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The extent to which interannual variability in Arctic sea ice influences the midlatitude circulation has been extensively debated. While observational data supports the existence of a teleconnection between November sea ice in the Barents-Kara region and the subsequent winter circulation, climate models do not consistently reproduce such a link, with only very weak inter-model consensus. We show, using the EC-Earth3 climate model, that while a deterministic ensemble of coupled simulations shows no evidence of such a teleconnection, the inclusion of stochastic parameterizations to the ocean and sea ice component of EC-Earth3 results in the emergence of a robust teleconnection comparable in magnitude to that observed. We show that this can be accounted for entirely by an improved ice-ocean-atmosphere coupling due to the stochastic perturbations. In particular, the inconsistent signal in existing climate model studies may be due to model biases in surface coupling, with stochastic parameterizations being one possible remedy.

This study introduces a new flow‐dependent distribution sampling (FDDS) scheme for air–sea coupling. The FDDS scheme is implemented in a climate model and used to improve the simulated mean and variability of atmospheric and oceanic surface fields and thus air–sea fluxes. Most coupled circulation models use higher resolutions in the sea ice and ocean compared to the atmospheric model component, thereby explicitly simulating the atmospheric subgrid‐scale at the interface. However, the commonly applied averaging of surface fields and air–sea fluxes tends to smooth fine‐scale structures, such as oceanic fronts. The stochastic FDDS scheme samples the resolved spatial ocean (and sea ice) subgrid distribution that is usually not visible to a coarser‐resolution atmospheric model. Randomly drawn nodal ocean values are passed to the corresponding atmospheric boxes for the calculation of surface fluxes, aiming to enhance surface flux variability. The resulting surface field perturbations of the FDDS scheme are based on resolved dynamics, displaying pronounced seasonality with realistic magnitude. The AWI Climate Model is used to test the scheme on interannual time‐scales. Our set‐up features a high ocean‐to‐atmosphere resolution ratio in the Tropics, with grid‐point ratios of about 60:1. Compared to the default deterministic averaging, changes are largest in the Tropics leading to an improved spatial distribution of precipitation with bias reductions of up to 50%. Enhanced sea‐surface temperature variability in boreal winter further improves the seasonal phase locking of temperature anomalies associated with the El Niño–Southern Oscillation. Mean 2m temperature, sea ice thickness and concentration react with a contrasting dipole pattern between hemispheres but a joint increase of monthly and interannual variability. This first approach to implement a flow‐dependent stochastic coupling scheme shows considerable benefits for simulations of global climate, and various extensions and modifications of the scheme are possible.

We introduce and study the impact of three stochastic schemes in the EC-Earth climate model: two atmospheric schemes and one stochastic land scheme. These form the basis for a probabilistic Earth system model in atmosphere-only mode. Stochastic parametrization have become standard in several operational weather-forecasting models, in particular due to their beneficial impact on model spread. In recent years, stochastic schemes in the atmospheric component of a model have been shown to improve aspects important for the models long-term climate, such as El Niño–Southern Oscillation (ENSO), North Atlantic weather regimes, and the Indian monsoon. Stochasticity in the land component has been shown to improve the variability of soil processes and improve the representation of heatwaves over Europe. However, the raw impact of such schemes on the model mean is less well studied. It is shown that the inclusion of all three schemes notably changes the model mean state. While many of the impacts are beneficial, some are too large in amplitude, leading to significant changes in the model's energy budget and atmospheric circulation. This implies that in order to maintain the benefits of stochastic physics without shifting the mean state too far from observations, a full re-tuning of the model will typically be required.

We present a new energy backscatter parametrization for primitive equation ocean models at eddy-permitting resolution, specifically for unstructured grids. Traditional eddy parametrizations in terms of viscosity closures lead to excessive dissipation of kinetic energy when used with eddy-permitting meshes. Implemented into the FESOM2 ocean model, the backscatter parametrization leads to a more realistic total dissipation of kinetic energy. It maintains a reservoir of dissipated energy and reinjects this subgrid energy at larger scales at a controlled rate. The separation between dissipation and backscatter scales is achieved by using different-order differential operators and/or spatial smoothing. This ensures numerical model stability. We perform sensitivity studies with different choices of parameter settings and viscosity schemes in a configuration with a baroclinically unstable flow in a zonally reentrant channel with a horizontally uniform mesh. The best backscatter setup substantially improves eddy-permitting simulations at 1/4° and 1/6° resolution, bringing them close to a 1/12° eddy-resolving reference. Improvements are largest for levels of kinetic energy and variability in temperature and vertical velocity. A selected optimal default scheme is then tested in a mixed resolution setup – a channel with narrow transitions between an eddy-permitting and an eddy-resolving subdomain. The backscatter scheme is able to adapt dynamically to the different resolutions and moves the diagnostics closer to the high resolution reference throughout the domain. Our study is a first step toward using backscatter in global variable-mesh ocean models and suggests potential for substantial improvements of ocean mean state and variability at reduced computational cost.

Capturing mesoscale eddy dynamics is crucial for accurate simulations of the large-scale ocean currents as well as oceanic and climate variability. Eddy-mean flow interactions affect the position, strength and variations of mean currents and eddies are important drivers of oceanic heat transport and atmosphere-ocean-coupling. However, simulations at eddy-permitting resolutions are substantially underestimating eddy variability and eddy kinetic energy many times over. Such eddy-permitting simulations will be in use for years to come, both in coupled and uncoupled climate simulations. We present a set of kinetic energy backscatter schemes with different complexity as alternative momentum closures that can alleviate some eddy related biases such as biases in the mean currents, in sea surface height variability and in temperature and salinity. The complexity of the schemes reflects in their computational costs, the related simulation improvements and their adaptability to different resolutions. However, all schemes outperform classical viscous closures and are computationally less expensive than a related necessary resolution increase to achieve similar results. While the backscatter schemes are implemented in the ocean model FESOM2, the concepts can be adjusted to any ocean model including NEMO.

Ocean models at eddy‐permitting resolution are generally overdissipative, damping the intensity of the mesoscale eddy field. To reduce overdissipation, we propose a simplified, kinematic energy backscatter parametrization built into the viscosity operator in conjunction with a new flow‐dependent coefficient of viscosity based on nearest neighbor velocity differences. The new scheme mitigates excessive dissipation of energy and improves global ocean simulations at eddy‐permitting resolution. We find that kinematic backscatter substantially raises simulated eddy kinetic energy, similar to an alternative, previously proposed dynamic backscatter parametrization. While dynamic backscatter is scale‐aware and energetically more consistent, its implementation is more complex. Furthermore, it turns out to be computationally more expensive, as it applies, among other things, an additional prognostic subgrid energy equation. The kinematic backscatter proposed here, by contrast, comes at no additional computational cost, following the principle of simplicity. Our primary focus is the discretization on triangular unstructured meshes with cell placement of velocities (an analog of B‐grids), as employed by the Finite‐volumE Sea ice‐Ocean Model (FESOM2). The kinematic backscatter scheme with the new viscosity coefficient is implemented in FESOM2 and tested in the simplified geometry of a zonally reentrant channel as well as in a global ocean simulation on a 1/4° mesh. This first version of the new kinematic backscatter needs to be tuned to the specific resolution regime of the simulation. However, the tuning relies on a single parameter, emphasizing the overall practicality of the approach.

Numerical weather prediction and climate models comprise a) a dynamical core describing resolved parts of the climate system and b) parameterizations describing unresolved components. Development of new subgrid-scale parameterizations is particularly uncertain compared to representing resolved scales in the dynamical core. This uncertainty is currently represented by stochastic approaches in several operational weather models, which will inevitably percolate into the dynamical core. Hence, implementing dynamical cores with excessive numerical accuracy will not bring forecast gains, may even hinder them since valuable computer resources will be tied up doing insignificant computation, and therefore cannot be deployed for more useful gains, such as increasing model resolution or ensemble sizes. Here we describe a low-cost stochastic scheme that can be implemented in any existing deterministic dynamical core as an additive noise term. This scheme could be used to adjust accuracy in future dynamical core development work. We propose that such an additive stochastic noise test case should become a part of the routine testing and development of dynamical cores in a stochastic framework. The overall key point of the study is that we should not develop dynamical cores that are more precise than the level of uncertainty provided by our stochastic scheme. In this way, we present a new paradigm for dynamical core development work, ensuring that weather and climate models become more computationally efficient. We show some results based on tests done with the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS) dynamical core.

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy and improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing longstanding climate biases and relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups which show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface and cryosphere of comprehensive weather and climate models (a) gives rise to more reliable probabilistic forecasts of weather and climate and (b) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics and turbulence is reviewed, its relevance for the climate problem demonstrated, and future research directions outlined., Comment: 26 pages, 15 figures. Final published version

In this study we demonstrate the potential of a kinetic energy backscatter scheme for use in global ocean simulations. Ocean models commonly employ (bi)harmonic eddy viscosities causing excessive dissipation of kinetic energy in eddy‐permitting simulations. Overdissipation not only affects the smallest resolved scales but also the generation of eddies through baroclinic instabilities, impacting the entire wave number spectrum. The backscatter scheme returns part of this overdissipated energy back into the resolved flow. We employ backscatter in the FESOM2 multiresolution ocean model with a quasi‐uniform 1/4° mesh. In multidecadal ocean simulations, backscatter increases eddy activity by a factor 2 or more, moving the simulation closer to observational estimates of sea surface height variability. Moreover, mean sea surface height, temperature, and salinity biases are reduced. This amounts to a globally averaged bias reduction of around 10% for each field, which is even larger in the Antarctic Circumpolar Current. However, in some regions such as the coastal Kuroshio, backscatter leads to a slight overenergizing of the flow and, in the Antarctic, to an unrealistic reduction of sea ice. Some of the bias increases can be reduced by a retuning of the model, and we suggest related adjustments to the backscatter scheme. The backscatter simulation is about 2.5 times as expensive as a simulation without backscatter. Most of the increased cost is due to a halving of the time step to accommodate higher simulated velocities.

A new global climate model setup using FESOM2.0 for the sea ice-ocean component and ECHAM6.3 for the atmosphere and land-surface has been developed. Replacing FESOM1.4 by FESOM2.0 promises a higher efficiency of the new climate setup compared to its predecessor. The new setup allows for long-term climate integrations using a locally eddy-resolving ocean. Here it is evaluated in terms of (1) the mean state and long-term drift under pre-industrial climate conditions, (2) the fidelity in simulating the historical warming, and (3) differences between coarse and eddy- resolving ocean configurations. The results show that the realism of the new climate setup is overall within the range of existing models. In terms of oceanic temperatures, the historical warming signal is of smaller amplitude than the model drift in case of a relatively short spin-up. However, it is argued that the strategy of ‘de-drifting’ climateruns after the short spin-up, proposed by the HighResMIP protocol, allows one to isolate the warming signal. Moreover, the eddy-permitting/resolving ocean setup shows notable improvements regarding the simulation of oceanic surface temperatures, in particular in the Southern Ocean.

State-of-the-art global ocean circulation models used in climate studies are only passing the edge of becoming “eddy-permitting” or barely eddy-resolving. Such models commonly suffer from overdissipation of mesoscale eddies by routinely used subgrid dissipation (viscosity) operators and a resulting depletion of energy in the large-scale structures which are crucial for draining available potential energy into kinetic energy. More broadly, subgrid momentum closures may lead to both overdissipation or pileup of eddy kinetic energy and enstrophy of the smallest resolvable scales. The aim of this chapter is twofold. First, it reviews the theory of two-dimensional and geostrophic turbulence. To a large part, this is textbook material with particular emphasis, however, on issues relevant to modeling the global ocean in the eddy-permitting regime. Second, we discuss several recent parameterizations of subgrid dynamics, including simplified backscatter schemes by Jansen and Held, stochastic superparameterizations by Grooms and Majda, and an empirical backscatter scheme by Mana and Zanna.

A new global climate model setup using FESOM2.0 for the sea ice‐ocean component and ECHAM6.3 for the atmosphere and land surface has been developed. Replacing FESOM1.4 by FESOM2.0 promises a higher efficiency of the new climate setup compared to its predecessor. The new setup allows for long‐term climate integrations using a locally eddy‐resolving ocean. Here it is evaluated in terms of (1) the mean state and long‐term drift under preindustrial climate conditions, (2) the fidelity in simulating the historical warming, and (3) differences between coarse and eddy‐resolving ocean configurations. The results show that the realism of the new climate setup is overall within the range of existing models. In terms of oceanic temperatures, the historical warming signal is of smaller amplitude than the model drift in case of a relatively short spin‐up. However, it is argued that the strategy of “de‐drifting” climate runs after the short spin‐up, proposed by the HighResMIP protocol, allows one to isolate the warming signal. Moreover, the eddy‐permitting/resolving ocean setup shows notable improvements regarding the simulation of oceanic surface temperatures, in particular in the Southern Ocean.

Members in ensemble forecasts differ due to the representations of initial uncertainties and model uncertainties. The inclusion of stochastic schemes to represent model uncertainties has improved the probabilistic skill of the ECMWF ensemble by increasing reliability and reducing the error of the ensemble mean. Recent progress, challenges and future directions regarding stochastic representations of model uncertainties at ECMWF are described in this paper. The coming years are likely to see a further increase in the use of ensemble methods in forecasts and assimilation. This will put increasing demands on the methods used to perturb the forecast model. An area that is receiving a greater attention than 5 to 10 years ago is the physical consistency of the perturbations. Other areas where future efforts will be directed are the expansion of uncertainty representations to the dynamical core and to other components of the Earth system as well as the overall computational efficiency of representing model uncertainty.

In global ocean models, the representation of small-scale, high-frequency processes considerably influences the large-scale oceanic circulation and its low-frequency variability. This study investigates the impact of stochastic perturbation schemes based on three different subgrid-scale parameterizations in multidecadal ocean-only simulations with the ocean model NEMO at 1° resolution. The three parameterizations are an enhanced vertical diffusion scheme for unstable stratification, the Gent–McWilliams (GM) scheme, and a turbulent kinetic energy mixing scheme, all commonly used in state-of-the-art ocean models. The focus here is on changes in interannual variability caused by the comparatively high-frequency stochastic perturbations with subseasonal decorrelation time scales. These perturbations lead to significant improvements in the representation of low-frequency variability in the ocean, with the stochastic GM scheme showing the strongest impact. Interannual variability of the Southern Ocean eddy and Eulerian streamfunctions is increased by an order of magnitude and by 20%, respectively. Interannual sea surface height variability is increased by about 20%–25% as well, especially in the Southern Ocean and in the Kuroshio region, consistent with a strong underestimation of interannual variability in the model when compared to reanalysis and altimetry observations. These results suggest that enhancing subgrid-scale variability in ocean models can improve model variability and potentially its response to forcing on much longer time scales, while also providing an estimate of model uncertainty.

Ensemble experiments with a climate model are carried out in order to explore how incorporating a stochastic ice strength parameterization to account for model uncertainty affects estimates of potential sea ice predictability on time scales from days to seasons. The impact of this new parameterization depends strongly on the spatial scale, lead time and the hemisphere being considered: Whereas the representation of model uncertainty increases the ensemble spread of Arctic sea ice thickness predictions generated by atmospheric initial perturbations up to about 4 weeks into the forecast, rather small changes are found for longer lead times as well as integrated quantities such as total sea ice area. The regions where initial condition uncertainty generates spread in sea ice thickness on subseasonal time scales (primarily along the ice edge) differ from that of the stochastic sea ice strength parameterization (along the coast lines and in the interior of the Arctic). For the Antarctic the influence of the stochastic sea ice strength parameterization is much weaker due to the predominance of thinner first year ice. These results suggest that sea ice data assimilation and prediction on subseasonal time scales could benefit from taking model uncertainty into account, especially in the Arctic.

The influence of a stochastic sea ice strength parametrization on the mean climate is investigated in a coupled atmosphere–sea ice–ocean model. The results are compared with an uncoupled simulation with a prescribed atmosphere. It is found that the stochastic sea ice parametrization causes an effective weakening of the sea ice. In the uncoupled model this leads to an Arctic sea ice volume increase of about 10–20% after an accumulation period of approximately 20–30 years. In the coupled model, no such increase is found. Rather, the stochastic perturbations lead to a spatial redistribution of the Arctic sea ice thickness field. A mechanism involving a slightly negative atmospheric feedback is proposed that can explain the different responses in the coupled and uncoupled system. Changes in integrated Antarctic sea ice quantities caused by the stochastic parametrization are generally small, as memory is lost during the melting season because of an almost complete loss of sea ice. However, stochastic sea ice perturbations affect regional sea ice characteristics in the Southern Hemisphere, both in the uncoupled and coupled model. Remote impacts of the stochastic sea ice parametrization on the mean climate of non-polar regions were found to be small.

The ice strength parameter P* is a key parameter in dynamic/thermodynamic sea ice models that cannot be measured directly. Stochastically perturbing P* in the Finite Element Sea Ice–Ocean Model (FESOM) of the Alfred Wegener Institute aims at investigating the effect of uncertainty pertaining to this parameterization. Three different approaches using symmetric perturbations have been applied: 1) reassignment of uncorrelated noise fields to perturb P* at every grid point, 2) a Markov chain time correlation, and 3) a Markov chain time correlation with some spatial correlation between nodes. Despite symmetric perturbations, results show an increase of Arctic sea ice volume and a decrease of Arctic sea ice area for all three approaches. In particular, the introduction of spatial correlation leads to a substantial increase in sea ice volume and mean thickness. The strongest response can be seen for multiyear ice north of the Greenland coast. An ensemble of eight perturbed simulations generates a spread in the multiyear ice comparable to the interannual variability of the model. Results cannot be reproduced by a simple constant global modification of P*.