Yurovskaya Maria

Kudryavtsev Vladimir

Chapron Bertrand

Collard Fabrice

Ocean surface current retrieval from space: The Sentinel-2 multispectral capabilities

Keywords: Ocean currents, Sea surface optical images, Wave dispersion relation, Time lag, Wave breaking, Sentinel-2, Satellite methods

The Sentinel-2 MultiSpectral Instrument (MSI) collects multiple spectral band images, corresponding to specific sensing wavelengths and spatial resolutions, i.e. 10 m, 20 m and 60 m, respectively. Images are collected one at the time with a given time-lag between observations. Under favorable conditions, spatiotemporal characteristics of propagating ocean surface waves can thus uniquely be retrieved. A method for surface current vector field reconstruction is then developed. Demonstrated over different deep ocean regions, the retrieved surface current fields well compare with medium-resolution ocean circulation model or derived-velocities from altimeter measurements. At finer scales, the surface wave-conservation law is recovered, with the associated relationship between current vorticity and wave-ray curvature. Over shallow water regions, the wave propagation properties well follow sea depth variations, consistent with ETOPO1 data. Finally, time-lag between detector bands can also be exploited to estimate speed and direction properties of detected surface wave breaking whitecaps. An analysis of velocity reconstruction errors further reveals that Sentinel-2 MSI inter-channel co-registration is realized with an accuracy better than 0.1 pixel. Overall, these results confirm very promising capabilities of optical imagery to provide direct surface current velocity measurements from space, over relatively large areas, O(100 km), with a spatial resolution down to O(1 km).

Highlights

► A method is developed for surface current reconstruction from Sentinel-2 images ► It is based on cross-spectral phase estimation between images from different bands ► Retrieved current fields well compare with model and altimeter measurements ► Over shallow water regions, sea depth is reconstructed ► Inter-channel time delay is used to estimate speed and direction of large whitecaps

Introduction

An area of unfilled promise in satellite ocean remote sensing is the development of a direct inversion of upper ocean surface current characteristics.

From precise sea level measurements, satellite altimeters greatly help reveal balanced motions to describe large to meso-scale ocean dynamics properties. Indeed, away from the equator, a sea level gradient results as a pressure gradient, to be balanced by the Coriolis force associated to a current flow. This is the geostrophic balance. Altimeter-derived currents thus provide a good representation of large scale depth-integrated currents. However, surface currents are certainly not always in geostrophic balance, and also reflect interactions with upper ocean wind and wave motions. Altimeter measurements cannot fully capture multi-scale variability of the ocean circulation, especially within the uppermost surface layers, which remains a challenge for theoretical and practical ocean modeling. Techniques using Doppler radar measurements (e.g. [START_REF] Goldstein | Interferometric radar measurement of ocean surface currents[END_REF]; [START_REF] Chapron | Direct measurements of ocean surface velocity from space: Interpretation and validation[END_REF]; [START_REF] Romeiser | Quality assessment of surface current fields from terrasar-x and tandem-x along-track interferometry and doppler centroid analysis[END_REF]; [START_REF] Rodriguez | Estimating ocean vector winds and currents using a Ka-band pencil-beam doppler scatterometer[END_REF]) can provide more direct measurements, but also face a number of difficulties. Not solely related to platform attitude issues, inversion algorithm definitions must account for detected orbital motions of waves, including wave breaking effects [START_REF] Johannessen | Direct ocean surface velocity measurements from space: Improved quantitative interpretation of envisat asar observations[END_REF]; [START_REF] Hansen | Simulation of radar backscatter and doppler shifts of wave-current interaction in the presence of strong tidal current[END_REF]; [START_REF] Martin | Towards wide-swath highresolution mapping of total ocean surface current vectors from space: Airborne proof-of-concept and validation[END_REF]; [START_REF] Martin | Simultaneous ocean surface current and wind vectors retrieval with squinted sar interferometry: Geophysical inversion and performance assessment[END_REF]; [START_REF] Yurovsky | Sea surface ka-band doppler measurements: Analysis and model development[END_REF]).

Overlooked, techniques from photographs and video recordings of the sea surface have long been demonstrated and reported in various field studies (e.g., [START_REF] Barber | A Diffraction Analysis of a Photograph of the Sea[END_REF]; [START_REF] Dugan | Water depth and surface current retrievals from airborne optical measurements of sur-face gravity wave dispersion[END_REF]; [START_REF] Dugan | Surface current measurements using airborne visible image time series[END_REF]; [START_REF] Leckler | Analysis and Interpretation of Frequency-Wavenumber Spectra of Young Wind Waves[END_REF]; [START_REF] Rascle | Intense deformation field at oceanic front inferred from directional sea surface roughness observations[END_REF]; Yurovskaya et al. (2018)). Today, with the significant improvement of optical instruments, like event cameras [START_REF] Rebecq | Emvs: Event-based multi-view stereo -3d reconstruction with an event camera in real-time[END_REF]), stereo systems [START_REF] Fedele | Space-time measurements of oceanic sea states[END_REF]) and relatively simple remote controlled measurements from drones (Yurovskaya et al. (2018a); Yurovskaya et al. (2018)), improved spatio-temporal properties of the ocean surface can be readily obtained.

From a satellite perspective, optical imagery also provides high resolution sea surface images over large areas. As presently available, an ensemble of satellite missions (e.g Landsat-8, Sentinel-2a and 2b, RapidEye, among others) not only often enable to distinguish individual ocean surface waves from acquired images, but also provide means to characterize spatio-temporal ocean surface wave displacements. Indeed, the specific viewing geometry of the satellite radiometers offers time-lagged acquisitions for different spectral channels. Near-simultaneous measurements can thus be exploited to estimate local displacements, such as moving objects on the sea surface, river ice debris [START_REF] Kääb | River ice flux and water velocities along a 600 km-long reach of lena river, siberia, from satellite stereo[END_REF]), ships [START_REF] Takasaki | Speed vector measurement of moving objects using jers-1/ops data[END_REF]), surface wave fronts [START_REF] De Michele | Direct measurement of ocean waves velocity field from a single spot-5 dataset[END_REF]), but also wave breakers that often manifest in satellite optical images as localized bright events. An overview of motion detection methods from near-simultaneous satellite images is given in [START_REF] Kääb | Motion detection using near-simultaneous satellite acquisitions[END_REF].

For Sentinel-2 measurements, cross-spectral analysis between images collected in two specific bands, was first demonstrated to retrieve surface wave directional properties and current characteristics (Kudryavtsev et al. (2017a,b)).

This initial methodology was then further improved to reconstruct the surface current velocity vector [START_REF] Yurovskaya | Wave spectrum and surface current retrieval from airborne and satellite sunglitter imagery[END_REF]). In this present work, the aim is to further test the instrument capabilities, applying the proposed methodology for different cases and over different ocean regions. For deep sea cases, the analysis concentrates on the applicability of the principle of wave action conservation, and more specifically the expected relationship between current vorticity and wave-ray curvature [START_REF] Kenyon | Wave refraction in ocean currents[END_REF]; [START_REF] Quilfen | Storm waves focusing and steepening in the agulhas current: Satellite observations and modeling[END_REF]). Over shallow water regions, changes of wave dispersion properties are then further shown to help reveal sea depth variations. Finally, time-lag between detector bands is further exploited to estimate, from space, speed and direction of detected surface wave breaking whitecaps, key for direct measurements of momentum and gas fluxes.

The structure of the paper is as follows. Section 2 introduces Sentinel-2 MSI time-lagged measurements, and the method to retrieve current and bathymetry information. Examples, including whitecap velocities, are given in Section 3. Discussion in Section 4 covers applicability of the proposed approach, possible error sources and estimation of velocity reconstruction accuracy.

Sentinel-2 MSI data and Methodology

MSI time-lagged data

Sentinel-2A and Sentinel-2B multispectral (MSI) instruments are composed of 13 spectral bands (443-2190 nm) with different spatial resolutions, ranging from 10 m to 60 m, to cover a swath width of 290 km formed by 12 sensor clusters. Due to a specific sensor configuration, i.e. the relative detector alignment, there is a parallax angle between both neighbor clusters and spectral channel sensors inside each cluster. It leads to inter-cluster and inter-band short-time lags that can be estimated from a viewing geometry as

dt = D/V D = H tan 2 θ 1 + tan 2 θ 2 -2tanθ 1 tanθ 2 cos(ϕ 1 -ϕ 2 ), ( 1
)
where H is the altitude of the satellite, θ 1,2 and ϕ 1,2 zenith and azimuth view angles of the same point in two different bands, V is the satellite speed and D the length of satellite track. Compared to Eq. ( 22) by Kudryavtsev et al. (2017a), the absolute satellite speed and flight distance are considered in Eq. (1), instead of ground ones, as the viewing angles are defined from ground to sensor.

While this is not critical for an overall estimation of wave dispersion characteristics (Kudryavtsev et al. (2017a,b)), a more precise dt value is essential to best retrieve local velocities, as discussed in Section 4.

Values for H and V are calculated from satellite coordinates, given in MSI auxiliary files. The time values for each band and strip (cluster) are also directly listed in metadata information. As tested, both ways to estimate the time lags give similar results, within 1-2% precision. The summary of inter-band and inter-cluster relative time shifts is reported in Fig. 1

Current Vector and Ocean Depth Reconstruction

To derive wave dispersion characteristics, the approach follows Kudryavtsev et al. (2017a). Consider I 1 , I 2 , image brightness fragments in B02 and B04, respectively, their coherence and phase spectra are: with Î1,2 , Fourier transform, and * its complex conjugation. Following linear surface wave theory, the phase spectrum in absence of current is

Coh = abs( Î1 Î2 * ) Î1 Î1 * • Î2 Î2 * , (2)
F = arg( Î1 Î2
F 0 = dt gktanh(kh), (4)
where g is gravity, k wavenumber, and h water depth.

In presence of a surface current, the surface wave dispersion is modified. The upper ocean is moving with a current velocity U, very slowly varying with position, i.e. varying over a scale much larger than the peak wavelength of the wave system, typically from 1 km to 20 km. To first order, this surface current locally, e.g. O(1 km), Doppler-shifts the phase as:

F = F 0 + kU • dt. (5)
In terms of phase velocity, C = F/(kdt), a transect of the phase spectrum along the wave direction provides an estimate of the corresponding surface current projection, as a measurable deviation between C(k j ) and C 0 (k j ):

U j = C -C 0 = F/(kdt) -tanh(kh)g/k,
or for deep sea conditions (kh >> 1):

U j = F/(kdt) -g/k. (6)
For deep water conditions or when the ocean depth is known, the inclination of the plane (F -F 0 )/dt in the wavenumber space gives the current magnitude and direction. In this case Eq. ( 5) can be solved using the least square method, over points k j with coherence (2) exceeding some pre-assigned threshold value (Coh = 0.8 in present calculations).

For unknown h, the least square method is unstable. Over areas with detected waves much longer than the water depth (kh << 1), the problem can reduce to zero current (Eq. ( 4)) to provide an estimated bathymetry.

The longer the waves, the more accurate is this procedure. The analysis now solely concentrates on the peak wavenumber k p . The time-lagged data is not anymore necessary, as the wave frequency conserves:

gk p tanh(k p h) = const = gk 0 , h(k p ) = 1 k p atanh k 0 k p , (7)
where k 0 is the wave peak wavenumber in the deep water region.

To note,a surface current should not significantly impact the estimated depth. For a 1 m/s flow, the term kU is generally much smaller than k √ gh, down to 5-10 m water depth. Signs of phase spectra indicate the propagation direction of detected wave systems. For clarity, only points with coherence level larger than 0.8 are considered. In our case (dt > 0), negative phase shift corresponds to the direction waves are propagating to.

Algorithm Implementation

The curves U j (k), using (6) along transects shown on Fig. 2, f, j (dashed lines), are plotted in Fig. 2, l. A linear approximation, U j = const, is obtained. A negligible current is found around point 1, and a surface current estimate of about 1.7 m/s is found for point 2.

Planes (F -F 0 ) for these two image fragments are presented in Fig. 2, g,

Results

Ocean Surface Current

Repeated over other image fragments, where waves are clearly distinguished, this procedure helps to reconstruct a current field throughout the satellite observation areas. As obtained, the resulting current field, shown in Fig. 3, a, is in a good qualitative agreement with altimeter derived estimates, Fig. 2 one. This ''overestimation" is also systematic for the other cases considered below. Besides some isolated false points, an artificial strip-like structure is apparent in Fig. 3, a. This is an indication of a small systematical error inside images taken from different clusters. This error can arise from both inter-band geolocation inaccuracy and the time lag estimate. As further analyzed in Section 4, the former factor is the most significant for Sentinel-2 images.

Examples of surface current reconstruction over other ocean regions, the

Bathymetry

Another Sentinel-2 image, overlapping an intense current region, is reported on Fig. 5. This snapshot contains a part of the Gulf Stream, and was acquired on 2016-05-14, 15:59, over the Florida shelf Atlantic region.

The part of the current field covered by the MSI image is consistent with altimeter-derived estimates, Fig. 5, a, d, e. The current frontal location is well-delineated and matches both altimeter gradients and brightness peculiarities on optical image (not shown). In line with previous results, the retrieved current is slightly stronger than the altimeter-derived one. Analysis also reveals an uniform flow of about 0.5 m/s, detected towards East-Southeast, probably associated to the tidal current, and thus not present in altimeter products.

In the shelf area, the total dispersion relation, accounting for the water depth, must be considered, Eq. ( 5), to estimate the flow velocity. Indeed, as obtained from Fig. 5, b, the waves traveling from the East are significantly modified by the bottom topography, shortening from 120 m in the East to 80 m at the coast. This measurable effect can help to solve the inverse problem, i.e. to estimate the ocean depth through Eq. ( 7). As anticipated, Fig. 5, c, f, display very good agreement of the reconstructed bathymetry and ETOPO1

Global Relief Model (www.ngdc.noaa.gov/mgg/global/).

Small scale surface current

All above examples confirm an overall qualitative agreement with largescale altimeter-derived estimates. As understood, these medium-resolution products cannot be used to evaluate detected fine structures of the retrieved current fields. A case, reported in Fig. 6 For more in-depth analysis, the accuracy of current reconstruction can be indirectly controlled by checking the expected frequency conservation law, following from kinematic equations for wave rays in the geometrical optics approximation (e.g. [START_REF] Phillips | The Dynamics of the Upper Ocean[END_REF]):

ω = ω 0 + kU = const, (8)
where ω 0 = gktanh(kh) is the wave intrinsic frequency of surface water waves and ω is the detected frequency of the surface gravity wave propagating in a current region.

As obtained and reported on Fig. 6,c, ω 0 , estimated from the brightness peak wavenumber, strongly fluctuates in the region of intense non-uniform current. On the opposite, the total frequency ω 0 + kU, Fig. 6,d, is much smoother, in line with the current field reconstruction.

Differentiation of Eq. ( 8) reduces it to one-dimensional expressions, eliminating the unknown constant:

-dω 0 /dx = d(k x U x + k y U y )/dx -dω 0 /dy = d(k x U x + k y U y )/dy, (9)
In terms of wave-ray trajectories, an interesting consequence of these kinematic equations is the expected relation between the radius of curvature R of the wave-rays, the wave group velocity c g and the vertical component of the current vorticity, assuming c g >> U [START_REF] Kenyon | Wave refraction in ocean currents[END_REF]:

c g /R = (rotU) z . ( 10
)
Both Eq. ( 9) and Eq. ( 10) can then be used to check the validity of all retrieved current fields. U and ω 0 derivatives can be estimated, using a least square method inside areas encompassing sufficient number of points, to ensure reliable surface current estimates. Ray curvature is estimated following the same procedure, through the derivatives of the wave vector direction α:

1 R = ∂α ∂r = ∂α ∂x cos α + ∂α ∂x sin α. ( 11
)
The comparison between left and right parts of Eq. ( 9) and Eq. ( 10), for the cases shown in Fig. 3 and Fig. 4, is presented Fig. 7. Mean values of each parameter (gray dots) are calculated around every point inside small 0.2 o square image fragments. Results first appear highly scattered. This is mainly induced from unstable estimations of the derivatives and their combinations from spatially non-uniform fields. This is especially evident for cases with multiple wave systems for which the chosen wavenumber peak may belong to any of co-existing wave trains. The ray curvature is also very sensitive and difficult to evaluate (Eq. ( 11), Fig. 7, bottom) given the small dynamic range of wave direction values inside each squared area. Yet, binaveraging (magenta/purple squares) improves estimates, close to the mean expected one-to-one line (black). Overall, the retrieved current fields are thus generally consistent with the conservation law principle.

Whitecap Velocities

To further take advantage of the time-lagged Sentinel-2 MSI acquisitions, the direct displacements of moving coherent targets can also be performed.

For ocean applications, a 1-s time-lag is sufficient to study motion and periodicity of whitecaps forming during wave breaking events [START_REF] Donelan | Periodicity in whitecaps[END_REF]. In the example shown Fig. 8, upper line, fragments from different parts of the Sentinel-2 observations, considered in Fig. 2 and Fig. 3 (Somali), are combined to construct RGB-images. The red color corresponds to the initial signal, i.e. adjusted B02 or B04 brightness. The green color corresponds to the same signal, acquired 1 s latter. The blue color corresponds to the averaged signal. Whitecaps are usually smaller than Sentinel-2 pixel resolution (10 m), but wave breaking events are clearly detected. Motions of wave breaking fronts can then be obtained. Inter-channel correlation function provides object displacement and thus, their velocity and direction [START_REF] Kubryakov | Reconstructing large-and mesoscale dynamics in the black sea region from satellite imagery and altimetry data. a comparison of two methods[END_REF]). Peak positions of the resulting correlation functions, shown in Fig. 8, f-j, correspond to the mean direction of the whitecap propagation.

The estimated velocities range between 5 m/s and 8 m/s, comparable to the phase and group velocities of the dominant waves, about 9 m/s and 4.5 m/s, respectively.

Discussion: Method Applicability and Accuracy

This methodology to infer surface current velocity shall apply to any space-borne optical multi-channel images, having inter-channel time-lag of order of seconds, and sufficient spatial resolution to resolve surface waves.

A necessary condition is indeed the visibility of surface wave modulations to analyse their propagation properties. With pixel resolution of order 10 m, this is usually fulfilled in most of the sun glint area. Except within the very specular part of the glint or too far from it, surface waves are well detected. Other factors can prevent the analysis of wave dispersion characteristics: clouds, surface roughness features like slicks, ship tracks or objects on the sea surface, including bright whitecaps. Whitecaps are often present in frontal current regions, and not solely during windy conditions.

Yet, the methodology appears quite robust. As demonstrated, Fig. 3 and Fig. 7, a (Somali case), a surface current field was retrieved under high wind conditions with numerous detectable whitecaps.The retrieved current values may then be overestimated over the most active wave breaking area (North-East part). Future investigations shall thus be necessary to better assess possible biases induced by visible whitecaps.

Results also depend on the directional spread of the wave spectrum, and the relative wave-current direction. Waves propagating perpendicular to a current direction are only weakly impacted. The procedure described in Section 2 can not apply. Ideally, wave systems exhibiting a large directional spread will help. Technically, a solution is to design an instrument with increased multi-angle bi-static detector capability, to combine high angular sampling with high spatial resolution [START_REF] Rascle | Sunglint images of current gradients at high resolution: Critical angle and directional observing strategy[END_REF]).

Accurate estimation directly depends on the time-lag between acquisitions, and their co-registration error. To retrieve surface wave propagation characteristics, time-lags should be long enough to provide a reliable crossspectral phase estimate, but short enough to ensure strong coherency between the two consecutive observations. For a time shift dt and displacement dx, with systematic errors ∆t and ∆x, respectively, the velocity estimate error

is ∆v = v - vdt + ∆x dt + ∆t = v ∆t dt + ∆t - ∆x dt + ∆t . ( 12
)
The first term in ( 12 Increasing the time-lag reduces the error (green line). But, a 5% time-lag error leads to 0.5 m/s uncertainty in velocity estimate for 50 m waves. In our present analysis, dt has been estimated with an accuracy of about 1%

(Section 2). The associated error is then negligible compared to the error related with co-registration precision.

Conclusion

Satellite sun glint images of the sea surface often provide highly powerful means to observe and quantify small-scale spatial variations of currents, wind and surfactants. In this paper, the Sentinel-2 MultiSpectral Instrument A method is applied to estimate the surface current from images of the sea surface, taken from two particular Sentinel-2 bands with a time delay of order 1 second. The measured deviation from the expected linear surface wave dispersion relationship directly relates to surface current impacts. The waverays, wavevenumber and dispersion fields, w(k), can cover a fairly wide range of angles to serve the reconstruction of the total surface current vector. In the absence of current, and shallow water conditions, the dispersion variations are determined by the ocean depth variations.

For MSI, the largest time-lag between acquisitions using 10-m resolution bands, is of order 1 s. To improve surface current determination, optimized acquisitions could consider video-like acquisitions, rather than two snapshots.

Already, the reconstructed current fields appear valuable. In absence of ground-truth information, results well compare, at large to medium spatial scales, with altimeter-derived geostrophic current estimates. At higher resolution, the analysis satisfy conservation laws, as obtained from wave-ray kinematic equations.

The possibility to estimate the speed and direction of large whitecaps, has also been tested. Again, this is opening for future investigations, as a potential key capability to infer direct measurements of momentum and gas fluxes.

As discussed for reliable current reconstruction, MSI images should be co-registered with an accuracy better than 0.03 pixel. For Sentinel-2 MSI measurements, this is generally fulfilled.

Overall, these different results demonstrate very encouraging prospects to combine different satellite measurements (altimeter, optical, radar). The design of dedicated future satellite missions to precisely retrieve surface cur-rents at high resolution, may thus build upon a satellite constellation, building from standard altimeter data, to medium resolution measurements (future SWOT mapping altimeter), completed with multi-angle bi-static optical measurements [START_REF] Kudryavtsev | Imaging mesoscale upper ocean dynamics using synthetic aperture radar and optical data[END_REF]

Figure 1 :

 1 Figure 1: Inter-cluster and inter-band time lag (relative to the earliest acquisition) in MSI Sentinel-2 data.

Figure ( 2

 2 Figure (2) provides the step-by-step algorithm to estimate the projection of the current velocity in the wave propagation direction. To illustrate the methodology, a Sentinel-2 image is considered (Fig.2, b), acquired August, 27th, 2016 at 06:46 in the region of the Somali current. This current is flowing from the South, rotating clockwise near the Somali peninsula. This large scale current is generally well captured by altimeter measurements (GlobCurrent surface current data, www.globcurrent.org), as reported in Fig.2, a. The current front is further clearly distinguished using MSI optical data, as colored waters from the Africa coast are very well delineated. A fragment of the frontal area is shown in Fig.2, c, with two squared areas of size 1 km x 1 km marked inside (2) and outside (1) the current. Zooming in (Fig.2, d, h), the detected wavy patterns for these two areas are apparently quite different: a dominant wave system in the upper area, and a more entangled multi-modal wave structure inside the current. The respective coherence fields, Eq. (2), and phase shift spectra, Eq. (3), are shown in subplots (e)-(f) and (i)-(j).

Figure 2 :

 2 Figure 2: (a) Current field on 2016-08-27 near Somalia according to altimeter data; (b) MSI Sentinel-2 image, obtained on 2016-08-27, 06:46; (c) image fragment with current front manifestation; (d) zoomed image fragment around point 1; (e) coherence for bands B02 and B04; (f) phase shift spectrum; (g) observed and theoretical phase difference; (hk) the same as (d)-(g) but for fragment 2; (l) current velocity retrieval for the directions marked with dashed lines in (f) and (j); (m) plane approximation of (F -F 0) plotted in (k).

  Fig. (3), b, c. Respective correlation coefficients, given in figure titles, show high statistical significance of the result. Both retrieved current amplitude and direction variability generally follow altimeter-derived estimates. The retrieved flow is stronger than the time-and spatial-averaged altimeter derived

Figure 3 :

 3 Figure 3: Current field retrieved from Sentinel-2 bands B02 and B04 for the case from Fig. 2 (a) and scatter plots of measured versus geostrophic current velocity (b) and direction (c).

  , typically encompass large spatial variability of the surface current at small scales. Sentinel-2 MSI image was acquired on April, the 3rd 11:33, in North-East Atlantic, a region with intense tidal currents. MARC model (Modeling and Analysis for Coastal Research, http://marc.ifremer.fr/en/results/currents/), Fig. 6, a, forecasts currents up to 3 m/s, over the North-North-East part, around Ouessant Island, at the time of the acquisition. Strong current variability at small scales, O(1000 m), is seemingly recovered with the proposed method, Fig. 6, b. Again, when results in neighbor strips systematically differ, it is likely indicating inter-channel geolocation imperfection in one or both clusters.

  ) r.h.s. indicates the time-lag uncertainty. The second one is the image co-registration error. Time-lag uncertainty increases with decreasing dt, i.e. the larger the time-lag the better the accuracy of the velocity estimation. Though not equivalent, spatial and temporal errors can occasionally compensate each other: a systematic displacement will appear as an additional current. A constant ∆x/dt adds to the estimated phase velocity c(k), and thus to the respective current projection. A temporal error distorts c(k) with a coefficient dt/(dt + ∆t). The influence of both terms in (12) is shown in Fig. 9, for 1 s and 2 s inter-band time-lags. For the bands with 10 m resolution and 1 s time-lag, a co-registration accuracy better than 0.1 m (0.01 pixel) is required to ensure reliable velocity estimate, down to 0.1 m/s.Examples in Section 3 demonstrate that surface currents down to 0.3 m/s are correctly retrieved, except for the case shown on Fig.6. For this case, the current magnitudes from neighbor strips systematically differ by about 1 m/s. Accordingly, B02-B04 inter-band matching accuracy is better than 0.1 pixel, and for most cases, better than 0.03 pixel. MSI co-registration accuracy seems to outclass the values listed in the Sentinel-2 data quality report, where 0.168 pixel is stated for B02 and B04 (sentinel.esa.int).

  properties and capabilities are further demonstrated.. Sentinel-2 instruments collect multiple spectral band images, corresponding to specific sensing wavelength and spatial resolution, i.e. 10 m, 20 m, and 60 m. Because images are acquired one at the time, with a fixed time-lag between observations, spatiotemporal characteristics of propagating ocean surface waves can uniquely be retrieved, including motions of whitecaps.

  ;[START_REF] Rascle | Sunglint images of current gradients at high resolution: Critical angle and directional observing strategy[END_REF]). Combining high angular diversity and pixel spacing, multi-angle optical measurements could also include polarization capabilities to help separate sunglint radiance from water-leaving, skyglint, and whitecap contributions[START_REF] Harmel | Estimation of the sunglint radiance field from optical satellite imagery over open ocean: Multidirectional approach and polarization aspects[END_REF]). While limited to favorable day-light and cloud-less conditions, Sentinel-2 MSI observations already offer essential means for multivalidation purposes: local wind, waves and current transformations and interactions. Future investigations are necessary to better assess biases, possibly induced by detected whitecaps. To note, the combined capability to track whitecaps and surface wave field transformation shall also further be explored to map and inform complex wave-current interactions[START_REF] Rascle | Surface roughness imaging of currents shows divergence and strain in the wind direction[END_REF];[START_REF] Ardhuin | Small-scale open ocean currents have large effects on wind wave heights[END_REF]) in the vicinity of ocean fronts and coastal areas.

Figure 4 :

 4 Figure 4: (a) Geostrophic current from altimeter data in the region of Agulhas current on the 4th of January, 2016 (left) and 28th of November, 2017 (center), and the Gulf of Mexico on 2018-04-09 (right); (b) respective surface currents retrieved from Sentinel-2 MSI images; (c) wavelengths and directions reconstructed from brightness spectra peak wavenumber; (d)-(e) scatter plots of measured versus geostrophic current velocity and direction (black solid lines show interval-averaged values, dashed line in (d), left, is the same, but for points U < 2 m/s).

Figure 5 :

 5 Figure 5: (a) MSI-derived current field (points with arrows) overlapping geostrophic current field in West Atlantic on the 14th of May, 2016; (b) wavelengths and directions obtained from Sentinel-2 image brightness; (c) ocean depth reconstructed through the wave dispersion relation from MSI image (dots) and ETOPO1 data (background); (d)-(e) scatter plots of geostrophic vs measured current velocity and direction; (f) scatter plot of ETOPO1 bathymetry vs reconstructed ocean depth.

Figure 6 :

 6 Figure 6: (a) Tidal current in the North of Biscay Bay on the 3rd of April, 11:30, according to MARC model; (b) current reconstructed from Sentinel-2 snapshot obtained on the 3rd of April, 11:33; (c) wave frequencies derived from image brightness spectra; (d) total wave frequency, ω 0 + kU, calculated using MSI-derived current vectors.

Figure 7 :(

 7 Figure 7: (a)-(d) left and right parts of Eq. 9 for every point (gray dots) in Fig. 3 and Fig. 4 (Somali current (a), Agulhas (b)-(c) and Gulf of Mexico (d)); squares are interval-averaged data; (e)-(k) left and right parts of Eq. 10 for the same cases as in (a)-(d).

Figure 8 :

 8 Figure 8: (a)-(e) RGB-compositions of MSI image fragments containing manifestation of wave breaking events. Red (earlier) and green (later) are the modified brightness signals of Sentinel-2 channels B02/B04, blue is their average, time lag is 1 s; (f)-(j) corresponding correlation functions; the location of maximum indicates event speed and direction.

Figure 9 :

 9 Figure 9: The absolute error of velocity estimate for 1 s and 2 s time lags (color) and different time lag estimation error ∆t (for 50 m waves), and inter-channel matching accuracy ∆x. ∆x and ∆t are of different signs here.

Acknowledgments

The authors are grateful to Vladimir Dulov for the discussion and useful comments, and to anonymous Reviewers whose valuable suggestions helped to improve the paper. The work was supported by Russian Science Foundation via grant 17-77-30019 and the Ministry of Education and Science of the Russian Federation under the State Assignment No. 0827-2018-0003, also supported through the ESA projects SArONG under contract 4000117644/16/NL/FF/gp and GlobCurrent under contract 4000109513/13/ILG. The Copernicus Sen-


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Bentamy Abderrahim

Intramonth oscillations of Atlantic ITCZ observed in SMAP satellite salinity

The time variability of wind and rainfall in the Atlantic Intertropical Convergence Zone (ITCZ) has a wide oscillation spectrum that includes strong intra-month periodicities. These latter short-period oscillations span from individual convection lifecycle events of a few hours to longer pentad and multi-week convective cluster periods. This study reports on measured ITCZ rain variability at periods of a few weeks and its imprint on sea surface salinity (SSS) observed using satellite remote sensing. Despite small amplitude of variations of only 0.1-0.2 psu, these changes are shown to be detectable in radiometer SSS estimates collected by the Soil Moisture Active Passive (SMAP) satellite. They are shown to develop in the mid-Atlantic ITCZ latitude band and to follow its seasonal meridional progression. These rain-correlated sea surface signatures appear quasi-synchronously across a wide range of longitude. Both the ITCZ-related seasonal migration and high zonal propagation speeds distinguish these intra-month SSS oscillations from that of tropical instability waves (TIW), with TIWs having periods greater than 1 month and slower westward propagation. While detection of tropical Atlantic TIW salinity signatures using satellite data has received significant attention, it appears that atmospheric freshwater forcing impacts on the upper ocean at these shorter periods represents an additional process resolvable from space using SMAP. Correlation analyses of precipitation and winds indicate that low latitude convection clusters are accompanied by an upward Ekman pumping anomaly, which uplifts saltier water to surface layers diluted by enhanced precipitation. These vertical processes modify the salt balance and change the phase relationship between the oceanic SSS response and the atmospheric freshwater forcing.

Introduction

One of the major sources of intraseasonal variations of near surface salinity in the tropical oceans is associated with oceanic tropical instability waves (TIW). Mixed layer current perturbations produced by TIWs induce cusp-shaped features in the sea surface temperature (SST) (e.g., [START_REF] Weisberg | Instability Waves in the Equatorial Atlantic Ocean[END_REF], sea surface salinity (SSS), (e.g., [START_REF] Grodsky | Tropical Instability Waves at 0°N, 23°W in the Atlantic: A Case Study Using Pilot Research Moored Array in the Tropical Atlantic (PIRATA) Mooring Data[END_REF], sea surface height (SSH) (e.g., [START_REF] Polito | Oceanic and Atmospheric Anomalies of Tropical Instability Waves[END_REF], and Chlorophyll-a (Chl-a) (e.g., [START_REF] Mcclain | Satellite Ocean-Color Observations of the Tropical Pacific Ocean[END_REF]). In the Pacific, wave-induced meridional excursions of salty and cold equatorial water periodically produce negatively correlated SST and SSS signatures that propagate westward at characteristic TIW speed of less than about 1 m s -1 , periods of 20-40 days, and wavelengths of 2 1000-2000 km e.g., [START_REF] Chelton | Observations of Coupling between Surface Wind Stress and Sea Surface Temperature in the Eastern Tropical Pacific[END_REF]). In the Atlantic, TIW signatures are generally similar to Pacific TIWs but have somewhat shorter wavelengths (< 1000 km), e.g., [START_REF] Lee | The Influence of Salinity on Tropical Atlantic Instability Waves[END_REF].

TIW-induced sea surface salinity structures have been detected in satellite salinity data obtained from orbiting L-band radiometers [START_REF] Lee | Aquarius Reveals Salinity Structure of Tropical Instability Waves[END_REF]; [START_REF] Yin | SMOSSea Surface Salinity Signals of Tropical Instability Waves[END_REF]. Differing from SST and SSH, TIW SSS signatures in the Eastern Pacific were found strongest at the equator. The satellite SSS imagery revealed that the dominant westward propagation speed of TIW at the equator is twice as fast as the TIW phase speed widely reported in the literature, which is mostly based on observations of SST and SSH away from the equator. These intraseasonal salinity perturbations are not simply TIW manifestations. They can also have an important effect on the magnitude of baroclinic energy transfer cascades in the tropical oceans due to significant meridional gradient of salinity (that between the saline equator and relatively fresh ocean of the Intertropical Convergence Zone, ITCZ) and the corresponding large magnitude of TIW-salinity perturbations, which contribution to water density perturbations is significant [START_REF] Grodsky | Tropical Instability Waves at 0°N, 23°W in the Atlantic: A Case Study Using Pilot Research Moored Array in the Tropical Atlantic (PIRATA) Mooring Data[END_REF][START_REF] Lee | The Influence of Salinity on Tropical Atlantic Instability Waves[END_REF].

Atmospheric boundary layer interactions with TIW-induced SST gradients can result in remarkably coupled spatio-temporal variations of winds, wind curl, and wind divergence [START_REF] Chelton | Observations of Coupling between Surface Wind Stress and Sea Surface Temperature in the Eastern Tropical Pacific[END_REF]. The coupling between SST gradients and winds confirms earlier observations indicating that surface winds respond to SST-induced changes in marine atmospheric boundary layer thermal stability (e.g., [START_REF] Beal | The Influence of the Marine Atmospheric Boundary Layer on ERS 1 Synthetic Aperture Radar Imagery of the Gulf Stream[END_REF]. Moreover, TIW-modulation of the wind divergence may also induce organization in atmospheric convection and rainfall, with additional impacts on the original TIW-related surface salinity perturbations. While such equatorial TIW salinity signatures and eddy salinity signatures [START_REF] Melnichenko | Signature of Mesoscale Eddies in Satellite Sea Surface Salinity Data[END_REF]; [START_REF] Hasson | Intraseasonal Variability of Surface Salinity in the Eastern Tropical Pacific Associated With Mesoscale Eddies[END_REF]) have received significant attention, surprisingly, there has been less examination of tropical ocean salinity change due to atmospheric freshwater forcing at frequencies higher than seasonal and apart from TIW influences. TIW-induced wind perturbations represent one example of local air-sea interactions that contribute to the cluster organization of tropical convection. On much larger scales, the most notorious organization is associated with the Madden-Julian Oscillation (MJO), a 30-to 90-day variability in the tropical atmosphere that propagates eastward at approximately 4 to 8 m s -1 .

MJO oscillations exhibit maximum amplitude over the Indian and western Pacific Oceans and 3 their impacts on the upper ocean have been detected in satellite remote sensing salinity (e.g., [START_REF] Shinoda | Large-Scale Oceanic Variability Associated with the Madden-Julian Oscillation during the CINDY/DYNAMO Field Campaign from Satellite Observations[END_REF][START_REF] Guan | Aquarius Surface Salinity and the Madden-Julian Oscillation: The Role of Salinity in Surface Layer Density and Potential Energy[END_REF]. Although (Foltz and McPhaden 2004) reported wind oscillations in a similar frequency band (30-70day) over the Atlantic, the MJO impacts east of the dateline, including the Atlantic sector, are less prominent. In the tropical Atlantic, the intraseasonal 30-80 day eastward-propagating convection and rainfall clusters (similar to the MJO) have been observed by [START_REF] Gu | Intraseasonal Variability in the Equatorial Atlantic-West Africa during March-June[END_REF]. These rainfall anomalies appear first in the northwestern tropical Atlantic right off the coast of South America and gradually extend eastward to cover the entire basin. In the Atlantic ITCZ, a shorter scale, 15-20 day variability is also present, which [START_REF] Tomaziello | Intraseasonal Variability of the Atlantic Intertropical Convergence Zone during Austral Summer and Winter[END_REF] associate with mid-latitude Rossby wave trains in the cold Hemisphere. The above two significant spectral peaks reflect in rainfall and winds not only over the Atlantic but also in tropical West Africa as well e.g. [START_REF] Maloney | Intraseasonal Variability of the West African Monsoon and Atlantic ITCZ[END_REF].

The global view provided by satellite imagery has helped to illustrate that tropical convection can be organized at a wide range of spatial and temporal scales, from mesoscale convective systems to planetary-scale Madden-Julian Oscillations [START_REF] Kiladis | Convectively Coupled Equatorial Waves[END_REF], scales that are virtually impossible to observe without such imagery. In monsoon regions, precipitation can appear to be organized on monthly and shorter periods [START_REF] Krishnamurti | Oscillations of a Monsoon System. Part I. Observational Aspects[END_REF]. In the Atlantic ITCZ, spatially coherent bi-weekly oscillations in winds and rainfall associated with the west African monsoon have been observed by [START_REF] Grodsky | Coupled Land/Atmosphere Interactions in the West African Monsoon[END_REF]. At shorter periods, the tropical convection is normally clustered by waves that move eastward, or westward, either along the equator or within the ITCZ [START_REF] Kiladis | Convectively Coupled Equatorial Waves[END_REF]. Such convectively-coupled equatorial waves introduce a band intra-month organization in the tropical convection and rainfall within bands that seasonally migrate with the ITCZ. This paper uses multi-year satellite datasets over the tropical Atlantic to identify likely precipitation events associated with convective clusters that are organized in a few week-long oscillations and, in turn, their imprint on SSS as measured using data from the Soil Moisture Active Passive (SMAP) satellite mission. While L-band radiometer imaging has shown some capability to detect the impact of strong individual rain events on both horizontal and vertical gradients of near surface ocean salinity [START_REF] Boutin | Satellite and In Situ Salinity: Understanding Near-Surface Stratification and Subfootprint Variability[END_REF][START_REF] Boutin | Interannual Anomalies of SMOS Sea Surface Salinity[END_REF] and even infer rainfall from SSS data [START_REF] Supply | Precipitation Estimates from SMOS Sea-Surface Salinity[END_REF], continuous satellite monitoring of 4 such events is not feasible due to the polar-orbit satellite sampling issues (full coverage requires roughly 3 days with a repeat cycle of 8 days), which allows systematic detection only of integral impact of cumulated rainfall [START_REF] Boutin | Sea Surface Freshening Inferred from SMOS and ARGO Salinity: Impact of Rain[END_REF]. Here, we focus instead on the satellite detection of the possible time-integrated ocean impacts of organized convection on SSS considering the longer time scale of convective/rainfall clusters with periods of about 3 weeks.

Satellite salinity missions operate in the L-band (1.4 GHz) where water emissivity depends on salinity. The background Earth thermal radiation in this band is almost 7 orders of magnitude weaker than in the infrared band widely used for SST. Such weak L-band radiation makes SSS retrieval challenging. Nevertheless, satellite SSS is reasonably close (to within 0.2 psu) to quasisynchronous in-situ data in the tropics (e.g., [START_REF] Lee | Consistency of Aquarius Sea Surface Salinity with Argo Products on Various Spatial and Temporal Scales[END_REF]. But such SSS accuracy is about 3% of its global ocean range (32 -38 psu) in comparison to 0.1 °C accurate SST, which accuracy is about 0.3% of its range (0 -30 °C). Although the time mean dilution by ITCZ rainfall reaches ~1 psu and is routinely detectable, the detection of smaller magnitude signals is not apriori achievable. This paper shows that besides well-known intraseasonal ocean SSS variations associated with TIW, there exist atmospheric-induced component of intraseasonal SSS associated with convection clustering. Regardless of its small amplitude of 0.1 -0.2 psu, it is detectable by satellite SSS remote sensing.

Wind-induced intraseasonal ocean oscillations are known to exist in the equatorial wave guide (e.g., [START_REF] Grodsky | Variability of Upwelling and Chlorophyll in the Equatorial Atlantic[END_REF], but are also present at higher latitudes. Part of the impetus for this study comes from [START_REF] Krishnamurti | Oscillations of a Monsoon System. Part I. Observational Aspects[END_REF] and [START_REF] Grodsky | Coupled Land/Atmosphere Interactions in the West African Monsoon[END_REF] who identified the presence of approximately bi-weekly oscillations in both surface wind and rainfall in Indian and west African monsoon systems. Such oscillations are tied with the corresponding monsoon and are seasonally present along with the monsoon. But, as demonstrated further, similar intramonth transients are present in the tropical atmosphere (precipitation, winds) and ocean response (SSS) all year long and occupy vast areas of the tropical open-ocean beyond coastal regions affected by monsoons.

To describe and analyze these intramonth oscillations, the presentation is organized in the following way. First, we demonstrate the presence of accorded intramonth variations in precipitation and satellite-observed SSS in the central north tropical Atlantic, which meridional location follows the ITCZ. Next, we perform correlation analyses between intramonth variations 5 of SSS, precipitation, and surface wind divergence that show an almost out-of-phase relationship between SSS and precipitation variations. This out-of-phase relationship suggests that other factors besides the pure surface forcing are involved, among which the ocean Ekman pumping and the fast relaxation of rain-induced salinity anomalies are found contributing to the phase characteristics of SSS response. Finally, we discuss precipitation and wind satellite data to illustrate how atmospheric convective clusters originate and propagate along the Atlantic ITCZ.

Data and methods

Satellite salinity: This study relies on satellite SSS from the Soil Moisture Active Passive (SMAP) mission. Global Level 3 SMAP SSS is available daily as an 8-day running mean on a 0.25° grid (Version 3) produced by the Remote Sensing Systems, www.remss.com/missions/smap, [START_REF] Meissner | The Salinity Retrieval Algorithms for the NASA Aquarius Version 5 and SMAP Version 3 Releases[END_REF]. The surface footprint of each measurement is 39 x 47 km so the effective resolution is close to 40 km. On monthly and ~100 km scales, satellite SSS values match with in-situ measurements in the warm tropics to within ~0.2 psu, [START_REF] Lee | Consistency of Aquarius Sea Surface Salinity with Argo Products on Various Spatial and Temporal Scales[END_REF]. Due to several limitations (e.g., remaining residual error due to extra-terrestrial radiation, ionospheric effects, land-sea transitions, and sea surface roughness impacts on the radiometer brightness temperatures), satellite SSS often exhibit systematic seasonally-dependent biases versus ground truth [START_REF] Meissner | Sensitivity of Ocean Surface Salinity Measurements From Spaceborne L-Band Radiometers to Ancillary Sea Surface Temperature[END_REF]). As shown by several studies (e.g., [START_REF] Boutin | Interannual Anomalies of SMOS Sea Surface Salinity[END_REF], the SSS anomaly (SSSA) determined from the background longer-term satellite SSS data, (i.e., the difference computed relative to a slow varying SSS signal, such as a monthly satellite-based SSS climatology) is significantly less affected by these seasonal biases. The filtering procedure effectively removes such retrieval artifacts along with any actual slow varying SSS component. For the entire SMAP observation period (April 2015 -onward), the intra-month SSS variation at each grid point was estimated as the difference of observed SSS from its monthly moving mean.

Other satellite data: Satellite SST data come from the Canadian Meteorological Centre. Here we use the level 4 SST produced by combining infrared, microwave, and in-situ daily analyses resampled at 0.25° spatial resolution. These SST data are used for the SMAP SSS processing and included in SMAP data files. The using of microwave-derived SST is important in this cloudy ITCZ region. To characterize the surface wind, we use the gridded daily 10m neutral winds from the ASCAT scatterometer onboard the European Meteorological Satellite 6 Organization MetOp which are described in [START_REF] Bentamy | Gridded Surface Wind Fields from Metop/ASCAT Measurements[END_REF]) and available at (ftp.ifremer.fr/ifremer/cersat/products/gridded/MWF/L3/ASCAT).

The precipitation data set is the Tropical Rainfall Measuring Mission (TRMM) Level 3 3B42v7 [START_REF] Huffman | The TRMM Multisatellite Precipitation Analysis (TMPA): Quasi-Global, Multiyear, Combined-Sensor Precipitation Estimates at Fine Scales[END_REF]. This is constructed by merging active and passive TRMM microwave along with microwave-calibrated infrared measurements (http://dx.doi.org/10.5067/TRMM/TMPA/3H/7). The TRMM orbit is specifically designed to achieve rapid repeat sampling at low latitudes. The TRMM data set has 0.25°× 0.25° spatial resolution and is available from 1998 -2018.

Results

General characteristics of intramonth salinity variations

In order to explore such transient rainfall-induced SSS features using SMAP SSSA data, we choose to focus on an area where local precipitation is the primary term in the surface salinity budget. The large scale SSS distribution in the tropical Atlantic reflects the meridional pattern of the net freshwater flux with higher SSS in the evaporative subtropics and fresher SSS in the rainy tropical belt (Fig. 1a). Within the fresh tropical belt, the meridional position of SSS minimum roughly coincides with the ITCZ and there is also some significant west-to-east asymmetry.

While the time mean ITCZ rainfall and corresponding wind convergence are apparently lower in the west (Figs. 1b,c), the SSS is fresher there in response to Amazon-Orinoco freshwater river discharge. The band of fresh SSS associated with these river discharge and advection extends from the shelf out into the central tropical Atlantic, reflecting seasonal eastward transport in the North Equatorial Counter Current (NECC). However, in the central tropical Atlantic (around 30°W), there exists a local SSS maximum in otherwise fresh zonal SSS band that separates relatively fresher water to the east and to the west of it. This implies different freshwater forcing mechanisms for the eastern and western edges of the basin. While the western fresh pole is primarily influenced by river discharge (e.g., Foltz et al. 2004;Coles et al. 2013), the eastern pole is more strongly driven by the local net freshwater forcing. In the east, this latter assumption is corroborated by mostly eastward local zonal currents associated with the NECC, which deflect the entrance of Gulf of Guinea fresh waters. Moreover, twin model experiments with the same atmospheric forcing but differing river discharges show that the entire eastern pole of fresh SSS is present even in simulations completely lacking any river discharge, including the Congo River 7 (Dr. Ricardo Matano of OSU, personal communication, see also [START_REF] Vizy | Influence of the Amazon/Orinoco Plume on the Summertime Atlantic Climate[END_REF] for changes in atmospheric patterns). In the meridional plane, there exists also a northward displacement of the low salinity belt relative to the latitudinal position of ITCZ rainfall. This displacement is attributed to the time mean northwestward Ekman transport produced by the northeasterly trade winds (e.g., [START_REF] Grodsky | A Curious Local Surface Salinity Maximum in the Northwestern Tropical Atlantic[END_REF][START_REF] Yu | Sea-Surface Salinity Fronts and Associated Salinity-Minimum Zones in the Tropical Ocean[END_REF].

Spatial structure of the time mean magnitude of intramonth SSS variability amplifies near the western and eastern boundaries due to river discharge impacts (Fig. 1d). More certainly, it is organized into two zonally elongated bands. The southern band extends along and just north of the equator and reflects the presence of intramonth, approximately 17-day TIWs [START_REF] Grodsky | Tropical Instability Waves at 0°N, 23°W in the Atlantic: A Case Study Using Pilot Research Moored Array in the Tropical Atlantic (PIRATA) Mooring Data[END_REF][START_REF] Lyman | Distinct 17-and 33-Day Tropical Instability Waves in Subsurface Observations*[END_REF][START_REF] Lee | Aquarius Reveals Salinity Structure of Tropical Instability Waves[END_REF]. The second band of increased SSS variability is located to the north of the equatorial band and is connected to the area of strong SSS variability in the western boundary (Fig. 1d), notably via the retroflection of the North Brazil Current. But in the central Atlantic, the SSS variability in the northern band is dominantly driven by the corresponding atmospheric forcing (Figs. 1e,f). This was discussed in previous studies (e.g., [START_REF] Yu | A Global Relationship between the Ocean Water Cycle and Near-Surface Salinity[END_REF][START_REF] Martins | Spatial and Temporal Scales of Sea Surface Salinity Variability in the Atlantic Ocean[END_REF][START_REF] Tzortzi | Spatial and Temporal Scales of Variability in Tropical Atlantic Sea Surface Salinity from the SMOS and Aquarius Satellite Missions[END_REF]. Intramonth SSS variability in the central Atlantic box and its causes will be further explored here by correlation analyses of oceanic and atmospheric fields.

The atmospheric-driven nature of intramonth SSS oscillations can be inferred via their meridional behavior seen in Fig. 2a. Averaged over the zonal extent of the central Atlantic box (30°W-15°W, see Fig. 1a for the box location), the area of enhanced intramonth SSS variability in Fig. 2a closely follows the meridional ITCZ and wind divergence anomaly (𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑A) displacements (compare Figs. 2a,2b,and 2d). These intramonth oscillations occur quasisynchronously with latitude (to within the temporal resolution of Fig. 2a) and coherently with rainfall and surface wind divergence oscillations (Fig. 2b,2d). Using spatial averaging over the central north tropical Atlantic box (Fig. 1a), which is 15°-wide in longitude, allows filtering out the majority of Atlantic TIW signatures.

In contrast with SSSA, Fig 2c suggests that the SST change does not follow intramonth ITCZ variations. The latter variations do display an equatorial band of SST variability associated with high frequency TIWs. Some of these TIW-induced variations are also detectable in intramonth SSS, especially in summer (Fig. 2a). SST oscillations are also amplified in the northeasterly 8 trade wind regime north of the ITCZ. The latter observation may suggest that organized ITCZ clustered rainfall leads to wind perturbations that extend well away from these rainfall clusters, which, in turn, modify SST through their impact on latent heat fluxes. These wide spread wind anomalies will be demonstrated in composite patterns analyzed below.

A longitude-time view of intramonth SSS (Fig. 3a) confirms that salinity variability is observed quasi-instantaneously over 30°W-15°W longitude band and is associated with fast-moving variations in atmospheric forcing. Along with the atmospherically-induced signal, a westward propagating TIW-induced signal is also present and distinguishable in all variables shown in Fig. 3, in particular, during the equatorial low rainfall period of the summer of 2015. This remaining TIW-related signal is still distinguishable after 15° zonal averaging even though the characteristic wavelength of Atlantic TIW (< 1000 km, e.g., [START_REF] Grodsky | Tropical Instability Waves at 0°N, 23°W in the Atlantic: A Case Study Using Pilot Research Moored Array in the Tropical Atlantic (PIRATA) Mooring Data[END_REF]) is normally smaller than that for Pacific TIW that is evident by sample SST fields in Fig. 4. Spatial averaging over the central north tropical Atlantic box allows for significant (but not complete) filtering out of TIW-related signals and thus emphasizing of longer scale variability associated with atmospheric transients.

Correlation between intramonth SSS and precipitation

Temporal SSS variations in the central tropical Atlantic box show that they are organized in at least two frequency bands (Fig. 5). Low frequency (>30 days) box-averaged SSS (see Fig. 1a for the box location) essentially depicts the seasonal cycle with distinct semi-annual variations (Fig. 5a) on top of the significant interannual variability. Fig 5b suggests these semi-annual SSS variations can be largely explained by the semi-annual seasonal cycle of surface freshwater forcing that peaks twice a year with north-south ITCZ migration across the box (e.g., Foltz et al. 2004). Some remaining disconnect between magnitudes of the low frequency SSS and precipitation variations, especially noticeable during a fresh period in autumn 2017, reflects the presence of notorious interannual variability and suggests that other factors including the background vertical stratification (mixed layer depth) and the ocean currents may also impact SSS variations. 9

Visual inspection of intramonth variations indicates an apparent negative correlation between precipitation enhancements and SSS decreases that are clearly seen in 8-day averaged raw data in Figs. 5a, 5b. Note that precipitation in Fig. 5b is also 8-day averaged to match the 8-day SSS averaging of satellite SMAP gridded salinity. The period of these precipitation and SSS oscillations is approximately 3 weeks (spectra are discussed later). The negative correlation between SSS and precipitation variations suggests the dominant role that surface freshwater flux plays in driving central tropical Atlantic SSS at a wide range of seasonal and intraseasonal periods. For intramonth periods, this negative correlation is further detailed in Fig. 5c, showing that the majority of positive/negative SSS deviations coincide with negative/positive precipitation change. Such a phase relationship is not fully expected because the maximum dilution is expected by the end of the rainfall event, which implies a π/4 phase delay between SSS freshening and rainfall.

As expected from Fig. 2a, the area of negatively correlated intramonth SSS and precipitation migrates meridionally following seasonal displacements of the ITCZ (Fig. 6). It shifts northward in the boreal summer and autumn and then back towards the equator in the winter and spring.

The magnitude of the correlation is statistically significant (Fig. 6) but normally doesn't exceed 0.5. This weak level may be attributed to the SSS noise because the relatively weak magnitude of intramonth SSS (< 0.2 psu) is near the edge of satellite retrieval accuracy (e.g., [START_REF] Lee | Consistency of Aquarius Sea Surface Salinity with Argo Products on Various Spatial and Temporal Scales[END_REF]).

Another possible explanation may be the satellite's temporal SSS data coverage, which employs 8-day averaging for gridded fields. Such averaging of independent in-swath satellite observations may alias on longer periods and thus limit the magnitude of intramonth correlations.

Lagged correlation between timeseries of parameters area-averaged over the central tropical

Atlantic box indicates that zero-lag correlation shown in Fig. 6 yields nearly the highest magnitude (Fig. 7b). Only a slight delay (a few days) between peaks of near-surface wind divergence and precipitation (Fig. 7a) is observed, and this is similar for precipitation and SSS (Fig. 7b).

Ekman pumping impact on intramonth SSS

The characteristic amplitude of intramonth SSS is about 𝛿𝛿𝛿𝛿 = 0.1 psu (Fig. 5c). In terms of the mixed layer salt budget, the magnitude of 𝛿𝛿𝛿𝛿 is roughly consistent with the magnitude of 10 organized rainfall oscillations in the ITCZ, 𝛿𝛿𝛿𝛿 = 5 mm day -1 (Figs. 2b,5c). This level would give an SSS variation of, 𝛿𝛿𝛿𝛿 = 𝑆𝑆𝑆𝑆𝑆𝑆 𝐷𝐷 𝛿𝛿𝛿𝛿 = 0.05 psu, if acted on for 𝛿𝛿𝛿𝛿 = 14 days and with a typical local ocean mixed layer depth of 𝐷𝐷 = 50 m. Although it is only a half of the observed 𝛿𝛿𝛿𝛿 = 0.1 psu, it is known that intense ITCZ rainfall produces shallow barrier layers, see e.g., Fig. 2 in [START_REF] Liu | Observed Subseasonal Variability of Oceanic Barrier and Compensated Layers[END_REF]. Hence, surface freshwater flux anomalies may act on a layer shallower than 𝐷𝐷 = 50 m and thus induce stronger SSS oscillations. Although the magnitude of 𝛿𝛿𝛿𝛿 is roughly consistent with the surface forcing scenario, the observed anticorrelation between SSS and precipitation variations (rather than rainfall leading SSSA integrated effects) suggests that other factors besides the pure surface forcing are involved (Fig. 5c).

While the approximately out-of-phase relationship (negative correlation) between div𝑑𝑑 and precipitation is fully expected for tropical convection events, the almost out-of-phase relationship between precipitation and ocean SSS response is surprising. If the salinity rate of change was solely balanced by the precipitation (𝜕𝜕𝛿𝛿/𝜕𝜕𝛿𝛿~𝛿𝛿𝛿𝛿), this would imply a so-called quadrature phase relationship between precipitation and salinity, (rainfall variation, 𝛿𝛿𝛿𝛿, leads SSSA integrated effect, 𝛿𝛿𝛿𝛿, by a quarter of period). The observed deviation from this phase relationship suggests that other factors must contribute to intramonth salinity change. In fact, it is assumed that organized precipitation (convection) clusters are accompanied by anomalous wind curl, which alters the Ekman pumping, 𝑊𝑊 EK = -1/𝜌𝜌 w curl(𝜏𝜏 x /𝑓𝑓, 𝜏𝜏 y /𝑓𝑓). Here, (𝜏𝜏 x , 𝜏𝜏 y ) are the zonal and meridional surface wind stress components, 𝜌𝜌 w is the water density, and 𝑓𝑓 is the Coriolis parameter. Lagged correlation in Fig. 7c illustrates the presence of in-phase variations between intramonth precipitation and 𝑊𝑊 EK (upward 𝑊𝑊 EK is positive). Hence, for low latitude convective clusters, the upward Ekman pumping brings saltier water to the surface that mixes with waters diluted by enhanced precipitation.

Correlation between Ekman pumping and convective clusters may be caused by organized cyclonic winds associated with the clusters, or by alternative factors. Fig. 8 explores likely alternatives showing several ocean and atmosphere parameters averaged over typical wet and dry events in the central Atlantic. These events are defined as periods when the magnitude of boxaveraged intramonth precipitation anomaly exceeds its standard deviation (2.5 mm day -1 ). Note, that this threshold is lower than rainfall standard deviation in Fig. 1e, where grid point rather 11 than box averaged values are shown. Due to the rainfall dilution, it is expected that wet and dry composites correspond to fresh and salty anomalies, respectively (Figs. 8a,b). The characteristic magnitude of intramonth SSS anomalies is about 0.1 psu in line with Fig. 5c. Wet and dry events are accompanied by convergent and divergent wind patterns, respectively, with the sign agreeing with corresponding changes in atmospheric convection and related precipitation (Figs. 8c,d).

Wind velocity and curl anomalies associated with changes in intramonth precipitation are roughly symmetrical versus the center latitude of the box, but the pattern of 𝑊𝑊 EK is not (Figs. 8e,f). This asymmetry is related to the latitudinal dependence of the Coriolis parameter, which amplifies the magnitude of 𝑊𝑊 EK approaching the equator. This latitudinal asymmetry is characteristic of Ekman pumping at low latitudes. As a result, during wet/dry events, the box averaged 𝑊𝑊 EK is upward/downward, respectively. This vertical exchange then partially balances anomalous net freshwater forcing, impacting the salt budget and altering the phase relationship between the oceanic SSS response and rainfall.

Discussions

To provide further insight into the correlations discussed above, an expanded example of shortterm wind and precipitation shifts at intramonth event scale is next examined for the November-December 2017 timeframe singled out in Fig. 5c. Fig. 9 provides a 2-day average spatiotemporal view for one positive/dry (Fig. 9 b-h) and a following negative/wet (Fig. 9 j-p) SSSA period. The results indicate a high correspondence between event-mean precipitation (Figs. 9a,9i) and SSS (see Fig. 5c). There exists an apparent difference in mean precipitation values temporally averaged over a salty event (27 November -10 December of 2017) and a fresh event (10 -23 December of 2017). But, it should be noted that zonally continuous band of ITCZ rainfall is represented only in time averages while 2-day snapshots are dominated by mesoscale convective systems (Fig. 9). These systems are thus seen in both precipitation and wind patterns but are unresolved in 8-day SSS averages. During the salty event (Fig. 9, b-h), the mid-Atlantic ITCZ was relatively quiet, especially during the first week (27 November -2 December). In the next week (3-10 December), the ITCZ intensified starting with a cluster of enhanced rainfall over the western tropical Atlantic area adjacent to South America (3-4 December). Interestingly, this area of enhanced rainfall is associated with atmospheric convection over the ocean and doesn't extend over the land. Next, this enhanced rainfall cluster propagated eastward along the 12 time mean ITCZ, at a speed of 6 to 7 m s -1 , finally reaching the Gulf of Guinea in about one week.

The above episode of eastward propagation of convection during 3-10 December is the only dryperiod clear episode in Fig. 9. During the fresh event (10-23 December, Fig. 9, j-p), there is no apparent eastward propagation of convection clusters. The main differences between precipitation fields for wet and dry events is in the generally higher magnitude of rainfall for wet events and the larger number of days of depressed rainfall for dry events (more quiet rainfall days during dry periods). suggests that much of 8-day averaged precipitation/SSSA variation (Fig. 5c) is, in fact, an integration of high frequency (1-4 day) mesoscale convective events. As mentioned before, immediate surface ocean impacts of such precipitation spikes are unresolved in 8-day SSS averages, but the integrated oceanic effects in this mid-Atlantic region are apparent.

As noted before, many factors, including wind stirring, Ekman pumping, and others, contribute to fresh rain lenses decay. For each individual rainfall event, the SSS keeps freshening until the cessation of rainfall, which introduces the phase delay with a characteristic time-scale corresponding to individual rain event duration. Because SMAP SSS resoles only longer time scales (> 8 days), it can detect the dilution effect of convective clusters only. Each such cluster includes multiple individual rain events. In terms of cumulative freshwater deposit, these clusters are equivalent to the combined effect of individual rainfall events. But for fast decaying anomalies, the physical lag between SSS response and cumulative rainfall is not defined by the time scale of convective clusters. It remains the same as that for individual rainfall events and is defined by the short time-scale of individual rain events. This suggests that the integrated effect of intermittent rainfall leads to different phase delays between rainfall and salinity response depending on the characteristic decay time of fresh salinity anomalies. As schematically illustrated in Fig. 11, a phase delay comparable with rainfall cluster time scales would happen only if the signature of the precipitation (associated low SSS anomaly) remains for a significant time at the ocean surface (slow decay case), and thus slowly accumulates precipitation from the entire rainfall cluster. In contrast, if fresh anomalies decay considerably 13 between individual rainfall events, the corresponding phase delay is smaller and defined by the characteristic duration of individual rainfall events (fast decay case). The observed negative correlation between precipitation and SSS anomalies (Fig. 7b) suggests the second, fast decay case. This is corroborated by the observed near surface salinity anomaly decay time of less than 1 day [START_REF] Drushka | Understanding the Formation and Evolution of Rain-Formed Fresh Lenses at the Ocean Surface[END_REF].

In late fall through spring, the ITCZ shifts southward towards the equator, and a wide spectrum of atmospheric oscillations is observed over the central Atlantic box (Fig. 12a). Like in Fig. 10, the spectral analysis in Fig. 12 depicts few-day oscillations, approximately 3-week oscillations, and also longer (about 50-to 60-day) oscillations. The latter band of oscillations was described by e.g., [START_REF] Gu | Intraseasonal Variability in the Equatorial Atlantic-West Africa during March-June[END_REF], but it was removed from our main analysis in order to focus on intramonth frequencies. Both 3-week and ~50-day oscillations are reflected in SSS and manifest in the corresponding peaks of the SSS spectrum. When the ITCZ shifts northward, the spectrum of precipitation becomes smoother while 3-week and ~50-day peaks hold (Fig. 12b). Despite even stronger precipitation oscillations in summer months, they are not apparently reflected in the box-averaged SSS (Fig. 12b). During these months, the band of SSS oscillations shifts northward following rainfall and weak winds in the ITCZ (Fig. 2a). During this period, the southeasterly trade winds amplify over the fixed central north tropical Atlantic box area. Hence, the decreased level of SSS oscillations during the period shown in Fig. 12b simply reflects that these amplified winds stir rainfall fresh water vertically and thus decrease the magnitude of SSS response.

Summary

In summary, it is known that wind and rainfall in the Atlantic ITCZ experience a wide spectrum of oscillations, including intra-month periodicities. However, the impact of such episodic rainfall on the surface ocean freshwater in the tropics at similarly small time and space scales is largely unknown. Some of these periodicities are related to the presence of approximately bi-weekly oscillations of wind and rainfall in the West African monsoon [START_REF] Grodsky | Coupled Land/Atmosphere Interactions in the West African Monsoon[END_REF]. But, such monsoonal oscillations are tied with the corresponding monsoon and are seasonally present along with the monsoon. Here it is demonstrated that accorded intramonth transients are present in the tropical atmosphere and near-surface ocean salinity all year long, occupy vast areas of internal ocean affected by ITCZ rainfall, and extend beyond coastal regions affected by monsoons. Although such rain-induced SSS oscillations are expected to occur across the entire 14 tropical Atlantic, their examination is limited to the central north tropical Atlantic box where the surface net freshwater forcing is the leading driver of SSS and where river discharge effects are less important.

This study reports on the presence of approximately 3 week ocean-atmosphere oscillations which result from organized groups of mesoscale tropical convection clusters and their apparent imprints on satellite-derived sea surface salinity (SSS). These SSS oscillations have a relatively small amplitude of up to 0.2 psu but are clearly are detectable in Soil Moisture Active Passive (SMAP) SSS retrievals at resolutions as short as 8-days and spatial scales of 50-100 km. These SSS oscillations are produced by the corresponding precipitation oscillations, which are most intense in the ITCZ. As a result, the SSS oscillations develop in the ITCZ latitude band and follow its seasonal meridional displacements. They also develop quasi-synchronously in a wide range of longitudes. These seasonal displacements and high zonal speeds distinguish rainfallforced intramonth salinity oscillations from signatures of tropical instability waves (TIW) which normally have periods exceeding 1 month and distinct slow westward propagation.

Lagged correlation of intramonth SSS and precipitation timeseries box-averaged over the central Atlantic box (30°W-15°W, 2°N-6°N) indicates only a slight delay (< 2 -3 days) between peaks of high precipitation and SSS decrease. The almost out-of-phase relationship between ~3 -week precipitation events and ocean SSS response is unexpected. If the salinity rate of change was balanced by the precipitation only, it would imply a quadrature (π/4 ) phase delay between precipitation and salinity variations, with negative salinity anomaly peaking at the end of a rainy period. The deviation from this phase relationship implies that other factors, including salt anomaly dissipation, also contribute at intramonth periods. Besides commonly considered vertical turbulent dissipation, we also show that low latitude organized precipitation (convection) clusters are accompanied by an upward Ekman pumping anomaly that entrains saltier water to surface layers diluted by enhanced precipitation. All these vertical processes contribute to fast (~1 day) rainfall lenses decay and modify the salt balance and change the phase relationship between the oceanic SSS response and the atmospheric freshwater forcing. This leads to almost out-of-phase relationship suggesting that maximum dilution coincides with rainfall peaks even on time scales of few-week rainfall clusters.

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Fig. 10

 10 Fig. 10 recalls this small sub-segment of the region of interest box-averaged intramonth SSS, wind and rainfall data. Comparison of Fig. 10 and with Fig. 9 variations in daily precipitation

Figures 588 Figure 1 .Figure 3 .Figure 4 .Figure 5 .

 5881345 Figures 588

Figure 6 .Figure 7 .

 67 Figure 6. Temporal correlation of intramonth variations of sea surface salinity and precipitation for each season. Black contours show 3 mm day -1 precipitation to illustrate the ITCZ position. Correlation magnitude > 0.14 is statistically significant at the 99% level. 597 598

Figure 8 .Figure 12 .

 812 Figure 8. Composite maps of anomalies corresponding to (a, c, e) wet and (b, d, f) dry events in the central Atlantic box (black rectangle) for (a, b) SSS, (c, d) divU, and (e, f) Ekman pumping velocity (WEK). Events are defined as periods when the magnitude of box averaged intramonth rainfall exceeds its standard deviation. Arrows show corresponding intramonth wind anomaly composites. Central latitude of the box is shown by magenta in (e, f).

Acknowledgements This research was supported by the NASA Ocean Salinity Science Team (OSST) grants NNX17AK08G and NNX17AK02G. All data providers are acknowledged for making their products freely available. SMAP salinity data are produced by Remote Sensing Systems and sponsored by the NASA/OSST.