Existing weather models are known to have poor skill at forecasting rainfall over East Africa, where there are regular threats of drought and floods. Improved forecasts could reduce the effects of these extreme weather events and provide significant socioeconomic benefits to the region. We present a novel machine learning-based method to improve precipitation forecasts in East Africa, using postprocessing based on a conditional generative adversarial network (cGAN). This addresses the challenge of realistically representing tropical rainfall, where convection dominates and is poorly simulated in conventional global forecast models. We postprocess hourly forecasts made by the European Centre for Medium-Range Weather Forecasts Integrated Forecast System at 6-18h lead times, at $0.1^{\circ}$ resolution. We combine the cGAN predictions with a novel neighbourhood version of quantile mapping, to integrate the strengths of machine learning and conventional postprocessing. Our results indicate that the cGAN substantially improves the diurnal cycle of rainfall, and improves predictions up to the $99.9^{\text{th}}$ percentile ($\sim 10 \text{mm}/\text{hr}$). This improvement extends to the 2018 March–May season, which had extremely high rainfall, indicating that the approach has some ability to generalise to more extreme conditions. We explore the potential for the cGAN to produce probabilistic forecasts and find that the spread of this ensemble broadly reflects the predictability of the observations, but is also characterised by a mixture of under- and over-dispersion. Overall our results demonstrate how the strengths of machine learning and conventional postprocessing methods can be combined, and illuminate what benefits machine learning approaches can bring to this region.

We assess the ability of neural network emulators of physical parametrization schemes in numerical weather prediction models to aid in the construction of linearised models required by 4D-Var data assimilation. Neural networks can be differentiated trivially, and so if a physical parametrization scheme can be accurately emulated by a neural network then its tangent-linear and adjoint versions can be obtained with minimal effort, compared with the standard paradigms of manual or automatic differentiation of the model code. Here we demonstrate this idea by emulating the non-orographic gravity wave drag parametrization scheme in an atmospheric model with a neural network, and deriving its tangent-linear and adjoint models. We demonstrate that these neural network-derived tangent-linear and adjoint models not only pass the standard consistency tests but also can be used successfully to do 4D-Var data assimilation. This technique holds the promise of significantly easing maintenance of tangent-linear and adjoint codes in weather forecasting centres, if accurate neural network emulators can be constructed.

Most Earth-system simulations run on conventional CPUs 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 bit. 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 65504. 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 3.8x on A64FX with Float16. Adding a compensated time integration the speedup is 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.

The need for high precision calculations with 64-bit or 32-bit floating-point arithmetic for weather and climate models is questioned. Lower precision numbers can accelerate simulations and are increasingly supported by modern computing hardware. This paper investigates the potential of 16-bit arithmetic when applied within a shallow water model that serves as a medium complexity weather or climate application. There are several 16-bit number formats that can potentially be used (IEEE half precision, BFloat16, posits, integer and fixed-point). It is evident that a simple change to 16-bit arithmetic will not be possible for complex weather and climate applications as it will degrade model results by intolerable rounding errors that cause a stalling of model dynamics or model instabilities. However, if the posit number format is used as an alternative to the standard floating-point numbers the model degradation can be reduced to a tolerable minimum. Furthermore, a number of mitigation methods, such as rescaling, reordering and mixed-precision, are available to make model simulations resilient against a precision reduction. If mitigation methods are applied, 16-bit floating-point arithmetic can be used successfully within the shallow water model. The results show the potential of 16-bit formats for at least parts of complex weather and climate models where rounding errors would be entirely masked by initial condition, model or discretization error.

Semi-implicit time-stepping schemes for atmosphere and ocean models require elliptic solvers that work efficiently on modern supercomputers. This paper reports our study of the potential computational savings when using mixed precision arithmetic in the elliptic solvers. Precision levels as low as half (16 bits) are used and a detailed evaluation of the impact of reduced precision on the solver convergence and the solution quality is performed. This study is conducted in the context of a novel semi-implicit shallow-water model on the sphere, purposely designed to mimic numerical intricacies of modern all-scale weather and climate (W&C) models. The governing algorithm of the shallow-water model is based on the non-oscillatory MPDATA methods for geophysical flows, whereas the resulting elliptic problem employs a strongly preconditioned non-symmetric Krylov-subspace solver GCR, proven in advanced atmospheric applications. The classical longitude/latitude grid is deliberately chosen to retain the stiffness of global W&C models. The analysis of the precision reduction is done on a software level, using an emulator, whereas the performance is measured on actual reduced precision hardware. The reduced-precision experiments are conducted for established dynamical-core test-cases, like the Rossby-Haurwitz wavenumber 4 and a zonal orographic flow. The study shows that selected key components of the elliptic solver, most prominently the preconditioning and the application of the linear operator, can be performed at the level of half precision. For these components, the use of half precision is found to yield a speed-up of a factor 4 compared to double precision for a wide range of problem sizes.