Tim Palmer

Abstract:

Numerical weather prediction and climate models comprise a) a dynamical core describing resolved parts of the climate system and b) parameterizations describing unresolved components. Development of new subgrid-scale parameterizations is particularly uncertain compared to representing resolved scales in the dynamical core. This uncertainty is currently represented by stochastic approaches in several operational weather models, which will inevitably percolate into the dynamical core. Hence, implementing dynamical cores with excessive numerical accuracy will not bring forecast gains, may even hinder them since valuable computer resources will be tied up doing insignificant computation, and therefore cannot be deployed for more useful gains, such as increasing model resolution or ensemble sizes. Here we describe a low-cost stochastic scheme that can be implemented in any existing deterministic dynamical core as an additive noise term. This scheme could be used to adjust accuracy in future dynamical core development work. We propose that such an additive stochastic noise test case should become a part of the routine testing and development of dynamical cores in a stochastic framework. The overall key point of the study is that we should not develop dynamical cores that are more precise than the level of uncertainty provided by our stochastic scheme. In this way, we present a new paradigm for dynamical core development work, ensuring that weather and climate models become more computationally efficient. We show some results based on tests done with the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS) dynamical core.

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.