Tim Palmer

Abstract:

The next generation of weather and climate models will have an unprecedented level of resolution and model complexity, and running these models efficiently will require taking advantage of future supercomputers and heterogeneous hardware. In this paper, we investigate the use of mixed-precision hardware that supports floating-point operations at double-, single- and half-precision. In particular, we investigate the potential use of the NVIDIA Tensor Core, a mixed-precision matrix-matrix multiplier mainly developed for use in deep learning, to accelerate the calculation of the Legendre transforms in the Integrated Forecasting System (IFS), one of the leading global weather forecast models. In the IFS, the Legendre transform is one of the most expensive model components and dominates the computational cost for simulations at a very high resolution. We investigate the impact of mixed-precision arithmetic in IFS simulations of operational complexity through software emulation. Through a targeted but minimal use of double-precision arithmetic we are able to use either half-precision arithmetic or mixed half/single-precision arithmetic for almost all of the calculations in the Legendre transform without affecting forecast skill.

Abstract:

Posit numbers, a recently proposed alternative to floating-point numbers, claim to have smaller arithmetic rounding errors in many applications. By studying weather and climate models of low and medium complexity (the Lorenz system and a shallow water model) we present benefits of posits compared to floats at 16 bit. As a standardised posit processor does not exist yet, we emulate posit arithmetic on a conventional CPU. Using a shallow water model, forecasts based on 16-bit posits with 1 or 2 exponent bits are clearly more accurate than half precision floats. We therefore propose 16 bit with 2 exponent bits as a standard posit format, as its wide dynamic range of 32 orders of magnitude provides a great potential for many weather and climate models. Although the focus is on geophysical fluid simulations, the results are also meaningful and promising for reduced precision posit arithmetic in the wider field of computational fluid dynamics.

Abstract:

© 2018 Royal Meteorological Society Studies conducted by the UK Met Office reported significant skill in predicting the winter North Atlantic Oscillation (NAO) index with their seasonal prediction system. At the same time, a very low signal-to-noise ratio was observed, as measured using the “ratio of predictable components” (RPC) metric. We analyse both the skill and signal-to-noise ratio using a new statistical toy model, which assumes NAO predictability is driven by regime dynamics. It is shown that if the system is approximately bimodal in nature, with the model consistently underestimating the level of regime persistence each season, then both the high skill and high RPC value of the Met Office hindcasts can easily be reproduced. Underestimation of regime persistence could be attributable to any number of sources of model error, including imperfect regime structure or errors in the propagation of teleconnections. In particular, a high RPC value for a seasonal mean prediction may be expected even if the model's internal level of noise is realistic.