Sea waves impact on turbulent heat fluxes in the Barents 1 Sea according to numerical modeling

. This paper investigates the impact of sea waves on turbulent heat fluxes in the Barents Sea. The 10 COARE algorithm, meteorological data from reanalysis and wave data from the WWIII wave model results were 11 used. The turbulent heat fluxes were calculated using the modified Charnock parameterization for the roughness 12 length and several parameterizations, which explicitly account for the sea waves parameters. A catalog of storm wave 13 events and a catalog of extreme cold-air outbreaks over the Barents Sea were created and used to calculate heat fluxes 14 during extreme events. 15 The important role of cold-air outbreaks in the energy exchange between the Barents Sea and the atmosphere 16 is demonstrated. A high correlation was found between the number of cold-air outbreaks days and turbulent fluxes of 17 sensible and latent heat, as well as with the net flux of long-wave radiation averaged over the ice-free surface of the 18 Barents Sea during a cold season. 19 The differences in the long-term mean values of heat fluxes calculated using different parameterizations for 20 the roughness length are small and are on average 1-3% of the flux magnitude. Parameterizations of Taylor and 21 Yelland and Oost et al. on average lead to an increase of the magnitude of the fluxes, and the parameterization of 22 Drennan et al. leads to a decrease of the magnitude of the fluxes over the entire sea compared to the Charnock 23 parameterization.

exchange exists for the Barents Sea, although the importance of CAOs has been stressed earlier (Smedsrud et al., 122 2013).

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Furthermore, CAOs create favorable conditions for enhancing wind speed over water, which leads to further 124 intensification of the energy exchange. The wind speed increase is primarily associated with the formation of large 125 horizontal temperature gradients and strong baroclinicity. This can lead to the intensification of cyclones and 126 mesocyclones (Kolstad, 2015), formation of jets and wind shear along the lower tropospheric fronts (Grønas and 127 Skeie, 1999), convergence lines (Savijärvi, 2012), and low-level jets (Brümmer 1996; Chechin et al., 2013;Chechin 128 and Lüpkes, 2019). Although the highest wind speeds over the Barents Sea have the orographic origin (e.g., the 129 Novaya Zemlya Bora (Moore, 2013)), it was shown (Kolstad, 2015) that in cyclones, the wind speed reaches its 130 maximum value when intense cold advection takes place in their rear part. In addition, intense turbulent exchange in 131 the convective boundary layer effectively transports momentum down to the lower atmospheric layer increasing the 132 near-surface wind speed (Chechin et al., 2015).

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In this paper, we consider the influence of sea waves on turbulent heat fluxes in the Barents Sea. Heat fluxes 134 were calculated using the COARE 3.0 algorithm and NCEP/CFSR reanalysis data with the Charnock roughness

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In this work, the computations were made using the ST1 scheme (Tolman, 2014). To account for the 159 nonlinear interactions of the waves, the Discrete Interaction Approximation (DIA) model (Hasselmann and 160 Hasselmann, 1985) was used, which is a standard approximation for calculation of nonlinear interactions in all 161 modern wave models.

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To take into account ice effects on the wave development, the IC0 scheme was used, where the grid point is 163 considered as ice-covered if the ice concentration was larger than 0.25. Thus, the exponential attenuation of wave 164 energy adjusted for the sea ice concentration at a given point was added.

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In the shallow water, the increase in wave height as waves approach the shore and the related wave breaking 166 after waves reach the critical value of steepness were taken into consideration. The whitecapping effect taken into 167 account in the ST1 scheme. The standard JONSWAP scheme was used to take the bottom friction into account. The

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spectral resolution of the model is 36 directions (Dq = 10°), the frequency range consists of 36 intervals (from 0.03 to 169 0.843 Hz).

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The calculations were performed using the original unstructured grid, which is based on the bottom 171 topography data from ETOPO1 database and detailed nautical charts (Figure 1). This unstructured grid consists of    In this paper, we used the output results of the wave model with time step 3 hours from 1979 to 2017 for each 198 node of the unstructured grid.

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Based on the wave model results, a study of storm activity was carried out according to the POT (Peak Over  where α -Charnock parameter, ggravity acceleration, akinematic viscosity coefficient (Andreas, 1989).

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Equation (3) is the modified Charnock formula (Smith, 1988), in which the second term on the right side describes the where H ssignificant wave height, L pspectral peak wavelength.

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Here c p -phase wave speed associated with spectral peak, which is expressed through the wave length as  2017 (with a slightly better spatial resolution than CFSR, were interpolated from the ~0.2˚ grid to ~0.3˚ grid to match 257 the CFSR resolution. The wind speed was used at 10 m height, air temperature and humidity were used at 2 m height.

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Reanalysis data are also available at isobaric levels, the lower of which is 1000 hPa. However, we preferred to take

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Here, we define the CAO index I cao as the daily potential temperature difference between the ocean surface 287 and the 700 hPa height. For each day, I cao was averaged over the ice-free part of the Barents sea. Figure 3 shows the where the latter is the 30-day running multiyear standard deviation of I cao .

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The dashed curve in Figure 3 represents the threshold value + which we use as a criteria for CAO 297 identification, namely 298 (7)

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According to the criteria (7), we identify CAOs as those cases when I cao values are above the dashed curve in Also, an equally important parameter is the wavelength, which is used in the parametrizations O2 and D3. In

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The Barents Sea is characterized by a high frequency of storm wave events, which provide a long swell in the 330 extinction stage (i.e., "old seas") and limit the applicability of the Charnock formula. As shown in (Myslenkov et al., which is obviously associated with the reduced strength of the westerlies.

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A slight negative trend of the CAO days is seen in Figure 7. To a large extent, it can be explained by an

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The frequency of CAOs with easterly wind over the Barents Sea is significant and represent up to 16% of all 371 CAOs (Figure 8b). During CAOs, the highest frequency of occurrence have northerly (30%) and north-easterly (27%)

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winds. The wind rose in CAOs differs from the wind rose in all cases during the cold season (Figure 8a). In particular, 373 the prevailing wind direction over the Barents sea in winter is from the south. Moreover, the winds having southerly 374 and westerly components are the strongest.

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The CAOs role in the heat exchange between the Barents Sea and the atmosphere is demonstrated by Figure   376 9. The latter shows the turbulent fluxes of sensible and latent heat, and , respectively, the net longwave radiative

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We stress that the values of fluxes shown in Figure 9 are averaged over the ice-free part of the Barents Sea. It 393 is important to keep in mind that there is a large interannual variability of the area of sea ice cover in the Barents Sea.

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This is another important factor, along with the number of CAO days, influencing the heat loss.

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One might also expect that the ice edge retreat further north leads to a larger fetch over which the cold air

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It can be concluded that the mean pattern of heat fluxes in the Barents Sea is largely contributed by storms. cold-air outbreaks, as for storm waves, are several times smaller than when considering long-term means.

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The average values of the flux difference during cold-air outbreaks are smaller than during storms, but the

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The extreme values of the difference, which can reach 700 W m -2 , are also greatest in the case of 539 simultaneously observed storms and cold-air outbreaks. Figure 20 shows case when the difference in sensible heat

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We obtained the mean annual distribution of the height and wavelength in the Barents Sea from wave 570 modelling results. Estimates of the storm activity from 1979 to 2017 were also obtained, confirming its high 571 interannual variability. Based on the data of wave modeling, a catalog of storm waves with the wave height exceeding 572 5 m was created. This catalog was used to calculate heat fluxes during storms.

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The catalog of extreme CAOs over the Barents Sea was also obtained. It is shown that the extreme CAOs are with discrepancies in meteorological parameters reproduced by the CFSR reanalysis and locally observed on the ship.

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We estimated the algorithm error as 4 W m -2 for sensible heat flux and 8 W m -2 for latent heat flux, which is within 585 the accuracy of the eddy-covariance method during ship measurements.

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The parametrization, the degree of dependence in the former is lower than in the latter.

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The difference between the experiments with parameterization D3 and C55 is almost the same in all cases 610 and always decreases (modulo) from west to east of the sea, actually resembling the mean distribution of wave height.

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Experiments with parameterizations T1 and O2 deviate most strongly from the Charnok parametrization in those areas