A power law for reduced precision at small spatial scales: Experiments with an SQG model. (15th August 2018) - Thornes, Tobias; Düben, Peter; Palmer, Tim
Abstract : Representing all variables in double‐precision in weather and climate models may be a waste of computer resources, especially when simulating the smallest spatial scales, which are more difficult to accurately observe and model than are larger scales. Recent experiments have shown that reducing to single‐precision would allow real‐world models to run considerably faster without incurring significant errors. Here, the effects of reducing precision to even lower levels are investigated in the Surface Quasi‐Geostrophic system, an idealised system that exhibits a similar power‐law spectrum to that of energy in the real atmosphere, by emulating reduced precision on conventional hardware. It is found that precision can be reduced much further for the smallest scales than the largest scales without inducing significant macroscopic error, according to a −4/3 power law, motivating the construction of a "scale‐selective" reduced‐precision model that performs as well as a double‐precision control in short‐ and long‐range forecasts but for a much lower estimated computational cost. A similar scale‐selective approach in real‐world models could save resources that could be re‐invested to allow these models to be run at greater resolution, complexity or ensemble size, potentially leading to more efficient, more accurate forecasts. Abstract : Numerical atmospheric models could be made more energy‐efficient by reducing the numerical precision with which less‐important calculations are performed. The Surface Quasi‐Geostrophic (SQG) equations, based on the Navier–Stokes equations that describe Earth's atmosphere, exhibit an Earth‐like turbulent energy cascade and weather‐like features such as the vortex shedding shown above. In this article, we emulate reduced precision in a spectral numerical SQG model and show that less precision is required at smaller spatial scales according to a power law.