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General circulation models (GCMs) are the foundation of weather and climate prediction1,2. GCMs are physics-based simulators that combine a numerical solver for large-scale dynamics with tuned representations for small-scale processes such as cloud formation. Recently, machine-learning models trained on reanalysis data have achieved comparable or better skill than GCMs for deterministic weather forecasting3,4. However, these models have not demonstrated improved ensemble forecasts, or shown sufficient stability for long-term weather and climate simulations. Here we present a GCM that combines a differentiable solver for atmospheric dynamics with machine-learning components and show that it can generate forecasts of deterministic weather, ensemble weather and climate on par with the best machine-learning and physics-based methods. NeuralGCM is competitive with machine-learning models for one- to ten-day forecasts, and with the European Centre for Medium-Range Weather Forecasts ensemble prediction for one- to fifteen-day forecasts. With prescribed sea surface temperature, NeuralGCM can accurately track climate metrics for multiple decades, and climate forecasts with 140-kilometre resolution show emergent phenomena such as realistic frequency and trajectories of tropical cyclones. For both weather and climate, our approach offers orders of magnitude computational savings over conventional GCMs, although our model does not extrapolate to substantially different future climates. Our results show that end-to-end deep learning is compatible with tasks performed by conventional GCMs and can enhance the large-scale physical simulations that are essential for understanding and predicting the Earth system.

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Non-periodic solutions are an essential property of chaotic dynamical systems. Simulations with deterministic finite-precision numbers, however, always yield orbits that are eventually periodic. With 64-bit double-precision floating-point numbers such periodic orbits are typically negligible due to very long periods. The emerging trend to accelerate simulations with low-precision numbers, such as 16-bit half-precision floats, raises questions on the fidelity of such simulations of chaotic systems. Here, we revisit the 1-variable logistic map and the generalised Bernoulli map with various number formats and precisions: floats, posits and logarithmic fixed-point. Simulations are improved with higher precision but stochastic rounding prevents periodic orbits even at low precision. For larger systems the performance gain from low-precision simulations is often reinvested in higher resolution or complexity, increasing the number of variables. In the Lorenz 1996 system, the period lengths of orbits increase exponentially with the number of variables. Moreover, invariant measures are better approximated with an increased number of variables than with increased precision. Extrapolating to large simulations of natural systems, such as million-variable climate models, periodic orbit lengths are far beyond reach of present-day computers. Such orbits are therefore not expected to be problematic compared to high-precision simulations but the deviation of both from the continuum solution remains unclear.

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Most Earth-system simulations run on conventional central processing units in 64-bit double precision floating-point numbers Float64, although the need for high-precision calculations in the presence of large uncertainties has been questioned. Fugaku, currently the world's fastest supercomputer, is based on A64FX microprocessors, which also support the 16-bit low-precision format Float16. We investigate the Float16 performance on A64FX with ShallowWaters.jl, the first fluid circulation model that runs entirely with 16-bit arithmetic. The model implements techniques that address precision and dynamic range issues in 16 bits. The precision-critical time integration is augmented to include compensated summation to minimize rounding errors. Such a compensated time integration is as precise but faster than mixed precision with 16 and 32-bit floats. As subnormals are inefficiently supported on A64FX the very limited range available in Float16 is 6 × 10-5 to 65,504. We develop the analysis-number format Sherlogs.jl to log the arithmetic results during the simulation. The equations in ShallowWaters.jl are then systematically rescaled to fit into Float16, using 97% of the available representable numbers. Consequently, we benchmark speedups of up to 3.8x on A64FX with Float16. Adding a compensated time integration, speedups reach up to 3.6x. Although ShallowWaters.jl is simplified compared to large Earth-system models, it shares essential algorithms and therefore shows that 16-bit calculations are indeed a competitive way to accelerate Earth-system simulations on available hardware.

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International outdoor athletics championships are typically hosted during the summer season, frequently in hot and humid climatic conditions. Therefore, we analyzed the association between apparent temperature and heat-related illnesses occurrence during international outdoor athletics championships and compared its incidence rates between athletics disciplines. Heat-related illnesses were selected from illness data prospectively collected at seven international outdoor athletics championships between 2009 and 2018 using a standardized methodology. The Universal Thermal Climate Index (UTCI) was calculated as a measure of the apparent temperature based on weather data for each day of the championships. Heat-related illness numbers and (daily) incidence rates were calculated and analyzed in relation to the daily maximum UTCI temperature and between disciplines. During 50 championships days with UTCI temperatures between 15℃ and 37℃, 132 heat-related illnesses were recorded. Average incidence rate of heat-related illnesses was 11.7 (95%CI 9.7 to 13.7) per 1000 registered athletes. The expected daily incidence rate of heat-related illnesses increased significantly with UTCI temperature (0.12 more illnesses per 1000 registered athletes/°C; 95%CI 0.08-0.16) and was found to double from 25 to 35°C UTCI. Race walkers (RR = 45.5, 95%CI 21.6-96.0) and marathon runners (RR = 47.7, 95%CI 23.0-98.8) had higher heat-related illness rates than athletes competing in short-duration disciplines. Higher UTCI temperatures were associated with more heat-related illnesses, with marathon and race walking athletes having higher risk than athletes competing in short-duration disciplines. Heat-related illness prevention strategies should predominantly focus on marathon and race walking events of outdoor athletics championships when high temperatures are forecast.

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Hundreds of petabytes are produced annually at weather and climate forecast centers worldwide. Compression is essential to reduce storage and to facilitate data sharing. Current techniques do not distinguish the real from the false information in data, leaving the level of meaningful precision unassessed. Here we define the bitwise real information content from information theory for the Copernicus Atmospheric Monitoring Service (CAMS). Most variables contain fewer than 7 bits of real information per value and are highly compressible due to spatio-temporal correlation. Rounding bits without real information to zero facilitates lossless compression algorithms and encodes the uncertainty within the data itself. All CAMS data are 17× compressed relative to 64-bit floats, while preserving 99% of real information. Combined with four-dimensional compression, factors beyond 60× are achieved. A data compression Turing test is proposed to optimize compressibility while minimizing information loss for the end use of weather and climate forecast data.

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