2.1 The model architecture and coupling framework

EC-Earth is a modular Earth system model (ESM) that is collaboratively developed by the European consortium with the same name. The current generation of the model, EC-Earth3, was developed after CMIP5, and version 3.3 is used for CMIP6 experiments.

EC-Earth3 comprises model components for various physical domains and system components describing atmosphere, ocean, sea ice, land surface, dynamic vegetation, atmospheric composition, ocean biogeochemistry, and the Greenland Ice Sheet. The component models are described in Sect. 3. The atmosphere and land domains are covered by ECMWF's IFS cycle 36r4 (based on IFS system 4, https://www.ecmwf.int/sites/default/files/elibrary/2011/11209-new-ecmwf-seasonal-forecast-system-system-4.pdf, last access: 18 March 2022), which is supplemented with a coupling interface to allow boundary data exchange with other components (ocean, dynamic vegetation, aerosols, and atmospheric chemistry). The NEMO3.6 (Madec and the NEMO team, 2008; Madec et al., 2015) and LIM3 (Vancoppenolle et al., 2009; Rousset et al., 2015) models are the ocean and sea ice components, respectively. Biogeochemical processes in the ocean are simulated by the PISCES model (Aumont et al., 2015). Both LIM3 and PISCES are code-wise integrated in NEMO. Dynamical vegetation, land use, and terrestrial biogeochemistry are provided by LPJ-GUESS (Smith et al., 2014; Lindeskog et al., 2013). Aerosols and chemical processes in the atmosphere are described by TM5 (van Noije et al., 2014). The ice sheet model PISM (Bueler and Brown, 2009; Winkelmann et al., 2011; The PISM Team, 2019) is optionally utilized to model the Greenland Ice Sheet.

An overview of five ESM model configurations is given in this section. Descriptions are schematic, and more detailed specifications will be given in forthcoming publications. Table 1 lists the configurations and their composition, while Table 2 shows the commonly used resolutions for CMIP6.

Table 1Configurations of the EC-Earth model for CMIP6; the name of the configuration is used as source_id in the CMIP6 context.

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Table 2Commonly used resolutions for CMIP6. The suffixes LR and HR are added to the name of the model configuration where applicable (e.g., EC-Earth3-Veg-LR).

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Most of the model components are coupled through the OASIS3-MCT coupling library (Craig et al., 2017), while some software components include more than one model component, e.g., the sea ice model being a part of the ocean model. A new coupling interface has been developed and implemented to allow a flexible exchange between the model components (see Sect. 3). The OASIS3-MCT coupler provides a technical means of exchanging (sending and receiving) two- and three-dimensional coupling fields between different model components on their different grids. Of the above-named model components, NEMO, LIM3, and PISCES exchange data directly via shared data structures. Thus, EC-Earth3 is implemented following a multi-executable MPMD (multiple programs, multiple data) approach. The model components run concurrently, and a message-passing interface (MPI) is used for parallelization within the components. A potential configuration of all components is illustrated in Fig. 1, which also shows coupling links and frequencies. Note that a configuration including all possible components is not implemented in practice.

Figure 1Coupling links and typical frequencies at standard resolution between all components that potentially can be coupled. Existing configurations include subsets of component models and associated couplings.

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In order to manage different configurations at both build time and runtime, EC-Earth3 includes tools to store and retrieve configuration parameters for different model configurations, computational platforms, and experiment types. This allows consistent control of the build and run environments and improves reproducibility across platforms and use cases.

Initial and forcing data (see Table 13), in the form of data files, are provided centrally for the EC-Earth community, and the data are versioned and check-summed for reproducibility.

For EC-Earth3 a tool was developed to convert the native model output to CF-compliant (“Climate and Forecast” standard) NetCDF format (i.e., Climate Model Output Rewriter, CMOR), thus fulfilling the CMIP6 Data Requests for the model intercomparison projects (MIPs) that the community is contributing to (van den Oord et al., 2022, 2017, https://github.com/EC-Earth/ece2cmor3/ (last access: 18 March 2022), https://doi.org/10.5281/zenodo.1051094, van den Oord, 2017).

2.2 Basic configurations EC-Earth3 and EC-Earth3-Veg

EC-Earth3 is the standard configuration consisting of the atmosphere model IFS (Sect. 3.1) including the land surface module HTESSEL (Sect. 3.2) and the ocean model NEMO3.6 with the sea ice module LIM3 (Sect. 3.5). Coupling variables are communicated between the different component models (see Sect. 3) via the OASIS3-MCT coupler. The physical interfaces are defined by specifying the variables exchanged and the algorithms used.

At the atmosphere–ocean interface, we follow the principle that the ocean provides state variables and the atmosphere sends fluxes (Table 3). Flux formulations correspond to the documentation of IFS CY36R1, Sect. 3, at https://www.ecmwf.int/en/publications/ifs-documentation (last access: 18 March 2022). Atmosphere fluxes are remapped onto the ocean grid by a nearest-neighbor distance-based Gauss-weighted interpolation. The energy (solar and non-solar radiation) and mass (evaporation and precipitation) fluxes are treated with a conservation post-processing method during coupling, in which the residual (target minus source grid integrals) is distributed over the target grid proportional to the original interpolated value. This does not constitute a locally conservative method, but it does conserve mass and energy of the coupling fields. The “sensitivity of non-solar heat flux” in Table 3 refers to the sensitivity with respect to sea ice surface temperature. The variable is used by the sea ice model to distribute the non-solar heat fluxes over different ice categories.

Table 3Variables and fluxes exchanged at the ocean–atmosphere interfaces.

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Table 4Variables and fluxes provided to the ocean via the runoff mapper.

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The freshwater runoff from land to ocean is derived from a runoff mapper (Table 4). It uses OASIS3-MCT to interpolate local runoff and ice-shelf calving (from Greenland and Antarctica) to the ocean. The runoff and calving received from the atmosphere and from the surface model HTESSEL are interpolated onto 66 hydrological drainage basins, remapped onto an intermediate grid by the same method and same post-processing as described above for the mass flux. The resulting runoff to the ocean is evenly and instantaneously distributed along several ocean coastal points connected to each hydrological basin in the vicinity of the major river outlet. The runoff is even distributed vertically. The distribution depths are taken (read in from a file) from an ocean-only simulation using a feature of NEMO to save these depths when the NEMO input parameter ln_rnf_depth_ini is set to true in the namelist. For a detailed description of the method we refer to the NEMO documentation (https://www.nemo-ocean.eu/doc/node53.html, last access: 18 March 2022).

In order to avoid a significant long-term sea surface height reduction in coupled model runs due to a net precipitation–evaporation (P–E) imbalance in the EC-Earth3 atmosphere of about −0.016 mm d⁻¹ in the historical period, the coupled model implements a runoff flux corrector, which amplifies river runoff by 7.95 % in order to compensate for this effect. The compensating flux by the corrector is calculated separately for different resolutions, since different resolutions give different results. The effects are also described in the section “Low-resolution configuration”. Correctors are derived for observed climate and applied throughout future scenario periods without change. Comparing the P–E imbalance in CMIP6 historical runs with 4×CO₂ experiments, we find that the P–E imbalance does not change significantly.

EC-Earth3-Veg is a configuration extending EC-Earth3 by the interactively coupled second-generation dynamic global vegetation model LPJ-GUESS, which is described together with the coupling principles in Sect. 3.3. Here we provide the variables exchanged through the coupler.

The coupling interface between the atmosphere and vegetation (Table 5) is characterized by the atmospheric model sending the driving variables, as well as selected biogeophysical soil parameters computed within HTESSEL. LPJ-GUESS returns vegetation parameters for both high and low vegetation categories needed for computing surface energy and water exchange in HTESSEL. This ensures that EC-Earth makes best use of both the advanced biophysics in the HTESSEL land surface model and the state-of-the-art vegetation dynamics, land use functionality, and terrestrial biogeochemistry (carbon and nitrogen) in LPJ-GUESS. Since HTESSEL and LPJ-GUESS have very different soil water schemes (LPJ-GUESS updates soil moisture separately in each patch and stand type for each grid cell – see Sect. 3.3, whereas HTESSEL simulates soil moisture per grid cell), the water cycle is discontinuous and each model operates its own water cycle. The water cycle of LPJ-GUESS is thus loosely coupled to the rest of EC-Earth by means of the driving variables sent by HTESSEL/IFS (Boysen et al., 2021). However, the conservation of moisture in the climate system is not affected by coupling to LPJ-GUESS.

Table 5Variables exchanged between the atmosphere and the vegetation model, with a coupling frequency of 1 d (in standard and low resolution).

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The land mask for the atmosphere is binary and is derived from GTOPO30 (see Sect. 11.2 and 11.4 in the IFS documentation (https://www.ecmwf.int/en/publications/ifs-documentation, last access: 18 March 2022). The ocean mask is binary as well, and a remapping of coupling fields between the atmosphere and ocean grid is carried out by the coupler OASIS_MCT.

2.2.1 Atmospheric tuning of EC-Earth3 and EC-Earth3-Veg

The atmospheric component of EC-Earth has been tuned with the goal of achieving a reasonably small radiative imbalance at the top of the atmosphere (TOA) at standard resolution (T255L91 – to which we refer in the following) in present-day atmosphere stand-alone (AMIP) runs using the CERES_EBAF_Ed4.0 dataset as a reference (Loeb et al., 2018). In particular, the goal was to minimize the mean weighted absolute error in the global means of the net radiative flux at the surface, the TOA longwave flux, longwave cloud forcing, and shortwave cloud forcing, with the first two fluxes considered the most important. The net radiative flux at the surface included the latent heat contribution associated with snowfall, which is not included in the latent heat flux stored by IFS. A series of convective and microphysical atmospheric tuning parameters was identified that are listed in Table 6. Similar parameters have also been commonly used for the tuning of other climate models (e.g., Mauritsen et al., 2012). An additional critical radius for the autoconversion process of liquid cloud droplets, added in EC-Earth3, was considered for tuning (see Rotstayn, 2000, for a discussion on the use of such parameters for model tuning). Changes in the tuning parameters have been adopted to avoid values too different from the original IFS CY36R4 values. In order to proceed with tuning, the sensitivity of the model radiative fluxes to changes in these parameters was determined through a series of short (6 years) AMIP runs for present-day conditions. The resulting linear sensitivities considerably accelerate the tuning process and reduce the number of simulations needed, allowing for the construction of a linear “tuning simulator” used to predict the impact of different combinations of tuning parameter changes on the target radiative fluxes and the determination of combinations providing an optimal score. An iterative process was followed, alternating the construction of new sets of tuning parameters using the known sensitivities, AMIP tuning runs for present-day conditions (20 years, from 1990 to 2010), and the following construction of a new set of tuning parameters to correct the residual biases, allowing for rapid convergence to a desired radiative balance. During this process model biases in other fields were monitored using a Reichler and Kim (2008) metric. Following a suggestion by ECMWF, we reintroduced a condensation limiter for clouds in the code, which had been removed in CY36R4 but then reintroduced in later cycles starting from CY37R2. Apart from improving the upper-tropospheric distribution of humidity in IFS, this change has an important impact on radiative fluxes (more than +1.6 W m² in net flux at TOA), making it a useful tool for tuning the global radiative balance. The atmospheric tuning process showed that energy conservation in IFS is severely dependent on the time step used. For example, at standard resolution, reducing the time step from 2700 to 900 s changes net surface fluxes by −2 W m², mainly due to an increase in low clouds, possibly due to resolution-dependent parameterizations. This issue has been improved in later operational versions at ECMWF. In final model configurations time steps ranging from 900 s (high resolution) to 3600 s (low resolution) have been used; see Table 2.

Table 6Atmospheric tuning parameters changed in EC-Earth compared to IFS CY36R4. The table reports the new values adopted for T255L91 EC-Earth3 and EC-Earth3-Veg tuning.

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A similar tuning procedure was also used to find alternative tuning parameter sets for other configurations (EC-Earth3-AerChem, EC-Earth3-LR, and EC-Earth3-Veg-LR). The atmospheric tuning for EC-Earth3 and EC-Earth3-Veg is the same, as is the case for EC-Earth3-LR and EC-Earth3-Veg-LR. This is because the vegetation fields used for EC-Earth3 were derived from dynamic vegetation model runs. Therefore, there are only very small differences between the two configurations (with and without dynamic vegetation) for each resolution in terms of the impact of vegetation on the global energy balance.

2.3 EC-Earth3-AerChem

EC-Earth3-AerChem (van Noije et al., 2021) is the configuration with interactive aerosols and atmospheric chemistry used in the Aerosol and Chemistry Model Intercomparison Project (AerChemMIP; Collins et al., 2017). In this configuration, TM5 is used to simulate tropospheric aerosols and chemistry based on the CMIP6 emission pathways for aerosols and chemically reactive gases. The resolution of TM5 is 3 × 2^∘ (longitude × latitude) with 34 vertical levels and a top at 0.1 hPa. IFS and NEMO have the same resolutions as in the standard configuration. TM5 and IFS exchange fields with a 6 h frequency. TM5 receives a large set of 2D and 3D meteorological fields from IFS and provides 3D distributions of aerosols, ozone (O₃), and methane (CH₄) in return. Table 7 lists the fields exchanged between IFS and TM5 through the coupler.

Table 7Variables exchanged with a 6 h frequency between the atmosphere and the chemical transport model (CTM) TM5 in EC-Earth3-AerChem.

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2.4 EC-Earth3-CC

EC-Earth3-CC is the configuration that includes a description of the carbon cycle, which is used for the Coupled Climate–Carbon Cycle Model Intercomparison Project (C4MIP; Jones et al., 2016). EC-Earth3-CC allows simulations with emissions forcing rather than with prescribed concentrations only as in the ScenarioMIP. This configuration uses a single carbon tracer in the atmosphere, advected by a version of TM5 with a reduced number of vertical levels (10 instead of 34), to simulate the transport of CO₂ through the atmosphere. The resolution and coupling frequency for the exchange between IFS and TM5 are the same as for the interactive aerosols and chemistry version of TM5 (EC-Earth3-AerChem) described in the preceding section. In effect the data transfer in both directions is much reduced. The CO₂ exchange with the ocean and terrestrial biosphere is calculated in PISCES and LPJ-GUESS, respectively, based on surface mixing ratios from the previous day received from TM5.

PISCES calculates the air–sea CO₂ flux at every time step after solving for carbon chemistry in seawater. This flux is proportional to the difference in pCO₂ between the atmosphere and the surface of the ocean. The exchange of CO₂ between the ocean and TM5 is realized once a day after accumulating the flux over each grid cell over 24 h. Furthermore, physical transport of passive tracers in the ocean presents a slight artificial mass imbalance. To prevent it from becoming significant for carbon during the spin-up we applied a uniform correction to dissolved inorganic carbon at the end of each year, after taking into account all sources and sinks.

A variant of EC-Earth-CC can also be run concentration-driven by excluding TM5. PISCES and LPJ-GUESS then read a uniform global atmospheric CO₂ concentration.

Tables 8 and 9 list the fields exchanged between the CTM on the one hand and the vegetation and ocean biogeochemistry models on the other hand through the coupler.

Table 8Variables exchanged with a 24 h frequency between the vegetation model LPJ-GUESS and the chemical transport model TM5 in EC-Earth3-CC. ^* Fluxes occur once a year and are distributed evenly over the following year.

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Table 9Variables exchanged with a 24 h frequency between the chemical transport model TM5 and the ocean biogeochemistry model PISCES.

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2.5 EC-Earth3-GrIS

EC-Earth3-GrIS is a configuration that couples the EC-Earth3-Veg to the Parallel Ice Sheet Model v1.1 (PISM, Sect. 3.8). It is used to model the Greenland Ice Sheet (GrIS) evolution and its feedback with the climate system in the Ice Sheet Model Intercomparison project (ISMIP6; Nowicki et al., 2016). GrIS handles the ice sheet dynamical and thermodynamical processes, including ice flow, subglacial hydrology, bed deformation, and the basal ice melt.

In the configurations EC-Earth3 and EC-Earth3-Veg, ice sheets are represented by a perennial snow layer of 9 m water equivalent. Snowfall on these areas is immediately redistributed into the ocean as ice to prevent excessive snow accumulation. Perennial snow albedo and snow density are fixed at 0.8 and 300 kg m⁻³, respectively, and the snowpack is in thermal contact with the underlying soil. In EC-Earth3-GrIS, the surface parameterization in EC-Earth3 is adjusted in order to better account for the presence of the ice sheet. The modifications include introduction of an explicit ice sheet mask obtained from PISM into HTESSEL and application of values representative of an ice sheet to calculate the surface energy balance and subsurface heat and energy transfer for glacierized grid points. In addition, if a grid cell is with an ice sheet but no snow cover (i.e., bare ice), the ice can melt and contribute to surface runoff if the energy flux at the surface is positive. Furthermore, a time-varying snow albedo parameterization is introduced for snow on ice sheets (Helsen et al., 2017) in EC-Earth3-GrIS. The parameterization allows the dependence of snow albedo on snow aging, melt, and refreezing. For fresh snow a maximum value of 0.85 is used. Under dry non-melting conditions, aging may reduce the snow albedo to 0.75, and during snowmelt the albedo decreases to a lower limit of 0.6. The albedo of refrozen meltwater is set to 0.65.

The new land ice physics described above are used for EC-Earth3 low-resolution configurations, in particular for PMIP experiments. For other resolutions, there is no coupling to the ice sheet model. Instead, the ice sheet mask can either be read in as boundary conditions or defined by snow depth exceeding a certain threshold (9 m).

The fields exchanged between EC-Earth and PISM are listed in Table 10. Information is exchanged once a year with monthly variations. IFS provides forcing fields of surface mass balance (SMB) and subsurface temperature to PISM. The SMB is calculated from precipitation, evaporation, and runoff. PISM returns the ice topography and ice mask to IFS and the calving (mass and energy) and basal melt (mass) fluxes to NEMO.

Table 10Variables exchanged between the atmosphere model IFS and the ice sheet model PISM, as well as between the ocean model NEMO and ice sheet model PISM. Information is exchanged once a year with monthly variations.

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2.6 HPC of different configurations

The increasing capabilities of ESMs, such as EC-Earth3, and the ability to perform large community experiments, such as CMIP6, are strongly linked to the amount of HPC capacity available and to the efficient use of these resources. As such, CMIP6 is an excellent opportunity to study the computational performance of ESMs, in particular for models such as EC-Earth3 that are developed and used by a wide range of institutions and integrated on different computational platforms.

The computational performance of EC-Earth3 has been evaluated in order to achieve different goals:

• to detect performance bottlenecks for future improvements,

• to compare the performance of different computational platforms used by the consortium and evaluate how different hardware can affect the performance of EC-Earth, and

• to compare different model configurations to analyze which components or calculations represent bottlenecks in the execution.

A first optimization and performance analysis of a preliminary version of EC-Earth3 (EC-Earth3P-HR) was presented in Haarsma et al. (2020). This particular version, which was used in the context of the H2020 PRIMAVERA project (Roberts et al., 2018), was integrated at both standard and high resolutions following the HighResMIP protocol (Haarsma et al., 2016). In Haarsma et al. (2020), the high-resolution configuration was analyzed in order to detect performance bottlenecks and to provide solutions for these. The high resolution was used for this purpose because of easier detectability of problems related to the scalability and computational efficiency.

The rest of this section will focus on the performance of the standard-resolution version of EC-Earth3 in order to fulfill the second and third goals presented.

The evaluation was done through a set of metrics independent of the platform and of the underlying parallel programming models. To make this possible, the EC-Earth standard-resolution configuration discussed hereafter was analyzed through CPMIP, a computational performance model intercomparison project (MIP) presented by Balaji et al. (2017). This analysis is done in two levels. The first level (Table 11) includes basic performance metrics for four different platforms (Rhino, RN; Marenostrum4, MN4; ECMWF-CCA, CCA; and Beskow, BK) in order to compare the performance of two configurations (EC-Earth3 and EC-Earth-Veg) on those different platforms. The second level (Table 12) includes the complete set of CPMIP metrics collected on Marenostrum4 for EC-Earth3.

Table 11Basic CPMIP metrics of EC-Earth3 and EC-Earth3-Veg with standard resolution for four different architectures and platforms: Marenostrum4 (MN4, LENOVO SD530), Rhino (RN, BullX B500), ECMWF-CCA (CCA, CRAY XC40), and Beskow (BK, CRAY XC40). The basic metrics are SYPD (simulated years per day), ASYPD (actual simulated years per day), CHSY (core hours per simulated year), and parallelization (number of MPI processes used).

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In Table 11 SYPD measures the model speed by counting the number of years the model could simulate within a 24 h period, given a certain configuration and computational platform. ASYPD is measured for a long-running experiment and includes queueing time, taking into account the sharing of HPC resources. CHSY measures the computational cost of the model for the given configuration and computational platform. Finally, parallelization represents the number of MPI processes used.

Comparing EC-Earth3 on two platforms (MN4 and RN) with similar parallelization, the BullX B500 experiment is slightly faster than the LENOVO SD530 experiment, but it also uses more resources and as a consequence the CHSY is slightly higher. On the other hand, we can obtain similar performance in BullX B500 and LENOVO SD530 experiments, even though the BullX B500 experiment is run on a platform with technology 5 years older, proving that configurations without an expensive computation can be simulated efficiently in more commodity clusters. Obviously, as shown in Haarsma et al. (2020), the performance of more demanding configurations will be affected by several issues, such as the MPI communications overhead, and a better network will ensure that better hardware will obtain better performance too. Finally, the experiment with EC-Earth3 on CCA proves that the user can achieve a similar efficiency using a setup with fewer processes and obtaining a similar CHSY, though the results will need more time to be executed.

It is important to note that the workflow of these experiments comprises different steps, with dependencies between them. This is especially true when the storage is a constraint and simulation steps need data from prior steps before post-processing. In such cases, the way these dependencies are handled may have an impact on the overall throughput.

LENOVO SD530 experiments at BSC were run using a workflow management tool called Autosubmit. This tool handles dependencies in an automatic way and is able to pack multiple tasks or simulation steps in the same job execution, which may reduce the amount of job queuing and thus have an impact on the ASYPD. This does not necessarily explain the differences between the three platforms in the study given the different use policies, load on the machine from other users, scheduling parameters, and usage existing among them.

The BullX B500 and CRAY XC40 (on BK platform) experiments are not directly comparable because the CRAY XC40 experiment includes LPJ-GUESS as a vegetation component. Both simulations use the same parallel resources, and the performance of the CRAY XC40 experiment on BK is lower. The results suggest that LPJ-GUESS is less efficient than the other components present in the standard configuration of EC-Earth and that this difference in performance is largely due to the way the output is performed. The problem is to be studied to improve it in the future. A new approach is under development to improve the computational efficiency of LPJ-GUESS. On the other hand, the EC-Earth-Veg configuration run in the CRAY XC40 experiment on CCA suggests that when the execution time of IFS and NEMO components is long enough (since we are using fewer parallel resources for their execution), the LPJ-GUESS component is not a bottleneck anymore, achieving a CHSY only slightly higher. However, the single point to take into account in this case is that the user will need more time to finish the simulations, since the SYPD is lower compared to the setup used on the BK platform.

These results will be used to compare the computational performance of EC-Earth with other models running the same CMIP6 configuration or with a similar complexity. However, preliminary results from the collection (provided by other institutions) prove that the efficiency of EC-Earth (comparing CHSY among models with a similar complexity or number of grid points) seems to show good results on average from the computational performance side. The cost of indirect processes such as coupling or output costs is also similar to the results obtained by other models.

3.1 Atmosphere

The atmosphere component of the EC-Earth model is based on the Integrated Forecast System (IFS) CY36R4 of the European Centre for Medium-Range Weather Forecasts (ECMWF). This specific cycle of the IFS was part of ECMWF's operational seasonal forecast system S4 (https://www.ecmwf.int/sites/default/files/elibrary/2011/11209-new-ecmwf-seasonal-forecast-system-system-4.pdf, last access: 18 March 2022). IFS solves the hydrostatic primitive equations using a two-time-level, semi-implicit, semi-Lagrangian discretization. Horizontal derivatives are computed in spectral space, while the computation of advection, the physical parameterizations, and in particular the nonlinear terms is conducted on the linear reduced Gaussian grid. The IFS is documented extensively at https://www.ecmwf.int/en/publications/ifs-documentation (last access: 18 March 2022) (for example https://www.ecmwf.int/sites/default/files/elibrary/2010/9232-part-iii-dynamics-and-numerical-procedures.pdf (last access: 18 March 2022) for the dynamics and https://www.ecmwf.int/sites/default/files/elibrary/2010/9233-part-iv-physical-processes.pdf (last access: 18 March 2022) for the physical processes). Here we only document the updates to the original IFS that were necessary for making long climate simulations.

The physical aspects of the atmosphere model in EC-Earth needed some adjustments and updates compared to the original IFS CY36R4. Most of these modifications are not necessary for numerical weather prediction (NWP) or even seasonal forecasts but are crucial when running long climate simulations (decadal, centennial, or longer) or simulations under different climate conditions (e.g., future scenarios or paleo-simulations).

The semi-Lagrangian advection scheme of IFS does not conserve mass or energy in the NWP version. A dry air mass conservation fixer has been available in IFS since CY25R1 and is active in EC-Earth to correct global pressure for the gain or loss of atmospheric mass. Similarly, to conserve humidity during transport we backported a simple proportional fixer from IFS cycle CY38R1 (Rasch and Williamson, 1990; Diamantakis and Flemming, 2014). This significantly reduced the bias of the average global precipitation–evaporation balance in the model from about +0.030 to −0.017 mm d⁻¹ and consistently (due to the associated latent heat of condensation) in the radiative balance in the atmosphere from about −1.65 W m² (a source of energy) to about −0.25 W m² .

The IFS CY36R4 version adopted for EC-Earth3 produces a reasonable quasi-biennial oscillation (QBO) in the tropical stratosphere when running at the standard resolution (T255L91), but not for any other available horizontal or vertical resolutions. Therefore, we substituted the original version-dependent latitudinal profile of the momentum flux in the non-orographic gravity wave scheme (which was originally developed ad hoc for the ECMWF system 4 seasonal forecast system) with a resolution-dependent parameterization of non-orographic gravity wave drag by backporting changes later introduced in IFS CY40R1 (see Davini et al., 2017a, for more details). This change allowed EC-Earth to recover a realistic QBO at all resolutions considered without deteriorating the jet streams.

Convection in the NWP version of IFS CY36R4 reaches its maximum around local noon in contrast to observations that peak later in the afternoon. A closure described by Bechtold et al. (2014) improving the diurnal cycle of convection has been implemented in EC-Earth3. For EC-Earth3, Rayleigh friction was activated in EC-Earth IFS for all resolutions to avoid unphysically large wind speeds at higher resolution.

In atmosphere-only simulations, the sea ice albedo is taken from a look-up table with climatological monthly values for sea ice albedo (Ebert and Curry, 1993) that take into account the annual cycle of highly reflective snow cover during winter and spring and the darker surface of melting sea ice during summer. In the coupled model, the sea ice albedo is computed in the sea ice model LIM3, and the updated values are used by the atmospheric component. The broadband sea ice albedo from LIM3 is then mapped on six shortwave bands with a mapping function.

The time stepping scheme needed technical adjustments to avoid an overflow of integer time step counters in order to allow making simulations beyond 32 768 time steps. The IFS output is saved in the GRIB1 data format, which also has a limit in the number of time steps that can be saved. This limit was overcome in EC-Earth3 by setting the time step to 0 and updating the GRIB-encoded reference time instead each time that output is written.

CMIP6 requires transient climate forcings to account for the change in atmospheric composition and other external drivers of the climate (e.g., insolation). The necessary interfaces to read the prescribed greenhouse gas concentrations, aerosol optical properties, stratospheric aerosols, stratospheric ozone, and insolation have been implemented in the IFS code in EC-Earth. Table 13 lists the sources and versions of the CMIP6 forcing datasets.

Well-mixed greenhouse gases (WMGHGs) explicitly included in EC-Earth's radiation scheme are CO₂, CH₄, nitrous oxide (N₂O), CFC-12, and CFC-11. Together these are responsible for about 98 % of the total radiative forcing by WMGHGs in 2014 compared to 1850 (Meinshausen et al., 2017). The radiative effects of the remaining WMGHGs (HCFC-22, CFC-113, CCl4) are accounted for in terms of CFC-11 equivalents (Meinshausen et al., 2017). The mixing ratios of each of the WMGHGs that are explicitly included and not provided by TM5 are prescribed by scaling their monthly zonal mean climatologies as used in IFS by a single time-dependent global factor. In this way, the global mean surface mixing ratios are forced to their CMIP6 pathways (Meinshausen et al., 2017). To reduce discontinuities, the scale factors are calculated on a monthly basis by interpolation of the time series of annual values provided by CMIP6. Any delays due to transport from the surface to the upper parts of the atmosphere are ignored in this approach.

Tropospheric aerosols are either simulated interactively in TM5 (in the EC-Earth3-AerChem configuration) or prescribed as a pre-industrial climatology plus an anthropogenic contribution (all other configurations). The pre-industrial aerosol background is specified using a monthly climatology based on TM5. This climatology was obtained from an offline TM5 simulation driven by ERA-Interim meteorology for the years 1981–1985 using CMIP6 anthropogenic emissions for the year 1850. The radiative and cloud effects of the pre-industrial aerosols are calculated based on the ERA-Interim reanalysis and the same set of variables as when aerosols are interactively simulated by TM5. The anthropogenic contribution is specified following the simple plume approach of MACv2-SP (Stevens et al., 2017), which provides a simplified parametric representation of the optical properties (extinction, single-scattering albedo, and asymmetry factor) of the anthropogenic contribution to the tropospheric aerosol burden (relative to 1850 levels), consistent with the CMIP6 time series of historical (Stevens et al., 2017) and future (Fiedler et al., 2019) anthropogenic emissions. In EC-Earth, MACv2-SP is coupled with the IFS radiation scheme to compute the optical properties for the 14 wavelength bands of the SW radiation. More precisely, the optical properties are calculated at the band mean wavelengths weighted by the incoming solar radiation. In addition, MACv2-SP provides a simple way to account for the effect of anthropogenic aerosols on clouds. Specifically, it provides a scale factor for the cloud droplet number concentration (CDNC) in each column based on the vertically integrated optical depth at 550 nm.

In the EC-Earth3-AerChem, aerosol impacts on clouds are included by calculating CDNC depending on the modal number and mass concentrations from TM5, following Abdul-Razzak and Ghan (2000). For all other model configurations the CDNC corresponds to pre-industrial aerosol conditions and an additional scaling factor from MACv2-SP that is included to account for the cloud forcing by anthropogenic aerosols. The resulting forcing includes contributions due to both cloud reflectivity and cloud lifetime effects, as the lifetime of clouds explicitly depends on CDNC. Currently only the activation and autoconversion of liquid cloud droplets are linked explicitly to ambient aerosol concentrations. For ice clouds the EC-Earth3 model still retains the parameterization from the original IFS CY36R4.

As EC-Earth3 uses MACv2-SP in combination with a pre-industrial aerosol climatology, natural aerosol variability is only accounted for via the prescribed seasonal cycle of the climatology. Furthermore, MACv2-SP only captures the seasonal cycle and long-term changes in the optical properties and the derived CDNC impact factor of anthropogenic aerosols. Diurnal variability in aerosol amounts or properties is not explicitly described. Day-to-day variability is only included to the extent captured by the seasonal cycles of the pre-industrial climatology and MACv2-SP. Of the interannual variability in the amount and properties of anthropogenic aerosols, only the long-term changes in plume strengths, which are assumed to covary with the 11-year averaged emissions of SO_x plus NH₃ in the associated countries, are accounted for. Changes in the spectral distribution of the optical properties, the single-scattering albedo, and asymmetry factor of anthropogenic aerosols due to long-term changes in their size distribution and composition are ignored by MACv2-SP.

Stratospheric aerosols are prescribed using the CMIP6 dataset of aerosol radiative properties, which covers the period 1850 to 2014 and for the more recent period is based on satellite data assembled by Thomason et al. (2018). The dataset consists of monthly resolved zonal mean fields, which are provided at the 14 shortwave (SW) and 16 longwave (LW) bands of the IFS's radiation schemes. For the SW scheme, the extinction, single-scattering albedo, and asymmetry factor are specified, whereas only the absorption is taken into account for the LW scheme, since aerosol scattering in the LW is neglected in the atmospheric component of EC-Earth. Forcing data are vertically interpolated beforehand for the 62- and 91-level configurations, taking into account the seasonality of model level heights, whereas horizontal and monthly to daily interpolation is done online. When interpolating or averaging the radiative property fields, they are first made extensive by including the appropriate weighting factors (e.g., extinction is converted to optical depth, single-scattering albedo to absorption optical depth, and likewise for the asymmetry factor). The forcing located below the online-diagnosed thermal tropopause level is excluded. This implementation is used in all current EC-Earth3 configurations with the exception of the EC-Earth3P-HR configuration, which uses a simplified implementation based on a monthly vertically integrated, latitude-dependent aerosol optical depth (AOD) forcing at 550 nm, which is then vertically distributed across the stratosphere. In both implementations, it is possible to set the forcing fields to a constant background distribution computed as the time average over 1850 to 2014. This background forcing is applied in pre-industrial control and future simulations, as recommended in the CMIP6 protocol.

The land use forcing dataset (LUH2) from CMIP6 (Hurtt et al., 2020) cannot be used directly as input to IFS because it does not provide the same vegetation cover or type categories as those used by the land surface scheme in IFS (HTESSEL; van den Hurk et al., 2000; Balsamo et al., 2009; Dutra et al., 2010; Boussetta et al., 2013) but instead provides agricultural management information and land use transitions that are annually updated. The vegetation cover, leaf area index (LAI), and vegetation type that are needed for the land surface scheme and albedo parameterization in IFS can be simulated by the dynamic vegetation model LPJ-GUESS (Smith et al., 2014). This happens automatically in the EC-Earth3-Veg configuration wherein the dynamic vegetation model, which uses the LUH2 dataset as an input, is active, but for all other configurations the required vegetation cover and type need to be precomputed. This is done by first making all CMIP6 experiments with the EC-Earth3-Veg configuration and saving the vegetation variables that can then be reused when making the same experiment with other model configurations.

The orbital parameters of the original IFS CY36R4 are fixed for present-day conditions following the recommendations of the International Astronomical Union (ARPEGE-Climate Version 5.1, 2008), which is sufficient for simulations of the recent past or near future. However, for paleo-simulations in PMIP the orbital parameters need to be variable or set fixed for a different time period. Orbital parameters and insolation are computed using the method of Berger (1978). Using this formulation, the insolation can be determined for any year within 10⁶ years of 1950 CE. The formulation determines the Earth–Sun distance factor and solar zenith angle. The annual cycle and diurnal cycle of solar insolation are represented with a repeatable solar year of exactly 365 d and with a mean solar day of exactly 24 h, respectively. The repeatable solar year does not allow for leap years. The orbital state may be specified in one of two ways. The first method is to specify a year, which is held constant during the integration for an equilibrium simulation or varies yearly for a transient simulation. The second method is to specify the orbital parameters: eccentricity, longitude of perihelion, and obliquity. This set of values is sufficient to specify the complete orbital state. For example, settings for piControl integrations under 1850 CE conditions are obliquity of 23.549, eccentricity of 0.016764, and longitude of perihelion of 100.33.

Table 12CPMIP metrics analysis for EC-Earth3 on Marenostrum4. Complete CPMIP metrics are shown in this table: resolution complexity (Cmpx), SYPD (simulated years per day), ASYPD (actual simulated years per day), CHSY (core hours per simulated year), parallelization, JPSY (Joules per year simulated), Coup. C. (coupling cost), Mem. B.(memory bloat), DO (data output cost), and DI (data intensity). From left to right we have resolution (Resol) as the total number of grid points for all the components used (ocean, atmosphere, and so on). Cmpx includes all prognostic variables of a model. JPSY quantifies the energy cost of the execution. Coup. C. represents the cost associated with the coupling among components (including interpolation and communication calculations; 8 % in this case with respect to the total execution time). Mem. B. is the division between the theoretical memory and the real one. DO is the cost of the output process (12 % in this case with respect to the total execution time). DI is the output volume in GB per day of simulation.

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Table 13CMIP6 forcing datasets used by EC-Earth3 and EC-Earth3-Veg for DECK (diagnostic, evaluation, and characterization of klima) and historical experiments. All datasets are available from https://esgf-node.llnl.gov/search/input4mips/ (last access: 18 March 2022). A more detailed description of the CMIP6 forcing datasets is available at http://goo.gl/r8up31 (last access: 18 March 2022).

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3.2 Land surface and vegetation

The Hydrology Tiled ECMWF Scheme of Surface Exchanges over Land (HTESSEL; van den Hurk et al., 2000; Balsamo et al., 2009; Dutra et al., 2010; Boussetta et al., 2013) is the land surface model interfacing with the atmospheric boundary layer and solving the energy and water balance at the land surface in EC-Earth. HTESSEL discretization, for each grid point, solves for up to six different land surface tiles that may be present over land (bare ground, low and high vegetation, intercepted water by vegetation, and vegetation-shaded and exposed snow). Surface radiative, latent heat, and sensible heat fluxes are calculated as a weighted average of the values over each tile.

The discretization in HTESSEL is such that coexistence in each grid point of more than one type of low and high vegetation, respectively, is not allowed. Therefore, for each grid point and for both low and high vegetation cover, a dominant type (dominant meaning the type with the higher relative area fraction for either high or low vegetation) is identified, T_l and T_h , and a vegetation coverage for high and low vegetation types, C_h and C_l, is specified.

Vegetation types and vegetation coverage can be

1. prescribed from a static land use map from the Global Land Cover Characteristics (GLCC, standard HTESSEL configuration; van den Hurk et al., 2000; Balsamo et al., 2009; Dutra et al., 2010; Boussetta et al., 2013),

2. interactively provided when coupled with LPJ-GUESS, or

3. prescribed from a previous simulation with LPJ-GUESS.

When the tile fractions are prescribed from GLCC, vegetation density is parameterized according to the Lambert–Beer law of extinction of light under a vegetation canopy and is therefore allowed to change as a function of leaf area index (LAI) for both low and high vegetation as described in Alessandri et al. (2017). Otherwise, LPJ-GUESS provides its own consistently simulated background tile fractions and vegetation densities.

The coupling of biophysical parameters in HTESSEL has been enhanced since CMIP5 (Weiss et al., 2014), for which only the surface resistance to evapotranspiration and water intercepted and directly evaporated from vegetation canopies were made to depend on LPJ-GUESS vegetation dynamics. In the version for CMIP6, as used in EC-Earth3-Veg, the surface albedo (including the shading effect of high vegetation), surface roughness length, and soil water exploitable by roots for evapotranspiration also vary following the variability of the effective vegetation cover. The improved representation of the effective vegetation cover variability brought a significant enhancement of the EC-Earth performance over regions where the land–atmosphere coupling is strong, in particular over boreal winter middle to high latitudes (Alessandri et al., 2017).

To represent time-dependent albedo for each grid point, a new scheme has been adopted that computes the total surface albedo (A_tot) as a weighted combination of contributions from the albedo of the low and high vegetation types present in each grid point (a_v(type), which is a function of the low or high vegetation type), plus a time-constant background soil albedo (a_s, a function of space):

where Cloweff and Chigheff are the effective fractional coverages for low and high vegetation, and T_l and T_h are the low and high vegetation types, respectively, at each grid point. The background soil albedo was adopted from the map from Rechid et al. (2009), and a look-up table of the albedo values a_v for each vegetation type was estimated using least square minimization of errors against available monthly climatology of snow-free monthly MODIS albedo (Morcrette et al., 2008).

3.3 Dynamic vegetation and terrestrial biogeochemistry

LPJ-GUESS (Smith et al., 2001, 2014; Lindeskog et al., 2013; Olin et al., 2015a, b), a process-based second-generation dynamic vegetation and biogeochemistry model, is the terrestrial biosphere component of EC-Earth globally simulating vegetation dynamics, land use and land management following the LUH2 dataset (Hurtt et al., 2020), and both carbon (C) and nitrogen (N) cycling in terrestrial ecosystems. LPJ-GUESS has been evaluated in numerous studies (Smith et al., 2014; Wårlind et al., 2014) and reproduces vegetation patterns, dynamics, and productivity, C and N fluxes and pools, and hydrological cycling from global to regional scales, in line with independent datasets and comparable models (e.g., Piao et al., 2013; Zaehle et al., 2014; Sitch et al., 2015; Peters et al., 2018).

LPJ-GUESS is a new component in EC-Earth3 (Boysen et al., 2021), though it has previously been coupled to EC-Earth v2.3 (Weiss et al., 2012; Alessandri et al., 2017) using a simplified coupling scheme in which updates to leaf area index (LAI) alone were transferred between the sub-models.

LPJ-GUESS is one of the first vegetation sub-models interactively coupled to an atmospheric model, in which the size, age structure, temporal dynamics, and spatial heterogeneity of the vegetated landscape are represented and simulated dynamically. Such functionality has been argued to be essential for correctly capturing biogeochemical and biophysical land–atmosphere interactions on longer timescales (Purves and Pacala, 2008; Fisher et al., 2018) and has been shown to improve realism compared with more common area-based vegetation schemes (Wolf et al., 2011; Pugh et al., 2018). Different plant functional types (PFTs) co-occur in natural and managed stands governed by climate, atmospheric CO₂ (Meinshausen et al., 2017; Riahi et al., 2017), and N deposition (Hegglin et al., 2021) forcings. Evolving stand structure impacts growth, survivorship, and the outcome of competition by affecting the availability of the key resources: light, space, water, and nitrogen. Disturbances due to management actions such as forest clearing, prognostic wildfires, and a stochastic generic disturbance regime affect patches at random, inducing biomass loss and resetting vegetation succession (Hickler et al., 2004). N-cycle-induced limitations on natural vegetation and crop growth, C–N dynamics in soil biogeochemistry, and N trace gas emissions are included (e.g., Smith et al., 2014; Olin et al., 2015a, b) as are biogenic volatile organic compound (VOC) emissions (Hantson et al., 2017).

Meteorological inputs imposed on LPJ-GUESS are daily fields of surface air temperature and 25 cm soil temperatures, precipitation, and net shortwave and net longwave radiation from IFS/HTESSEL (Table 5). LPJ-GUESS calculates its own soil moisture for potential plant uptake in all patches in each of the six simulated stands independently of the single grid-cell-averaged hydrology scheme used in HTESSEL.

Vegetation dynamics are simulated on six stand types in the land portion of the grid cell (excluding large water bodies based on the static LUH2 ice and water fraction information), five stands having dynamic grid cell fractions consistent with the LUH2 dataset, namely natural, pasture, urban, crop, and irrigated crop, and one, peatland, having a fixed grid cell fraction derived from the GLCC global map used in the standard HTESSEL configuration – see Sect. 3.2. The LUH2 dataset, including land cover fractions, management options (N fertilization in this case), and land cover transitions, are read in yearly after aggregation to the atmospheric and land surface model resolution in a preprocessing step. A total of 10 woody and two herbaceous PFTs compete in the natural stand (Smith et al., 2014), whereas two herbaceous species, one each conforming to the C₃ and C₄ photosynthetic pathways, are simulated on pasture, urban, and peatland fractions. The crop stands each have five crop functional types (CFTs) representing the properties of global crop types and encompassing the classes found in the LUH2 database, namely both annual and perennial C₃ and C₄ crops, as well as C₃ N fixers (Lindeskog et al., 2013).

At the end of each day, LPJ-GUESS calculates the effective cover for low (high) vegetation, C_l (C_h), and LAI for low (high) vegetation, LAI_low (LAI_high), taking into account phenology and stand fractions in the grid cell. Dominant high and low vegetation types corresponding to the standard HTESSEL types are calculated and sent by LPJ-GUESS to IFS/HTESSEL on 31 December each year. These six fields link the vegetation dynamics and land use in LPJ-GUESS to the biophysical processes simulated at the land surface in HTESSEL, namely albedo, latent and sensible heat exchange, runoff, and momentum exchange.

In the EC-Earth-CC configuration, LPJ-GUESS is coupled to TM5 in addition to IFS and exchanges additional fields to enable prognostic global C cycle calculations. Spatiotemporally variable surface CO₂ concentrations are sent by TM5 to LPJ-GUESS (and PISCES) to replace the annual and global mean CO₂ concentrations used in the EC-Earth-Veg configuration. LPJ-GUESS sends daily averaged fields of net ecosystem C exchange (i.e., uptake or release) to TM5 to complement the surface C exchange with the ocean calculated in PISCES (see below), thereby completing the carbon cycle in EC-Earth-CC. This daily flux includes contributions from net primary production (NPP), heterotrophic respiration (Rh), wildfires, land use (including crop and pasture harvest), and natural disturbances on non-managed land. Since some processes in LPJ-GUESS are simulated with a yearly time step (e.g., wildfires, disturbance, establishment of new individuals and mortality, land use change), these annual fluxes are distributed evenly throughout the year and added to the daily NPP and Rh fluxes the following year to conserve carbon mass. Negative NPP fluxes account for CO₂ uptake by vegetation.

3.4 Atmospheric chemistry

The Tracer Model version 5 (TM5) is the atmospheric composition model of EC-Earth (van Noije et al., 2014) used in the EC-Earth3-AerChem and EC-Earth3-CC configuration. It can be used for the interactive simulation of carbon dioxide (CO₂), methane (CH₄), ozone (O₃), tropospheric aerosols, and other trace gases. These components are prescribed in IFS from forcing datasets (see Sect. 3.1) if not provided interactively by TM5. Other well-mixed greenhouse gases and stratospheric aerosols are prescribed in all configurations. This section briefly describes how the various components are configured.

As an alternative to the scaling approach for WMGHGs presented in Sect. 3.1, the 3D distributions of CO₂ and CH₄ can be calculated online by TM5. In the EC-Earth-CC configuration a single-tracer version of TM5 is used for simulating the transport of CO₂ through the atmosphere. Anthropogenic emissions of CO₂ are prescribed following the CMIP6 historical inventory (Hoesly et al., 2018) or future scenarios (Gidden et al., 2019). Exchange of CO₂ with the ocean and terrestrial biosphere is included by coupling TM5 to PISCES and LPJ-GUESS, respectively (see Sect. 3.3). An important feature of the model is that the transport in TM5 is mass-conserving (Krol et al., 2005). For the simulation of CH₄, a version of TM5 that includes atmospheric chemistry and aerosols is used (van Noije et al., 2021). A recent description of the chemistry scheme applied in EC-Earth has been presented by Williams et al. (2017). Emissions of aerosols and chemically reactive gases are taken from the CMIP6 historical datasets for anthropogenic sources (Hoesly et al., 2018) and biomass burning (van Marle et al., 2017) or the corresponding CMIP6 scenario datasets (Gidden et al., 2019). To force the CH₄ simulation to follow the pathway provided by CMIP6, its surface mixing ratios are nudged towards the monthly zonal means from CMIP6 interpolated to daily values. Moreover, because TM5 lacks a comprehensive stratospheric chemistry scheme, the CH₄ mixing ratios in the stratosphere are nudged towards a monthly zonal mean observational climatology representative for the 1990s (interpolated to daily values), scaled by a global factor based on the CMIP6 time series of global annual mean surface values. To calculate the scale factor, we assume a 1-year delay between the mixing ratios at the surface and in the stratosphere (Meinshausen et al., 2017) and a reference value based on a 10-year average.

The chemical production of water vapor (H₂O) by oxidation of methane in the stratosphere is included in IFS in a similar way as in the standard version of IFS. The assumption made in the standard version of IFS is that

where square brackets denote local mixing ratios (in ppmv) and the constant is set to 6.8 ppmv based on observations for the present day. To account for long-term variations in CH₄, in EC-Earth it is assumed instead that

where

Here [CH₄]S(t) is the monthly varying global mean surface mixing ratio obtained by linear interpolation from the CMIP6 time series of annual values, and [CH₄]0S is a reference value for the present day, which is set to 1.78 ppmv.

Ozone is simulated by TM5. As for CH₄, TM5 applies a nudging scheme for O₃ in the stratosphere. In EC-Earth3, the mixing ratios are nudged towards daily zonal means obtained from the CMIP6 dataset.

For aqueous-phase chemistry in the troposphere, the acidity of cloud droplets is calculated assuming a uniform CO₂ mixing ratio following the CMIP6 time series of annual global mean surface values.

TM5 simulates tropospheric aerosols, namely sulfate, black carbon, primary and secondary organic aerosol, sea salt, and mineral dust, in four size ranges describing nucleation, Aitken, accumulation, and coarse modes using the M7 aerosol microphysical model (Vignati et al., 2004). In addition, it simulates the total mass of ammonium, nitrate, and methane sulfonic acid (MSA). Optical properties of the aerosol mixture are calculated based on Mie theory in combination with the mixing assumptions described by van Noije et al. (2014).

For calculation of the SW radiative effects of the aerosol mixture, TM5 provides the extinction, single-scattering albedo, and asymmetry factor at the 14 wavelength bands of the SW radiation scheme (using the same wavelength values as in MACv2-SP). In addition, TM5 provides the particle number and component mass mixing ratios for each of the M7 modes, plus the total mass mixing ratios of nitrate and MSA. LW absorption is calculated based on the mass mixing ratios of the M7 components using absorption efficiencies from IFS. The contribution of the aerosol mixture described by MACv2-SP and/or TM5 to SW extinction and LW absorption is removed above the tropopause, where the stratospheric aerosol dataset from CMIP6 is applied. The tropopause level is diagnosed online following the thermal tropopause definition of the World Meteorological Organization (WMO, 1957), as detailed by Reichler et al. (2003). Where the thermal tropopause does not exist according to this definition, tropospheric and stratospheric aerosols are merged at the 100 hPa level.

3.5 Ocean

The ocean component of the EC-Earth model is the Nucleus for European Modelling of the Ocean (NEMO; Madec and the NEMO team, 2008; Madec et al., 2015) that includes the ocean model OPA (Océan Parallélisé), the LIM3 sea ice model (see Sect. 3.6), and the PISCES biogeochemistry model (see Sect. 3.7). The CMIP6 version of the EC-Earth model uses NEMO3.6 (revision r9466) in combination with the ORCA1 shared configuration (regular ORCA1, not eORCA1).

OPA is a primitive equation model of ocean circulation. Prognostic variables are velocity, hydrostatic pressure, sea surface height, and thermohaline variables (potential temperature and salinity). The distribution of variables is given by a three-dimensional Arakawa-C-type grid (Arakawa and Lamb, 1977). OPA uses a partial step implementation for the geopotential z^* coordinate (grid boxes do not continue below topography) and a diffusive bottom boundary layer scheme (similar to that of Beckmann and Döscher, 1997) with implicit bottom friction to mix dense water down a slope.

NEMO allows for various choices for the physical sub-grid-scale parameterizations as well as the numerical algorithms. EC-Earth uses the turbulent kinetic energy (TKE) scheme for vertical mixing. The vertical eddy viscosity and diffusivity coefficients are computed from a 1.5 turbulent closure model based on a prognostic equation for the turbulent kinetic energy and a closure assumption for the turbulent length scales. This turbulence closure model has been developed by Bougeault and Lacarrère (1989) in atmospheric cases, adapted by Gaspar et al. (1990) for oceanic cases, and embedded in OPA by Blanke and Delecluse (1993).

Since the CMIP5 version of EC-Earth, major changes in the TKE schemes have been implemented: it now includes a Langmuir cell parameterization (Axell, 2002), the Mellor and Blumberg (2004) surface wave breaking parameterization, and a time discretization which is energetically consistent with the ocean model equations (Burchard, 2002; Marsaleix et al., 2008). A mixed layer eddy parameterization following Fox-Kemper et al. (2008) has been newly implemented in NEMO3.6. An enhanced vertical diffusion and a double diffusive mixing parameterization are part of the OPA code in EC-Earth. Since CMIP5, a tidal mixing parameterization has been added to OPA (de Lavergne et al., 2020).

Horizontal tracer diffusion is described by the Gent–McWilliams (Gent and McWilliams, 1990) parametrization of mesoscale eddy-induced turbulence.

The ORCA family is a series of global ocean grid configurations. The ORCA grid is a tripolar grid based on the semi-analytical method of Madec and Imbard (1996). ORCA1 with a resolution of about 1^∘ is used for standard- or low-resolution simulations, and ORCA025 (resolution 0.25^∘) is used for high-resolution simulations with EC-Earth3-HR. A meridional grid refinement of 1/3∘ in the tropics allows a partial representation of tropical instability waves. There are 75 vertical levels in the ocean with an upper level of about 1 m and 24 levels distributed over the uppermost 100 m.

The main difference of the OPA version used in EC-Earth compared to the reference OPA version of NEMO3.6 is that the parameterization of the penetration of TKE below the mixed layer due to internal and inertial waves is switched off (nn_etau = 0). This has been done because the penetration of TKE below the mixed layer caused a surface layer of warm summer water masses in the North Atlantic convection areas that is too deep, which leads to a breakdown of the Labrador Sea convection within a few years and a strongly underestimated Atlantic Meridional Overturning Circulation (AMOC) in EC-Earth. A minor modification compared to the standard NEMO setup from the ORCA1-shared configuration for NEMO (ShacoNemo) is an increased tuning parameter rn_lc (0.2) in the TKE turbulent closure scheme that directly relates to the vertical velocity profile of the Langmuir cell circulation. Consequently, the Langmuir cell circulation is strengthened.

3.6 Sea ice

The sea ice component is version 3.6 of the Louvain-la-Neuve Ice Model (LIM; Vancoppenolle et al., 2009; Rousset et al., 2015), which works directly on the NEMO environment, including the ORCA grid. LIM3.6 is based on the Arctic Ice Dynamics Joint EXperiment (AIDJEX) framework (Coon et al., 1974), combining the ice thickness distribution (ITD) framework, the conservation of horizontal momentum, an elastic–viscous–plastic rheology, and energy-conserving halo-thermodynamics (Vancoppenolle et al., 2009). All of these components of the sea ice model have been introduced or revised since CMIP5.

The ice thickness distribution framework was introduced (Thorndike et al., 1975) to deal with meter-scale variations in ice thickness, which cannot be resolved explicitly but should preferably be accounted for, as many sea ice processes, in particular growth and melt, depend nonlinearly on thickness h. In practice, this is achieved by treating h as an independent variable, leading to the introduction in discrete form of L=5 thickness categories, each characterized by a specific set of state variables (namely ice concentration, ice volume per unit area, snow volume per unit area, ice enthalpy, snow enthalpy, sea ice salt content). Ice and snow enthalpy also depend on vertical depth in the ice (z). All sea ice state variables Xijl,l=1,…,L are updated due to transport and thermodynamic processes. The default choice of five categories, with the upper category above 4 m, has been shown to provide reasonable results at an acceptable computing cost (Massonnet et al., 2019).

Vertical sea ice motions are irrelevantly small and hence neglected, and the sea ice velocity field reduces to its horizontal components. The 2D ice velocity vector is considered the same for all categories and stems from the horizontal momentum conservation equation. The internal stress term is formulated assuming that sea ice is a viscous–plastic material, i.e., assuming viscous ice flow at very small deformation and plastic flow (stress independent of deformation) above a plastic failure threshold. This threshold lies on an elliptical yield curve in the principal stress component space, whose size can be changed by tuning the classical ice strength parameter P*=20 000 following the classical formulation of Hibler (1979). The horizontal momentum equation is resolved using the elastic–viscous–plastic (EVP) C-grid formulation of Bouillon et al. (2009) using 120 sub-time steps. Once the velocity field is computed, the sea ice state variables are transported horizontally using the second-order moment-conserving scheme of Prather (1986).

Ice thermodynamics are based on the Bitz and Lipscomb (1999) enthalpy formulation and account for dynamic changes in ice salinity through temperature- and salinity-dependent thermal properties (Ono, 1968; Pringle et al., 2007). The salt entrapment and drainage parameterizations follow from Vancoppenolle et al. (2009): each category is characterized by a dynamic mean salinity, from which a profile shape is derived for the computation of the vertical diffusion of heat. The broadband surface albedo of each ice category empirically depends on ice thickness, snow depth, surface temperature, and cloud fraction based on a reformulation of the Shine and Henderson-Sellers (1985) parameterization that solves a few inconsistencies associated with state transitions (e.g., snow/no snow), following Grenfell and Perovich (2004), and is tuned to match observations of Brandt et al. (2005). The impact of melt ponds is implicitly accounted for through imposed changes on the albedo activated when the surface temperature is 0 ^∘C. Energy, salt, and mass conservations have been carefully checked within the ice component and its interfaces with the atmosphere and ocean (Rousset et al., 2015).

All surface fluxes are computed in the atmosphere, and the IFS atmospheric model has only one ice thickness category. The solar and non-solar heat fluxes are therefore distributed on the different sea ice categories in LIM3, taking into account the differences in albedo and temperature among the sea ice categories in each grid point.

During the tuning phase it was found that the Arctic sea ice volume grew to unrealistically high values, especially during phases with reduced AMOC. An analysis showed that the thermal conductivity of snow needed a slight reduction (rn_cdsn = 0.27) to reduce basal growth and increase bottom melt (see also Sect. 2).

3.7 Ocean biogeochemistry

PISCES-v2 (Pelagic Interactions Scheme for Carbon and Ecosystem Studies volume 2) is a biogeochemical model that simulates the nutrient cycle and the inorganic and organic carbon cycle, and it comprises lower trophic phytoplankton and zooplankton (Aumont et al., 2015). It has two functional groups for phytoplankton (nanophytoplankton, including calcite producers, and diatoms that can produce siliceous shells) and two size classes for zooplankton (mesozooplankton and microzooplankton). The growth rate of phytoplankton depends on photosynthetically available radiation (PAR) intensity and temperature. A limitation for primary production is computed based on the availability of the main nutrients (P, N, Si, Fe). In the case of low nitrate concentrations, nitrogen fixation by diazotrophic cyanobacteria is parameterized in waters warmer than 20 ^∘C (Aumont et al., 2015). PISCES uses a constant P / N / C ratio of 1/16/122 for primary production. Organic particulate matter produced by food-web processes in the euphotic layer is represented by two size classes. These sink throughout the water column with different velocities while being decomposed into dissolved inorganic nutrients (DIN, DOP) and dissolved inorganic carbon (DIC). A further pool for dissolved organic matter (DOM) is fed by phytoplanktonic exudation and excretion by zooplankton. DOM in PISCES represents only the semi-labile fraction, with turnover times ranging from months to years, and it is further remineralized at a constant rate. PISCES includes two different chemistry models to describe iron pool interactions. In EC-Earth3 we use the complex model by Tagliabue and Arrigo (2006). The global river and atmospheric deposition input of nutrients are not balanced to match the fraction lost by sediment burial. For this reason, PISCES allows for a homogeneous correction towards global mean values for alkalinity, nitrate, phosphate, and silicate. Furthermore, physical transport of passive tracers presented a slight artificial mass imbalance. To prevent it from becoming significant for carbon during the spin-up we applied a uniform correction to dissolved inorganic carbon at the end of each year after taking into account all sources and sinks.

With respect to climate studies PISCES is capable of simulating the relevant processes of the marine carbon cycle; i.e., it comprises the soft-tissue carbon pump and the carbonate counter-pump to realistically simulate the feedback of the marine carbon cycle to the climate.

The air–sea gas exchange for carbon dioxide and oxygen is parameterized according to Wanninkhof (1992). The interface to the seafloor is given by basic assumptions for the exchange between the active sediment layer and the water bottom layer where different assumptions are made for the burial efficiency for silicate, calcite, and particular organic matter (see Aumont et al., 2015, for further details).

PISCES is part of the community model NEMO and runs on the same model grid. In EC-Earth3 the horizontal resolution is about 1^∘ (ORCA1) with 75 vertical levels. Advection and diffusion of the 24 biogeochemical tracers are done in the hydrodynamic ocean model. A detailed description of the PISCES reference version is given in Aumont et al. (2015). In EC-Earth3 PISCES can be run in passive mode or with feedback to the atmosphere by prognostically simulating air–sea carbon fluxes and contributing to determining atmospheric pCO₂ when the global carbon cycle is fully closed in the case that the atmospheric chemistry model TM5 and the terrestrial biosphere model LPJ-GUESS are also enabled. A feedback to the ocean physics is not foreseen; i.e., the thermal effect of light absorption by chlorophyll on water temperature is not communicated to NEMO (although possible).

3.8 Greenland Ice Sheet

The Parallel Ice Sheet Model v1.1 (PISM; Bueler and Brown, 2009; Winkelmann et al., 2011; The PISM Team, 2019) is used in the EC-Earth3-GrIS configuration to model the Greenland Ice Sheet (GrIS) evolution in the climate system. PISM is an open-source model jointly developed by a group of universities available from http://www.pism-docs.org (last access: 18 March 2022). While all surface processes over an ice sheet (such as the snow layer) are modeled in EC-Earth3, PISM handles the ice sheet dynamical and thermodynamical processes, including ice flow, subglacial hydrology, bed deformation, and the basal ice melt.

The spatial domain of PISM is built on a three-dimensional, equidistant polar stereographic grid. The equations are solved with an adaptive time stepping procedure. Boundary conditions include subsurface temperature and mass balance on the ice surface (provided by EC-Earth3), bedrock elevation, and bed geothermal heat flux (considered to be invariant geographic conditions).

PISM considers the ice sheets as a slow, nonlinearly viscous isotropic fluid characterized by a creeping flow induced by gravitational forces and constrained by the conservation laws of momentum, mass, and energy for ice. A combination of two shallow ice approximations, the non-sliding shallow ice (SIA) and the shallow shelf (SSA) approximations, is applied, depending on the ice regime (Bueler and Brown, 2009). The former is applied to bed-frozen parts of the ice sheets, while the latter is applied to ice shelves and also used as a sliding law in areas with low basal resistance. This hybrid formulation enables the modeling of fast-flowing ice streams and outlet glaciers and is commonly used for simulations of whole ice sheets for which it is too expensive to solve the full set of stress balance equations.

The ice velocities are determined from geometry (i.e., ice thickness and ice surface elevation), ice temperature, and basal strength using momentum–stress balance equations. The ice thermodynamics are formulated as the energy balance based on enthalpy that enables solutions for polythermal ice masses (Ashwanden et al., 2012) and the Glen–Paterson–Budd–Lliboutry–Duval flow law (Lliboutry et al., 1985) that accounts for softening of the ice as the liquid water fraction increases. The ice flow law is a single power law in which the exponent can be selected independently for the SIA and SSA. Furthermore, an enhancement factor is used to account for the anisotropic nature of the ice.

The subglacial processes are resolved by the sliding law that relates the basal sliding velocity to the basal shear stress. PISM uses a pseudo-plastic sliding law and the Mohr–Coulomb model for yield stress that depends on the till friction angle and the effective pressure of the saturated till. The latter is based on a subglacial routing scheme, and the basal melt rate is calculated from energy conservation across the ice–bedrock layer. A geothermal heat flux map is applied at the basal boundary to account for the heat entering the ice sheet from below. Ice bed deformation is approximated by the viscoelastic deformable Earth model formulated in Bueler et al. (2007).

Calving of marine-terminating glaciers at the ocean boundary is parameterized in PISM as the model does not have a good representation of the narrow fjord systems of the marine outlet at the considered resolution. Several calving schemes are implemented in PISM to cope with different conditions, including eigencalving, von Mises calving, thickness calving, and flow-kill calving. A commonly used calving scheme for GrIS is adapted from the von Mises yield criterion, which is suited for ice flows confined in narrow valleys and fjords (Morlighem et al., 2016). The parameterization assesses the calving speed from the amount of ice fracturing.

3.9 Lake treatment

EC-Earth3 has no explicit lake model. All grid points in the atmosphere model that are covered with less than 50 % water in the land–sea mask are assumed to be land and use the HTESSEL scheme as described above. Grid points with more than 50 % water are considered water, and the water temperature, sea ice cover, and sea ice temperature in these points are updated by the coupler. This process is straightforward for grid points over the ocean, but for inland water bodies such as large lakes this implies an extrapolation of temperature, for example, from the nearest unmasked grid point in the ocean model. This method potentially leads to problems in lakes where the closest ocean point is much further north such as the Great Lakes for which the closest ocean point is the Hudson Bay. This constellation implies colder lakes and longer sea ice cover, which has an impact on the local climate (e.g., lake breeze) around these lakes.

5.1 Temperature

The time series of the global annual mean near-surface air temperature (TAS) is shown in Fig. 4. Reanalysis data from ERA5 and ERA-20C are shown for comparison. Compared to ERA5 the model ensemble has a warm bias of about 0.5 K in the global mean. ERA5 can be considered more relevant for the global mean TAS in comparison with ERA-20C because ERA5 has stronger observational constraints and updated physical parameterization in the underlying global model, while ERA-20C is limited to assimilation of daily surface pressure and surface winds over the ocean (Poli et al., 2016).

Figure 4Global annual mean TAS (in K) from the EC-Earth2.3 (red, for CMIP5) and EC-Earth3 (blue, for CMIP6) ensembles for (a) global mean, (b) land only, and (c) ocean only. Ensemble means are shown as thick lines, and the ensemble spread is shown as a shaded area. Global annual mean TAS from the ERA5 (black, solid) and ERA-20C (black, dashed) reanalyses is shown for comparison.

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The bias in the EC-Earth3 global mean TAS is mainly due to a warmer ocean and especially due to a strong warm bias in the Southern Ocean, as we will show below. Another feature is the large ensemble spread shown as a shaded area around the ensemble mean. The difference between the coldest and warmest ensemble member is 0.8 K on average. For further comparison, the CMIP5 ensemble of EC-Earth2.3 is also shown, which is about 1.2 K colder and indicates a smaller spread among the 10 members in comparison to the current 20-member ensemble. When analyzing the long piControl run we found that the EC-Earth3 model oscillates between two states that are characterized by low or high values of the AMOC, cold or warm North Atlantic temperatures, and more or less sea ice in the Arctic, with a period of about 200 years. The temperature difference over the North Atlantic is large enough to have a discernible impact on the global mean TAS, resulting in a warm and a cold state. The model can remain in either of these states for several decades before turning to the other state, with transitions occurring at irregular intervals. We speculate here that the oscillation decreases with the warming climate. This is indicated by a larger ensemble of historical and scenario simulations than shown here. The exact processes as well as the triggers for the oscillation are still under investigation on the basis of the larger ensemble and will be presented in a later study. However, it is already clear that the large differences between the warmest and coldest member of the ensemble of historical simulations are related to the two states of the model climate, i.e., whether the initial states for the historical run stem from the cold or warm phase of the piControl run, and that transitions between different states occur during the historical simulation.

The TAS trend after 1980 is found to be stronger in the EC-Earth3 ensemble mean (0.25 K per decade) than in the ERA5 reanalysis (0.18 K per decade). However, when looking at the warming during the entire historical period by comparing the mean TAS from 1851–1880 against 1981–2010 we find that the model warmed by 0.7 K, which is only slightly higher than the 0.63 K estimate for the observed warming (IPCC; Hoegh-Guldberg et al., 2018)

To study the EC-Earth3 recent past climate we focus on the period 1980–2010. The ensemble mean spatial TAS is compared to ERA5 for this period in Fig. 5. We find cold TAS biases over the land regions and the Arctic and warm biases over the Southern Ocean and Antarctica as well as for the stratocumulus regions of the continents (Fig. 5b). The individual member biases have a large spread in the Northern Hemisphere as previously mentioned, while the Southern Hemisphere biases are similar for all members as seen in the zonal mean bias plot (Fig. 5d). The CMIP5 ensemble EC-Earth2.3 is colder than ERA5 except over the Southern Ocean (Fig. 5c), and the spread is much smaller than for EC-Earth3 (Fig. 5d).

Figure 5(a) ERA5 1980–2010 mean TAS (in ^∘C); (b) EC-Earth3 and (c) EC-Earth2.3 ensemble mean biases compared to ERA5 (^∘); (d) zonal annual mean TAS from the EC-Earth2.3 (blue, CMIP5) and EC-Earth3 (red, CMIP6) ensembles.

Most coupled climate models suffer from a warm Southern Ocean (SO) bias (Hyder et al., 2018). In EC-Earth3 configurations, the warm bias is found in all seasons. Large parts of the bias have been attributed to biases in shortwave cloud radiative effects. Modifications in the cloud scheme and the representation of supercooled liquid water made in more recent versions of IFS, including cycle 45r1 (Forbes and Ahlgrimm, 2014; Forbes et al., 2016), together with the introduction of the new ecRad radiation scheme in cycle 43r3 (Hogan et al., 2017), have been shown to substantially reduce these biases.

6.1 Sea level pressure

EC-Earth3 mean sea level pressure (PSL) fields are close to ERA5 as shown in Fig. 7. The PSL bias of individual members and the ensemble values are within 1.5 hPa compared to ERA5 except over Antarctica where the pressure is between 0.5 and 2 hPa too high, while over the Southern Ocean the pressure is 1 hPa too low. The variability, measured as the annual standard deviation, of EC-Earth3 PSL is very close to ERA5, indicating realistic surface winds (not shown) and modes of variability as shown later in this section.

Figure 7Upper panel: mean PSL 1980–2010 (hPa) for ERA5 (a) and for the EC-Earth3 ensemble bias compared to ERA5 (b). Lower panel: interannual standard deviation (hPa) for ERA5 (c) and for the EC-Earth3 ensemble (d).

6.2 Zonal wind

An overview of the atmospheric circulation is shown in Fig. 8, where the yearly averaged biases of the zonal component of wind of EC-Earth2.3 and EC-Earth3 are assessed against ERA5. Zonal averages (Fig. 8a, b) show that both models are characterized by an underestimation of the Southern Hemisphere jet, which is larger in the upper troposphere. However, EC-Earth3 shows a reduction of this negative bias compared to EC-Earth2.3.

Figure 8(a, b) Biases (colored shading) of the zonally averaged zonal component of wind for EC-Earth2.3 (a) and EC-Earth3 against ERA5 reanalysis over the 1980–2010 period. Contours show the ERA5 climatology. (c, d) Biases (colored shading) of the 250 hPa zonal component of wind for EC-Earth2.3 (a) and EC-Earth3 against ERA5 reanalysis over the 1980–2010 period. Contours show the ERA5 climatology. Root mean square error, mean bias, and the number of ensemble members used are reported in each panel.

Similar improvements are seen in the Northern Hemisphere: here EC-Earth2.3 was characterized by a negative bias on the order of −5 m s⁻¹ in the core of the upper-tropospheric jet stream, while EC-Earth3 shows limited bias with a slight overestimation on its equatorward side at the tropopause level.

Looking at upper-level zonal wind patterns (Fig. 8c, d) it can be seen that considerable improvements have been obtained for the Pacific jet, which is strongly underestimated in EC-Earth2.3 and shows a minor southward bias in EC-Earth3. Conversely, the North Atlantic jet still shows a poleward displacement – extending from the western Atlantic up to eastern Europe – of the same magnitude in both configurations. A southward displacement of the subtropical jet over Africa also emerges in EC-Earth3.

Overall, CMIP6 EC-Earth3 shows a reduction of the bias when compared with CMIP5 EC-Earth2.3. This is confirmed by smaller figures for both root mean squared error and mean bias shown in the top of each panel in Fig. 8. Larger biases in both models are observed when looking at specific seasons (not shown): EC-Earth3 shows overall smaller biases in DJF and larger biases in JJA than its CMIP5 predecessor. In general, EC-Earth3 is characterized by an underestimation of the winter jet and by an overestimation of the equatorward component of the tropical jet in the summer hemisphere. An underestimation of the winter stratospheric polar vortex – stronger in the Southern Hemisphere – is also found.

6.3 Blocking

Atmospheric blocking – the recurrent long-lasting quasi-stationary high-pressure system developing at the exit of the jet streams in midlatitudes (Woolings et al., 2018) – is assessed in Fig. 9 for both EC-Earth2.3 and EC-Earth3 against ERA5 reanalysis. Analysis of blocking is relevant for climate models considering both (1) the large impact on regional weather that blocking has in both summer and winter seasons (e.g., Sillmann et al., 2011; Schaller et al., 2018) and (2) the constant struggle that GCMs experience in correctly simulating the observed blocking frequencies (e.g., Masato et al., 2013; Davini and D'Andrea, 2020). Blocking is shown here as percentage of blocked days per season following the definition of Davini and D'Andrea (2020), according to which a bidimensional blocking index based on the reversal of the geopotential height gradient at 500 hPa is used.

Figure 9Biases for the blocking frequency according to the Davini and D'Andrea (2020) index for EC-Earth2 (a, c) and EC-Earth3 (b, d) against ERA5 reanalysis over the 1980–2010 period. Contours show the ERA5 climatology. Panels (a) and (b) are winter, and panels (c) and (d) are summer. Root mean square error, mean bias, and the number of ensemble members used are reported in each panel.

Small differences arise from the comparison between EC-Earth2.3 and EC-Earth3, supported by the negligible changes in root mean squared error and mean bias reported in each panel. Both models are in line with the CMIP5 and CMIP6 multi-model mean (see Davini and D'Andrea, 2020). The most evident improvement is the reduced bias in winter North Pacific blocking in EC-Earth3 compared to its predecessor. However, both EC-Earth2.3 and EC-Earth3 show the common underestimation of winter European blocking with similar magnitude. It is interesting to notice that while in EC-Earth2.3 the winter European bias is characterized by a north–south dipole probably associated with an equatorward displacement of the Atlantic eddy-driven jet, in EC-Earth3 the dipole is located on the east–west axis, suggesting the presence of a jet that is too penetrative over the European continent (Fig. 9a, b).

Larger biases are seen in summer: negligible differences between EC-Earth2.3 and EC-Earth3 are also found, with slightly larger North Pacific and European blocking biases observed in EC-Earth3.

6.4 Sea ice

We compare EC-Earth3 historical ensemble mean sea ice variables and spread to observations and reanalysis datasets.

The ensemble mean of EC-Earth3 slightly overestimates the Arctic sea ice area (Fig. 10), whereby the ensemble spread encases the OSI SAF satellite observations (Lavergne et al., 2019). The trend in the Arctic sea ice area over 1980–2014 is captured well by the model during March and September (Fig. 10).

Figure 10Time series of Arctic (a, c) and Antarctic (b, d) sea ice area for both EC-Earth3 (ensemble mean as thick solid lines) and satellite observations (OSI SAF as blue dash-dotted lines and NSIDC as dashed lines). The EC-Earth3 ensemble minimum up to maximum value is represented by the shading around the ensemble mean.

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Interestingly, the modeled summer Arctic sea ice area minimum occurs in August instead of September as in observations. This result is in agreement with previous studies using NEMO-LIM forced by atmospheric forcing (Rousset et al., 2015; Docquier et al., 2017) and several coupled CMIP6 models including NEMO as an ocean component (Keen et al., 2021). The exact reason for the minimum sea ice area occurring in August is not clear (Keen et al., 2021).

While the total Arctic sea ice area is captured well by the model, there are large regional differences in the sea ice concentration between EC-Earth3 and satellite observations (Fig. 11). In March, the model overestimates the concentration near the ice margins in the Atlantic sector, including the Labrador, Greenland–Iceland–Norwegian (GIN), and Barents seas, while the concentration is underestimated by the model in the Bering Sea. In September, the sea ice concentration is generally overestimated by the model at the ice margins, with exceptions in the Kara, Laptev, and Chukchi seas, where the concentration is underestimated.

Figure 11Difference in Arctic sea ice concentration in percent between the ensemble mean of EC-Earth3 and OSI SAF observations in September (a) and March (b), averaged over 1980–2010.

The total Arctic sea ice volume is higher in the ensemble mean of EC-Earth3 compared to the PIOMAS reanalysis (Fig. 12). The PIOMAS volume is close to the lower edge of the EC-Earth3 ensemble spread, which is considerably large, of about 30×10³ km³ in the 1980s and 1990s. This is consistent with the Arctic sea ice being generally thicker in the model compared to PIOMAS (Fig. 13). In September, the Arctic sea ice is clearly too thick in the model with a bias up to 2 m compared to PIOMAS. In March, the Arctic sea ice thickness is overestimated by EC-Earth3 in the central Arctic, while in the Bering and Karas seas the thickness is lower compared to PIOMAS.

Figure 12Time series of September (orange, upper panel) and March (blue, lower panel) Arctic sea ice volume for EC-Earth3 (thin solid lines representing the ensemble mean), EC-Earth3-Veg (dashed lines representing the ensemble mean), the CMIP5 version of EC-Earth (dotted lines), and PIOMAS reanalysis (thick solid lines). The EC-Earth3 and EC-Earth3-Veg ensemble minimum and maximum are represented by the same line style as their means, but with transparent shading added around the ensemble means.

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We chose PIOMAS as a reference product for sea ice thickness and volume because of the relatively long available time frame (i.e., from 1979 to now) compared to observational products, which cover much shorter periods. Uncertainties in PIOMAS are related to the underlying ocean and sea ice models, to the atmospheric forcing, and to the observational data available to the assimilation scheme. PIOMAS ice thickness estimates agree well with the ICESat ice thickness retrievals for the central Arctic, the area for which submarine data are available, with a mean difference smaller than 0.1 m, while differences outside this area are larger (Schweiger et al., 2011). Also, PIOMAS spatial thickness patterns agree well with ICESat thickness. PIOMAS appears to overestimate thin ice thickness and underestimate thick ice. The latter feature partly explains the higher ice thickness in EC-Earth3 in the central Arctic compared to PIOMAS (Fig. 13).

Figure 13Difference in Arctic sea ice thickness between the ensemble mean of EC-Earth3 and PIOMAS in September (a) and March (b), averaged over 1980–2010.

While the EC-Earth3 historical ensemble represents the Arctic sea ice area relatively well, it clearly underestimates the Antarctic sea ice area (Fig. 10) by ∼ 5 million km² in September and ∼ 2 million km² in March. This underestimation is linked to the warm bias in the Southern Ocean (Fig. 4) and is visible for all areas around Antarctica during the Southern Hemisphere summer (Fig. 14). The underestimation is more pronounced close to the ice edge than in the central pack ice during the Southern Hemisphere winter (Fig. 14). Also, the modeled trend in Antarctic sea ice area in both September and March is slightly negative, while observations show a slightly positive trend over 1979–2014 (Fig. 10). However, including the most recent years (after 2014), the observed Antarctic sea ice area does not exhibit any significant trend (Meredith et al., 2019).

Figure 14Difference in Antarctic sea ice concentration between the ensemble mean of EC-Earth3 and OSI SAF observations in September (a) and March (b), averaged over 1980–2010.

Due to the absence of reliable long-term reanalysis and/or observational products for Antarctica, we do not show maps of sea ice thickness in the Southern Hemisphere.

6.5 AMOC

The Atlantic Meridional Overturning Circulation (AMOC) is connected with a northward flow of warm and salty water in the upper layers of the Atlantic Ocean and exports of cold and dense water southward in the deeper layers (Buckley and Marshall, 2016). The ensemble mean of the AMOC stream function obtained from the EC-Earth3 ensemble simulations (Fig. 15a), after being averaged over 1980–2010, features the expected overturning clockwise circulation cell with a maximum transport of 18 Sv centered at around 35^∘ N and a depth of 1000 m. Compared to the 12-member ensemble mean of EC-Earth 2.3 (Brodeau and Koenigk, 2016) used for CMIP5 (no figure), the CMIP6 version of EC-Earth presented here has a stronger AMOC closer to observations (Smeed et al., 2018).

Figure 15(a) AMOC stream function in the depth and latitude plane for the EC-Earth3 ensemble mean, averaged over 1980–2010 (in Sv). (b) Standard deviation of AMOC between the members. The x axis denotes degrees latitude.

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The ensemble mean time series of the AMOC index, defined as the maximum volume transport stream function between 24.5 and 27.5^∘ N, covers values from well within the range of the RAPID-MOCHA array observations (Smeed et al., 2017). The ensemble mean shows a weak decrease of about 0.5 Sv from the year 1850 to 1876 with a relatively steady period until 1931 around 17.5 Sv, followed by an increase of around 2 Sv until 1980 and a decrease afterwards. Individual members of the ensemble vary between 2 and 5 Sv, with the upper range matching the RAPID observational variability well. It has to be noted that the RAPID data are available only for the last 20 years. Several other studies with ocean models forced by atmospheric reanalysis data (e.g., Yeager and Danabasoglu, 2014; Huang et al., 2012) show a later increase in AMOC between 1980 and the 1990s and a decrease after the mid-1990s. Most CMIP5 models also show a later decrease in AMOC, mainly after the year 2000 (e.g., Collins et al., 2013; Cheng et al., 2013).

There is a wide range of variability (Fig. 15b) between ensemble members, possibly because each member starts from a different initial condition that evolves differently depending on the state of the model's internal variability. The variation between members occurs mainly at depth of 1000–2000 m and between 0 and 40^∘ N, and it has a pattern and magnitude similar to the AMOC multidecadal variability (Fig. 2 in Boulton et al., 2014). A first analysis suggests that the lowest AMOC strength values correspond to extended periods with absent deepwater formation and expanded sea ice in the Labrador Sea. Our preliminary analysis suggests that those ensemble members with similar initial conditions (in terms of SST and SAT) have similar curves in their AMOC index time series. This further suggests that those members with a more realistic initial state might be better in capturing the AMOC variability. Nevertheless, time series of 12 individual members (out of 20 members) show a roughly similar trend after 1950.

The AMOC (Fig. 16) shows a variability of 70 to 100 years as in ECHAM5 and the Max Planck Institute Ocean Model (Jungclaus et al., 2005) but a narrower range than the variability of 50–200 years in CCSM4 (Danabasoglu et al., 2012). One reason that could explain the somewhat long period of variability for our EC-Earth simulations is that the modeled sea ice is extending too far into the Labrador Sea, which keeps AMOC in a weaker state for a longer period of time before recovering. In CMIP5, most models without the convection were also covered by sea ice in the Labrador Sea in winter (Heuzé, 2017).

Figure 16Time series of maximum AMOC (maximum between 24.5–27.5^∘ N) for ensemble mean (black), low quartile (purple), high quartile (pink), ensemble minimum (blue), and ensemble maximum (red) are shown for 19 members of EC-Earth3. Observation data are shown with green from RAPID-MOCHA array observations (Smeed et al., 2017).

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Figure 17Ocean northward heat transport: the blue curve is the ensemble mean, and the light blue shading is delimited by the ensemble minimum and maximum. The black curve is taken from Trenberth et al. (2019). The hydrographic measurements at 26^∘ N (RAPID) and 57^∘ N (OSNAP) are shown as vertical bars.

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The ocean heat transport (Fig. 17) is related to the AMOC. North of 20^∘ N it shows values slightly lower than observation estimates from Trenberth et al. (2019) that cover the period from 2000–2014.

6.6 Modes of variability

Since the North Atlantic Oscillation (NAO) is one of the most relevant modes of variability for the European climate, we assess its representation separately. The NAO is characterized by atmospheric oscillation between the Arctic and the subtropical Atlantic and can also be defined through changes in surface pressure (Hurrell et al., 2003). During winter, the positive phase of NAO has been defined when the difference between the Icelandic low-pressure center and the Azores high-pressure center is intensified: conversely, a negative NAO phase is when this difference is weaker than usual. The NAO pattern is estimated by calculating the leading empirical orthogonal function (EOF) of the detrended December to February (DJF) monthly sea level pressure (SLP) anomalies over the Atlantic sector (20–80^∘ N, 90^∘ W–40^∘ E). The ERA-20C and both EC-Earth ensemble means show very similar spatial patterns (Fig. 20), with EC-Earth2.3 showing more intense negative values over Iceland and less intense positive values over the Bay of Biscay and northern Spain when compared to EC-Earth3 and observations.

Overall the representation of the NAO in EC-Earth3 shows minor improvements with respect to EC-Earth2.3: the root mean square error (RMSE) of EC-Earth3 is 0.64 compared with 0.52 for EC-Earth2.3.

Previous assessments of coupled models have found that the CMIP5 and CMIP3 models represent NAO very similarly as in reanalyses, with no general improvements of CMIP5 compared to CMIP3 models (Davini and Cagnazzo, 2014).

In EC-Earth3, the ENSO spatial patterns and amplitude are well represented (not shown). In order to assess the variability of ENSO in the EC-Earth3 ensemble we calculated the Niño3.4 SST power spectra (Fig. 18) for the model and for the HadISST observational dataset (Rayner et al., 2003). HadISST shows the highest peak at 5.5 years and a range of periods between 3.3 and 3.7 forming the second highest peak. The mean of the EC-Earth3 ensemble spectra shows the highest peak at around 3.7 years. Some individual members show their main peak at about 5.5 years, similar to the HadISST dataset. Most of the ensemble members (two with the highest peaks) show their maximum in the 3–4-year period.

Figure 18Power spectra of Niño3.4 sea surface temperature (SST) time series for HadISST observations (black thick line), 20 EC-Earth3 ensemble members (light green lines), and 4 EC-Earth 2.3 ensemble members (cyan lines). The EC-Earth3 and EC-Earth2.3 ensemble means are shown as green and blue thick lines, respectively. The Niño3.4 is calculated between latitudes 5^∘ N–5^∘ S and longitudes 170–120^∘ W. The power spectra were calculated for the 1900–2009 period.

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EC-Earth3 shows larger ENSO spectral power than EC-Earth2.3, with an ensemble mean closer to the HadISST observations, especially in frequencies with high energy. Thus, we see a clear improvement in the representation of ENSO in EC-Earth3. Similar improvements were seen earlier for CMIP5 models (Jha et al., 2014). While the frequency distribution in EC-Earth3 is distinctly improved compared to EC-Earth2.3, a challenge is still seen in representing distinct peaks in the power spectrum.

The range among the ENSO spectra of different members is considerable. Climatologically, most ensemble members show only small differences over the tropics when compared with the whole ensemble mean. Although the members with the most energetic ENSO share some climatological features (cold Arctic and Labrador seas) compared to the ensemble mean, the reason why they have developed a more energetic ENSO remains unclear.

Previous studies have shown that winters of El Niño have an impact on the circulation over the North Atlantic, favoring a negative phase of the NAO in the late winter (e.g., García-Serrano et al., 2011) teleconnected via the extratropical Pacific–North American (PNA) pattern (Enfield and Mayer 1997; Giannini et al., 2000). This nonstationary relationship between ENSO and the atmospheric variability over the North Atlantic and European sector is already reproduced in the internal variability behavior of coupled ocean–atmosphere systems in CMIP5 simulations (López-Parages et al., 2016)

To better assess this relationship between ENSO and NAO, we calculated the regression of the Niño3.4 index on sea level pressure (SLP) for the winter season (December to February, DJF) for ERA-20C reanalysis and for both EC-Earth ensembles (EC-Earth3 and EC_Earth2.3) (Fig. 19). As reported by previous studies (Wallace and Gutzler, 1981), a positive PNA-like pattern arises with an intensified lower Aleutian low and lower pressure over the eastern United States. This low pressure extends along the North American east coast into the central North Atlantic Ocean, while there is higher pressure over and between Iceland and Scandinavia, a pattern that is similar to a negative phase of NAO (Fig. 19). The EC-Earth3 ensemble demonstrates a high resemblance to ERA-20C (Fig. 19), which is much improved compared to the EC-Earth2.3 ensemble (Fig. 19). The latter shows weaker SLP anomalies, which can be associated with a weaker ENSO intensity in EC-Earth2.3 compared to the newer EC-Earth3 and to observations. Thus, EC-Earth3 gives a clear improvement of the ENSO–NAO link.

Figure 19Regression of Niño3.4 SST index onto sea level pressure during winter (DJF) for the ERA-20C reanalysis (a), 20-member EC-Earth3 ensemble mean (b), and 4-member EC-Earth2.3 ensemble mean (c). Analyses are based on 3-month means for December–February.

Previous research has linked La Niña and El Niño events to the positive and negative NAO patterns (Fereday at al., 2020). Although this link is relatively weak due to the fact that internal atmospheric variability is large in the North Atlantic European (NAE) region (Brönnimann, 2007), it depends on ENSO strength (Jiménez-Esteve and Domeisen, 2019; Toniazzo and Scaife, 2006). Therefore, a more energetic ENSO (more comparable in scale with observations) such as in the current EC-Earth3 could impact the intensity and sign of NAO.

The PNA pattern in EC-Earth3 shows strong spatial similarities with ERA-20C, which is an improvement compared to EC-Earth2.3 (not shown). RMSEs are respectively 0.9 and 0.54. EC-Earth3 also shows a more realistic behavior than EC-Earth2.3 with respect to typical features of the PNA patterns, i.e., an above-average surface pressure over the subtropical Pacific (west of Hawaii) and over western Canada, together with below-average surface pressure over the North Pacific Ocean and along the southeastern United States.

The quasi-biennial oscillation (QBO) dominates the interannual variability in the tropical stratosphere (Baldwin et al., 2001). As in most climate models, the vertical discretization and the parameterization of gravity waves are crucial (e.g., Bushell et al., 2020) for a realistic representation of the QBO in EC-Earth.

In EC-Earth 2.3, with 62 vertical levels and without an ad hoc tuning, the zonal wind in the equatorial band is easterly on average, reaching −35 m s⁻¹ close to the 5 hPa level (Fig. 21a). Note that results in this panel are based on model level outputs interpolated onto equivalent pressure levels. CMIP5 pressure level outputs are available only up to 20 hPa for other ensemble members.

Figure 20Regression of sea level pressure (SLP) anomalies to the NAO index during winter (December to February) for the ERA-20C reanalysis (a), 20-member EC-Earth ensemble mean (b), and 4-member EC-Earth2.3 ensemble mean (c).

Figure 2110 years of the equatorially (within 5^∘ from the Equator) averaged monthly mean zonal wind in EC-Earth2.3 (r12i1p1, a) and EC-Earth3 (r4i1p1f1, b) as a function of time and altitude. Easterly winds are shaded in gray, and the contour interval is 5 m s⁻¹. The peak-to-peak amplitude profiles of the equatorial zonal wind, estimated from the temporal standard deviation for the period 1980–2010, are reported in (c) for ERA5 (black), 12 CMIP6 (red), and 6 CMIP5 (blue) ensemble members. In panel (d) the Fourier spectra at the 30 hPa level for ERA5 (black) and the same experiments in panel (c) are shown. Only for panel (a) are the results for EC-Earth2.3 interpolated onto pressure levels from native model levels.

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Like other models participating in CMIP6 (Richter et al., 2020), the realism of the modeled QBO is notably improved in EC-Earth3, with 91 vertical levels and a revised gravity wave scheme (see Sect. 3.1). A marked alternation of easterly and westerly zonal wind shears can be seen between approximately 100 and 5 hPa in Fig. 21b. While a realistic QBO-like oscillation has been obtained, there is no improvement in the zonal wind above 5 hPa, as it remains easterly year-round without a clear sign of any stratospheric semi-annual oscillation. This phenomenon, linked with the QBO, is also driven by vertically propagating waves (Smith et al., 2019).

From the comparison of the amplitude profiles with ERA5 (Fig. 21c), it is clear that, even if still underestimated, the zonal wind variability in the EC-Earth3 ensemble members is improved with respect to those of EC-Earth2.3. As with other climate models (Bushell et al., 2020), the maximum of the oscillation peaks somewhat higher (at 10 hPa) in EC-Earth3 than in the reanalysis (closer to 20 hPa).

In Fig. 21d we also report the Fourier spectra at the 30 hPa (25 km) level, again including ERA5 and ensemble members from EC-Earth2.3 and EC-Earth 3. For the CMIP5 model only the annual harmonic stands out, whereas the EC-Earth 3 spectrum at 30 hPa resembles that of ERA5 much more closely, despite the modeled QBO being slightly faster.

6.7 Carbon cycle components

As an outlook to the EC-Earth3-CC configuration, we present first results here from the carbon cycle components of one member of the historical experiment. In this configuration, the physical climate is equivalent to that of the EC-Earth3-Veg configuration. However, besides the land vegetation and biogeochemistry model, the ocean biogeochemistry model has been activated. The latter describes the evolution of biogeochemical tracers in the ocean, but it does not have any feedback on climate. Both land vegetation and ocean biogeochemistry were equilibrated with a 1600-year-long spin-up keeping atmospheric CO₂ at pre-industrial level (284.32 ppm). The completion of the spin-up was assessed following the recommendation of C4MIP (Jones et al., 2016), with both the ocean and land C stocks having to drift by less than 10 Pg C per century. Once this condition was met, a piControl simulation and historical simulation were started from the same initial conditions.

The ocean's cumulative C uptake between 1870 and 2014 is 150.78 Pg C, in good agreement with the estimate of 155 ± 20 Pg C by the Global Carbon Project (GCP) 2015 for the same period (Le Queré et al., 2015). The average air–sea CO₂ exchange between the atmosphere and the ocean for the period 1981–2014 is compared here to the observation-based reconstruction of Landschutzer et al. (2016) for the same period (Fig. 22). The overall spatial distribution of the air–sea CO₂ flux is in broad agreement with observations, with the largest differences occurring at high latitudes. In particular, in the Southern Ocean EC-Earth3-CC exhibits a large negative bias (i.e., more outgassing) in some regions due to the presence of extended periods of unrealistic open-sea convection. In the North Pacific and North Atlantic, EC-Earth3-CC has a stronger CO₂ uptake than observations, likely due to a deeper mixed layer and frequent active convection in the Labrador Sea, respectively.

Figure 22Air–sea CO₂ flux averaged over the period 1982–2014 for EC-Earth3-CC (a), the observation-based reconstruction by Landschutzer et al. (2016; b), and their difference (c).

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In Fig. 23 we show CO₂ fluxes from the land and ocean components of EC-Earth3 for the period 1960–2014. The ocean CO₂ sink (SOCEAN; Fig. 23c) of the EC-Earth3-CC historical simulation closely follows the multi-model mean of the GCP 2019 (Friedlingstein et al., 2019), with differences in variability due to the mismatch between climate in EC-Earth-CC and the atmospheric forcing products used in the GCP. Land fluxes (computed from two historical EC-Earth3-Veg runs, one with dynamic land use change and management and one with land use fixed at 1850 levels) have increased following increased atmospheric CO₂ and temperature, but these show a stronger interannual variability in both emissions from land use change (ELUC; Fig. 23a) and terrestrial CO₂ sink (SLAND; Fig. 23b) compared to the estimates from the DGVMs in GCP 2019. This interannual variability originates from both climate differences between EC-Earth3-Veg and the observation-based forcing, which includes the right timing of weather events like El Niño in the offline simulations used for the GCP (Harris et al., 2014) and the mismatch between the dynamic vegetation in LPJ-GUESS compared to the land use dataset LUH2 (Hurtt et al., 2020) that dictates where and when land use change occurs.

Figure 23CO₂ exchanges between the atmosphere and the terrestrial biosphere for (a) CO₂ emissions from land use change (ELUC) and (b) land CO₂ sink (SLAND) with individual DGVMs (gray), the multi-model mean (dark green), and its range (±1σ, light green shading) from GCP overlaid with EC-Earth3-Veg fluxes (black). Panel (c) shows the CO₂ exchange between the atmosphere and ocean (SOCEAN) with individual ocean models (gray), the multi-model mean (dark blue), and its range (±1σ, light blue shading) from GCP overlaid with EC-Earth3-CC fluxes (black).

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