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Motivated by recent advances in operational weather forecasting, we study theefficacy of low-precision arithmetic for climate simulations. We develop aframework to measure rounding error in a climate model which provides astress-test for a low-precision version of the model, and we apply our methodto a variety of models including the Lorenz system; a shallow waterapproximation for flow over a ridge; and a coarse resolution global atmosphericmodel with simplified parameterisations (SPEEDY). Although double precision (52significant bits) is standard across operational climate models, in ourexperiments we find that single precision (23 sbits) is more than enough andthat as low as half precision (10 sbits) is often sufficient. For example,SPEEDY can be run with 12 sbits across the entire code with negligible roundingerror and this can be lowered to 10 sbits if very minor errors are accepted,amounting to less than 0.1 mm/6hr for the average grid-point precipitation, forexample. Our test is based on the Wasserstein metric and this providesstringent non-parametric bounds on rounding error accounting for annual meansas well as extreme weather events. In addition, by testing models using bothround-to-nearest (RN) and stochastic rounding (SR) we find that SR can mitigaterounding error across a range of applications. Thus our results also provideevidence that SR could be relevant to next-generation climate models. Whilemany studies have shown that low-precision arithmetic can be suitable onshort-term weather forecasting timescales, our results give the first evidencethat a similar low precision level can be suitable for climate.

Climate Modelling in Low-Precision: Effects of both Deterministic & Stochastic Rounding