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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]

Stochastic schemes, designed to represent unresolved subgrid‐scale variability, are frequently used in short and medium‐range weather forecasts, where they are found to improve several aspects of the model. In recent years, the impact of stochastic physics has also been found to be beneficial for the model's long‐term climate. In this paper, we demonstrate for the first time that the inclusion of a stochastic physics scheme can notably affect a model's projection of global warming, as well as its historical climatological global temperature. Specifically, we find that when including the "stochastically perturbed parametrization tendencies" (SPPT) scheme in the fully coupled climate model EC‐Earth v3.1, the predicted level of global warming between 1850 and 2100 is reduced by 10% under an RCP8.5 forcing scenario. We link this reduction in climate sensitivity to a change in the cloud feedbacks with SPPT. In particular, the scheme appears to reduce the positive low cloud cover feedback and increase the negative cloud optical feedback. A key role is played by a robust, rapid increase in cloud liquid water with SPPT, which we speculate is due to the scheme's nonlinear interaction with condensation. Plain Language Summary: Accurate estimates of the extent of global warming by 2100 are crucial for determining effective climate policies. However, large uncertainties still remain, due in large part to uncertainties in the response of clouds to global warming. Model uncertainties arise largely from the need to crudely estimate the effects of processes too small to represent perfectly (given the limits of current computing power). "Stochastic schemes" aim to represent such errors, thereby, potentially, improving climate models. Indeed, many such improvements have been found over the last decade. In this paper, we show that the inclusion of such a scheme in one particular climate model has the effect of reducing the projected global warming by 10%. We link this to the scheme having changed the response of clouds to global warming. A potential consequence of this result is that carefully calibrated stochastic schemes could, by representing model errors, improve the accuracy of global warming projections. Key Points: The inclusion of a stochastic scheme reduces climate sensitivity in a general circulation modelThis reduction, of around 10%, is linked to changes in cloud cover and cloud optical depth feedbacksWell‐calibrated stochastic schemes may give more accurate global warming projections [ABSTRACT FROM AUTHOR]

This study assesses the medium‐range flow‐dependent forecast skill of Euro‐Atlantic weather regimes: the positive and negative phases of the North Atlantic Oscillation (NAO+ and NAO−), Atlantic ridge (ATLR), and Euro‐Atlantic blocking (EABL), for extended winters (November–March) in the periods 2006/2007–2013/2014 and 1985/1986–2013/2014 using The Interactive Grand Global Ensemble (TIGGE) and the National Oceanic and Atmospheric Administration (NOAA)'s Global Ensemble Forecasting System (GEFS) reforecast datasets, respectively. The models show greater‐than‐observed (smaller‐than‐observed) frequencies of NAO− and ATLR (NAO+) with forecast lead time. The increased frequency of NAO− is not due to its excess persistence but due to more frequent transitions mainly from ATLR, but also from NAO+. In turn, NAO+ is under‐persistent. The models show the highest probabilistic skill for forecasts initialised on NAO− and the NAO− forecasts during the TIGGE period. However, the GEFS reforecast during the period 1985/1986–2013/2014 revealed that these recent high skills reflect the occurrence of four long‐lasting (>30 days) NAO− events in 2009/2010–2013/2014 and that the skill for forecasts initialised on NAO− before 2009/2010 (the longest duration was 22 days and the second‐longest 16 days) was the lowest. The longer the NAO− events persist, the higher the skill of forecasts initialised on NAO−. The skill dependency on regime duration is less clearly observed for the other regimes. In addition, the GEFS reforecast also revealed that the highest skill of the NAO− forecasts during the period 1985/1986–2013/2014 is attributed to the higher skill of the NAO− forecasts during the active NAO− periods. The EABL forecasts initialised on ATLR show the lowest skill, followed by the NAO− (EABL) forecasts initialised on NAO+ or ATLR (NAO+). These results suggest that the recent models still have difficulties in predicting the onset of blocking. [ABSTRACT FROM AUTHOR]

The Stochastically Perturbed Parametrization Tendencies (SPPT) scheme is used at weather and climate forecasting centres worldwide to represent model uncertainty that arises from simplifications involved in the parametrization process. It uses spatio-temporally correlated multiplicative noise to perturb the sum of the parametrized tendencies. However, SPPT does not distinguish between different parametrization schemes, which do not necessarily have the same error characteristics. A generalization to SPPT is proposed, whereby the tendency from each parametrization scheme can be perturbed using an independent stochastic pattern. This acknowledges that the forecast errors arising from different parametrizations are not perfectly correlated. Two variations of this 'independent SPPT' (iSPPT) approach are tested in the Integrated Forecasting System (IFS). The first perturbs all parametrized tendencies independently, while the second groups tendencies before perturbation. The iSPPT schemes lead to statistically significant improvements in forecast reliability in the Tropics in medium-range weather forecasts. This improvement can be attributed to a large, beneficial increase in ensemble spread in regions with significant convective activity. The iSPPT schemes also lead to improved forecast skill in the extratropics for a set of cases in which the synoptic initial conditions were more likely to result in European 'forecast busts'. Longer 13 month simulations are also considered to indicate the effect of iSPPT on the mean climate of the IFS. [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]

Programmable hardware, in particular Field Programmable Gate Arrays (FPGAs), promises a significant increase in computational performance for simulations in geophysical fluid dynamics compared with CPUs of similar power consumption. FPGAs allow adjusting the representation of floating-point numbers to specific application needs. We analyze the performance-precision trade-off on FPGA hardware for the two-scale Lorenz '95 model. We scale the size of this toy model to that of a high-performance computing application in order to make meaningful performance tests. We identify the minimal level of precision at which changes in model results are not significant compared with a maximal precision version of the model and find that this level is very similar for cases where the model is integrated for very short or long intervals. It is therefore a useful approach to investigate model errors due to rounding errors for very short simulations (e.g., 50 time steps) to obtain a range for the level of precision that can be used in expensive long-term simulations. We also show that an approach to reduce precision with increasing forecast time, when model errors are already accumulated, is very promising. We show that a speed-up of 1.9 times is possible in comparison to FPGA simulations in single precision if precision is reduced with no strong change in model error. The single-precision FPGA setup shows a speed-up of 2.8 times in comparison to our model implementation on two 6-core CPUs for large model setups. [ABSTRACT FROM AUTHOR]

Forecast verification is important across scientific disciplines, as it provides a framework for evaluating the performance of a forecasting system. In the atmospheric sciences, probabilistic skill scores are often used for verification, as they provide a way of ranking the performance of different probabilistic forecasts unambiguously. In order to be useful, a skill score must be proper: it must encourage honesty in the forecaster and reward forecasts that are reliable and have good resolution. A new score, the error-spread score (ES), is proposed, which is particularly suitable for evaluation of ensemble forecasts. It is formulated with respect to the moments of the forecast. The ES is confirmed to be a proper score and is therefore sensitive to both resolution and reliability. The ES is tested on forecasts made using the Lorenz ′96 system and found to be useful for summarizing the skill of the forecasts. The European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble prediction system (EPS) is evaluated using the ES. Its performance is compared with a perfect statistical probabilistic forecast: the ECMWF high-resolution deterministic forecast dressed with the observed error distribution. This generates a forecast that is perfectly reliable if considered over all time, but does not vary from day to day with the predictability of the atmospheric flow. The ES distinguishes between the dynamically reliable EPS forecasts and the statically reliable dressed deterministic forecasts. Other skill scores are tested and found to be comparatively insensitive to this desirable forecast quality. The ES is used to evaluate seasonal range ensemble forecasts made with the ECMWF System 4. The ensemble forecasts are found to be skilful when compared with climatological or persistence forecasts, though this skill is dependent on the region and time of year. [ABSTRACT FROM AUTHOR]