Background to the Super-Droplet Model (SDM)

Cloud microphysics remains an integral and under-represented element of the climate system. Not only does this limit our understanding of clouds themselves, but also causes some of the largest uncertainties in climate modelling as a whole. Such a predicament is only exacerbated by Global Storm Resolving Models (GSRMs), the new generation of climate models which have storm-resolving resolutions O(1km) and parametrise radiation, sub-grid turbulence, and microphysics [SlingoJBatesPBauerPaeal22] [SSJ+19] [SSAea19] [SBW+19]. GSRMs have all but irradicated their parametrisations of convection, leaving microphysical parametrisations to replace them as one of their leading sources of uncertainty [MvLWF+20]. State of the art climate models have thus accentuated the need to better understand and model cloud microphysics.

The recently established Super-Droplet Model (SDM) is a promising alternative to conventional bulk and bin models for cloud microphysics. Briefly, SDM replaces traditional modelling of condensate distributions with Lagrangian particles, so called ‘super-droplets’, that act as representatives for the condensate populations of a cloud. A super-droplet has a multiplicity which defines how many ordinary condensate particles it represents. Whilst most microphysical processes, for example condensation and evaporation, are modelled exactly how ordinary condensates would be, some processes are modelled probabilistically instead. Indeed, the defining feature of SDM is that collisions of super-droplets are determined Monte-Carlo simulation such that the outcome of collisions converges towards the stochastic behaviour of a direct numerical simulation (DNS) as the number of super-droplets increases. As has been shown in numerous studies, SDM can reproduce the results of bin models at comparable computational cost, but without suffering from the spatial and spectral broadening caused by numerical diffusion [DWP19] [AS13] [AGRG10] [ARH+08].

In comparison with bulk and bin models, SDM has a number of important conceptual and computational advantages [MvLWF+20]. The Lagrangian perspective and the reduced number of assumptions make SDM easier to interpret physically, and therefore a more appealing model. Particularly promising is that SDM can readily incorporate the multitude of attributes of real droplets with only linearly increasing computational complexity. As a consequence super-droplets can, for example, naturally convey information about different aerosol properties, which could be used to understand how atmospheric emissions impact rainfall or cloud reflectivity (and therefore the Earth’s energy budget). Alternatively SDM is well suited to modelling the plethora of cloud ice structures, as super-droplet attributes could be designed so that different ice habits transition seamlessly between one another. This is in stark contrast to the “curse of dimensionality” which has plagued more complex bin and bulk models in recent decades [GMS+19]. The convergence properties of SDM are also a big factor in its conceptual appeal. As the number of super-droplets increases, SDM tends towards DNS - or in other words the closest model we have to “true” cloud microphysics. This property arises from the mathematical formulation of SDM and is not likewise fundamental to bulk and bin models.

From a computational perspective, whilst SDM is prohibitively expensive for current global climate simulations, it is ideally suited to future advances in HPC. The underlying simplicity of the model renders it highly parallelisable and well matched to trends favouring the use of many, extremely fast lightweight processors. As has been shown recently, this makes SDM ideally suited to supercomputers with graphics processing units (GPUs) [BA21] [DWP19] [AJPG15]. The growth of random access memory (RAM) is also favourable for SDM. Not only does it make SDM’s high memory usage less demanding, but it allows for the improvement of the model’s precision by enabling more super-sroplets to be simulated in a domain. It also allows more super-droplet attributes and microphysical processes to be incorporated into SDM, thus increasing the fidelity of the model to our understanding of cloud microphysics. With regard to HPC, SDM is highly scalable and advances in tandem.