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  • View in gallery

    (a) Seasonal cycle of surface temperatures in the tropical Atlantic from ERA-Interim reanalysis data (Dee et al. 2011) (1979–2013). The star marks the location of the buoy we use in this study, at 6°S, 8°E. It is part of the PIRATA array (Servain et al. 1998; Bourlès et al. 2019). (b) The seasonal cycle of SST from buoy data, averaged from daily data over 2014–18 and for the coupled global version of EC-Earth.

  • View in gallery

    Schematic of the coupled ocean atmosphere SCM version of EC-Earth used in this study. We force the atmosphere with temperature, moisture, and momentum advection. At the interface between the atmosphere and the ocean the model components exchange fluxes, among which the turbulent (latent and sensible heatflux: LH + SH) and radiative heat fluxes [shortwave (SW) and longwave (LW)] are indicated with arrows. The ocean further receives momentum forcing from the atmosphere (τ), and mass fluxes (not indicated). In the ocean column, vertical mixing is the only parameterized process solved for with the TKE scheme (MixTKE).

  • View in gallery

    Average SST at the buoy location at 6°S, 8°E in June for (a) 2014–18 and (b) 2014.

  • View in gallery

    June 2014 (top) atmosphere specific humidity, (middle) atmospheric temperature, and (bottom) ocean temperature at the buoy location at 6°S, 8°E in June, with atmospheric data from ERA-Interim and ocean temperature from (left) PIRATA data and (right) as modeled by the SCM (control). Ticks on the right-hand sides of the bottom row indicate levels at which ocean data are available. Atmospheric data are available on the same model level heights for ERA-Interim and the SCM.

  • View in gallery

    Control simulation (June 2014) surface fluxes, net shortwave (SW; red), net longwave (LW; blue), and the turbulent fluxes latent heat and sensible heat combined (LH + SH; green). Of the latter, latent heat is the much larger contribution. The sum of the surface fluxes is shown in black (TOT).

  • View in gallery

    Downward shortwave radiation from the PIRATA buoy and from the SCM control run, at 2- and 15-min temporal resolution, respectively.

  • View in gallery

    Daily integrals of the downward shortwave radiation flux during June from the PIRATA buoy from data received at 2-min intervals, the same interpolated to model time-step resolution of 15 min, and from the SCM control run.

  • View in gallery

    SST as simulated by the various atmospheric experiments described in the upper part of Table 1. The black line shows observed SST for comparison.

  • View in gallery

    (a) Surface fluxes as in Fig. 5, net surface shortwave radiation in red, net surface longwave in blue, turbulent fluxes in green, and total sum of fluxes in black/gray for the control experiment (solid lines), Atm ERA (dashed lines), T,Q ERA (dotted lines), and U,V ERA (dash–dotted lines. (b) The relative change of integrated surface fluxes with respect to the control experiment, in percent. Colors are as in (a). Note that because of the sign convention an increase in turbulent as well as longwave radiative flux translates to an increased in cooling.

  • View in gallery

    Root-mean-square SST errors in the parameter sweeps for CLC and Cdiff.

  • View in gallery

    SST as simulated by the various oceanic experiments described in the lower part of Table 1. The black line shows observed SST for comparison.

  • View in gallery

    (top) Atmospheric moisture, (middle) temperature, and (bottom) upper ocean temperature in (left) the control experiment and (right) at ideal Cdiff.

  • View in gallery

    Integrated surface fluxes over the time of the simulations in the Cdiff sweep. Turbulent components latent and sensible heat fluxes are combined in green; the radiative components shortwave and longwave are shown in red and blue, respectively.

  • View in gallery

    Root-mean-square SST errors in the parameter sweeps for Cdiff, with cubic fits. Stars mark the minimum SST RMSE on the fit.

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The Southeastern Tropical Atlantic SST Bias Investigated with a Coupled Atmosphere–Ocean Single-Column Model at a PIRATA Mooring Site

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  • 1 Meteorology and Air Quality, Wageningen University, Wageningen, and Research and Development of Weather and Climate Models, Royal Dutch Meteorological Institute, De Bilt, Netherlands
  • | 2 Research and Development of Weather and Climate Models, Royal Dutch Meteorological Institute, De Bilt, Netherlands
  • | 3 Meteorology and Air Quality, Wageningen University, Wageningen, Netherlands
  • | 4 Faculty of Geosciences, Utrecht University, Utrecht, Netherlands
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Abstract

Warm sea surface temperature (SST) biases in the tropical Atlantic Ocean form a longstanding problem in coupled general circulation models (CGCMs). Considerable efforts to understand the origins of these biases and alleviate them have been undertaken, but state-of-the-art CGCMs still suffer from biases that are very similar to those of the generation of models before. In this study, we use a powerful combination of in situ moored buoy observations and a new coupled ocean–atmosphere single-column model (SCM) with parameterization that is identical to that of a three-dimensional CGCM to investigate the SST bias. We place the SCM at the location of a Prediction and Research Moored Array in the Tropical Atlantic (PIRATA) mooring in the southeastern tropical Atlantic, where large SST biases occur in CGCMs. The SCM version of the EC-Earth state-of-the-art coupled GCM performs well for the first five days of the simulation. Then, it develops an SST bias that is very similar to that of its three-dimensional counterpart. Through a series of sensitivity experiments we demonstrate that the SST bias can be reduced by 70%. We achieve this result by enhancing the turbulent vertical ocean mixing efficiency in the ocean parameterization scheme. The underrepresentation of vertical mixing in three-dimensional CGCMs is a candidate for causing the warm SST bias. We further show that surface shortwave radiation does not cause the SST bias at the location of the PIRATA mooring. Rather, a warm atmospheric near-surface temperature bias and a wet moisture bias contribute to it. Strongly nudging the atmosphere to profiles from reanalysis data reduces the SST bias by 40%.

Denotes content that is immediately available upon publication as open access.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Anna-Lena Deppenmeier, deppenme@ucar.edu

Abstract

Warm sea surface temperature (SST) biases in the tropical Atlantic Ocean form a longstanding problem in coupled general circulation models (CGCMs). Considerable efforts to understand the origins of these biases and alleviate them have been undertaken, but state-of-the-art CGCMs still suffer from biases that are very similar to those of the generation of models before. In this study, we use a powerful combination of in situ moored buoy observations and a new coupled ocean–atmosphere single-column model (SCM) with parameterization that is identical to that of a three-dimensional CGCM to investigate the SST bias. We place the SCM at the location of a Prediction and Research Moored Array in the Tropical Atlantic (PIRATA) mooring in the southeastern tropical Atlantic, where large SST biases occur in CGCMs. The SCM version of the EC-Earth state-of-the-art coupled GCM performs well for the first five days of the simulation. Then, it develops an SST bias that is very similar to that of its three-dimensional counterpart. Through a series of sensitivity experiments we demonstrate that the SST bias can be reduced by 70%. We achieve this result by enhancing the turbulent vertical ocean mixing efficiency in the ocean parameterization scheme. The underrepresentation of vertical mixing in three-dimensional CGCMs is a candidate for causing the warm SST bias. We further show that surface shortwave radiation does not cause the SST bias at the location of the PIRATA mooring. Rather, a warm atmospheric near-surface temperature bias and a wet moisture bias contribute to it. Strongly nudging the atmosphere to profiles from reanalysis data reduces the SST bias by 40%.

Denotes content that is immediately available upon publication as open access.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Anna-Lena Deppenmeier, deppenme@ucar.edu

1. Introduction

Tropical Atlantic Ocean sea surface temperatures (SST) display large variability on interannual time scales, and a strong seasonal cycle. State-of-the-art coupled general circulation models (CGCMs) struggle to capture the cooling in the southeastern tropical Atlantic, as a result of which they suffer from large warm SST biases in that region (Richter and Xie 2008; Richter et al. 2012; Wang et al. 2014). These biases hamper efforts to reliably predict societal relevant climate events (Stockdale et al. 2006), such as the West African monsoon and the Atlantic Niño.

In boreal summer, the southeastern tropical Atlantic cools strongly and rapidly. Simultaneously, a cold tongue forms on the equatorial eastern Atlantic, extending as far as 20°W (Fig. 1a, visible in June, July, and August). In boreal autumn, the cold tongue recedes and the cold waters in the southeast warm gradually.

Fig. 1.
Fig. 1.

(a) Seasonal cycle of surface temperatures in the tropical Atlantic from ERA-Interim reanalysis data (Dee et al. 2011) (1979–2013). The star marks the location of the buoy we use in this study, at 6°S, 8°E. It is part of the PIRATA array (Servain et al. 1998; Bourlès et al. 2019). (b) The seasonal cycle of SST from buoy data, averaged from daily data over 2014–18 and for the coupled global version of EC-Earth.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

On the southeastern edge of the cold tongue (6°S, 8°E), located in the region of strong annual cooling (Fig. 1b), the Prediction and Research Moored Array in the Tropical Atlantic (PIRATA; Servain et al. 1998; Bourlès et al. 2019) offers observational data to fill the gap of our knowledge of the ocean and air–sea interaction processes in this region. At the location of this buoy, SSTs cool by several degrees during boreal summer (Fig. 1b). The cooling in three-dimensional CGCMs is much weaker, as indicated at the example of EC-Earth, also in Fig. 1b. The insufficient cooling leads to the large typical positive SST biases in the region. The largest SST biases occur very close to the coast around the Angola Benguela frontal zone (Xu et al. 2014a), where biases can be as large as 8°C (Koseki et al. 2018). Harlaß et al. (2015) and Milinski et al. (2016) have recently shown the importance of atmospheric resolution for reducing these coastal biases, and Small et al. (2014) stressed the importance of an additional high-resolution ocean component. Smaller, but sizeable, biases are found at the location of the buoy (Toniazzo and Woolnough 2014; Voldoire et al. 2019). During the first five months of the year, the three-dimensional model accurately captures the SST in the southeastern tropical Atlantic. With the onset of the strong cooling the bias develops and is first sizeable in June. This makes June the ideal month to study the bias, as it is the month in which it establishes.

Recently, the seasonal heat budget at this site has been analyzed by Scannell and McPhaden (2018) for the five years in which daily data record is available. The authors find that in boreal summer horizontal advection contributes only in a minor role to the heat budget, and that rather reduced shortwave forcing and vertical turbulent entrainment into the upper ocean mixed layer are the main causes for the observed SST cooling. The latter process occurs at scales too small to be explicitly captured in the ocean component of three-dimensional models, and has to be added via parameterization. The specifics of the parameterization determine the strength of the mixing included in the model. The underrepresentation of this vital process is a strong candidate for producing the warm bias (Hazeleger and Haarsma 2005; Exarchou et al. 2017; Planton et al. 2018).

Other origins of the warm bias have been suggested to arise in the atmosphere, for example, from excessive shortwave radiation (Huang et al. 2007; Hu et al. 2008) or insufficient wind forcing (Richter et al. 2012; Voldoire et al. 2014; Koseki et al. 2018) or from an atmospheric moisture bias (Hourdin et al. 2015). A recent multimodel study highlights the role of wind stress forcing in the bias development (Voldoire et al. 2019), but also shows that it cannot explain the entire bias and sometimes even has limited effect (as is the case for EC-Earth, which we use here). Other studies have highlighted the contribution of the ocean model (Xu et al. 2014b), its horizontal and vertical resolution (Seo et al. 2006; Doi et al. 2012; Small et al. 2014), advection (Goubanova et al. 2019), and turbulent processes (Hazeleger and Haarsma 2005; Exarchou et al. 2017; Planton et al. 2018) to the bias formation. The question of the southeastern tropical Atlantic warm bias is not yet resolved and more analysis is clearly necessary to trace its origins.

In this study, we use an ocean–atmosphere coupled single-column version of the coupled GCM EC-Earth (Hazeleger et al. 2010) to investigate the bias formation in the southeastern tropical Atlantic, at the location of the 6°S, 8°E PIRATA mooring. With the single-column model (SCM) we can investigate processes active on very short time scales. This is impractical, if not impossible, with the three-dimensional model. With the coupled SCM, as opposed to the standalone version of the atmosphere and the ocean, we can investigate coupled air–sea processes, and the effect of the model bias in one component on the other component. In this work we first test the impact of the atmosphere on the ocean, and then focus on ocean parameterization.

The short runtime of the SCM allows us to perform a range of sensitivity experiments and explore the parameter space that determines the short time scale processes of our interest. By choosing a location for which in situ data are available, we are able to closely compare and evaluate the model performance. Additionally, we can employ observed data to force the model.

The paper is structured as follows. We describe the model in section 2. In section 3 we describe the data used in this study, and the setup of the SCM experiments. In section 4, we evaluate the SCM performance (section 4a), before moving on to atmospheric sensitivity experiments (section 4b) and ocean experiments (section 4c). The results are summarized and discussed in section 5.

2. Model description

We use a novel coupled ocean–atmosphere SCM Hartung et al. (2018) derived from the three-dimensional host model EC-Earth (after Hazeleger et al. 2010, 2012). Optimal settings for SCM experiments are explored in Hartung et al. (2018), where the model is initially described. Here, we briefly repeat the description of the model setup.

The SCM consists of the Nucleus for European Modelling of the Ocean (NEMO) ocean model, version 3.6 (Madec et al. 2016), which includes the sea ice model LIM3 (Vancoppenolle et al. 2008), and the Open Integrated Forecasting System cycle 40r1 (https://confluence.ecmwf.int/display/OIFS/About+OpenIFS) for the atmosphere, with the land surface model H-Tessel (Balsamo et al. 2009). Coupling between the ocean and atmosphere is handled by OASIS3-MCT (Valcke 2013), similar to the way the components couple in three-dimensional EC-Earth.

OpenIFS solves the one-dimensional primitive equations for momentum [Eqs. (1) and (2)], thermodynamics [Eq. (3)], and moisture [Eq. (4)] for the atmosphere:
ut=η˙uη+Fu+f(υυg)+Pu+uruτa,
υt=η˙υη+Fυf(uug)+Pυ+υrυτa,
Tt=η˙Tη+FT+RTωcpp+PT+TrTτa,and
qt=η˙qη+Fq+Pq+qrqτa.
The vertical coordinate η merges orography with pressure coordinates in the free atmosphere. The term η˙ is the vertical velocity in this coordinate, and ω is the vertical velocity in pressure coordinates; u and υ are the horizontal velocity components, with their geostrophic contributions ug and υg; f is the Coriolis parameter; R is the universal gas constant and cp is the heat capacity (both for moist air); and p is pressure. The terms Fi are horizontal advection of momentum, temperature, and moisture, and Pi are parameterizations of subgrid-scale processes. The parameterized processes include radiative transfer, convection, and clouds, with its own prognostic equations for cloud liquid and ice, rain and snow water content and cloud cover. These parameterizations have been the subject of intensive research, and are not the focus of this study. Profiles can be nudged to reference states for ur, υr, Tr, and qr with a time scale τa.
The surface energy budget is
(1αi)(1fRs,i)Rs+RTεσTsk,i4+SHi+LHi=QT=Λsk,i(Tsk,iT1).
The subscript i indicates that the surface grid box is subdivided into tiles, and hence a single gridbox can consist of partly ocean and partly sea ice (or land surface). The shortwave radiation at the surface Rs is absorbed with fraction fRs,i and reflected with albedo αi; RT is downward longwave radiation, ε is the surface emissivity, and σ is the Stefan–Boltzmann constant; SH and LH are the sensible and latent heat flux, respectively; QT is the total surface heat flux; Tsk,i and Λsk,i are tiled skin layer temperature and conductivity, respectively, and T1 is the upper ocean (or sea ice) layer temperature. In our case there are ocean tiles only.
The one-dimensional ocean model is based on the hydrostatic equation, conservation of temperature T and salinity S [Eqs. (8) and (9)], the momentum equations [Eqs. (6) and (7)], and the equation of state ρ = ρ(T, S, ρ) [polyEOS80-bsq function in Fofonoff and Millard (1983)]:
ut=zAvmuz+fυ,
υt=zAvmυzfu,
Tt=zAvtTz+1ρocpI(Fsol,z)z+QT,and
St=zAvtSz+EP,
where f is the Coriolis parameter as above, ρo is the ocean reference density (1035 kg m−3), and u and υ are the horizontal momentum components. The first terms on the right-hand side of Eqs. (6)(9) describe the effect of turbulent mixing on the ocean column; Avm and Avt are the vertical turbulent viscosity and diffusivity coefficients, respectively. The coefficients have to be determined via a turbulence closure paramterisation scheme, which is described below. In the one-dimensional model, vertical turbulent mixing is the only parameterized process. The term I(Fsol,z) is the penetrative part of the surface solar radiation, and EP is the freshwater flux at the ocean surface from evaporation and precipitation. Nudging to reference profiles is, at the moment, not implemented in the model. Scannell and McPhaden (2018) find horizontal advection to play only a very minor role in the heat budget, which justifies the use of the 1D model without applying large-scale forcing at this location.
At the coupling interface between the atmosphere and the ocean, the ocean receives wind stress, turbulent, and radiative surface fluxes (split into solar and nonsolar), and the freshwater budget from the atmosphere. This impacts the boundary conditions of the ocean according to the following equations, where z is the depth of the column, and τu and τυ are the horizontal wind stress components:
Avmuz=τuρ0,
Avmυz=τυρ0,
AvtTz=Qtρ0cp,and
AvtSz=(EP)S0ρ0.

The subscript 0 denotes the surface layer. The setup of the SCM and the processes relevant to this study are schematically shown in Fig. 2.

Fig. 2.
Fig. 2.

Schematic of the coupled ocean atmosphere SCM version of EC-Earth used in this study. We force the atmosphere with temperature, moisture, and momentum advection. At the interface between the atmosphere and the ocean the model components exchange fluxes, among which the turbulent (latent and sensible heatflux: LH + SH) and radiative heat fluxes [shortwave (SW) and longwave (LW)] are indicated with arrows. The ocean further receives momentum forcing from the atmosphere (τ), and mass fluxes (not indicated). In the ocean column, vertical mixing is the only parameterized process solved for with the TKE scheme (MixTKE).

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

Turbulent vertical mixing in the ocean

As mentioned above, the subgrid-scale parameterization of the ocean part of the SCM consists solely of turbulent vertical mixing. It is based on a turbulent kinetic energy (TKE) closure scheme (Blanke and Delecluse 1993; Gaspar et al. 1990; Madec et al. 2016), which solves for the turbulent coefficients Avt and Avm with the prognostic TKE equation:
e¯t=CWI|τ|ρ0+wLC3HLC+Avm[(uz)2+(υz)2]AvtN2+z(Avme¯z)Cεe¯3/2ldiss+CWFe¯exp(z)
The change of available TKE e¯ in time is the sum of the following contributions to the TKE budget, in the order of appearance on the right-hand side: production by wind input at the surface, Langmuir cell contributions, production by shear, destruction by stratification, vertical diffusion, Kolmogorov dissipation, and internal and surface wave breaking. In Eq. (14), CWI is a parameter for the wind input, |τ| is the wind stress, ωLC is the Langmuir circulation velocity, and HLC is the depth of the Langmuir cell. The Langmuir circulation strength is calculated according to
wLC=CLCussin(πzHLC),
with us = 0.377(|τ|)1/2; HLC is dependent on the column stability given by N2, and CLC is a coefficient influencing the circulation strength.
Furthermore, N2 is the Brunt–Väisälä frequency, and Cε and ldiss are the dissipation coefficient and length scale. The latter is calculated according to
ldiss=(2e¯/N2)1/2
and is furthermore bound by phyical considerations (e.g., the length close to the surface cannot be larger than the distance to the surface); CWF is the wave breaking coefficient indicating the fraction of energy that penetrates below the mixed layer.
The turbulent coefficients Avm and Avt, vertical eddy viscosity and diffusivity, are calculated according to Eqs. (17) and (18):
Avm=Cdifflmixe¯and
Avt=Avm/Prt.
Here, Cdiff is a coefficient for which the numerical value has to be derived from observations; it is related to the vertical eddy mixing efficiency (Gaspar et al. 1990). The term lmix is the mixing length across which the turbulence can act, equal to ldiss. The Prandtl number Prt in Eq. (18) is dependent on the Richardson number Ri = N2/(∂U/∂z)2, but in fact is equal to 1 in all cases considered. Hence, Avm and Avt have the same value.
Of the coefficients denoted by Ci, some are more certain than others. For example, Cε is generally agreed to take on the value 0.7 (Gaspar et al. 1990). Similarly, CWI (wind input coefficient) and CWF (wave fraction penetration below the mixed layer) are chosen to represent the average impact of medium-aged waves. The Langmuir coefficient, on the other hand, is set to 0.15 as a default but can assume values up to 0.45 (Axell 2002). The value of Cdiff can be estimated according to
Cdiff=0.5γPrtCε,
where Cε = 0.7 and Prt = 1. For the ocean vertical mixing efficieny γ, observational estimates exist. From these measurements it results that Cdiff can assume values between 0.035 and 0.28 (Gaspar et al. 1990). Osborn (1980) estimates Cdiff = 0.07, Oakey (1982) finds Cdiff between 0.04 and 0.13, Moum et al. (1989) suggest a value between Cdiff = 0.04 and 0.17, Lilly et al. (1974) find γ = 0.33, and therefore Cdiff = 0.1, and Weinstock (1978) suggests Cdiff = 0.28. The default value in NEMO, Cdiff = 0.1, is on the lower end of the possible values for Cdiff. Considering the large observational uncertainty, we propose experiments investigating the climate system sensitivity of this parameter.

3. Experimental setup

The SST bias in CGCMs typically peaks in boreal summer, coinciding with the period of rapid observed cooling. We first examine whether the SCM displays similar behavior, focusing on June, when the observed cooling is strongest and the bias begins to develop. We perform an ensemble of five simulations for the years in which there are high-temporal-resolution buoy observations available (2014–18).

To account for large-scale circulation impacts, the SCM is forced with horizontal wind, temperature, and moisture advection. This forcing is extracted from 3-hourly ERA-Interim data (Dee et al. 2011) from the grid point closest to the buoy. The grid point is approximately 50 km away (5.96°S, 8.44°E). We assume that the large-scale circulation in the region is spatially homogeneous enough to justify using the data of this grid point for forcing the experiments, rather than averaging over a box around the buoy. Additionally, the vertical profiles of wind, temperature, and moisture above 3 km are nudged to ERA-Interim profiles with a relaxation time scale τa = 6 h. This ensures realistic evolution of the atmosphere, while leaving sufficient freedom in the marine boundary layer. ERA-Interim data are used to validate the atmosphere column simulation. Additionally, we use high-temporal-resolution shortwave radiation data from the buoy.

For the ocean initialization we use daily vertical temperature and salinity profiles from the PIRATA buoy (Servain et al. 1998; Rouault et al. 2009). Temperature data are available down to 500 m, and salinity down to 120 m. Below these depths, we extend the profiles with monthly mean profiles from the ECMWF ocean reanalysis system ORAS4 (Balmaseda et al. 2013). These are adjusted to match the bottom temperature and salinity of the buoy data. From there the ocean evolves freely throughout the simulation, without nudging to reference profiles. Chlorophyll data from Sea-viewing Wide Field-of-view Sensor Ocean Color Data from the NASA Goddard Space Flight Center are used to take into account heating by solar penetration (NASA Goddard Space Flight Center 2014).

Sensitivity experiments

The sensitivity experiments performed for this study are listed in Table 1. Only settings that deviate from the control experiment are specified in the table.

Table 1.

Sensitivity experiments performed with the coupled SCM, and their overall root-mean-square SST and surface shortwave radiation (SSR) biases with respect to PIRATA observation. The upper part of the table lists experiments with changes in the atmosphere, and the lower part lists experiments with changes in the ocean. All experiments are performed for the period of 1–30 June 2014. For the sweeps we note the minimum RMSE at optimal parameter value (marked with asterisks).

Table 1.

First, we test the impact of atmospheric biases on SSTs. We perform a simulation in which we replace the shortwave radiation the ocean receives with observed shortwave radiation from buoy data (experiment “Shortwave”).

Furthermore, to test the contribution of other surface fluxes we perform an experiment in which we nudge the horizontal wind components, as well as the temperature and moisture profiles from ERA-Interim down to the surface with a relaxation time scale that is equal to the model time step (15 min; “UVTQ ERA”). In two separate experiments we nudge only the horizontal wind components to ERA-Interim profiles and T and Q to control profiles, and vice versa (experiments “U,V ERA” and “T,Q ERA”).

Second, we perform sensitivity experiments in which we test the intrinsic ocean contribution to the SST bias. In the absence of advection, we focus on the parameterization of vertical turbulent mixing. Two coefficients in this scheme lend themselves for sensitivity experiments: CLC and Cdiff. Both parameters are highly uncertain, due to differing measurement results by which they are constrained. As mentioned above, CLC is set to 0.15 as a default, but can physically be as large as 0.54 (Axell 2002). In “CLC sweep” we perform a suite of sensitivity experiments in which we vary this parameter.

In the sensitivity experiment suite “Cdiff sweep” we test the impact of Cdiff by performing a sweep of SCM integrations in which we vary its value in the physical plausible possible range between 0.035 and 0.28 (see section 4a).

Last, we test the influence of ocean stratification on the calculation of the vertical turbulent coefficients. Stratification enters the computation of the turbulent coefficients via the Brunt–Väisälä frequency N2, the frequency at which a displaced mass element oscillates around its location in a static case; N2 is used to calculate the mixing length lmix, the distance across which the turbulent mixing can act [equal to the dissipation length scale ldiss; Eq. (16)]:
lmix=ldiss=(2e¯/N)1/2.
Via the mixing length, N enters into the calculation of the vertical eddy coefficients [Eq. (17)]. In the sensitivity experiment “NPIR2” we test the impact of (erroneous) model stratification on the SST bias. Instead of allowing the model to calculate N2 from its own active tracer profiles, we replace them with high-temporal-resolution profiles from observations. The replacement happens at the point where N2 is calculated exclusively, and is not equivalent to ocean nudging.

4. Results

a. Temperature bias in the single-column model

During the first four days of the simulation, the SCM ensemble follows the observed cooling very well (Fig. 3a). In that time, SST cool by almost a degree in both the observations and the model. However, the daily cycle is considerably stronger in the model than in the observations. Both the daily maximum and minimum SST are over/underestimated by the model.

Fig. 3.
Fig. 3.

Average SST at the buoy location at 6°S, 8°E in June for (a) 2014–18 and (b) 2014.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

After the initial phase, observed SST continue to decrease strongly, in total by almost three degrees at the end of the month. The model cools by less than two degrees. In a gradual build-up, the SST bias grows to 1.1°C at the end of the simulation. This bias is smaller than that of most state-of-the-art coupled GCMs, but it is only slightly smaller than the bias in the three-dimensional version of EC-Earth (Exarchou et al. 2017; Voldoire et al. 2019, and Fig. 1b). The SST bias in this region in initialized EC-Earth simulations grows to approximately 1°C during June (Deppenmeier et al. 2020).

For the sensitivity experiments in this paper, we choose a year that represents the ensemble average well. In 2014, model SSTs follow observed SSTs closely during the first five days (Fig. 3b). Daily maximum temperatures are overestimated, much like in the ensemble average. From day 6 onward, the SCM cannot reproduce the observed cooling. A warm SST bias builds up gradually, and reaches 2°C at the end of the month.

In the control simulation the SCM displays a root-mean-square error (RMSE) in atmospheric temperature of 0.81°C and moisture excess of 9.2 × 10−4 kg kg−1 in the lowest kilometer of the atmosphere (see comparison of SCM and ERA-Interim in Fig. 4, upper panels). The qualitative evolution of both moisture and temperature is well captured by the model. The air cools and dries throughout June. However, in the SCM the atmospheric column is too warm and too moist. The wet bias is already present at the very beginning of the simulation, when SSTs are still very close to the ones observed. This indicates that it arises in the atmosphere. It is indeed also present in an atmosphere only (AMIP-type) simulation (not shown). The 10-m temperature warm bias grows with time, but the wet bias is largest in the beginning and remains relatively stable thereafter. Near-surface temperatures in an AMIP-type simulation are cooler than in the coupled simulation, especially after 5–10 days of runtime (not shown).

Fig. 4.
Fig. 4.

June 2014 (top) atmosphere specific humidity, (middle) atmospheric temperature, and (bottom) ocean temperature at the buoy location at 6°S, 8°E in June, with atmospheric data from ERA-Interim and ocean temperature from (left) PIRATA data and (right) as modeled by the SCM (control). Ticks on the right-hand sides of the bottom row indicate levels at which ocean data are available. Atmospheric data are available on the same model level heights for ERA-Interim and the SCM.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

Below the ocean surface, temperatures in the first 10 m decrease steadily throughout the month in the buoy measurements (Fig. 4, left-hand side of bottom panel). At depths between 10 and 30 m, the measurements show very short time scale variability, leading to rapid and short-lived deepening and shallowing of the thermocline. Near-surface ocean temperatures in the SCM also decrease, but less so than in observations. In the model, the thermocline deepens monotonically and diffuses throughout the month (Fig. 4, bottom panel right-hand side). This trend is not visible in the observational data. Similar to what we have observed for the daily cycle of SST, upper ocean temperature in the SCM displays a stronger diurnal cycle than the buoy data. In the model, a shallow warm near-surface layer of up to 10-m depth develops every day.

The control simulation surface fluxes show a relatively constant shortwave radiation input, and similarly constant radiative and turbulent cooling (Fig. 5). In total, the SCM surface fluxes warm the ocean. The observed cooling therefore must be a result of cooling from below, which in the absence of advection must be caused by vertical turbulent entrainment of cold water into the warm surface layer.

Fig. 5.
Fig. 5.

Control simulation (June 2014) surface fluxes, net shortwave (SW; red), net longwave (LW; blue), and the turbulent fluxes latent heat and sensible heat combined (LH + SH; green). Of the latter, latent heat is the much larger contribution. The sum of the surface fluxes is shown in black (TOT).

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

To summarize, the SCM performs very well during the first days of the simulation. Thereafter, it rapidly develops a SST bias very similar to that of its three-dimensional counterpart. Atmospheric moisture is overestimated from the beginning of the simulation, and surface atmospheric temperatures increase simultaneously with the SST bias.

In the following, we investigate different reasons for the model biases and possibilities to alleviate them. First, we focus on impacts arising in the atmosphere in section 4b, and then on the ocean model itself in section 4c.

b. Surface forcing

A possible explanation for the warm SST bias could be excess shortwave radiation, which artificially heats the sea surface. This has been suggested for the eastern boundary region in the Pacific Ocean (Ma et al. 1996) and might be true also for the Atlantic (Huang et al. 2007; Hu et al. 2011; Zuidema et al. 2016). We investigate this possibility with two approaches. First, we compare the surface shortwave radiation from the SCM to the buoy measurements, to establish whether a positive shortwave radiation bias is present.

At first glance, the surface shortwave radiation time series of the SCM seems to suffer from a shortage of radiation rather than a surplus on most days in the simulation (Fig. 6). However, the two datasets cannot readily be compared, because of their differing time resolution. Model data are available at 15-min intervals, whereas buoy data are provided at 2-min intervals. To eliminate the apparent differences arising from differences in temporal resolution, and therefore differences in the representation of intermittency, we compute daily integrals of shortwave radiation (Fig. 7). The integrated daily amount of surface shortwave radiation in the SCM is very similar to the one observed. The difference between the total energy input during the length of the simulation depends only slightly on whether the original 2-min data from PIRATA are used or whether PIRATA data are interpolated to the 15-min resolution of the SCM. In the latter case, energy input between the model and the observations only differs by 0.05%. In the former case the energy difference amounts to 0.5% excess in the SCM as compared to PIRATA, 2382 kJ over the entire month. This difference is due to the high intermittency of observed surface radiation, which cannot be matched by the SCM output frequency. However, the excess shortwave radiation cannot account for the SST bias. An estimate of the SST tendency term due to heating ∂T/∂t = Q/(wcp), with an assumed seawater density ρw of 1020 kg m−3, a specific heat capacity cp of 4000 J kg−1 K−1, and a very shallow mixed layer depth h of 20 m, shows that the order of magnitude of heating due to this excess is 0.03°C. The surface solar radiation bias, hence, cannot explain the warm SST bias, which is larger by almost two orders of magnitude. This conclusion is consistent with those of other studies using EC-Earth (Exarchou et al. 2017; Voldoire et al. 2019; Deppenmeier et al. 2020).

Fig. 6.
Fig. 6.

Downward shortwave radiation from the PIRATA buoy and from the SCM control run, at 2- and 15-min temporal resolution, respectively.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

Fig. 7.
Fig. 7.

Daily integrals of the downward shortwave radiation flux during June from the PIRATA buoy from data received at 2-min intervals, the same interpolated to model time-step resolution of 15 min, and from the SCM control run.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

Atmospheric sensitivity experiments

Even though the difference in surface shortwave radiation is small, feedbacks involving it could still influence the SST bias. To test this hypothesis, we perform a coupled simulation in which the ocean receives observed shortwave radiation, instead of the one calculated by the atmospheric component (experiment “Shortwave”). Consistent with the conclusion from the shortwave radiation analysis, the SST bias in this simulation does not reduce. The SST evolution is hardly influenced during the time of the simulation (Fig. 8, green line). This solidifies the notion that surface shortwave radiation is not the main origin of the warm SST bias in the southeastern part of the cold tongue.

Fig. 8.
Fig. 8.

SST as simulated by the various atmospheric experiments described in the upper part of Table 1. The black line shows observed SST for comparison.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

In section 4a, we have seen that the near-surface atmosphere in the SCM is warm and wet biased. Both these biases could be a cause or consequence of the warm SST bias. To determine the impact of atmospheric biases on the SST bias, we investigate sensitivity experiments in which the atmosphere is unbiased (with respect to ERA-Interim). In this experiment (“Atm ERA”) the SST bias reduces from 1.25° to 0.69°C. The observed cooling now matches for approximately 10 days of the simulation (Fig. 8, red line). After that, the steep observed cooling can, again, not be reproduced by the model.

The reduction of SST bias is notable, however, and we investigate the cause further. A possible reason for the warm SST bias originating in the atmosphere is reduced forcing of the ocean due to underestimated winds. This theory has recently been supported by Xu et al. (2014b) and Voldoire et al. (2019). We test the influence of wind biases on the SST bias in the U,V ERA experiment. The wind forcing hardly impacts the simulation (Fig. 8, purple line). The SST RMSE decreases only by 0.05°C. Voldoire et al. (2019) show EC-Earth to be the least sensitive CGCM to the wind stress replacement. This is due to the small wind stress bias in the model compared to ERA-Interim. In the SCM, the wind stress bias is also small. As a consequence, wind stress nudging mostly changes the direction of the wind, but does not enhance its amplitude (not shown). Because the wind bias is small to begin with, this experiment does not much impact the surface flux budget (Fig. 9b) and hence has a very small impact on the RSME SST.

Fig. 9.
Fig. 9.

(a) Surface fluxes as in Fig. 5, net surface shortwave radiation in red, net surface longwave in blue, turbulent fluxes in green, and total sum of fluxes in black/gray for the control experiment (solid lines), Atm ERA (dashed lines), T,Q ERA (dotted lines), and U,V ERA (dash–dotted lines. (b) The relative change of integrated surface fluxes with respect to the control experiment, in percent. Colors are as in (a). Note that because of the sign convention an increase in turbulent as well as longwave radiative flux translates to an increased in cooling.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

The atmosphere furthermore exerts influence on the ocean surface via surface-level temperature and moisture, which impact the surface flux budget. It has recently been suggested that atmospheric moisture is a major cause for the warm SST bias (Hourdin et al. 2015). In the T,Q ERA experiment we remove the model bias of temperature and moisture with respect to ERA-Interim. This experiment is able to almost reproduce the cooling of Atm ERA. The SST RMSE in this simulation is reduced to 0.69°C.

In both experiments in which moisture and temperature are adjusted, an increase in turbulent surface fluxes drive the SST cooling by reducing the total surface flux going into the ocean (Fig. 9). The turbulent fluxes cool considerably more when atmospheric temperature and moisture are improved. The total surface flux in the sensitivity experiments with the latter variables from ERA-Interim even changes signal, and now cools the ocean rather than warming it, as in the control.

We have demonstrated the impact of the (near surface) atmosphere conditions as well as shortwave radiation on the SCM SST bias. While shortwave radiation is modeled accurately at the location of the buoy, the warm and moist near surface air bias contribute to the warm SST bias. In bias-reduced atmosphere simulations it is possible to reduce the SST RMSE from 1.25° to 0.69°C. This is a considerable reduction, but a sizeable SST bias remains, even if the atmosphere is unbiased. The origin of the remaining bias lies in the ocean interior. Hence, in the following section, we will turn our attention to the ocean.

c. Ocean model

Entrainment of cold water by turbulent vertical mixing plays a large role in the tropical upper ocean heat budget (Foltz et al. 2003; Moum et al. 2013; Hummels et al. 2014; Scannell and McPhaden 2018). If this process is underrepresented, due to, for example, inadequate parameterization, it can lead to warm SST biases. Too little cold water could be entrained into the shallow mixed layer from below, leading to insufficient cooling. In this section we examine influences on vertical turbulent mixing in the upper ocean and their effect on the SST.

The TKE scheme, as described in section 2, adds the contributions to the available TKE, and then infers the turbulent mixing coefficients, which determine mixing in the ocean column. The first source term of TKE is the Langmuir cell parameterization.

1) Langmuir circulation

Langmuir circulation is dependent on wind input at the surface, and the stability of the ocean column. Langmuir circulation can be an important contribution to entrainment by cool water at the bottom of the mixed layer (Skyllingstad and Denbo 1995). They appear generally above wind speeds of 3 m s−1 (Talley 2011), which is frequently crossed in our simulations (not shown). The strength of the parameterized circulation is dependent on the coefficient CLC, which has been set to 0.15 by Axell (2002). Its value can be increased, but the recommendation is to keep it below 0.54. Here, we test the whole parameter space between the two values.

Overall, there is a slight decrease in SST RMSE with increasing Langmuir coefficient (Fig. 10, green circles). It is notable, however, that the RMSEs between values of CLC = 0.15 and 0.45 are noisy, rather than showing a clear tendency. SST RMSE only decreases more consistently at values larger than 0.45. From the shape of the curve no clear recommendation can be made for the value of CLC, although higher values might be preferred, rather than the very low default value.

Fig. 10.
Fig. 10.

Root-mean-square SST errors in the parameter sweeps for CLC and Cdiff.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

2) Vertical mixing efficiency

Next, we test the response to increasing the vertical mixing efficiency in the TKE scheme. The vertical mixing coefficients Avt and Avm depend on Cdiff that represents the ocean mixing efficiency [Eqs. (17)(19)]. This factor is loosely constrained by measurements, but can assume values between 0.035 and 0.28. Here, we test the parameter space in the same manner as in section 1.

The SST RMSE is very sensitive to the value of Cdiff (Fig. 10, blue circles). At the default value Cdiff = 0.1, the RMS SST bias has a value of 1.25°C. At lower values (i.e., at less efficient mixing) the bias is even larger (up to 1.87°C at lowest Cdiff = 0.035), growing with decreasing Cdiff. SST RMSE values decrease rapidly with increasing Cdiff. The minimum bias is reached at Cdiff = 0.23; the bias then amounts to only 0.32°C. This is a reduction of 74% of the default bias. Between values of 0.2 and 0.25 for Cdiff, the bias is relatively stable and very low. When Cdiff is increased further, the SST RMSE increases again. This is due to the model sea surface then becoming too cold, leading to a cold bias with respect to observations.

At the optimal value for Cdiff, model SST follow observations well (Fig. 11, purple line). Enhancing turbulent vertical mixing in the ocean column within the physically plausible range can reduce the SST bias to approximately a quarter of its original amplitude. The parameter change in Cdiff enhances the turbulent heat flux (THF) across the mixed layer from 10.3 to 21.5 W m−2 [estimated from ∂T/∂t = Qnet + THF/(ρcph), with ρ = 1024 kg m−3, cp = 4000 J kg−1 K−1, and the mean diagnostic mixed layer depth h = 25]. This is in good agreement with values reported in the literature by Foltz et al. (2018) and Scannell and McPhaden (2018).

Fig. 11.
Fig. 11.

SST as simulated by the various oceanic experiments described in the lower part of Table 1. The black line shows observed SST for comparison.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

In the ocean column, the warm top layer formation is reduced with the optimal Cdiff as compared with the control (Fig. 12, bottom row), but not entirely removed. The diurnal cycle remains too strong compared to observations (as is also evident from SST; Fig. 11). Short time scale subsurface temperature variability as observed in PIRATA data (Fig. 4) is not present in the model, despite the increased vertical mixing activity.

Fig. 12.
Fig. 12.

(top) Atmospheric moisture, (middle) temperature, and (bottom) upper ocean temperature in (left) the control experiment and (right) at ideal Cdiff.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

Consistent with the cooler SST, near-surface atmospheric temperatures are also decreased. However, higher up the atmosphere strongly warms as compared to the control (Fig. 12, center row). The atmosphere was warmer than ERA-Interim to begin with (Fig. 4) and hence this is a degradation of model performance. The overestimation of near-surface moisture is increased near the surface, and aloft a dry region forms that is not observed in ERA-Interim. These atmospheric changes consistently occur in an AMIP-type simulation forced with observed SST (not shown). They are hence intrinsic to the atmospheric component of the coupled model, which is not the focus of the current study. Further investigation of this behavior might be the focus of an atmospheric study.

Surface fluxes along the Cdiff sweep decrease (Fig. 13). The higher Cdiff is, the cooler the sea surface, and as a consequence both the turbulent fluxes and the longwave radiation flux decrease. Shortwave radiation also decreases, although it is more complicated to place this decrease. Cooler surface temperatures might lead to more stratocumulus cloud cover due to increased boundary layer stability, but the response of clouds to the SST is very noisy. The dominant cloud type in the simulations is shallow convection cumulus, which reacts strongly to perturbations of SST in AMIP-type runs due to their chaotic nature (not shown). Considering that shortwave radiation is not overstimated in the control (Fig. 7), the reduced shortwave radiation with increased Cdiff is not a model improvement. However, it positively influences the SST bias.

Fig. 13.
Fig. 13.

Integrated surface fluxes over the time of the simulations in the Cdiff sweep. Turbulent components latent and sensible heat fluxes are combined in green; the radiative components shortwave and longwave are shown in red and blue, respectively.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

3) Vertical mixing efficiency in changed setting

We have demonstrated the beneficial effect of increasing the vertical ocean mixing on reducing RMSE SST. Setting Cdiff to a value twice as large as the default value, but still within the plausible physical range, results in a realistic simulation of SST. We have also demonstrated beneficial impact of correctly modeled near-surface temperature and moisture in the atmosphere. We wonder whether already improved simulations (such as Atm ERA) are less sensitive to the value of Cdiff. Therefore, we perform another set of parameter sweeps along the values of Cdiff for the nudged atmosphere experiment, and additionally for the shortwave forcing experiment.

Figure 14 shows SST RMSE depending on the value of Cdiff. The RMSEs have been fitted with a cubic function, and stars mark minimum values on the curve. All three sweeps reach a minimum in the Cdiff range between 0.2 and 0.25, and the RMSEs at their respective ideal Cdiff values are very similar. The lowest RMSE value is obtained when the atmosphere is nudged to the surface (Fig. 14, red). This suite is also least dependent on the value of Cdiff, as indicated by the relatively flat curve. Since the sea surface is already beneficially influenced by cooler near-surface temperatures in the atmosphere, the SST bias does not reach values as high as in the control.

Fig. 14.
Fig. 14.

Root-mean-square SST errors in the parameter sweeps for Cdiff, with cubic fits. Stars mark the minimum SST RMSE on the fit.

Citation: Journal of Climate 33, 14; 10.1175/JCLI-D-19-0608.1

All three curves, whether for the coupled simulation, the atmosphere nudged to the reanalysis state, or the shortwave radiation used from observations, reach their minimum around the same value of Cdiff, between 0.20 and 0.25 (Fig. 14). The SST biases obtained at these Cdiff values are very small, meaning that the summertime SST cooling is well represented. This highlights the dominant effect of vertical turbulent mixing on the ocean cooling. When there is enough vertical mixing, other factors, such as an improved atmosphere, do not much improve the simulation anymore. This result is hence a very strong indication of the importance of vertical turublent mixing, and implies that the value for Cdiff should be increased in three-dimensional simulation. Although the mean bias reduces, the intermittency of the ocean is not captured.

4) Stratification

We have established in section 4a that modeled SST as well as the upper 10 m of the ocean column display a stronger daily cycle than observed (Figs. 4 and 8). This warm top layer artifically stabilizes the ocean column. Ocean stability enters the TKE scheme in the form of the Brunt–Väisälä frequency N2 with a negative sign [Eq. (14)]. Increased stratification reduces the TKE available to create vertical ocean mixing. Furthermore, the stability enters into the calculation of the mixing length lmix [Eq. (16), and lmix = ldiss]. When e¯ decreases as a result of large N2, lmix decreases. Additionally, with lmix ∝ 1/N, the mixing length decreases even more. The term lmix enters into the calculation of the turbulent eddy coefficients via Eqs. (17) and (18). All of these effects cause vertical ocean mixing to decrease with increasing stratification.

Here, we test the effect of stratification on the ocean vertical mixing and on the SST bias. We replace model temperature and salinity with those from high-temporal-resolution PIRATA observations, which are less stratified. As a result, turbulent vertical mixing is increased (not shown). The enhanced mixing leads to a considerable reduction of the SST RMSE from 1.25°C in the control to 0.89°C in NPIR2. The SST bias is decreased by almost a third. This highlights the impact stratification asserts on ocean vertical mixing. In the SCM, a positive feedback loop involving stratification and vertical mixing likely grows the SST bias. Vertical mixing is insufficiently strong in the beginning, which leads to increased stratification. The ocean stability in turn reduces the TKE, which further decreases vertical mixing.

In the sensitivity experiment, Avt is less intermittent in the upper 5 m than in the control simulation (not shown). The continuously active mixing also occasionally penetrates the upper 10 m of the column, and toward the end of the simulation (day 25) displays very short term, but strong bursts in the upper 20 m. The effect of the enhanced mixing activity on SST is large (Fig. 11, green line). Especially after day 25, when “deeper” mixing bursts first occur, the sea surface cools considerably more than in the control simulation.

Note that the temperature and salinity fields used in this experiment contain high-frequency variability, for example from internal waves. The TKE parameterization includes a term for turbulence production by internal waves [see last term of Eq. (14)]. This could lead to double counting of this specific term on the one hand, and on the other hand some high-frequency variability from internal waves might be present in the 3D model that is absent in the SCM.

5. Discussion and summary

In this study, we use a coupled ocean–atmosphere SCM to investigate the warm SST bias in the tropical Atlantic Ocean. Such a bias establishes rapidly in three-dimensional coupled global circulation models throughout boreal summer. The warm bias is typically large in the southeast tropical Atlantic and occurs in most CGCMs.

We place the SCM at a PIRATA mooring location in the southeastern tropical Atlantic. This enables us to compare the model simulation to in situ point observations. For the average of the five years in which high-temporal-resolution buoy data are available, the SCM version of EC-Earth performs well in the first five days of the simulation. It then produces a SST bias very similar to that in the three-dimensional version of the model; the RMSE of the bias is 1.25°C. This makes the SCM a useful tool to investigate the origin of the bias and test possible ways to alleviate it.

For the case of 2014 we eliminate solar surface radiation as the main cause of the warm SST bias. This is in line with other studies (Exarchou et al. 2017; Voldoire et al. 2019; Deppenmeier et al. 2020). Forcing the ocean with observed surface shortwave radiation does not improve simulation of the SST. Note that the location in this study coincides with the trade cumulus region. Farther southeast, radiation may contribute to, or even be a main cause of, model biases. Near-surface temperature and moisture in the atmosphere, however, assert a considerable influence on simulated SSTs (producing an RMSE of 0.70°C, a reduction of 44%). Nudging winds to ERA-Interim profiles, on the other hand, hardly affects the SST. This is to be expected for EC-Earth, which has a relatively small wind bias (Voldoire et al. 2019).

While correcting the atmosphere improves the SST simulation, a sizable bias remains. We show that the bias can be reduced to a quarter of its original size by making physical changes in the ocean model alone. We increase the factor with which TKE is transformed to turbulence within its physical range by setting the vertical mixing efficiency coefficient Cdiff from its default value of 0.1 to its optimal value of 0.23. This reduces the SST bias to 0.34°C, the largest reduction we are able to achieve with any sensitivity experiment. Using the optimal value for Cdiff also improves the vertical ocean profile. A very stable and warm upper bias, visible in the control simulation, is reduced. However, the intermittency in observations is not captured, even in the experiments with highest mixing efficiency parameters. The large improvement of the ocean simulation with increased vertical mixing hints to vertical mixing being an underrepresented process in the SCM. Similarly, it is likely underestimated in the CGCMs, which use the same vertical mixing parameterization. It is, however, possible that part of the insufficient mixing in the SCM stems from neglecting remote forcing and equatorial/coastal wave propagation. Furthermore, mixing induced by shear variability deeper than the wind-driven shear might be underestimated in the current setup of the SCM in comparison the 3D model. Therefore, the ideal value in the SCM is not necessarily the ideal value for a CGCM. We recommend research aimed at improving vertical mixing parameterizations for other locations than the one explored here, as well as the impact of horizontal currents.

We test the influence of the Langmuir circulation coefficient. The model sensitivity to this parameter is much smaller than that to Cdiff, and there is no clear optimal value for CLC.

Furthermore, calculating vertical eddy coefficients with the correctly stratified profiles reduces the SST bias to 0.89°C. Upper ocean mixing is increased with the correct profiles, which reduces the SST bias. The artifical stable stratification in the control simulation leads to decreased mixing, which in turn leads to more stable stratification. This is a positive feedback that worsens the bias. Most likely, initial ocean vertical mixing is too low in the model, which then leads to the artificially stable column. This could hence be alleviated with an increase in the mixing efficiency.

In further experiments, we have also tested the maximum solar penetration depth, which has recently been suggested to assert large influence on SST (Exarchou et al. 2017). In this study, however, we find no reduction of the bias by increasing the depth from 23 m to either 30 or 50 m.

In this study, we demonstrate that both the atmosphere and the ocean contribute to the warm SST bias in the southeastern tropical Atlantic. We show that the bias can be considerably reduced by enhancing the vertical ocean mixing efficiency within its physically plausible range. The climate sensitivity to the ocean vertical mixing parameterization in the fully coupled global model EC-Earth is tested in a separate study (Deppenmeier et al. 2020) in which impacts on the atmospheric circulation and projected climate change are shown. More observations to better constrain the parameter Cdiff are desirable, so that it can be confirmed whether the larger value is indeed more appropriate for modeling ocean vertical mixing.

Acknowledgments

This study was supported by the EU FP7/2007–2013 PREFACE Project under Grant Agreement 603521. We acknowledge the GTMBA Project Office of NOAA/PMEL for the freely available PIRATA mooring data used as model forcing and for comparison. We acknowledge Kerstin Hartung for valuable collaboration and for help with identifying optimal settings for the SCM at this location.

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