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The response of the atmospheric boundary layer to mesoscale sea surface temperature (SST) is often characterized by a link between wind stress divergence and downwind SST gradients. In this study, an idealized simulation representative of a storm track above a prescribed stationary SST field is examined in order to determine in which background wind conditions that relationship occurs. The SST field is composed of a mid-latitude large-scale frontal zone and mesoscale SST anomalies. It is shown that the divergence of the surface wind can either correlate with the Laplacian of the atmospheric boundary layer temperature or with the downwind SST gradient. The first case corresponds to background situations of weak winds or of unstable boundary layers and the response is in agreement with an Ekman balanced adjustment in the boundary layer. The second case corresponds to background situations of stable boundary layers and the response is in agreement with downward mixing of momentum. Concerning the divergence of the wind stress, it generally resembles downwind SST gradients for stable and unstable boundary layers, in agreement with past studies. For weak winds, a correlation with the temperature Laplacian is still found to some extent. In conclusion, our study reveals the importance of the large-scale wind conditions in modulating the surface atmospheric response with different responses in the divergences of surface wind and wind stress.

Introduction

Satellite measurements have shown evidence of a local response of the atmospheric boundary layer to oceanic mesoscale structures (ranging from tens to hundreds of km). It takes the form of a positive correlation between wind stress and sea surface temperature (SST) anomalies at all latitudes [START_REF] Xie | Satellite observations of cool ocean-atmosphere interaction[END_REF]. Equivalent relationships exist with correlation of divergence of the wind stress with along-wind SST gradient, or wind stress curl and across-wind SST gradient [START_REF] Chelton | Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical pacific[END_REF][START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF][START_REF] O'neill | Observations of SST-induced perturbations of the wind stress field over the Southern Ocean on seasonal timescales[END_REF]. It was also revealed through the signature of ocean eddies in turbulent air-sea fluxes of sensible and latent heat [START_REF] Bourras | Response of the atmospheric boundary layer to a mesoscale oceanic eddy in the northeast Atlantic[END_REF], or in cloud cover and rain rates [START_REF] Frenger | Imprint of southern ocean eddies on winds, clouds and rainfall[END_REF].

The coupling between the atmosphere and narrow oceanic structures has been explored through various analyses of the horizontal-momentum budget in the boundary layer based on theoretical models [START_REF] Samelson | On the coupling of wind stress and sea surface temperature[END_REF][START_REF] Schneider | The atmospheric response to weak sea surface temperature fronts[END_REF] or idealized simulations [START_REF] Spall | Midlatitude wind stress-sea surface temperature coupling in the vicinity of oceanic fronts[END_REF][START_REF] Kilpatrick | Boundary layer convergence induced by strong winds across a midlatitude SST front[END_REF][START_REF] Kilpatrick | Atmospheric response to a midlatitude SST front: Alongfront winds[END_REF]. The general setting of these analyses was a large-scale wind blowing across (or along) an SST gradient, potentially leading to a change in the stability of the boundary layer. In locally unstable conditions (i.e. winds blowing from cold to warm waters), an increase of the downward transfer of momentum explains the correlation of wind or wind stress with SST anomalies [START_REF] Wallace | The influence of sea-surface temperature on surface wind in the eastern equatorial Pacific: Seasonal and interannual variability[END_REF][START_REF] Hayes | The influence of sea-surface temperature on surface wind in the eastern equatorial Pacific: Weekly to monthly variability[END_REF]). The mechanism of downward momentum mixing (hereafter DMM) was proposed to explain the relation between the divergence of wind stress and downwind SST gradients (e.g. [START_REF] Chelton | Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical pacific[END_REF][START_REF] O'neill | Observations of SST-induced perturbations of the wind stress field over the Southern Ocean on seasonal timescales[END_REF].

Another mechanism that is considered in the literature is related to surface pressure variations induced by SST structures. It was initially proposed as an important source of coupling at tropical latitudes [START_REF] Lindzen | On the role of sea surface temperature gradients in forcing low-level winds and convergence in the tropics[END_REF], and more recently as an important forcing for surface-wind convergence over mid-latitude SST fronts [START_REF] Feliks | Low-frequency variability in the midlatitude atmosphere induced by an oceanic thermal front[END_REF][START_REF] Minobe | Influence of the Gulf Stream on the troposphere[END_REF]). The mechanism is based on a thermal adjustment of the boundary layer to the underlying SST, which creates local variations of the hydrostatic pressure. Through a mechanism in terms of Ekman balance mass adjustment (hereafter EBMA), the divergence of the surface wind correlates with the Laplacian of sea level pressure. The latter is itself very close to the Laplacian of the atmospheric temperature if the boundary layer has adjusted to the underlying SST, which is more likely for low winds [START_REF] Brachet | Atmospheric circulations induced by a midlatitude SST front: A GCM study[END_REF][START_REF] Lambaerts | Atmospheric response to sea surface temperature mesoscale structures[END_REF].

At mid-latitudes the importance of the pressure term compared to vertical mixing still remains unclear, largely depending on the spatial scales [START_REF] Small | Air-sea interaction over ocean fronts and eddies[END_REF]) but also on the region of interest [START_REF] Shimada | Global analysis of the pressure adjustment mechanism over sea surface temperature fronts using AIRS/Aqua data[END_REF] or on the season that is considered [START_REF] Takatama | Diagnostics for near-surface wind response to the Gulf Stream in a regional atmospheric model[END_REF]. Moreover the two mechanisms can be active together to force a surface divergence response. For instance, in the Kuroshio Extension region, [START_REF] Putrasahan | Isolating mesoscale coupled ocean-atmosphere interactions in the Kuroshio Extension region[END_REF] show that the divergence of wind stress correlates with downwind SST gradients (see their Fig. 4). At the same time, divergence of surface wind correlates with the Laplacian of SST (see their Fig. 7) Most past studies have examined the time-average response (at least weekly averages) or the transient response (a few hours) of the atmospheric boundary layer to SST anomalies. As pointed out by [START_REF] Liu | Two types of surface wind response to the East China Sea Kuroshio front[END_REF], [START_REF] O'neill | The Gulf Stream Convergence Zone in the time-mean winds[END_REF] or [START_REF] Plougonven | Comments on "the gulf stream convergence zone in the time-mean winds[END_REF], the responses differ when considering averaged or transients fields. Here our goal is to determine the nature of the surface divergence response to mesoscale SST perturbations separating between classes of different large-scale wind conditions. For that purpose we use an idealized simulation of an atmospheric storm track above a frontal SST zone including a variety of oceanic structures of horizontal scales from 40 to 400 km.

Section 2 presents the configuration of the model with a brief description of the simulated storm track. We then document in section 3 the surface divergence response at the oceanic eddy scale by a composite analysis and we show that the simulations are consistent with observational results such as those of [START_REF] Frenger | Imprint of southern ocean eddies on winds, clouds and rainfall[END_REF]. Section 4 describes the spatial organization of the boundary layer response, investigating how the response mechanisms change for different synoptic-wind configurations. Differences between the responses in wind divergence and wind stress divergence are also investigated. Section 5 summarizes the results of the previous sections and compares them with previous studies.

Model description a. General configuration

The 3.6.1 version of the WRF model [START_REF] Skamarock | A description of the Advanced Research WRF Version 3, NCAR technical note[END_REF]) is used to simulate a characteristic mid-latitude storm track above a prescribed SST field. The model integrates the nonhydrostatic compressible moist Euler equations. Microphysics is represented with the [START_REF] Kessler | On the distribution and continuity of water substance in atmospheric circulation[END_REF] scheme, and convection with the [START_REF] Kain | Convective parameterization for mesoscale models: The kainfritcsh scheme. The representation of cumulus convection in numerical model[END_REF] scheme. The model uses the Yonsei University (YSU) parametrization [START_REF] Hong | A new vertical diffusion package with an explicit treatment of entrainment processes[END_REF] for the atmospheric boundary layer in conjunction with a Monin-Obukhov parametrization for surface layers (MM5 scheme). We do not include the effect of ocean surface currents in the wind stress calculation although it is known to affect the atmospheric boundary layer above oceanic eddies [START_REF] Renault | Modulation of wind work by oceanic current interaction with the atmosphere[END_REF][START_REF] Takatama | The role of back pressure in the atmospheric response to surface stress induced by the Kuroshio[END_REF].

The Cartesian domain, periodic in the zonal direction x, is of size L x × L y = 9216 × 9216 km.

Horizontal resolution is set to 18 km, and fifty η levels are used for the hydrostatic-pressure vertical coordinate, equally spaced in pressure. Top pressure is set to 36 hPa, corresponding to an altitude of approximately 20 km and 13 levels are below 2 km of altitude. Free-slip boundary conditions are used at the poleward and equatorial walls of the domain, and y = 0 corresponds to the equatorial side of the domain. A spatially varying Coriolis parameter is used with a largest β effect in the center of the domain. Typical values of these parameters correspond to 40

• N (see Appendix A).
The model is forced by using a gray-radiation scheme with an atmosphere transparent to water vapor and clouds, as proposed by [START_REF] Frierson | A gray-radiation aquaplanet moist GCM. Part I: Static stability and eddy scale[END_REF]. This forcing allows to mimic simple relaxation forcings on dry variables (e.g. [START_REF] Held | A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models[END_REF], but with the sole dependence on the SST field. The details of the radiative scheme are described in Appendix B.

b. Oceanic forcing

We prescribe the sea surface temperature field, stationary in time and composed of a large-scale meridional gradient and an eddying component:

SST (x, y) = SST (y) + e -(y-y sst ) 2 /l 2 0 × F(x, y) SST eddy (x,y) (1)
The large-scale front is described by

SST (y) = SST eq - SST eq -SST pol 2 1 + tanh y -y sst l sst (2)
with parameters defined in Table 1. SST ranges from SST pol = 275 K to SST eq = 295 K and is characterized by a smooth transition between warm and cold waters with an SST gradient of the order of 1 K/100 km.

The eddying component SST eddy (x, y) is obtained from a snapshot of a 2D turbulent field F(x, y) of a surface quasi-geostrophic (SQG) model [START_REF] Lapeyre | Impact of the small-scale elongated filaments on the oceanic vertical pump[END_REF] run for a domain size of L x /2 × L y /2 and extended by periodicity to the full domain. The SQG model was shown to adequately represent the upper ocean dynamics at mesoscale (see review of Lapeyre 2017).

F(x, y

) is normalized to get a standard deviation of 1.1 K and its zonal average is set to zero. Then it is multiplied with a Gaussian envelope to obtain the field SST eddy located where the meridional large-scale gradient of SST is the most intense.

Figure 1 shows the total SST field and the corresponding SST anomalies. The maximum value of |SST eddy | is 5.0 K but mesoscale SST anomalies have a relatively moderate signature in the total SST field which is characterized by a frontal region between y ≈ 3000 and 6000 km (Fig. 1a).

These anomalies display a variety of structures with mesoscale eddies of various diameters, as well as long and thin filaments of ∼50 km width attached to them (Fig. 1b, see also Fig. 5).

c. Mean state of the troposphere

A first simulation using SST as surface boundary condition was run for 4 years. Starting from its final state, a new simulation was then integrated over 8 years using the SST defined in (1). Outputs are saved twice a day, and the first three months are discarded as a spin-up period when computing statistics. The dynamical equilibrium obtaining by taking a time and zonal average is presented on Fig. 2.

A typical storm track forms as a response to the large-scale forcing: a tropospheric jet is located around y = 6000 km with a maximum speed larger than 25 m s -1 around p = 250 hPa. The height of the tropopause changes from 200 hPa on the equatorial side of the domain down to 400 hPa on the poleward side (not shown). The eddy poleward heat flux is maximum in the free troposphere at the center of the domain between y = 4000 km and y = 6000 km, while the eddy kinetic energy has its maximum slightly poleward at y = 5500 km (not shown). The simulated storm track is weaker than the southern-hemisphere storm track for which the zonal jet reaches values of 35 m s -1 but has realistic features of midlatitudes baroclinic zones. A more detailed analysis of the response of the storm track to the oceanic mesoscale SST field is carried out in [START_REF] Foussard | Storm tracks response to oceanic eddies in idealized atmospheric simulations[END_REF].

Composite analysis at the oceanic eddy scale

In order to assess the consistency of our idealized simulations with the observed relation between surface variables and SST anomalies, we first discuss the main features of the response of the atmospheric boundary layer to a typical mesoscale eddy. To that end, composites for cold and warm eddies are computed in the line of [START_REF] Park | Modification of surface winds near ocean fronts: Effects of Gulf Stream rings on scatterometer (QuikSCAT, NSCAT) wind observations[END_REF] or [START_REF] Frenger | Imprint of southern ocean eddies on winds, clouds and rainfall[END_REF]. For the sole purpose of identifying the position of the eddies, we use a method based on a wavelet packet decomposition (see details in [START_REF] Lapeyre | Impact of the small-scale elongated filaments on the oceanic vertical pump[END_REF][START_REF] Doglioli | Tracking coherent structures in a regional ocean model with wavelet analysis: Application to Cape Basin eddies[END_REF]). The procedure is to decompose SST eddy in elementary wavelets of compact support (using the Haar basis). Then wavelet coefficients smaller than a given value are filtered out. The field that is recomposed with the remaining wavelets is such that it is zero at a given point if it does not belong to an eddy. This allows to determine the precise location of each structure in order to compute the composites. The amplitude of an eddy is defined as the spatial average of the SST anomaly over the set of grid points within the eddy. The coordinates of its center are defined as their averaged values and the eddy radius is defined as R eddy = A /π, with A the area of the eddy (defined as the set of points belonging to the specific eddy). Only eddies with amplitude larger than 2 K are retained. This results in 16 warm and 16 cold eddies, with radii ranging from 81 to 145 km (see Fig. 1b).

For each eddy and each instantaneous snapshot, the large-scale background wind is defined as the average of the 10-meter wind within a square box of width equal to 10 radii centered on each eddy. This yields a direction (used for the rotation of different quantities) and an amplitude (used to separate strong and weak-wind conditions). For presentation of the composites, all fields, including sea surface temperature, are rotated so that the large-scale wind blows towards x > 0, and are translated so that the eddy center is at (x, y) = (0, 0). No spatial filtering has been applied to create the composites. Derivatives and Laplacian are computed using physical coordinates before rotation and translation are made. At the end, spatial coordinates are rescaled in units of eddy radii R eddy . Composites of surface wind speed (hereafter 10 m-winds) and SST created through this procedure show the usual response with accelerated (compared to environment) winds over warm SST anomalies and decelerated winds over cold SST anomalies (Fig. 3). Note that the asymmetry between warm and cold eddies in terms of wind acceleration or deceleration cannot be interpreted since too few eddies served to create the composite fields.

We now turn to the analysis of surface wind divergence. Rather than computing the mean divergence, we choose to separate the response depending on the large-scale wind speed. To that end, we have selected conditions with large-scale winds larger than 10 m s -1 (to be called strong-wind conditions) and smaller than 3 m s -1 (to be called weak-wind conditions). These categories correspond to 33% and 7% of instantaneous snapshots respectively. In the following, we only consider the response to warm eddies as the results with cold eddies are qualitatively similar, but with an opposite sign (not shown). Finally, we have tested that changing the thresholds does not change qualitatively the results.

The divergence of the surface wind reveals significant differences between strong and weakwind conditions (Fig. 4a and4d). Strong-wind conditions (Fig. 4a) are characterized by a dipolar spatial pattern with a divergent wind field upwind of the eddy and a convergent wind field downwind, with a typical amplitude of the order of 10 -5 s -1 . This is consistent with accelerated wind speeds over warm eddies and is similar to observations (e.g. [START_REF] Park | Modification of surface winds near ocean fronts: Effects of Gulf Stream rings on scatterometer (QuikSCAT, NSCAT) wind observations[END_REF][START_REF] Ma | Atmospheric responses to oceanic eddies in the Kuroshio Extension region[END_REF].

Note also that the downwind convergence is twice as large as the upwind divergence, which is generally not observed when doing averages over all weather conditions (e.g. [START_REF] Frenger | Imprint of southern ocean eddies on winds, clouds and rainfall[END_REF].

For weak-wind conditions (Fig. 4d), the situation is different as a strong monopolar convergence pattern is located slightly downwind of the warm eddy.

To determine the importance of the DMM and EBMA, the surface divergence was compared with the downwind SST gradient and the Laplacian of atmospheric temperature in the boundary layer. and4e) but, in both cases, we recover the standard dipolar pattern. For strong-wind conditions, the shape of the downwind SST gradient is similar in part to the shape of the surface divergence (compare Figs. 4a and4b), except for the surface convergence zone that extends further downstream (Fig. 4a). Another difference is that the downwind SST gradient has positive and negative poles with almost equal amplitude contrary to surface divergence for which some asymmetry is apparent. In weak-wind conditions, the downwind SST gradient differs from surface convergence with a monopolar shape for the later and a dipolar shape for the former (compare 4d and 4e).

For each wind condition, the Laplacian of boundary layer temperature ∇ 2 θ was computed as the Laplacian of the temperature averaged between the surface and 500 m. It is represented in Figs. 4c and 4f for strong and weak winds. For strong winds, it is intensified and negative in the downwind side of the SST anomaly and is located close to the region of largest surface convergence (compare Figs. 4a and4c). It thus seems that both the temperature Laplacian and the downwind SST gradient contribute in shaping the surface divergence pattern. This suggests that both DMM and EBMA may be important in setting the spatial variation of the surface divergence field. This result contrasts with the literature (e.g. [START_REF] Kilpatrick | Atmospheric response to a midlatitude SST front: Alongfront winds[END_REF] as, in general, the downwind SST gradient seems the dominant parameter especially at high winds. A notable difference with these studies is that they only consider simplified configurations with quasi-unidirectional fronts, so that the temperature Laplacian only comes from either the along or the cross-wind direction. On the contrary, due to the geometry of oceanic eddies, the Laplacian can have variations in both directions.

Indeed, in our simulation, it is found that about two thirds of the pressure Laplacian correspond to crosswind variations of pressure (not shown). Finally, in comparison to the temperature Laplacian, the SST Laplacian is centered over the oceanic eddy and is out of phase with the surface divergence (not shown). This is easily explained as the temperature anomaly that is generated above the warm oceanic eddy is advected downwind, so that SST and atmospheric temperature Laplacian do not correlate.

For weak-wind conditions, the temperature Laplacian is monopolar and negative above the SST anomaly because of weak temperature advection by the wind (Fig. 4f). Comparing Fig. 4d, 4e and 4f, we see that, the surface divergence pattern is highly correlated with the temperature Laplacian , while it is not the case when compared to the downwind SST gradient. Actually, because of the weak temperature advection, the SST Laplacian is correlated with the temperature Laplacian as well as with the surface divergence (not shown). This is in agreement with the results of Lambaerts A last remark concerns moderate-wind conditions (i.e. winds between 3 m s -1 and 10 m s -1 ).

In such conditions, it was found that the wind divergence response is between those for the two other wind conditions (not shown).

The difference in terms of the atmospheric response between weak and strong-wind conditions is reminiscent of results obtained by [START_REF] Chen | Oceanic eddy-driven atmospheric secondary circulation in the winter Kuroshio Extension region[END_REF] for eddies in the Kuroshio Extension region.

In their study, they separated two different classes, one with a dipolar pattern in divergence of surface wind (corresponding to 60% of the oceanic eddies that were observed) and one with a monopolar pattern (corresponding to 10% of the eddies). The first class was attributed to DMM while the second class to EBMA. An inspection of their Fig. 3c shows that, for the first class of eddies, the convergence maximum extends further downstream, a result consistent with our result for strong-wind conditions (Fig. 4a).

Atmospheric response to a turbulent field of mesoscale eddies

The previous section has characterized the response of the wind field at the oceanic eddy scale in a simulation forced by the ocean with no ocean-atmosphere coupling. It showed that our simulation with fixed SST compares well with observations for strong-wind conditions. We now turn to examine the spatial organization of the atmospheric response in relation with the oceanic turbulent field, i.e. for scales smaller than 400 km. This contrasts with studies focusing on eddy composites or unidimensional fronts. To this end, we focus on a part of the spatial domain, of width 1400 × 1400 km and centered at (x 0 , y 0 ) = (5400, 4500) km , i.e. close to the center of the SST front. Results that are discussed hereafter apply for other spatial regions as well within the band where oceanic eddies are present.

In the following, we consider anomalies from the large-scale environment. These turbulent-scale anomalies, denoted as ( ) ⋆ , are obtained (except for SST) by removing a large-scale component obtained by convoluting with a Gaussian kernel of radius r f ilter = 200 km. The SST anomaly SST eddy is given directly from the boundary condition through (1).

The anomaly of time-mean surface wind speed |U| ⋆ is presented in Fig. 5a. Here is the time average for the whole analysis period. It bears striking similarities with SST eddy with a correlation coefficient of r = 0.98 and a regression coefficient of 0.29 m s -1 K -1 . This is true for the anomalies associated with oceanic eddies, confirming results of the last section, but also for the filamentary structures in between. The regression coefficient (also called coupling coefficient) is in the range of the usual values derived from observations (e.g. [START_REF] O'neill | Covariability of surface wind and stress responses to sea surface temperature fronts[END_REF] or from models [START_REF] Song | Coupling between sea surface temperature and low-level winds in mesoscale numerical models[END_REF][START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF].

The time-mean response in the surface winds generally reflects convergence above warm eddies (such as eddies B or D in Fig. 5b) and divergence above cold eddies (eddies A or C). The divergence field does not bear resemblance with the downwind SST gradients (Fig. 5c) while there is a high correlation with the Laplacian of temperature in the boundary layer (compare shadings in Figs. 5b andd). As discussed in the previous section, such a comparison is not helpful to reveal in which wind conditions EBMA or DMM are important. This is probably due to the fact that, in this region, the time-mean wind is weak (not shown).

We propose below to contrast conditions of strong and weak winds as well as different wind directions to better assess the role of the background wind and of the stability of the boundary layer.

Several effects are anticipated: the wind speed will influence both how turbulent the boundary layer is, and how much advection decorrelates boundary layer temperature from SST. The direction of the wind will also play a role through the presence of a large-scale meridional SST gradient. For example, northerly winds will advect cold air above warm waters, inducing a larger temperature difference between ocean and atmosphere, and hence a more turbulent boundary layer.

a. Method

Composite atmospheric fields depending on large-scale wind conditions are built through the following steps. We consider the square box of size 900 × 900 km, centered at (x 0 , y 0 ) and located inside the previously used 1400 × 1400 km domain. The chosen box is large enough to be free of local wind variations induced by the SST anomalies, but not too large in order to cover separate synoptic weather patterns. To double the statistics, we also used the box centered at 1208, 4500) km since the SST eddy field was duplicated in longitude. We introduce the wind conditions as the couples U ls = (U ls , V ls ) for U ls = -10, -5, 0, 5, 10 m s -1 and V ls = -10, -5, 0, 5, 10 m s -1 (ls for large-scale). Then, for each 12-hour output, the instantaneous wind at 10 meters, U 10m , is averaged over the (900 km × 900 km) box and is sorted out according to which wind conditions (U ls ,V ls ) it belongs (within ±2.5 m s -1 ). Composite fields [ ] are finally constructed by averaging over all outputs belonging to each large-scale wind condition (U ls V ls ).

(x ′ 0 , y ′ 0 ) = (
In the following, we will consider composites for which more than 100 time outputs have been averaged. Finally, we introduce k = [ U 10m (x, y,t) ]/[ |U 10m (x, y,t)| ] as a composite vector in the wind direction and θ the average temperature from the surface to 500 m height.

b. Surface wind divergence

We now examine the differences of spatial structures in surface wind divergence for different wind conditions. Three large-scale wind conditions are considered in details: northerly strong winds (U ls = (0, -10) m s -1 ), weak winds (U ls = (0, 0) m s -1 ) and southerly strong winds (U ls = (0, 10) m s -1 ).

Figures 6a and 6b present the surface divergence anomaly [∇ • U 10m ] ⋆ (in colors) as well as k•∇SST eddy and [∇ 2 θ ] ⋆ (in contours), for northerly wind conditions (i.e. U ls = (0, -10) m s -1 ). At first glance, both [∇ 2 θ ] ⋆ and k • ∇SST eddy seem to correlate well with the surface wind divergence (correlation coefficients of r = 0.81 and 0.63, respectively, see Table 2). However inspecting with more attention Figs. 6a and 6b, we note that, at some particular locations, the spatial structures of the downwind SST gradient and the temperature Laplacian are quite different. First, narrow SST structures oriented parallel to the background wind such as the one to the South West of eddy A produce patterns of wind convergence ([∇ • U 10m ] ⋆ < 0) while k • ∇SST eddy is almost zero (Fig. 6a).

At this location, surface wind convergence is collocated with negative values of SST Laplacian (not shown) and with negative values of [∇ 2 θ ] ⋆ (see Fig. 6b). Also, for the the small warm eddy D, only a monopolar pattern of convergence of surface winds is seen which differs from the dipolar pattern of k • ∇SST eddy (Fig. 6a). In fact, at this location, the convergence region is associated with large values of temperature Laplacian [∇ 2 θ ] ⋆ (Fig. 6b). The significant correlation (r = 0.81) between surface wind divergence and temperature Laplacian and the similarity of spatial structures suggest that, for strong northerly winds, the surface wind divergence response is mostly due to EBMA. However because of temperature advection by the northerly wind, correlation of surface divergence with the SST Laplacian itself remains low, with a correlation coefficient of 0.18.

The weak-wind case is represented in Figs. 6c and6d. The surface divergence is found to be generally weaker than for northerly winds (compare Figs. 6a and6c). Looking at Fig. 6d, surface divergence and temperature Laplacian are well correlated (with a correlation coefficient of 0.63).

Also, there is a fair correspondence between SST Laplacian and surface divergence (correlation coefficient of 0.39), because the temperature anomalies lie almost above the SST anomalies (not shown). At particular locations (near eddy A, or in some filamentary structures in the northern part of the domain), the surface divergence resembles the downwind SST gradient (Fig. 6c). However, in many other places (such as eddies B, C, D), the two fields do not coincide with each other. We conclude that, in these weak-wind conditions, there is a preferential response following EBMA.

The situation is different for a southerly wind (Figs. 6e and6f) for which we see a clear correlation of the surface divergence with the downwind SST gradient (correlation coefficient of 0.83 see Tab. 2). This manifests in similar spatial structures not only for eddies B, C and D but also for the filamentary structures between them. The response above eddies B and C shows a typical dipolar structure of convergence/divergence corresponding to a DMM response. On the contrary, the connection between the surface divergence and the temperature Laplacian is less obvious when comparing the spatial structures of the two fields (Fig. 6f), although the spatial correlation is still high (around 0.48).

We now explore more quantitatively and systematically the atmospheric response by computing the correlation coefficients of surface divergence with either the downwind SST gradient (Fig. 7a)

or the temperature Laplacian (Fig. 7b) as a function of the wind conditions (U ls ,V ls ). Two regimes can be distinguished. The first one, for strong southerly (V ls > 0) or zonal winds, corresponds to a better correlation of the surface divergence with the downwind SST gradient than with the temperature Laplacian. On the contrary, for northerly (V ls < 0) or for weak winds, the surface divergence better correlates with the temperature Laplacian. However, there is still some correlation with the downwind SST gradient. This last result can be understood by the correlation that is found between k • ∇SST eddy and [∇ 2 θ ] ⋆ , as shown in Fig. 7c. A simple explanation of this correlation comes from the heat budget which can be approximated by

U ls • ∇[θ ] ⋆ ≈ γ (SST eddy -[θ ] ⋆ )
where the air-sea heat flux was replaced by a simple relaxation towards SST with a typical timescale γ -1 . If U ls points towards x > 0 with constant modulus, the quantity U ls • ∇ can be replaced by |U ls |∂ /∂ x. After some algebra, we have

1 γ |U ls | ∂ 2 [θ ] ⋆ ∂ x 2 + k • ∇[θ ] ⋆ = k • ∇SST eddy (3)
For a sufficiently strong wind (i.e. |U ls | × |∂ x SST eddy | ≫ γ|SST eddy |), the temperature anomaly above the surface heating will be advected downstream and the first term in the l.h.s. of (3) will dominate the second term. In this situation, we obtain a balance between downwind SST gradient and temperature Laplacian which explains the correlation between the two quantities. This is particularly true for strong winds with a southward component (Fig. 7c andtable 2). Note however that it involves the second derivative only along the wind direction, so that the total Laplacian may not be systematically related to the downwind SST gradient.

To understand why surface divergence correlates with downwind SST gradient in some situations, and with the temperature Laplacian in others, we examine the dependence on the wind conditions of the boundary layer height and the air-sea temperature difference, both spatially averaged over the domain of Fig. 5. The result is displayed in Fig. 8 and is significant in the sense than the mean change of both quantities between different wind conditions is larger than their change across the SST front (for a given wind condition). Northerly winds tend to be associated with high boundary layers (Fig. 8a) and an atmospheric temperature much colder than the underlying SST (Fig. 8b). This can be explained by the advection of cold air from the North, tending to decrease stability over the region that is examined. This results in a typical situation of strong turbulence in the boundary layer associated with a deep boundary layer. Southerly winds are associated with warm air advected in the region creating a stable boundary layer (Fig. 8b), which results in shallow boundary layers (Fig. 8a). These differences can explain the different response in terms of wind divergence as the surface pressure anomaly and the surface divergence tend to be proportional to the height of the boundary layer [START_REF] Feliks | Low-frequency variability in the midlatitude atmosphere induced by an oceanic thermal front[END_REF]). Conditions with higher boundary layers will result in stronger EBMA. This can be confirmed by examining the coupling coefficient, computed as the regression coefficient between wind speed anomalies and SST anomalies as a function of the background wind (U ls , V ls ). The coupling coefficient is the smallest for northerly winds corresponding to large-scale unstable boundary layers (Fig. 8c). For zonal or southerly winds (corresponding to large-scale stable boundary layers), the coupling coefficient increases with the wind speed, in agreement with [START_REF] Byrne | Atmospheric response to mesoscale sea surface temperature anomalies: Assessment of mechanisms and coupling strength in a high-resolution coupled model over the South Atlantic[END_REF] in their simulation of the Southern Ocean. This confirms that DMM is more efficient for southerlies, resulting in higher correlation between surface divergence and downwind SST gradient. As suggested by [START_REF] Skyllingstad | Effects of mesoscale sea-surface temperature fronts on the marine atmospheric boundary layer[END_REF] and [START_REF] Small | Air-sea interaction over ocean fronts and eddies[END_REF], the surface stability, rather than the boundary layer depth, is the more susceptible to explain this behavior.

Note that we repeated the analysis and compared the vertical velocity at 500 m (w ⋆ ) with downwind SST gradient or temperature Laplacian. For the weak-wind conditions (Fig. 9), as well as for the northerly case, the vertical velocity strongly correlates with the temperature Laplacian (with reversed sign) and not with the downwind SST gradient (Table 2). This is true at the scales of the main eddies, as well as at the scales of filaments (not shown). The correlation with the SST Laplacian remains small even in the weak wind case (correlation coefficient of 0.42 compared with 0.73 for the temperature Laplacian). For southerly winds, it is difficult to determine whether vertical velocities are similar to temperature Laplacian or to SST gradients. Instantaneous snapshots are sometimes characterized by a cold front present in the domain, in general oriented S-SW towards N-NE. Despite averaging over different snapshots, these fronts leave a residual signature in the vertical velocity field. As a result, the vertical velocity field does not display any organization at the scales of oceanic eddies (not shown).

c. Wind stress divergence

Several observational studies [START_REF] O'neill | Observations of SST-induced perturbations of the wind stress field over the Southern Ocean on seasonal timescales[END_REF][START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF]) pointed out a robust relation between wind stress divergence and downwind SST gradient. We now try to relate this result with the response of the surface divergence that we analyzed above.

If we neglect the role of surface oceanic currents, the wind stress vector τ is written using bulk formula,

τ = ρ 0 C d |U 10m | U 10m , (4)
with C d the drag coefficient [START_REF] Stull | An introduction to boundary layer meteorology[END_REF]. Divergences of surface wind and wind stress are then related by

∇ • τ = ρ 0 U 10m • ∇(C d |U 10m |) + ρ 0 C d |U 10m | ∇ • U 10m .
(5)

The first term on the r.h.s. of (5) describes the effect of spatial variations of stress-to-wind ratio (i.e. Laplacian, and this should also be the case for the last term of (5) as well.

To examine the sensitivity of wind stress divergence to the wind direction, we approximate ( 5) by

[∇ • τ] ≈ ρ 0 [U 10m ] • ∇ [ C d |U 10m | ] E stab + ρ 0 [ C d |U 10m | ] ∇ • [U 10m ] E div (6)
with a constant density ρ 0 = 1.2 kg m -3 . In the following, we will consider the anomalies from the large-scale environment, e.g. [∇ • τ] ⋆ . Quantities E stab and E div will refer to their anomalies.

Relation (6) was assessed and revealed to be valid with a r.m.s. error of about 20% and a good correlation between the wind stress and its approximation (6). The error rises to 38% for weak winds (because the sum of the two terms underestimates [∇ • τ] by 20%).

Figure 10a presents the divergence of the wind stress for northerly winds (U ls = (0, -10) m s For weak-winds conditions (U ls = (0, 0)), the wind stress is smaller than for the northerly case (ratio of r.m.s. of 0.38). E div is of comparable magnitude with E stab (r.m.s. of 0.40 × 10 -7 against 0.46 × 10 -7 N m -3 ). As in the previous case, E stab is found to be correlated with downwind SST gradients (see Fig. 10e) with a correlation coefficient of 0.94 while E div correlates with the temperature Laplacian (Fig. 10f) with a correlation coefficient of 0.70. Both terms significantly contribute to the wind stress spatial pattern: term E div generally dominates close to eddy centers (e.g. eddies B and D ) or far from the eddies (e.g. North of eddies C and D, Fig. 10f) while E stab dominates in smaller scale structures at the eddy peripheries such as near eddies A and C (Fig. 10e). Weak wind conditions are therefore prone to a correlation between wind stress divergence and temperature Laplacian, when considering scales around 200 km, while both downwind SST gradient and temperature Laplacian matter for smaller scales.

We now consider the case of southerly winds, i.e. U ls = (0, 10) m s -1 (Fig. 10g-i). First, the wind-stress divergence has an opposite sign with the case of northerly winds (compare Fig. 10a and 10g). This is related to the high correlation of [∇ • τ] ⋆ with k • ∇SST eddy (correlation coefficient of 0.93). Two reasons can be invoked: E stab is in general 61% larger than E div (table 4); E div (as well as surface divergence) is better correlated with k • ∇SST eddy than with [∇ 2 θ ] ⋆ .

More generally, for all wind conditions of U ls (except for weak winds), the correlation between wind stress divergence and downwind SST gradient is higher than 0.80 (Fig. 11a). The correlation with the temperature Laplacian is smaller (Fig. 11b) but still increases to values around 0.7 for northerly winds. The wind stress divergence response is clearly different from the surface wind divergence, as the correlation with the downwind SST gradient always dominates in the first case (Figs. 11a and11b), while both downwind SST gradient and temperature Laplacian were important for the second case (Figs. 7a and7b)

Figure 11c shows the value of the regression coefficient between wind stress divergence and downwind SST gradient for all wind conditions. Values are of the typical range of those found in the literature [START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF]. The first dependence of the regression coefficient is on the wind speed, consistent with observations (e.g. O'Neill et al. 2012). It is modulated by the direction of the large-scale background wind relative to the large-scale front, in agreement with the coupling coefficient between wind speed and SST (Fig. 8c).

We conclude that the response in wind stress divergence to SST anomalies depends both on the magnitude of the mean surface wind and on the stability of the atmospheric boundary layer. In strong-wind conditions, we essentially find a wind stress divergence proportional to the downwind SST gradient. This is true for stable as well as for unstable boundary layers and is in agreement dominates. It is responsible for a response related to the downwind SST gradient. The second effect comes from the direction and intensity of the wind (related to ∇ • U 10m ). Its contribution is large for unstable boundary layers in strong-wind conditions. In that case, the two effects add up as they have similar spatial characteristics. For weak winds, the contribution of the second effect becomes as important as the first one, in particular at scales around 200 km.

Conclusions

In the present study, the response of surface winds to SST anomalies associated with oceanic eddies has been explored in an idealized simulation of an atmospheric storm track. Two mechanisms are generally invoked to explain the response in terms of divergence of surface wind and wind stress. A first one is related to pressure adjustment (EBMA mechanism, Lindzen and Nigam 1987) while a second to downward momentum mixing (DMM mechanism, [START_REF] Wallace | The influence of sea-surface temperature on surface wind in the eastern equatorial Pacific: Seasonal and interannual variability[END_REF]. It is expected that the surface wind divergence resembles the Laplacian of the atmospheric temperature in the first case and the downwind SST gradient in the latter case. Our study has documented in which large-scale wind conditions one of the mechanisms is more active than the other. One advantage of our idealized simulation approach is that we could directly inspect the response in surface winds, contrary to other studies which considered equivalent neutral winds or wind stress.

Also, using instantaneous winds averaged in composites (grouping together similar large-scale wind conditions) allows to separate the rapid response without a temporal filter, in a manner similar to [START_REF] Byrne | Atmospheric response to mesoscale sea surface temperature anomalies: Assessment of mechanisms and coupling strength in a high-resolution coupled model over the South Atlantic[END_REF].

We first examined the response at the oceanic eddy scale through a composite analysis. It revealed that the surface wind divergence projects both onto the downwind SST gradient and onto the Laplacian of the atmospheric temperature in the boundary layer. For weak winds, the divergence of surface wind is proportional to the Laplacian of the boundary layer temperature. On the other hand, for strong winds, the surface divergence has a main pattern similar to the downwind SST gradient, but with a downstream extension (related to the temperature Laplacian spatial extension).

The atmospheric response was then investigated over a large region including a field of mesoscale oceanic eddies and filaments of scales between 40 and 400 km. The analysis revealed a more complex response that depends on the wind conditions, and more generally on the mean stability of the boundary layer. For large-scale unstable conditions or for weak winds, the divergence of the surface wind is correlated with the temperature Laplacian (corresponding to EBMA), while for large-scale stable conditions, it is correlated with downwind SST gradient (corresponding to DMM). For strong winds, the correlation of the surface divergence with the SST Laplacian is found to be small, due to the effect of the mean-wind advection.

Concerning the response in terms of wind stress divergence, a different picture is obtained. For strong winds, the divergence of wind stress is proportional to downwind SST gradient, even in large-scale unstable conditions. For weak winds, wind stress divergence is proportional to some extent to the temperature Laplacian. These results are valid at the scales of oceanic eddies, as well as smaller filamentary scales. This discussion shows that wind stress and surface wind divergences may behave differently considering their response to SST anomalies. We point out that such a distinction is rarely made in the literature and should be given greater consideration. Actually wind stress is directly related to the stability of the boundary layer while horizontal velocities in the atmosphere are less so but have a strong dependence on gradients of boundary layer temperature.

Several studies have examined the relevant parameters that set the atmospheric response sensitivity to DMM [START_REF] Spall | Midlatitude wind stress-sea surface temperature coupling in the vicinity of oceanic fronts[END_REF][START_REF] Small | Air-sea interaction over ocean fronts and eddies[END_REF][START_REF] Schneider | The atmospheric response to weak sea surface temperature fronts[END_REF][START_REF] Ayet | An analytical study of the atmospheric boundary layer flow and divergence over a SST front[END_REF]. The first one is related to the magnitude of the mean wind speed. Our study confirms that the relative importance of DMM increases with wind speed. This is shown by a better correlation of surface divergence with downwind SST gradient than with temperature Laplacian for strong winds, except in situations of winds blowing from cold to warm waters. A second important parameter is the spatial scale of the SST field [START_REF] Small | Air-sea interaction over ocean fronts and eddies[END_REF]. One would expect the smaller the lengthscale, the larger the sensitivity to DMM. However, for strong winds blowing from cold to warm waters, we found that EBMA still dominates with surface divergence proportional to temperature Laplacian down to 40 km. The dominance of EBMA over DMM (in terms of relation between surface wind divergence and temperature Laplacian or downwind SST gradient) was found to be related to the large-scale stability of the boundary layer. For unstable and deep boundary layers, an EBMA response is found, while DMM prevails for large-scale stable conditions. This may be related to the dependence of the pressure Laplacian to the mean height of the boundary layer (which favors EBMA) and to the dependence of the coupling coefficient (between wind and SST anomalies) on the stability (which favors DMM).

As the focus of the paper concerns the boundary layer and surface dynamics, we did a sensitivity study to the boundary layer parametrization scheme, using the Mellor-Yamada-Nakanishi-Niino (MYNN) scheme [START_REF] Nakanishi | An improved Mellor-Yamada level-3 model with condensation physics: Its design and verification[END_REF]. We obtained qualitatively similar results (see Fig. 12), but with different intensities in agreement with results of [START_REF] Lambaerts | Atmospheric response to sea surface temperature mesoscale structures[END_REF] and [START_REF] Perlin | Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations[END_REF]. A sensitivity to the number of vertical levels within the first 1000 m showed a weak dependence of the results on vertical resolution as well.

The present study has different limitations. The first one is the stationarity in time of the oceanic anomalies especially for scales below 50 km. However, because of the fast variability of the atmosphere, conditions of given wind do not occur over long timescales compared to the SST variability of the ocean. Therefore the composite analysis focuses only on the rapid response of the atmosphere and not on its time average which is tightly linked to fixed SST. Another limitation is the fact that ocean-atmosphere coupling was not considered although different feedbacks are known to modify the surface wind response to oceanic mesoscale anomalies. In particular, our parametrization of the surface atmospheric layer does not take into account ocean currents modulation on the wind work [START_REF] Renault | Modulation of wind work by oceanic current interaction with the atmosphere[END_REF][START_REF] Moulin | Momentum transfer between an atmospheric and an oceanic layer at the synoptic and the mesoscale: An idealized numerical study[END_REF][START_REF] Takatama | The role of back pressure in the atmospheric response to surface stress induced by the Kuroshio[END_REF]. Moreover the air-sea coupling tend to damp oceanic eddies through Ekman pumping at the scale of oceanic eddies [START_REF] Stern | Interaction of a uniform wind stress with a geostrophic vortex[END_REF][START_REF] Dewar | Some effects of the wind on rings[END_REF] as well at the scale of a turbulent eddy field [START_REF] Oerder | Impacts of the mesoscale ocean-atmosphere coupling on the Peru-Chile ocean dynamics: The current-induced wind stress modulation[END_REF]. A full air-sea coupling could reduce the SST amplitude and modulate the atmospheric response. These different mechanisms need to be taken into account in future studies.

Acknowledgments. This work was granted access to the HPC resources of IDRIS under the allocation A0020106852 made by GENCI (Grand Equipement National de Calcul Intensif). The authors want to thank Arnaud Czaja, Caroline Muller and Gwendal Rivière for useful discussion about this work and three anonymous reviewers for their time and numerous comments that significantly improved the clarity of the results and discussion.

APPENDIX A

Coriolis parameter

The Coriolis parameter f has the following dependence in y: ) This formula in addition to parameters in Table 1 allows to model a storm track with a Coriolis parameter that ranges between values at 27.6 and 55.6 • N. The β effect above the oceanic front has a realistic value of β max = 1.75 × 10 -11 m -1 s -1 , corresponding to its value at a latitude of 40 • N. In this way, we obtain a strong planetary vorticity gradient, which helps to maintain the eddy-driven jet to its mean position. Using a linear function for f with the same value of β = β max would lead to unrealistic values of f on the northern or southern part of the domain.

f (y) = f 0 + β max l β tanh y -y sst l β . ( A1

APPENDIX B

Radiative scheme

The radiative scheme that is used in our simulation is a gray radiation scheme following the ideas of [START_REF] Frierson | A gray-radiation aquaplanet moist GCM. Part I: Static stability and eddy scale[END_REF]. We introduce T as the absolute temperature and D the optical depth (with the convention D = 0 at the top of the atmosphere and D = D 0 at the surface). The equations for upward (F ↑ ) and downward (F ↓ ) radiative energy fluxes are

dF ↑ dD = F ↑ -σ T 4 (B1) dF ↓ dD = -F ↓ + σ T 4 (B2)
with σ the Stefan-Boltzmann constant. To close the system, the fluxes at the surface and at the top of the atmosphere are such that

F ↑ (D = D 0 ) = σ SST 4 (B3) F ↓ (D = 0) = 0 . (B4)
This choice of boundary conditions is different from [START_REF] Frierson | A gray-radiation aquaplanet moist GCM. Part I: Static stability and eddy scale[END_REF] and allows to constrain the forcing to almost entirely depend on the SST field.

We prescribe total optical depth D to be dependent only on latitude y and pressure p. The surface

optical depth D 0 (y, p = p 0 ) = D 0 (y) is such that D 0 (y) = D eq cos 2 π y 2 L y + D pole sin 2 π y 2 L y (B5)
Then we separate optical depths in the troposphere and stratosphere by introducing D T and D S such that

D = max(D T , D S ) , (B6)
with

D S (y, p) = 1 4 p p 0 D 0 (y) , (B7) D T (y, p) = (1 + D 0 ) p p 0 4κ 1 - ∆θ α SST log p p 0 4 -1 . (B8)
Table 1 summarizes the values of the various parameters.

In (B8), SST is the zonal average of SST and

α = 1 + D 0 2 + D 0 1/4 (B9)
D S is larger than D T in the highest atmospheric layers, and transition from one expression to the other roughly sets the height of the tropopause in our experiment.

In the model, the diabatic term due to radiative forcing is expressed in the temperature equation as

R = 1 ρ C p ∂ (F ↑ -F ↓ ) ∂ z (B10)
To understand the nature of this forcing, we can compute the potential temperature at radiative equilibrium θ Rad , i.e. when R = 0. Below the tropopause, D(y, p) = D T (y, p) and using (B1-B5) and (B8), we obtain

θ Rad (x, y) = α SST (x, y) -∆θ log p p 0 SST (x, y) SST (y) . ( B11
)
Since α is weakly dependent on y (ranging between 0.92 and 0.96), the gray-radiation scheme relaxes temperature towards a profile whose meridional gradient is proportional to ∂ SST /∂ y in zonal mean. Such a profile is similar to the radiative equilibrium of [START_REF] Held | A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models[END_REF].

To ensure that the boundary layer response does not depend on radiative parametrization choices, two other sensitivity runs were done. In the first one, SST (y) was replaced by SST (x, y) in (B8)

while in the second one, SST (x, y) was replaced by SST (y) in (B3) While radiative fluxes act either as an additional heat source or sink at the scale of the oceanic eddies in each experiment, the impact

(L x , L y ) in km (9216, 9216) (SST eq , SST pol ) in K (295, 275)
y sst in km 4500 (l sst , l 0 , l β ) in km ( 1000, 1500, 1500 )

f 0 in s -1 9.35 × 10 -5 β max in m -1 s -1 1.75 × 10 -11
∆θ in K 10 weak and southerly large-scale winds. Each quantity was computed over the domain displayed in Fig. 5. x (km) D B C A -0.9 -0 .9 -0 . 9 -0 . 9 -0 . 9

(D eq , D pole ) (6, 1.5) p 0 (in Pa) 10 5 TABLE 1. Common parameters. C([∇ • U 10m ] ⋆ , [∇ 2 θ ] ⋆ ) 0.81 0.63 0.48 C([∇ • U 10m ] ⋆ , k • ∇SST eddy ) 0.63 0.36 0.83 C([∇ • U 10m ] ⋆ , ∇ 2 SST eddies ) 0.18 0.39 0.08 C([∇ 2 θ ] ⋆ , k • ∇SST eddy ) 0.58 0.31 0.34 C([w] ⋆ , -[∇ 2 θ ] ⋆ ) 0.
706 707 Northerlies weak winds Southerlies C([∇ • τ] ⋆ , [∇ 2 θ ] ⋆ ) 0.73 0.58 0.43 C([∇ • τ] ⋆ , k • ∇SST eddy ) 0.91 0.68 0.93 C([∇ • τ] ⋆ , ∇ 2 SST
-0 .3 -0 .3 -0.3 -0 .3 -0 .3 -0 . 3 -0 .3 -0 .3 -0 .3 -0.3 -0.3 -0 .3 -0 .3 -0 .3 -0 . 3 -0.3 -0 .3 -0 .3 -0. 3 -0 .3 -0 . 3 0 .3 0. 3 0. 3 0 . 3 0 .3 0 . 3 0 . 3 0.3 0 . 3 0 .3 0. 3 0.3 0 . 3 0 . 3 0 . 3 0.3 0.3 0 . 3 0 . 3 0 . 3 0. 3 0 .3 0 . 3 0 . 3 0 . 3 0 . 3 0 .3 0 . 3 0 .3 0. 3 0.3 (f) ∇ •U 10m ∇ 2 θ y (km) -0 .9 -0 .9 -0 . 3 -0. 3 -0 .3 -0 .3 -0. 3 -0.3 -0 . 3 -0 .3 -0 . 3 -0.3 -0 .3 -0 .3 -0. 3 -0.3 0 .3 0 .3 0. 3 0 .3 0. 3 0. 3 0 . 3 0 . 3 0 . 3 0 . 3 0 . 3 0.3 0 . 3 0.3 0.3 0.3 0 .3 0 .3 0 .3
0 .9 0 .9 0 .9 0. 9 0.9 -0 .9 -0 . 9 -0 .9 -0 . 9 -0 .9 -0 .9 0 . 9 0 . 9 0 .9 0.9 0 . 9 0. 9 0.9 1 .5 x (km) -0.9 -0 .9 -0 .9 -0 . 9 -0 . 9 -0 . -0 .9 -0 .9 -0 .9 -0 .9 -0 .9 -0 .9 -0 . 0 .9 0 . 9 0 . 9 0 .9 0.9 0 .9 0. 9 0.9 1 .5

(c) ∇ •U 10m k •∇SST D B C A -0.9 -0 .9 -0.9 -0.3 -0 .3 -0 .3 -0 .3 -0 .3 -0 .3 -0 .3 -0 .3 -0 .3 -0 . 3 -0.3 -0 . 3 -0 . 3 -0 .3 -0 . 3 -0 .3 -0.3 -0 . 3 0.3 0.3 0. 3 0 .3 0.3 0 . 3 0.3 0 .3 0 . 3 0.3 0 .3 0. 3 0 .3 0 . 3 0 . 3 0 .3 0 . 3 0.3 0.3 0.9 (d) ∇ •U 10m ∇ 2 θ y (
-0 .3 -0. 3 -0 .3 -0. 3 -0 .3 -0 .3 -0 .3 -0 .3 -0 . 3 -0.3 -0 .3 -0.3 -0 . 3 -0.3 -0 .3 -0 .3 -0 . 3 -0.3 -0 . 3 -0 .

  et al. (2013) who examined the fast adjustment of the boundary layer from rest to a turbulent eddy SST field. A possible interpretation of this result can rely on the EBMA mechanism: the warm SST anomaly creates a warm temperature anomaly in the boundary layer, which then creates a convergence field in the Ekman layer.

  |τ|/|U 10m | = C d |U 10m |). Since both C d and |U 10m | vary with air-sea temperature difference, and hence to some extent with SST, we expect U 10m • ∇(C d |U 10m |) to be proportional to the downwind SST gradient. The second term on the r.h.s. of (5) describes the direct effect of the spatial variation of the wind direction, and more generally the divergence of the wind vector. As seen above, for an unstable boundary layer or for weak winds, [∇ • U 10m ] ⋆ is generally proportional to the temperature

  with the results of[START_REF] O'neill | Observations of SST-induced perturbations of the wind stress field over the Southern Ocean on seasonal timescales[END_REF] and[START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF]. It can be understood as the addition of two effects in the wind stress. The first one comes from the variation of the drag coefficient and the surface wind speed due to SST (in relation with ∇(C d |U 10m |)) and generally

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 9 .Fig. 10 .Fig. 12 .FIG. 2 .FIG. 4 .

 12345679101224 Fig. 1. (a) Total SST and (b) eddy SST fields, in K. In (b), black crosses mark centers of the eddies used to create composites following the method described in Section 3. . . . . . . . 41 Fig. 2. Time and zonal average of zonal wind (blue thick contours, in m s -1 ), potential temperature (black contours, in K), and meridional flux of potential temperature (red thick contours, in K m s -1 ). . . . . . . . . . . . . . . . . . . . . . . . 42 Fig. 3. Composites of surface wind speed |U 10m | (shading, in m s -1 ) and sea surface temperature SST (contours, in K), for (a) warm and (b) cold eddies. . . . . . . . . . . . 43 Fig. 4. Composites above warm eddies of (a, d) divergence of surface wind, (b, e) downwind SST gradient and (c, f) Laplacian of boundary layer temperature. (a-c) strong-wind conditions (wind speeds larger than 10 m s -1 ) and (d-f) weak-wind conditions (wind speeds smaller than 3 m s -1 ). Contours correspond to SST (in K). . . . . . . . . . . . . 44 Fig. 5. Anomaly of (a) time-mean surface wind speed |U 10m | ⋆ (in m s -1 ), (b) surface divergence (in 10 -5 s -1 ), (c) downwind SST gradient (in 10 -5 Km -1 ) and (d) Laplacian of atmospheric temperature (in 10 -10 Km -2 ). In contours, SST eddy (in K). Letters used to describe particular eddies on this figure are at the same spatial coordinates as those on Figs. 6, 9 and 10. . . . 45 Fig. 6. Composites of surface divergence (shadings, in 10 -5 s -1 ) for days with (a-b) northerly winds, (c-d) weak winds, and (e, f) southerly winds. In (a, c, e), contours correspond to downwind SST gradient (in 10 -5 K m -1 ). In (b, d, f), contours correspond to Laplacian of atmospheric boundary layer temperature (in 10 -10 K m -2 ). . . . . . . . . . . 46 Fig. 7. Correlation coefficient of surface wind divergence with (a) downwind SST gradient and (b) Laplacian of atmospheric boundary layer temperature, as a function of the large-scale background wind at 10 meters. (c) Correlation coefficient of downwind SST gradient with Laplacian of temperature. White squares denote insufficient number of snapshots for averaging over wind conditions. . . . . . . . . . . . . . . . . . . . 47 Fig. 8. (a) Boundary layer height (in m) and (b) difference between 0-500 m vertically averaged temperature θ and SST (in K). Both quantities are averaged in space and plotted as a function of the large-scale background wind at 10 meters. (c) Regression coefficient of wind-speed and SST anomalies as a function of the background wind (m s -1 K -1 ). . . . . . . . 48 Fig. 9. Composites of vertical velocity at 500 m (in mm s -1 ) for weak winds. Contours correspond to -[∇ 2 θ ] ⋆ (in 10 -10 K m -2 ). . . . . . . . . . . . . . . . . . . 49 Fig. 10. Composites of wind-stress divergence [∇ • τ] ⋆ (a, d, g), stability effect on wind-stress diver- gence E stab (b, e, h) and wind divergence effect on wind-stress divergence E div (c, f, i). Units are in 10 -7 N m -3 . Contours in (a, d, g) correspond to SST eddy (in K). Contours in (b, e, h) correspond to [U 10m ] • ∇SST eddy (in 10 -5 K m s -1 ). Contours in (c, f, i) correspond to [∇ 2 θ ] ⋆ (in 10 -10 K m -2 ). (a, b, c) strong northerly winds; (d, e, f) weak winds, (g, h, i) strong southerly winds. . . . . . . . . . . . . . . . . . . . . 50 Fig. 11. Correlation coefficient of wind stress divergence with (a) downwind SST gradient, (b) temperature Laplacian. (c) Regression coefficient of wind stress divergence and downwind SST gradient anomalies as a function of the large-scale background wind at 10 meters, in 10 -2 N m -2 K -1 . . . . . . . . . . . . . . . . . . . . . . 51

  FIG.6. Composites of surface divergence (shadings, in 10 -5 s -1 ) for days with (a-b) northerly winds, (cd) weak winds, and (e, f) southerly winds. In (a, c, e), contours correspond to downwind SST gradient (in 10 -5 K m -1 ). In (b, d, f), contours correspond to Laplacian of atmospheric boundary layer temperature (in 10 -10 K m -2 ).

FIG. 9 .

 9 FIG. 7. Correlation coefficient of surface wind divergence with (a) downwind SST gradient and (b) Laplacian of atmospheric boundary layer temperature, as a function of the large-scale background wind at 10 meters. (c) Correlation coefficient of downwind SST gradient with Laplacian of temperature. White squares denote insufficient number of snapshots for averaging over wind conditions.

  FIG. 10. Composites of wind-stress divergence[∇ • τ] ⋆ (a, d, g), stability effect on wind-stress divergence E stab (b, e, h) and wind divergence effect on wind-stress divergence E div(c, f, i). Units are in 10 -7 N m -3 . Contours in (a, d, g) correspond to SST eddy (in K). Contours in (b, e, h) correspond to [U 10m ] • ∇SST eddy (in 10 -5 K m s -1 ).Contours in (c, f, i) correspond to [∇ 2 θ ] ⋆ (in 10 -10 K m -2 ). (a, b, c) strong northerly winds; (d, e, f) weak winds, (g, h, i) strong southerly winds.

  FIG. 11. Correlation coefficient of wind stress divergence with (a) downwind SST gradient, (b) temperature Laplacian. (c) Regression coefficient of wind stress divergence and downwind SST gradient anomalies as a function of the large-scale background wind at 10 meters, in 10 -2 N m -2 K -1 .

  The downwind SST gradient k • ∇SST (x, y,t) = (U 10m (x, y,t)/|U 10m (x, y,t)|) • ∇SST (x, y)

	was computed for each time output and grid point, then put in the new reference frame. Figures 4b
	and 4e show this quantity, for strong and weak winds in the case of warm eddies. Due to our
	specific definition, the downwind SST gradient is different in amplitude for strong and weak-
	wind conditions (Figs. 4b

  This relation reflects the fact that variations of the drag coefficient C d and the surface wind speed are closely linked to SST variations. Indeed, the correlation coefficient of [∇ • τ] ⋆ with [k] • ∇SST eddy is 0.91 (Tab. 3) which is in agreement with the role of vertical stability in explaining the spatial patterns of wind stress divergence. Term E div tends to reinforce the divergence close to the eddy centers (e.g. eddies B and D) and also explains a significant part of [∇ • τ] ⋆ above filamentary structures in SST between eddies C and D or to the South West of eddy A. This is in agreement with a correlation coefficient of 0.73 between wind stress divergence and temperature Laplacian.

	-1 )
	while Figs. 10b and 10c present its two components following decomposition (6). Comparing

Figs.

10b and 10c

, term E stab is in general larger than term E div (r.m.s. ratio of 1.69, see Table 4). The role of DMM in shaping the wind stress divergence can be understood by realizing that E stab is proportional to the downwind gradient of SST with a correlation coefficient of 0.97 (see table

3

).

TABLE 2 .

 2 Correlation coefficients between different parameters related to wind divergence for Northerly,

		76	0.73	0.43
	C([w] ⋆ , k • ∇SST eddy )	0.50	0.16	0.08
	C([w] ⋆ , -∇ 2 SST eddies )	0.19	0.42	0.16

TABLE 3 .

 3 Correlation coefficients between different parameters related to wind stress divergence forNortherly, weak and southerly large-scale winds.

			Northerlies weak winds Southerlies
		rms( E stab ) in 10 -7	1.44	0.46	1.78
		rms( E div ) in 10 -7	0.85	0.40	1.10
		rms([∇ • τ] ⋆ ) in 10 -7	2.09	0.80	2.96
	710	TABLE 4. r.m.s. values of different parameters related to wind stress divergence for Northerly, weak and
	711	southerly large-scale winds.

on the main heat budget remained small and no major differences were obtained concerning the results of this paper.

577

LIST OF TABLES


Romain Garrouste
email: garroust@mnhn.fr

André Nel
email: anel@mnhn.fr

Alaskan Palaeogene insects: a challenge for a better knowledge of the Beringian 'route' (Odonata: Aeshnidae, Dysagrionidae)

Keywords: Insecta, Paleocene-Eocene, Beringia, Alaska, paleoclimate

Alaskan Palaeogene insects: a challenge for a better knowledge of the Beringian 'route' (Odonata: Aeshnidae, Dysagrionidae)

Introduction

The Alaska is a crucial area for the understanding of the insect paleobiogeography in relation to the successive Beringian land bridges (among others, [START_REF] Mantilleri | Phylogénie des Stereodermini Sharp, 1895, et description d'un nouveau genre afrotropical (Coleoptera: Brentidae)[END_REF][START_REF] Espeland | Ancient Neotropical origin and recent recolonisation: Phylogeny, biogeography and diversification of the Riodinidae (Lepidoptera: Papilionoidea)[END_REF][START_REF] Brunke | Dispersal of thermophilic beetles across the intercontinental Arctic forest belt during the early Eocene[END_REF][START_REF] Kim | West meets East: how do rainforest beetles become circum-Pacific? Evolutionary origin of Callipogon relictus and allied species (Cerambycidae: Prioninae) in the New and Old Worlds[END_REF][START_REF] Dorchin | Phylogeny, new generic-level classification, and historical biogeography of the Eucera complex (Hymenoptera: Apidae)[END_REF], and the climatic changes at high latitudes, especially during the hot-house episode of the Paleocene-Eocene. But the Alaskan insect fossil record remains very poor, except for recent progresses in the knowledge of the Pleistocene to Holocene entomofaunas. [START_REF] Grimaldi | Insects from the Upper Miocene Grubstake Formation of Alaska[END_REF] summarized the knowledge on pre-Pleistocene insects from Alaska. Only two Miocene (compression fossils) and a Late Cretaceous (amber) outcrops with insects are currently known. Paleocene and Eocene insects are only recorded through a few undescribed amber inclusions and traces of activities on plant remains, all from the Chickaloon Formation [START_REF] Sunderlin | Paleoclimatic and paleoecological implications of a Paleocene-Eocene fossil leaf assemblage, Chickaloon formation, Alaska[END_REF]).

Here we describe the first two Paleocene-Eocene insects from the Chickaloon Formation. One is a wing of an Aeshnidae sensu stricto, representing the oldest fossil record of this family. The second is a wing fragment of a damselfly.

Despite the recent descriptions of numerous Mesozoic dragonfly families of the clade

Aeshnoptera [START_REF] Bechly | Morphologische Untersuchungen am Flügelgeäder der rezenten Libellen und deren Stammgruppenvertreter (Insecta; Pterygota; Odonata), unter besonderer Berücksichtigung der Phylogenetischen Systematik und des Grundplanes der Odonata[END_REF], the modern dragonfly family Aeshnidae remains unknown in the Mesozoic (see [START_REF] Bechly | A revision and phylogenetic study of Mesozoic Aeshnoptera, with description of several new families, genera and species (Insecta: Odonata: Anisoptera)[END_REF][START_REF] Huang | A new Burmese amber hawker dragonfly helps to redefine the position of the aeshnopteran family Burmaeshnidae (Odonata: Anisoptera: Aeshnoidea)[END_REF]). In the Palaeogene, the important Mesozoic diversity and morphological disparity of the Aeshnoptera is drastically reduced to the Gomphaeschnidae Tillyard & Fraser, 1940 (also Mesozoic) and the Aeshnidae sensu lato.

Among the Aeshnidae sensu lato, the most 'basal groups ' Allopetaliidae Cockerell, 1913, Brachytronidae Cockerell, 1913, and Telephlebiidae Cockerell, 1913 are still unknown in the fossil record. [START_REF] Piton | Paléontologie du gisement éocène de Menat (Puy-de-Dôme), flore et faune[END_REF] described an isolated abdomen attributable to the Aeshnoidea from the Paleocene of Menat (France) but it is impossible to accurately attribute it to the Aeshnidae (even sensu lato) and no wing has been found in this outcrop. The oldest Aeshnidae sensu stricto is Huncoaeshna [START_REF] Petrulevičius | A new genus and species of darner dragonfly (Aeshnidae: Odonata) from the lower Eocene of Laguna del Hunco, Patagonia, Argentina[END_REF] from the lower Eocene of Argentina. Some nymphs attributable to the Aeshnidae are also known from the Eocene Baltic amber (Bechly & Wichard 2008). The Latest Eocene of the Isle of Wight and several Oligocene outcrops have lead numerous Aeshnidae belonging to extinct or extant genera (Nel et al., 1994[START_REF] Nel | Dragonflies and damselflies (Insecta: Odonata) from the Late Eocene of the Isle of Wight[END_REF].

Material and method

The Chickaloon Formation near Anchorage is well-known for its macroflora together with numerous traces of insect feeding activities on leaves, together with amber with some arthropod inclusions [START_REF] Sunderlin | Paleoclimatic and paleoecological implications of a Paleocene-Eocene fossil leaf assemblage, Chickaloon formation, Alaska[END_REF]. It is currently considered as straddling the Paleocene-Eocene boundary [START_REF] Triplehorn | Radiometrie age of the Chickaloon Formation of south-central Alaska: location of the Paleocene-Eocene boundary[END_REF][START_REF] Neff | Sedimentology, facies architecture and chemostratigraphy of a continental high-latitude Paleocene-Eocene succession -The Chickaloon Formation, Alaska[END_REF]. The old Baxter mine from where the insects come, is a well-known locality for fossil leaves, situated at 61 °42.6' N., 149°05' W [START_REF] Wolfe | Tertiary plants from the Cook Inlet region, Alaska. Tertiary biostratigraphy of the Cook Inlet region, Alaska[END_REF]. The palaeoenvironment corresponds to fluvio-lacustrine system surrounded by a forest under warm temperate conditions. The specimens were studied using a Nikon SMZ 1500 and a Nikon SMZ 25. Photographs were taken using a Nikon D800, dry and under alcohol. The nomenclature of the dragonfly wing venation is based on the interpretations of [START_REF] Riek | A new interpretation of dragonfly wing venation based upon Early Carboniferous fossils from Argentina (Insecta: Odonatoidea) and basic characters states in pterygote wings[END_REF], amended by [START_REF] Nel | Les 'Anisozygoptera' fossiles. Phylogénie et classification (Odonata)[END_REF][START_REF] Bechly | Morphologische Untersuchungen am Flügelgeäder der rezenten Libellen und deren Stammgruppenvertreter (Insecta; Pterygota; Odonata), unter besonderer Berücksichtigung der Phylogenetischen Systematik und des Grundplanes der Odonata[END_REF]. For the basal classification of the Aeshnoptera, we follow [START_REF] Bechly | A revision and phylogenetic study of Mesozoic Aeshnoptera, with description of several new families, genera and species (Insecta: Odonata: Anisoptera)[END_REF] and [START_REF] Ellenrieder | A phylogenetic analysis of the extant Aeshnidae (Odonata: Anisoptera)[END_REF] Oligaeschna Piton and Théobald, 1939 but the narrow area between IR2 and Rspl due to the nearly straight Rspl does not fit with these genera (Nel et al. 1994).

Basiaeschna alaskaensis has a narrow area with two rows of cells between IR2 and Rspl, and 'aeshnid bulla', and a nearly straight Rspl. This combination of structures can be found only in Epiaeschna and Basiaeschna. Epiaeschna differs from Basiaeschna alaskaensis in the distinctly forked IR2 and base of IR1 well distal to the pterostigmal brace, while it is below it in Basiaeschna alaskaensis [START_REF] Garrison | Dragonfly genera of the new world: an illustrated and annotated key to the Anisoptera[END_REF] Description. Wing apparently hyaline, except for a darker area at level of base of IR1; length of preserved part of wing 14.7 mm, width 7.4 mm; base of RP3/4 ca. 2.0 mm basal of subnodus; base of IR2 2.0 mm distal of that of RP3/4, opposite subnodus; 10 postnodal crossveins preserved, not really aligned with the 11 corresponding postsubnodal crossveins; base of RP2 four cells and 3.7 mm distal of that of IR2; no oblique vein 'O'; areas between IR2 and RP3/4 and between RP3/4 and MA not distally broadened in preserved part of wing; postdiscoidal area with one row of cells between discoidal cell and level of base of IR1, then greatly broadened, with two rows of cells; area between MP and CuA not distally broadened, with only one row of cells; cubito-anal area very broad, with four rows of cells between CuA and posterior wing margin.

Discussion. This wing is clearly that of Zygoptera or an Epiproctophora of the isophlebiopteran lineage for the gracile venation and pattern of organization of the bases of the branches of RP relatively to the position of the nodus. The very broad cubito-anal area is encountered in few families of this kind. Affinities with the Epiproctophora are unlikely because the base of IR2 is opposite subnodus while it is generally basal to it in this clade, especially in the Eocene family Pseudostenolestidae [START_REF] Garrouste | New Eocene damselflies and first Cenozoic damsel-dragonfly of the isophlebiopteran lineage (Insecta: Odonata)[END_REF]. The same character plus the absence of the oblique vein 'O' excludes affinities with the Sieblosiidae and the Latibasaliidae (Nel et al. 2005a[START_REF] Petrulevičius | Enigmatic and little known Odonata (Insecta) from the Paleogene of Patagonia and northwest Argentina[END_REF]. Affinities with the Caloptera Belyshev and Haritonov, 1983 are excluded because of the relatively distal position of the midfork [START_REF] Bechly | Morphologische Untersuchungen am Flügelgeäder der rezenten Libellen und deren Stammgruppenvertreter (Insecta; Pterygota; Odonata), unter besonderer Berücksichtigung der Phylogenetischen Systematik und des Grundplanes der Odonata[END_REF]. The Thaumatoneuridae Tillyard & Fraser, 1938 have a very different cubito-anal area with several posterior branches of CuA. The Frenguelliidae have also an oblique vein 'O' [START_REF] Petrulevičius | Frenguelliidae, a new family of dragonflies from the earliest Eocene of Argentina (Insecta: Odonata): phylogenetic relationships within Odonata[END_REF]. The Eocene Austroperilestidae have the base of IR2 aligned with the subnodus but an oblique vein 'O' (Petrulevičius & Nel 2005). This fossil better fits with the Dysagrionidae in the positions of the main veins, the broad cubito-anal area, and the absence of oblique vein 'O'. This family currently comprises the genera Congqingia Zhang, 1992 (early Cretaceous of China); Palaeodysagrion Zheng et al., 2017, Burmadysagrion Zheng et al., 2016, Electrodysagrion Zheng et al., 2017 ('mid Burmadysagrion has much narrower wings with narrow cubito-anal area [START_REF] Zheng | Burmadysagrioninae, a new subfamily (Odonata: Zygoptera: Dysagrionidae) from mid-Cretaceous Burmese amber[END_REF]. Our fossil differs from Petrolestes in the base of IR2 opposite the subnodus instead of being much more basal [START_REF] Garrouste | New Eocene damselflies and first Cenozoic damsel-dragonfly of the isophlebiopteran lineage (Insecta: Odonata)[END_REF]. It differs from Congqingia in the broader postdiscoidal area, the narrower area between MP and CuA and the position of the base of IR2 [START_REF] Zhang | Congqingia rhora gen. nov., spec. nov. -a new dragonfly from the Upper Jurassic of Eastern China (Anisozygoptera, Congquingiidae fam. nov.)[END_REF]. Electrodysagrion has the base of RP3/4 just basal of nodus, which is not the case in our fossil (Zheng et al. 2017a). Eodysagrion differs from our fossil in the broad area between MP and CuA four cells distal of nodus level [START_REF] Rust | The first damselflies from the Lowermost Eocene of Denmark, with a description of a new subfamily (Odonata, Zygoptera: Dysagrionidae)[END_REF].

Electrophenacolestes and Primorilestes have a base of RP3/4 well basal of nodus, a postdiscoidal area distally broad, but it differs from our fossil in the area between MP and CuA becoming broader three cells distal of nodus (Nel et al. 2005b, 2016[START_REF] Nel | The first Baltic amber dysagrionine damselfly (Odonata: Zygoptera: Thaumatoneuridae: Dysagrioninae)[END_REF][START_REF] Rust | The first damselflies from the Lowermost Eocene of Denmark, with a description of a new subfamily (Odonata, Zygoptera: Dysagrionidae)[END_REF]. Phenacolestes shares with our fossil the same position for the base of RP3/4, but its postdiscoidal area becomes broader more distally than in our fossil, while the area between MP and CuA remains narrow as in our fossil [START_REF] Calvert | The fossil odonate Phenacolestes, with a discussion of the venation of the legion Podagrion Selys[END_REF]. Dysagrion has a narrow area between MP and CuA, but differs from our fossil in the narrow postdiscoidal area and the area between RP3/4 and IR2 becoming distally very broad [START_REF] Nel | Les Lestoidea (Odonata, Zygoptera) fossiles: un inventaire critique[END_REF].

Palaeodysagrion is based on a wing base, with nearly no comparable structure with our fossil.

Nevertheless its cubito-anal area has only one row of cells opposite the nodus, instead of two in our fossil (Zheng et al. 2017b).

This fossil differs from all the dysagrionid genera, thus it probably corresponds to a new genus. Nevertheless we avoid naming it because of the lack of information on the basal structures of the wing, especially the discoidal cell.

Conclusion

Basiaeschna is clearly not a 'basal' taxon in the phylogeny of the Aeshnidae (Ellenrieder 2002: fig. 20). Thus its discovery in the Paleocene-Eocene strongly supports the hypothesis that the Aeshnidae sensu stricto diversified much earlier, probably during the Campanian-Maastrichian, more or less in accordance with the dating obtained by [START_REF] Letsch | Not going with the flow: a comprehensive time-calibrated phylogeny of dragonflies (Anisoptera: Odonata: Insecta) provides evidence for the role of lentic habitats on diversification[END_REF].

Unfortunately, no fossil Odonata is recorded from the Latest Cretaceous.

After [START_REF] Garrison | Dragonfly genera of the new world: an illustrated and annotated key to the Anisoptera[END_REF], the habitat of Basiaeschna janata is the 'forested rivers, streams and lakes with little shore vegetation, and oxygenated ponds'. It corresponds to the paleobiota of the Chickaloon Formation during the Paleocene -Eocene hothouse phase. Also, 57 M.a. ago the area was ca. 200 to 500 km southward [START_REF] Sunderlin | Warm paleoenvironmental indicators in the Paleocene/Eocene Chickaloon Formation, Matanuska Valley, Alaska[END_REF][START_REF] Sunderlin | Paleoclimatic and paleoecological implications of a Paleocene-Eocene fossil leaf assemblage, Chickaloon formation, Alaska[END_REF][START_REF] Sunderlin | Paleoenvironment and paleoecology of a Late Paleocene high-latitude terrestrial succession, Arkose Ridge Formation at Box Canyon, southern Talkeetna Mountains, Alaska[END_REF].

The discovery of a Basiaeschna supports temperate, warmer conditions than today in the area, favorable for Beringian interchanges.

The Paleocene-Eocene was an exceptional period for the hot-house conditions and for the Asiatic-North American interchanges, relatively well-documented by fossil plants and vertebrates [START_REF] Brikiatis | The De Geer, Thulean and Beringia routes: key concepts for understanding early Cenozoic biogeography[END_REF]), but relatively poorly known for the terrestrial arthropods, despite recent advances in the topic [START_REF] Archibald | New Dinopanorpidae (Insecta: Mecoptera) from the Eocene Okanagan Highlands (British Columbia, Canada and Washington State, USA)[END_REF][START_REF] Archibald | Ecology and distribution of Cenozoic Eomeropidae (Mecoptera), and a new species of Eomerope Cockerell from the Early Eocene McAbee locality, British Columbia, Canada[END_REF][START_REF] Archibald | Two new species of fossil Eomerope (Mecoptera: Eomeropidae) from the Ypresian Okanagan Highlands, far-western North America, and Eocene Holarctic dispersal of the genus[END_REF]. Generally the available information for insect Beringian interchanges is indirect, obtained through dating in molecular phylogenies [START_REF] Kim | West meets East: how do rainforest beetles become circum-Pacific? Evolutionary origin of Callipogon relictus and allied species (Cerambycidae: Prioninae) in the New and Old Worlds[END_REF][START_REF] Dorchin | Phylogeny, new generic-level classification, and historical biogeography of the Eucera complex (Hymenoptera: Apidae)[END_REF], or through discoveries of Palaeogene Eurasiatic fossils related to modern or fossil Nearctic taxa [START_REF] Archibald | Intercontinental dispersal of giant thermophilic ants across the Arctic during early Eocene hyperthermals[END_REF]. The same problem occurs with the three other 'routes' of De Geer, Thulean, and Turgai Strait (Fig. 4), even if some Paleocene insects are known from Spitzberg in De Geer 'route' [START_REF] Wappler | Wasp mimicry among Palaeocene reduviid bug from Svalbard[END_REF] (Nel & Petrulevičius 2010[START_REF] Li | New discoveries of Neogene hawker dragonflies (Insecta, Odonata, Aeshnidae) from Shandong province in China[END_REF]. The Dysagrionidae are known in the Palaeogene of North America, Central Asia, and Europe, but also in the 'mid' Cretaceous Burmese amber, suggesting faunal transfers between Eurasia and North America. The new Alaskan Dysagrionidae suggests that at least some of these transfers were made through the Beringian Bridge.

Basiaeschna is a widespread Eastern Nearctic monospecific genus, nowaday going west to Saskatchewan [START_REF] Garrison | Dragonfly genera of the new world: an illustrated and annotated key to the Anisoptera[END_REF][START_REF] Hutchings | Eight new or previously unrecorded species of Odonata (dragonflies) for Saskatchewan[END_REF]), thus its discovery in the North-Western part of the same region is not surprising. But it is surprising that Basiaeschna remains unknown in the Cenozoic of Eurasia.

Odonata are generally not the most frequent insects found as fossils. Thus these discoveries together with the presences of numerous traces of insect activities show that the Chickaloon Formation could potentially give a rich insect assemblage, important for future direct evidences of Palaeogene Beringian interchanges.

  Age and outcrop. Paleocene-Eocene, Chickaloon Formation, Premier Coal Group, new strip pit near Baxter Mine, Anchorage C-6 quad, Alaska.Description. An incomplete wing, with postero-basal half missing, probably hyaline (no trace of coloration under alcohol); length of fragment 35.0 mm, estimate wing length ca. 40.0 mm, wing 10.1 mm wide in part distal of nodus, distance between arculus and nodus ca. 13.0 mm, between nodus and pterostigma 15.3 mm, between pterostigma and apex 4.2 mm; pterostigma 4.8 mm long, 1.06 mm wide, covering three cells; pterostigmal brace present, distinctly oblique, and aligned with basal margin of pterostigma; Ax2 visible, ca. 10 secondary crossvein distal of Ax2 not well aligned with nine antenodal crossveins between ScP and RA; 14 postnodal crossveins not aligned with 14 postsubnodals; four antesubnodal crossveins above the Bq space; five Bqs crossveins; Mspl without strong concave bend, and with two rows of cells between it and MA; two rows of cells between Mpsl and MP; MA and RP3/4 parallel and MA with a weak concave bend before wing margin, two rows of cells between MA and RP3/4 in distal part; base of RP3/4 5.7 mm basal of nodus, that of IR2 3.8 mm; base of RP2 aligned with subnodus; oblique vein 'O' one cell distal of base of RP2; distal fork of IR2 nearly absent; three rows of cells in area between RP2 and IR2; RP2 parallel with anterior branch of IR2, making a distinct curve; one row of cells between RP1 and RP2 basal of pterostigma; base of IR1 at level of pterostigmal brace; Rspl nearly straight, with two rows of cells between it and IR2.Discussion. The presence of a RP2 modified to a characteristic curvature beneath the pterostigma is a synapomorphy of the Aeshnodea Bechly, 1996. Affinities with the Allopetaliidae Cockerell, 1913 are excluded because there is only one row of cells between RP1 and RP2 basal of the pterostigma. The presence of an anterior fork of IR2, even if it is rudimentary, supports an attribution to the Euaeshnodea Bechly et al., 2001. The presence of the characteristic (but weakly indicated) bulge in the distal part of the MA ('aeshnid bulla') supports an attribution to the Aeshnidae Leach, 1815. Telephlebia is excluded because of the well-developed pterostigmal brace and the rudimentary fork of IR2 in Basiaeschna alaskaensis sp. nov. Affinities with Brachytron and Aeschnophlebia are excluded because of the well-developed pterostigmal brace in Basiaeschna alaskaensis. The rudimentary fork of IR2 could indicate affinities with the Oplonaeschna Selys, 1883 and the Cenozoic

  . All the visible characters of Basiaeschna alaskaensis fit well with those of Basiaeschna, viz. a very rudimentary fork of IR2 (or even no fork at all), Rspl and Mspl nearly straight, 2-3 rows of cells between Rspl and IR2 and between Mspl and MA, a weak 'aeshnid bulla', one row of cells between RP1 and RP2, and same pattern of IR1. Two fossil taxa have been attributed to the genus Basiaeschna, viz. Basiaeschna separata Scudder, 1890 and Basiaeschna ashutasica Martynov, 1929, but later transferred into the genus Oligaeschna by Nel et al. (1994). Thus Basiaeschna alaskaensis is the first fossil species of the genus Basiaeschna. The Eocene South American genus Huncoaeshna Petrulevičius et al., 2010 has also a two-celled area between a nearly straight Rspl and IR2 and an unforked IR2 (Petrulevičius et al. 2010), but it differs from Basiaeschna alaskaensis in the presence of four rows of cells between IR2 and RP2, and it differs from Basiaeschna janata in the postdiscoidal area with 3-4 rows of cells just distal of discoidal triangle, instead of two in Basiaeschna janata. Material. Specimen USGS Paleobotany Loc 9870b, collection 'J. Wolfe & Hopkins 1962', stored at the National Museum of Natural History, Washington, USA. Age and outcrop. Paleocene-Eocene, Chickaloon Formation, Premier Coal Group, new strip pit near Baxter Mine, Anchorage C-6 quad, Alaska.

'

  Cretaceous of Myanmar); Dysagrion Scudder, 1878 (Eocene of Wyoming), Phenacolestes Cockerell, 1908 (Eocene of Colorado), Petrolestes Cockerell, 1927 (Eocene of Colorado and Germany), Eodysagrion Rust et al., 2008 (Eocene of Denmark), Electrophenacolestes Nel & Arillo, 2006 (Eocene Baltic amber), and Primorilestes Nel et al., 2005 (Eocene of Denmark, Russia and Miocene of Bulgaria).

Figure 1 .

 1 Figure 1. Basiaeschna alaskaensis sp. nov., holotype USGS Paleobotany Loc 9870a. A, photograph of wing. B, reconstruction. Scale bars: 5 mm.

Figure 2 .

 2 Figure 2. Basiaeschna alaskaensis sp. nov., holotype USGS Paleobotany Loc 9870a. Photograph under alcohol of costo-apical part of wing. Scale bar: 4 mm.

Figure 3 .

 3 Figure 3. Dysagrionidae genus and species undetermined, USGS Paleobotany Loc 9870b. A, photograph of wing. B, reconstruction. Scale bars: 5 mm.

Figure 4 .

 4 Figure 4. Palaeogeographical reconstruction of Earth during the Paleocene. The numbers point out the key geo-dispersal nodes discussed in the text: (1) Beringia, (2) Thulean route, (3) De Geer route, and (4) Turgai Strait. Map modified after Scotese, C.R. 2001. Atlas of Earth History, Volume 1, Paleogeography, PALEOMAP Project, Arlington, Texas, 52 pp. https://www.researchgate.net/publication/264741875_Atlas_of_Earth_History.

Etymology. Named after Alaska, state from which the fossil comes.

  for the classification of the extant Aeshnidae. Vein abbreviations are ScP

	Rpsl and Mspl supplementary radial and median veins; Bqs crossveins between RP1/2, IR2
	and 'O'; 'O' oblique vein between RP2 and IR2.
	Systematic palaeontology
	Order Odonata Fabricius, 1793
	Suborder Anisoptera Sélys, 1854
	Family Aeshnidae Rambur, 1842
	Genus Basiaeschna Sélys, 1883
	Included species. Basiaeschna janata (Say, 1839); Basiaeschna alaskaensis sp. nov.
	Basiaeschna alaskaensis sp. nov.
	(Figs 1-2)
	Diagnosis. Wing characters only. Pterostigma covering only three cells (four in B. janata);
	wing ca. 40 mm long, instead of ca. 34 mm in B. janata.
	Material. Holotype USGS Paleobotany Loc 9870a, collection 'J. Wolfe & Hopkins 1962',
	stored at the National Museum of Natural History, Washington, USA.
	subcostal posterior; RA radius anterior; RP radius posterior; IRxx intercalary radial veins;

  . The monospecific Eastern Nearctic genus Epiaeschna is a good example of such situation as it is well-represented in the fossil record by five Palaearctic species, viz. Epiaeschna pseudoheros Nel and Petrulevičius, 2010 (late Oligocene, France), Epiaeschna stauropolitana Martynov, 1927 (mid Miocene, Crimea),

	Epiaeschna magnifica (Martynov 1929) (late Oligocene, Kazakhstan), Epiaeschna gossi
	(Campion 1916) (middle-late Eocene, UK), Epiaeschna matutina (Zhang 1989) (Miocene,
	China)

Acknowledgements

We sincerely thank C.C. Labandeira and F. Marsh, curator and research assistant at the collections of fossil insects at the National Museum of Natural History, USA, for their hospitality at the Paleobiology Department and loan of the fossils.