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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 significantly reduced. Furthermore, 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. Plain Language Summary: 64‐bit floating‐point numbers are the standard number format for scientific computing in fluid dynamics, which allows for very precise calculations with negligible rounding errors. The need for calculations at this precision level has been questioned for weather and climate models, as errors are caused primarily by insufficient observations or deficiencies of the models themselves. Reducing numerical precision can accelerate simulations and low‐precision number formats are increasingly supported by modern computers. This paper investigates the potential of low numerical precision with numbers that only use 16 bit of information, when applied within simulations of weather and climate. The different number formats are applied in a two‐dimensional oceanic or atmospheric circulation model. There are several 16‐bit number formats that can potentially be used, all of which have considerably larger rounding errors than the standard 64‐bit numbers. A simple change to 16 bits for all calculations will not be possible as it will degrade simulation results. However, if mitigation methods are applied, 16‐bit calculations can be used successfully within the applications of this paper. The results show the potential of 16‐bit number formats for at least parts of complex weather and climate models. Key Points: Posit numbers reduce rounding errors compared to floating‐point numbers, enabling reliable shallow water simulations with 16‐bit arithmeticErrors caused by 16‐bit arithmetic are reduced with critical computations in 32 bit, which can be implemented on present‐day hardware16‐ or even 8‐bit communication between processors introduces negligible errors, providing a perspective for reduced data communication [ABSTRACT FROM AUTHOR]

The use of reduced numerical precision to reduce computing costs for the cloud resolving model of superparameterized simulations of the atmosphere is investigated. An approach to identify the optimal level of precision for many different model components is presented, and a detailed analysis of precision is performed. This is nontrivial for a complex model that shows chaotic behavior such as the cloud resolving model in this paper. It is shown not only that numerical precision can be reduced significantly but also that the results of the reduced precision analysis provide valuable information for the quantification of model uncertainty for individual model components. The precision analysis is also used to identify model parts that are of less importance thus enabling a reduction of model complexity. It is shown that the precision analysis can be used to improve model efficiency for both simulations in double precision and in reduced precision. Model simulations are performed with a superparameterized single-column model version of the OpenIFS model that is forced by observational data sets. A software emulator was used to mimic the use of reduced precision floating point arithmetic in simulations. [ABSTRACT FROM AUTHOR]

This paper sets out a new methodological approach to solving the equations for simulating and predicting weather and climate. In this approach, the conventionally hard boundary between the dynamical core and the sub-grid parametrizations is blurred. This approach is motivated by the relatively shallow power-law spectrum for atmospheric energy on scales of hundreds of kilometres and less. It is first argued that, because of this, the closure schemes for weather and climate simulators should be based on stochastic-dynamic systems rather than deterministic formulae. Second, as high-wavenumber elements of the dynamical core will necessarily inherit this stochasticity during time integration, it is argued that the dynamical core will be significantly over-engineered if all computations, regardless of scale, are performed completely deterministically and if all variables are represented with maximum numerical precision (in practice using double-precision floating-point numbers). As the era of exascale computing is approached, an energy- and computationally efficient approach to cloud-resolved weather and climate simulation is described where determinism and numerical precision are focused on the largest scales only. [ABSTRACT FROM AUTHOR]

Inexact hardware design, which advocates trading the accuracy of computations in exchange for significant savings in area, power and/or performance of computing hardware, has received increasing prominence in several error-tolerant application domains, particularly those involving perceptual or statistical end-users. In this paper, we evaluate inexact hardware for its applicability in weather and climate modelling. We expand previous studies on inexact techniques, in particular probabilistic pruning, to floating point arithmetic units and derive several simulated set-ups of pruned hardware with reasonable levels of error for applications in atmospheric modelling. The set-up is tested on the Lorenz '96 model, a toy model for atmospheric dynamics, using software emulation for the proposed hardware. The results show that large parts of the computation tolerate the use of pruned hardware blocks without major changes in the quality of short- and long-time diagnostics, such as forecast errors and probability density functions. This could open the door to significant savings in computational cost and to higher resolution simulations with weather and climate models. [ABSTRACT FROM AUTHOR]