Abstract
The continuous partial differential equations governing a given physical phenomenon, such as the Navier–Stokes equations describing the fluid motion, must be numerically discretized in space and time in order to obtain a solution otherwise not readily available in closed (i.e., analytic) form. While the overall numerical discretization plays an essential role in the algorithmic efficiency and physically-faithful representation of the solution, the time-integration strategy commonly is one of the main drivers in terms of cost-to-solution (e.g., time- or energy-to-solution), accuracy and numerical stability, thus constituting one of the key building blocks of the computational model. This is especially true in time-critical applications, including numerical weather prediction (NWP), climate simulations and engineering. This review provides a comprehensive overview of the existing and emerging time-integration (also referred to as time-stepping) practices used in the operational global NWP and climate industry, where global refers to weather and climate simulations performed on the entire globe. While there are many flavors of time-integration strategies, in this review we focus on the most widely adopted in NWP and climate centers and we emphasize the reasons why such numerical solutions were adopted. This allows us to make some considerations on future trends in the field such as the need to balance accuracy in time with substantially enhanced time-to-solution and associated implications on energy consumption and running costs. In addition, the potential for the co-design of time-stepping algorithms and underlying high performance computing hardware, a keystone to accelerate the computational performance of future NWP and climate services, is also discussed in the context of the demanding operational requirements of the weather and climate industry.
Highlights
Over the past few decades, operational numerical weather prediction (NWP) and climate models have evolved tremendously thanks to the continuous improvement of computing technologies and of the underlying algorithms at the foundations of these models
A numerical weather or climate model is constituted by a set of prognostic partial differential equations (PDEs) governing the fluid motion in the atmosphere and by all those physical processes acting at a subgrid scale, whose statistical effects on the mean flow are expressed as a function of resolvedscale quantities [64]
The path-based time-integration (PBTI) class, instead, solves the PDE problem in a single step, where the advection term is adsorbed into the path derivative and the right-hand side is formed by forcing terms only
Summary
Over the past few decades, operational NWP and climate models have evolved tremendously thanks to the continuous improvement of computing technologies and of the underlying algorithms at the foundations of these models. A numerical weather or climate model is constituted by a set of prognostic partial differential equations (PDEs) governing the fluid motion in the atmosphere (i.e., the geophysical flow) and by all those physical processes acting at a subgrid scale, whose statistical effects on the mean flow are expressed as a function of resolvedscale quantities [64]. The former is known as the dynamical core and represents the scale-resolved part of the model, whereas the latter are referred to as the physical parameterizations and include the under-resolved processes. The overall model is discretized in space and time via suitable algorithmic blocks to approximate the continuous system of equations, thereby providing a solution otherwise not readily achievable
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