Feedback of mesoscale ocean currents on atmospheric winds in high-resolution coupled models and implications for the forcing of ocean-only models

The repercussions of surface ocean currents for the near-surface wind and the air-sea momentum flux are investigated in two versions of a global climate model with :: an : eddying ocean. The focus is on the effect of mesoscale ocean current features at scales of less than 150 km, by considering high-pass filtered, monthly-mean model output fields. We find a clear signature of a mesoscale oceanic imprint in the wind fields over the energetic areas of the oceans, particularly along the extensions of the western boundary currents and the Antarctic Circumpolar Current. These areas are characterized by a positive correlation 5 between mesoscale perturbations in the curl of the surface currents and the wind curl. ::::::: Coupling :::::::::: coefficients ::::::: between ::: the :::: curl :: of ::: the :::::: surface ::::::: currents :::: and ::: the ::::: wind ::: curl :::: are :::::::: estimated ::::: using ::::: linear :::::::::: regression. The coupling coefficients are spatially nonuniform and show a pronounced seasonal cycle. The positive feedback of mesoscale current features on the near-surface wind acts in opposition to their :: the ::::::::::::: current-induced : damping effect on the wind stress. :::::: surface ::::: stress. :::: The ::::::::::: current-wind :::::::: feedback ::: thus ::::::: reduces ::: the :::::::::: well-known :::::::: damping :: of ::::::::: mesoscale ::::: eddies ::: by ::: the ::::::::::: current-stress ::::::::: interaction :::: that :: is :::::::: typically :::::::: accounted ::: for ::: by 10 :: the ::::: usage ::: of ::::::: ’relative ::::: winds’ :: in ::: the ::::::::::::::: stress-formulation :: of ::::: many ::::::: models. : A tentative incorporation of this feedback in the surface stress formulation of an eddy-permitting global ocean-only model leads to a gain in the kinetic energy of up to 10, suggesting a fundamental shortcoming of present ocean model configurations. :::: more :::::::: accurate ::::::::: mechanical :::::: surface :::::::: coupling ::::: when ::::::::: comparing :: to :::::: coupled ::::::::::: simulations.

Ocean Sci. Discuss., doi:10.5194/os-2017Discuss., doi:10.5194/os- -24, 2017 Manuscript under review for journal Ocean Sci. Discussion started: 12 April 2017 c Author(s) 2017. CC-BY 3.0 License. and eddy kinetic energies of an eddy-permitting global ocean model, based on a tentative implementation of the diagnosed spatially-variable, monthly-mean distribution of the current-wind coupling in the bulk surface stress formulation. 15 2 Methods & Models

Methods
Both atmospheric surface winds and ocean-surface currents determine the surface stress where ρ a is air density, C D the drag coefficient (note that C D also depends on the choice of α as |U − αu| is used for the calculation), U the 10m wind , u the ocean surface current and α a parameter representing the influence of ocean currents. 20 Note that we chose to use the wording 'surface stress' instead of the more commonly used 'wind stress' as the stress is not entirely determined by the wind. Since the wind speed is typically an order of magnitude larger than the ocean current speed, the challenge is to detect the imprint of ocean currents in the surface stress. Fortunately the inherent spatial and temporal scales of the atmosphere and the ocean are very different. While at mid-latitudes atmospheric mesoscale variability is typically associated with time scales of hours to days and spatial scales of hundreds to thousands of kilometers, the oceanic variability 25 is most energetic at time scales of days to weeks with spatial scales of tens of kilometers.
For assessing the imprint of the oceanic variability, we use monthly-mean model output from coupled atmosphere-ocean and forced ocean-only simulations and apply a spatial Hann-type high-pass filter to remove variability on scales longer than approximately 150km (see Appendix A for discussion of this choice and associated sensitivities). Model output closer than 30 150km to the coast is neglected as orographic and coastline effects may also introduce small-scale distortions to the wind (Perlin et al., 2007;Renault et al., 2016a).
The smallest spatial scales present in the data are emphasized further by considering the curl of the wind, of the surface stress and of the ocean surface currents in the quantification of the current-wind and current-stress linkage. Assuming linear relationship in the form the coupling coefficients s st and s w are estimated by linearly regressing the stress curl/wind curl as a function of the oceanic current vorticity. We note that other studies used bin averaging for the same quantities (Renault et al., 2016b), and for the relationship between the SST gradient and the wind curl or wind gradient (Chelton et al., 2007); however, a bin averaging was not found to be necessary here. Note also that the factor 10 2 is simply used to get coupling coefficients of O(1).
As a means to account for the partial re-energisation of the near-surface winds in the atmospheric forcing of uncoupled ocean models, Renault et al. (2016b) proposed to tweak the bulk formulation of the surface momentum flux by using (1) with α = 1 − s w . From their regional model results Renault et al. (2016b) estimated an s w = 0.23 ± 0.01 for the CCS. We extend this approach here by estimating the spatial distribution of the coupling coefficient s w from two global coupled simulations.
We then proceed to test the suggestion of Renault et al. (2016b) by forcing a set of global ocean-only simulations using (1) 15 with a spatially-varying parameter α in comparison to the classical 'absolute wind' and 'relative wind' forcing formulation.

Models
The coupled experiments GC2-N512 (hereafter C1/4) and GC2.  (Smith, 1988) with Charnock's coefficient of 0.018, with coupling frequencies of 3-hourly (for C1/4) and 1-hourly (for C1/12). For an extensive documentation of the model configurations and a discussion of the impacts of a resolved ocean mesocale in the simulations we refer to Hewitt et al. (2016). A discussion of the impact of the oceanic mesoscale on the thermal air-sea interaction, i.e. the SST -surface stress relationship, has been given by Roberts et al. (2016).
Here we consider the interaction due to momentum transfer at the oceanic mesoscale. The models were integrated for 19 years 25 (year 20 experienced some data loss), the last 15 years are used for the analysis. Even if 20 year runs might be too short for the deep ocean to spin up, they are sufficient for the surface coupling investigated in this study.
The ocean-only experiments are based on NEMO (version 3.4) in an ORCA025 configuration. This configuration uses a tripolar grid at a nominal resolution of 1/4 • , and 46 vertical levels with a resolution of 6m near the surface and 250m at 30 depth. Surface-forcing fields build on the Coordinated Ocean-Ice Reference Experiments (CORE, Large and Yeager, 2009;Griffies et al., 2009) and have a spatial resolution of 2 • . Turbulent air-sea fluxes are calculated using the bulk formulae given by Large and Yeager (2004). The experiments were started from a 30-yr spinup  and then carried out through 1989-2004. Four forced experiments were performed: with absolute winds (F α=0 ), relative winds (F α=1 ), and two experiments that use spatially and temporally variable α given by the distribution of the coupled experiments C1/4 (F α=C1/4 ) and C1/12 (F α=C1/12 ). Further details are given in the next section. The analysis uses the last 15 years of each integration.

Ocean current feedback on near-surface winds
Generally the momentum exchange between atmosphere and ocean is from the atmosphere to the ocean. In forced ocean models we find that for high-pass filtered data there is no relation between the curl of the surface current and the curl of the near-surface winds (Fig. 1 a). In coupled models, the surface stress also acts as the bottom boundary condition for the atmo-   s w ≈ 0.31 (C1/12).

30
The seasonality in the coupling coefficient and the different behaviour between GS and ACC regimes can be rationalized in terms of the stability of the near-surface atmosphere, as given by the vertical temperature gradient between 20m and 53m ( Fig.   3 red curves). The relationship between the atmospheric stability and the coupling coefficient s w suggests that the influence of the ocean surface currents is spread over a deeper atmospheric layer when its stability is weak. More specifically, for the GS region cold winds from the continent during winter lead to strong turbulent heat fluxes over the Gulf Stream that destabilize the near-surface atmosphere, reflected by a negative vertical temperature gradient. This implies that the partial re-energisation of the winds (due to the presence of ocean currents) in winter happens over a deeper layer than during summer when the near-surface atmosphere is stable (positive vertical temperature gradient). Accordingly the change in the near-surface wind 5 is smaller in winter as the gain of momentum is distributed over a deeper layer, resulting in a smaller s w than in summer.
During summer months the near-surface layers are relatively shallow which leads to stronger changes in near-surface winds due the presence of ocean currents, i.e. larger s w . While the amplitude of the seasonality is similar in the north-western Pacific  positive, resulting in a large mean s w and very little seasonal variability (Fig. 4). The lack of a seasonality in the near-surface 10 stability of the atmosphere also results in low correlation between the stability and s w .
The strength of the seasonal cycle of s w does vary with region. An illustration of the spatial distribution of the amplitude is given in Fig. 4, showing the temporal standard deviation of the monthly-mean values of s w . The main pattern is the contrast between the strong seasonality of the northern hemisphere WBCs and the core of the ACC reflecting the different seasonality 15 in the stability of the near-surface atmosphere. This is emphasized in Fig. 5, showing the correlation between the variability of s w and near surface stability (∂T /∂z).
The stability of the near-surface atmosphere tends to determine the strength of the coupling coefficient s w . Over the WBCE regions the variability of the near-surface stability is high and with that the variability of the coupling coefficient s w is also high. Positive correlations in Fig. 5   discussed in Appendix A.
The effect of the partial re-energisation of the atmospheric winds due to the influence of ocean surface currents in the surface 10 stress estimation is missing in the forcing formulation currently used for ocean-only models. Renault et al. (2016b) suggest to modify the velocity used in the bulk formulation (1) by U + s w · u − u, so that the wind U is re-energised by s w · u, where u is the ocean current velocity. We then use α = 1 − s w in (1) to force ocean-only models. As a test of its potential use in forced ocean-only models, following the suggestion of

Imprint of ocean surface currents on the surface stress
The presence of ocean surface currents is accounted for in the surface stress formulation (1

Assessment of impacts in a forced ocean model
The strength of the coupling between the curl of the ocean current and the curl of the surface stress (i.e., the choice of α) has implications for the ocean energetics. The part of the surface stress that is due to ocean surface currents acts as a damping mechanism for surface currents, hence for a larger α we expect to get a stronger damping, i.e., a weaker EKE. This is illustrated in Fig. 10a, by depicting the surface EKE (derived from the velocity deviations from annual mean velocity, based on time 5 series of 5-day mean values) over the Gulf Stream. F α=1 (F α=0 ) produces the lowest (highest) level of EKE, while F α=C1/4 and F α=C1/12 lie in between, relatively, close to F α=1 . A spatial view is given by a meridional section in the Pacific composed of a section through the Kuroshio Extension region at 218 • W and a section cutting through the equatorial and ACC region at 175 • W (Fig. 10 b). EKE levels are everywhere largest for F α=0 and smallest for F α=1 , while F α=C1/4 and F α=C1/12 values lie in between. More specifically, regional averages in EKE and mean kinetic energy (MKE) for F α=C1/4 (F α=C1/12 ) show 10 increases by 6% (6%) and 1% (1%) in the ACC, 12% (9%) and 2% (5%) in the Kuroshio, 15% (16%) and -1% (-1%) in the Gulf Stream, and 14% (12%) and 9% (8%) in the equatorial region (±5 • off the equator). A switch from relative to absolute winds shows even stronger changes in EKE and MKE. Direct comparison of EKE to the coupled simulations is not meaningful
here because differences in resolution and frequency of wind forcing (Hughes and Wilson, 2008;Zhai et al., 2012) and details of the ocean configurations account for larger differences in EKE than the choice of α.

Discussion
In two coupled high resolution ocean models, we find a linkage between ocean surface currents and surface winds with pronounced spatio-temporal variability. The strength of the coupling coefficient s w appears strongly affected by the atmospheric 5 stability. The present results extend the findings of the regional model study of Renault et al. (2016b) to the global oceanatmosphere system. By including this feedback in the bulk formulation of the momentum flux (1), with α = 1 − s w , using the spatially and temporally varying coefficient s w estimated from the coupled models, the forced models appeared to capture 13 Ocean Sci. Discuss., doi:10.5194/os-2017Discuss., doi:10.5194/os- -24, 2017 Manuscript under review for journal Ocean Sci. Discussion started: 12 April 2017 c Author(s) 2017. CC-BY 3.0 License. We note several limitations of the method applied here: (1) For small curls of the ocean currents, the coupling coefficients appear to be biased, and cannot be robustly estimated (cf. Fig. A2).
(2) The temporal and spatial scales of the atmosphere and ocean are not entirely separated. Therefore the results slightly vary with the cut-off length of the filter. (3) The results may depend on the parameterization of the vertical momentum flux in the atmospheric model. Further research should examine turbulence resolving atmospheric models, perhaps in conjunction with prescribed ocean currents, to understand how the state of the atmosphere modifies the response of near-surface winds in the presence of ocean currents.
The simulations presented here clearly show an imprint of the ocean surface currents on the surface stress and the near-surface 5 winds. Estimates of surface stress (e.g., from scatterometer measurements) or the winds simulated in coupled simulations should thus be regarded as containing an imprint of the surface ocean state. Using either of these to drive an ocean-only model may have undesirable effects because it provides a spurious source of energy to the ocean model (Xu and Scott, 2008). On the other hand, in data sets produced for the forcing of ocean models (e.g. Large and Yeager, 2004;Brodeau et al., 2010)  sion of the 'relative winds'-formulation in the form of (1) with α = 1 − s w , using a variable coefficient s w in conjunction with winds from reanalysis products (where the atmosphere is forced only by SST) to force global ocean-sea ice models. The possibility of developing a parameterization for s w based on atmospheric state parameters needs to be explored in further studies.

Appendix A: Energy spectra
An inspection of high-resolution coupled model output (Fig. A1) suggests an upper bound of about 200km for the transition between wavelengths where the atmosphere is more energetic and wavelengths where the ocean is more energetic. We find that this scale separation is sometimes more pronounced and in some regions not even valid and show this exemplarily for three locations: in a large box in the South Pacific, the atmospheric velocity spectral density dominates at all scales; in a rather small freedom (DOF).
Given any three dimensional data set (two space and one time dimension) there will be coherence, meaning that time and space points can be dependent on each other. Therefore the DOF estimation needs to consider both temporal and spatial DOF. For the temporal DOF of freedom we follow Bretherton et al. (1999), estimating the ratio of effective sample size (ESS, N * ) to sample size N 25 N * /N = 1 − r 1 r 2 1 + r 1 r 2 , while r 1,2 is the lag-one autocorrelation for dataset 1,2. If only one dataset is used r 1 = r 2 . For the spatial DOF estimation we use an adapted binomial method (B-method) of Livezey and Chen (1983) and Wang and Shen (1999), where a random time series is correlated with every spatial point since by chance some points will give a significant correlation with that random time series, the points with significant correlation share coherence, which is exploited to estimate the coherence of the field.
To estimate the total DOF of the given three-dimensional (with two spatial and one temporal dimension t) climate data set we combine the spatial (DOF S ) and temporal DOF estimation DOF total = DOF S · t · N * /N (C3)