Climate Prediction” (Shukla et al.

2009). The summit demanded that the grid spacings of climate models must decrease towards the 1 km scale to accurately represent key regional processes in the atmosphere without

parameterizing deep convection. This “grand challenge” can only be met by a significant boost of the available computing resources (Shukla et al. 2010) which reflects the tight coupling between scientific discoveries and HPC in climate and weather modelling (Washington et al. 2009). This is further discussed in Section 6.6.

High-resolution grid spacings under 10 km necessitate non-hydrostatic dynamical core designs since the scales of horizontal and vertical motions become comparable in these cloud-permitting or cloud-resolving model configurations. This invalidates the hydrostatic approximation that has been built into most GCM equation sets until very recently. Today, new dynamical core model

developments recognize that non-hydrostatic designs are paramount for the future GCM generation as e.g. reflected by Walko and Avissar (2008), Wedi et al. (2009), Ullrich and

Jablonowski (2012b), Skamarock et al. (2012) or Wood et al. (2014). At hydrostatic scales the non-hydrostatic models reproduce the non-hydrostatic solution, although typically at higher computational cost, and provide a seamless transition into the meso-scale flow regimes. This multi-scale GCM design allows the development of unified modelling systems (Palmer et al. 2008; Hurrell et al.

2009; Hoskins, 2013) that can be used for both local weather predictions and global climate

projections without any algorithmic dynamical core changes. However, this raises questions concerning the scale-awareness (or scale sensitivities) of the subgrid-scale physical

parameterizations that are not necessarily well suited for a wide range of resolutions, as briefly discussed further in Section 6.5.

As mentioned before high-resolution GCM modelling puts strong demands on HPC resources, and only very few modelling centres are currently equipped to handle the computational workload and data volumes. The big data volumes might even break existing data analysis and visualization software. Therefore, variable-resolution technologies have been emerging over the last decade, which build a bridge between the scientific and computational requirements. Variable-resolution GCMs place fine grid spacings in selected (non-moving) areas of interest while keeping the rest of the global domain at coarser resolutions. This technique even has the potential to replace

traditional Limited-Area Models (LAMs) that can be nested within a coarse-resolution host GCM and rely on periodic updates of the boundary conditions. These boundary data updates can cause inconsistencies, like the violation of mass conservation constraints, and numerical noise, which is often damped via diffusion in “sponge zones” (Harris and Durran, 2010). In addition, some LAMs employ a nudging (relaxation) of the high-resolution solution towards the large-scale flow

conditions of the host GCM to prevent the splitting between the LAM and GCM flow fields. This might become important for regional long-term climate modelling applications with LAMs. On the downside, the nudging compromises the versatility of regional climate assessments since the flow is not allowed to freely evolve in the high-resolution domain. Most often, the LAMs are also only coupled to the host model in a one-way interactive way and do not feed back the fine-grid

information to the coarse GCMs. These issues are not present in global variable-resolution models that automatically provide consistent two-way interactions (and thereby dynamic up- and

downscaling of flow features) between the coarse- and fine-resolution domains.

6.4.2 Variable-resolution

Variable-resolution GCMs come in many different flavours. Until about 2010, most

variable-resolution GCMs used a grid stretching technique, like the Schmidt (1977) transformation, to zoom into a single region of interest with high resolution. The papers by Fox-Rabinovitz et al. (2006), Tomita (2008) and McGregor (2013) provide a comprehensive review of various stretched-grid GCMs. More recently, variable resolution grids are provided as an option in selected GCMs that are built upon unstructured icosahedral, hexagonal or cubed-sphere grid topologies. Examples are the variable-resolution model ICON by the German Weather Service and the Max-Planck Institute for Meteorology (Gassmann, 2011a; Zängl et al. 2015), the model OLAM which is under

development at the University of Miami (Walko and Avissar, 2008, 2011), the cubed-sphere Finite-Volume GCM at the Geophysical Fluid Dynamics Laboratory (Harris and Lin, 2013, 2014), the Model for Predictions Across Scales (MPAS) for atmosphere and ocean simulations developed at the National Center for Atmospheric Research (NCAR) and the US Department of Energy’s (DoE) Los Alamos National Laboratory (Skamarock et al. 2012; Ringler et al. 2013; Rauscher et al. 2013;

Rauscher and Ringler, 2014; Park et al. 2013, 2014), and the Spectral Element (SE) version of the NCAR/DoE Community Atmosphere Model (CAM) (Guba et al. 2014; Zarzycki et al. 2014a, 2014b, 2015; Zarzycki and Jablonowski, 2014). The importance of variable-resolution and multi-scale modelling has also been recognized in the special issue on “Mesh Generation and Mesh

Adaptation for Large-Scale Earth System Modelling” by the journal Philosophical Transactions of the Royal Society A in 2009 (Nikiforakis, 2009 and other special issue articles), and the 2013-2014 special issue on the “Isaac Newton Institute Programme on Multiscale Numerics for the

Atmosphere and Ocean” by the journal Geoscientific Model Development (http://www.geosci-model-dev.net/special_issue27.html). The latter was a four-month program that took place in Cambridge, U.K., in 2012. It brought together the international research community in the pursuit to advance numerical, computational and Adaptive Mesh Refinement (AMR) techniques for

atmosphere and ocean GCMs (Ham et al. 2012; Weller et al. 2010, 2013b).

An example of a variable-resolution CAM-SE grid is depicted in Figure 1. The figure shows a high-resolution region with grid spacings of about 14 km in the inner domain. The grid then transitions to a grid spacing of 28 km (midlevel) and 55 km in the outermost domain. The figure also provides close-up views of the sharp transition regions.

Figure 1. Example of a non-moving variable-resolution mesh in the model CAM-SE

6.4.3 Adaptive mesh refinement

Dynamic adaptivity of the mesh (AMR) has been a topic of interest for many years and progress has been made towards the development of global models that can track objects and refine resolution as the objects develop smaller scales. Many 2D adaptive mesh refinement algorithms for e.g. the shallow-water equations on the sphere and x-z non-hydrostatic slice models in

Cartesian geometry have been documented in the literature. Examples are the AMR shallow water articles by Jablonowski et al. (2006), Läuter et al. (2007), St-Cyr et al. (2008), Weller (2009), Chen et al. (2011), Blaise and St-Cyr (2012), Marras et al. (2015), Aechtner et al. (2015) or

McCorquodale et al. (2015). Furthermore, adaptive x-z slice model configurations were explored by Skamarock and Klemp (1993), Müller et al. (2013) or Kopera and Giraldo (2014). A

comprehensive review of AMR techniques for atmosphere and ocean models has been provided by Behrens (2006). The 2D AMR assessments have served as an idealized test bed for adaptive 3D model developments. Very few 3D AMR models in spherical geometry have been developed so far, and this research field might become an emerging trend for future-generation GCMs. Among the adaptive 3D AMR approaches are the weather prediction model OMEGA (Bacon et al. 2000;

Gopalakrishnan et al. 2002), the anelastic adaptive moving mesh model of Kühnlein et al. (2012), the dynamical core AMR developments by Jablonowski et al. (2009) and the non-hydrostatic cubed-sphere Chombo-AMR model that is currently under development at DoE’s Lawrence Berkeley National Laboratory and the University of Michigan.

6.4.4 Model adaptivity

Another type of model adaptivity, where the model changes locally in a region of the domain, will also play an important role in future computing. It will be most effective when combined with hierarchical adaptive mesh and algorithm refinement techniques. These models can describe the same physics at different levels of fidelity at the same location or can describe different physics.

Model adaptivity can potentially exploit different levels of parallelism, asynchrony, and mixed precision and can minimize communication across layers. Model adaptivity (as well as AMR) could be tied to error control and uncertainty management to apply the finer-grained models only in those regions where the extra expense improves the solution accuracy. There are clearly opportunities in developing scalable adaptive algorithms, but more research is needed.