Internal Solitary Waves in the White Sea: Hot-Spots, Structure, and Kinematics from Multi-Sensor Observations

: A detailed picture of internal solitary waves (ISWs) in the White Sea is presented based on an analysis of historical spaceborne synthetic aperture radar (SAR) data and ﬁeld measurements. The major hot-spot of ISW generation locates in the southwestern (SW) Gorlo Strait (GS), characterized by the presence of strong tides, complex topography, and two distinct fronts. Here, pronounced high-frequency isopycnal depressions of 5–8 m were regularly observed during ﬂood and ﬂood/ebb slackening. Other regions of pronounced ISW activity are found near Solovetsky Islands and in the northwestern Onega Bay. The spatial and kinematic properties of the observed ISWs are linked to water depth, with larger wave trains and higher propagation speeds being observed over the deep regions. Direct estimates of ISW propagation speeds from sequential and single SAR images agree well, while theoretical ones obtained using a two-layer model overestimate the observed values by 2–3 times. This is explained by the effective modulation of ISW propagation speed during the tidal cycle by background currents that are not accounted for in the model. Enhanced values of diapycnic diffusion coefﬁcient in the pycnocline layer were registered near the frontal zones, where intense 14–17 m high ISWs were regularly observed.


Introduction
The White Sea (WS) is one of the most isolated and most commonly studied basins of the Arctic Ocean [1,2]. It is known for very strong tides and the most intense tidal energy dissipation in the Eurasian Arctic [3,4]. Powerful tidal dynamics create strong quasiperiodic semidiurnal tidal currents reaching 1.5 m/s [2]. Under such conditions, internal tides (ITs) of the dominant semidiurnal period should arise in areas where stratification is well expressed. As the models predict [5,6], ITs can have amplitudes of up to 10 m at generation sites, and due to the proximity to the critical latitude for the M 2 tide, they should dissipate locally, eventually evolving into wave trains of short-period internal solitary waves (ISWs) [7].
Oceanographic observations of the last decade have made it possible to detect significant short-term variabilities of currents, temperature, and salinity in various regions of the White Sea [8][9][10][11][12]. Strong thermocline oscillations associated with the propagation of short-period ISWs of 15-17 m height and periods of 15-20 min were repeatedly recorded in the southwestern part of the sea [13,14]. The formation of large-scale ISW trains generated due to tide-topography-frontal zone interactions in the eastern WS crossing the entire sea basin, and dissipating on the shallow western shelf were also reported in [15], based on an analysis of spaceborne synthetic aperture radar (SAR) data.
However, at the moment, there is no detailed information regarding the spatiotemporal distribution of ISWs in the White Sea that has been confirmed by long-term observations, nor their generation hot-spots, spatial and kinematic properties, or influence  Figure 1 shows the total spatial coverage of the study site using SAR data during the study period. As seen, the sea area was covered pretty well. Over 120 SAR images covered the Basin, Onega, and Dvina bays (OB and DB, respectively); and two major straits around Solovetsky Islands (SI), namely, Zapadnaya (west of SI) and Vostochnaya (east of SI). Solovetskaya Salma straits, hereinafter, are ZSSS and VSSS, respectively. A slightly lower number of data points, 80-100 images, was available over the periphery of the study region, i.e., in the northwestern part of the Kandalaksha Gulf, in the northeastern Gorlo Strait (GS), and in the southeastern OB. In SAR images, ISWs usually have very recognizable patterns of alternating bright and dark bands of enhanced and depressed radar backscatter of concentric form (see Figure 2), as ubiquitously demonstrated for both the Arctic regions [17][18][19][20][21][22] and the rest of the World Ocean [23][24][25][26][27]. In SAR images, ISWs usually have very recognizable patterns of alternating bright and dark bands of enhanced and depressed radar backscatter of concentric form (see Figure 2), as ubiquitously demonstrated for both the Arctic regions [17][18][19][20][21][22] and the rest of the World Ocean [23][24][25][26][27].
In this work, the surface manifestations of oceanic ISWs were visually detected in SAR images, and further analysis of their properties followed the methodology described in [28]. Following [28], once clear signatures of ISWs were detected, a curve matching the leading wave of each ISW train and a transect crossing the wave train in the propagation direction were drawn to estimate a number of spatial ISW properties. To reduce the speckle noise typical for SAR images of the sea surface, the values of normalized radar cross-section (NRCS or sigma 0 ) along the transect were calculated as a mean of 10 parallel transects, as has often been performed in similar studies (e.g., [24]). Then, using a mean sigma 0 profile along the transect, its orientation, and the image itself, we determined the following ISW properties: crest length (L c ) of the ISW train, its length (L), area (A), and propagation direction (d), the wavelength of the leading wave (λ 0 ), and the interpacket distance (λ g ) between sequential wave trains ( Figure 2). The latter was used to estimate the propagation speed (C p ) of ISWs, assuming that the generation of every new packet occurred every tidal period, with the lunar semidiurnal M 2 tide being the dominant tidal component in the White Sea [6]. In this work, the surface manifestations of oceanic ISWs were visually detected in SAR images, and further analysis of their properties followed the methodology described in [28]. Following [28], once clear signatures of ISWs were detected, a curve matching the leading wave of each ISW train and a transect crossing the wave train in the propagation direction were drawn to estimate a number of spatial ISW properties. To reduce the speckle noise typical for SAR images of the sea surface, the values of normalized radar cross-section (NRCS or sigma 0 ) along the transect were calculated as a mean of 10 parallel transects, as has often been performed in similar studies (e.g., [24]). Then, using a mean sigma 0 profile along the transect, its orientation, and the image itself, we determined the following ISW properties: crest length (Lc) of the ISW train, its length (L), area (A), and propagation direction (d), the wavelength of the leading wave (λ0), and the interpacket distance (λg) between sequential wave trains ( Figure 2). The latter was used to estimate the propagation speed ( ) of ISWs, assuming that the generation of every new packet occurred every tidal period, with the lunar semidiurnal M2 tide being the dominant tidal component in the White Sea [6]. Figure 2 shows an example of an enlarged Envisat ASAR image acquired on 13 August 2010 (18:30 UTC) depicting the clear signatures of two sequential ISW trains, T1 and T2, propagating southwest from the shallow GS toward the deep Basin. It also schematically shows how the different ISW properties are estimated from the 2D SAR image (Figure 2a) and from the variation of the SAR signal backscatter along the transect AB crossing the wave trains T1 and T2 (Figure 2b). The interpacket distance λg between the wave trains T1 and T2 is about 7 km, which equals to = 2 ⁄ = 7000 /12,4 · 3600 ≈ 0,16 m/s.  Figure 2 shows an example of an enlarged Envisat ASAR image acquired on 13 August 2010 (18:30 UTC) depicting the clear signatures of two sequential ISW trains, T1 and T2, propagating southwest from the shallow GS toward the deep Basin. It also schematically shows how the different ISW properties are estimated from the 2D SAR image ( Figure 2a) and from the variation of the SAR signal backscatter along the transect AB crossing the wave trains T1 and T2 (Figure 2b). The interpacket distance λ g between the wave trains T1 and T2 is about 7 km, which equals to C p = λ g /T M2 = 7000 m/12, 4·3600 s ≈ 0, 16 m/s. The spatial fields of an ISW probability and the mean values of their properties were then calculated on a horizontal grid of 40 × 40 cells with a cell size equal to about 110 km 2 .
The mean values of interpacket distances and propagation speeds were obtained only for the data of 2010 (comprising approximately half of all the SAR data used). The information on ocean depth corresponding to the center of each detected ISW train was derived from IBCAO version 3.0 [16].

In Situ Measurements
In situ observations were made in July-August, 2009-2014, in the two straits around the SI (the ZSSS and the VSSS), the Basin, the Onega Bay, the Gorlo Strait, and the Dvina Bay, at 14 polygons shown by white triangles in Figure 1. The observations included the installation of autonomous buoy stations and frequent oceanographic stations (scans) made from an anchored vessel. All works were carried out with the data binding to the tidal phase. Measurements were made when the wind speed was below 8 m/s. Systems of two or three buoy stations approximately 1-2 km apart were installed at each polygon. The duration of the observations lasted from one to three M 2 tidal cycles. Doppler flow profilers ADP SonTek-500 and ADCP Workhorse Sentinel 300 equipped with pressure and temperature sensors were installed near the bottom. The discreteness of the measurements was 2 min. In addition, JFE ALEC (https://www.jfe-advantech. co.jp/eng/products/ocean-ryusoku.html#aem1da, accessed on 28 August 2022) current meters were installed at 10, 13, 16, and 19 m depths. CTD instruments SBE-19plus (https: //www.seabird.com/sbe-19plus-v2-seacat-profiler-ctd/product?id=60761421596, accessed on 14 July 2022) and CTD-90M (https://www.sea-sun-tech.com/product/multiparameterprobe-ctd-90-memory/, accessed on 22 July 2022) were installed in the pycnocline layer. Data from the buoy stations were used mainly to obtain additional information about the hydrological conditions in the study area, and to assess the propagation velocity and the direction of the ISWs.
Basic information regarding the ISWs was obtained by scanning the water column from surface to bottom with CTD-90M and Cast Away (https://www.ysi.com/castaway-ctd, accessed on 17 August 2022) sensors from the anchored vessel. One "descent-ascent" scan cycle took about 1-2 min. The vertical properties of the ISWs were estimated from the observations of the thermocline depth that usually coincided with the pycnocline depth. Therefore, we also used the water temperature data for the analysis of the ISW properties. As shown in Figure 3, the time variations in the position of the thermocline allowed us to determine the height and the period of each wave passing through the polygon. The wave height was estimated as the average value between the height of the front and the rear slopes of a soliton, and the period of each wave was estimated as the time interval between the adjacent maxima of the isotherm (Figure 3). Oscillations with the periods from 3 to 60 min and a height of more than 1 m were considered as ISWs. The former was largely dictated by the technical constraints of the measurements, i.e., the lower limit (3 min) was determined by the shortest period of the repeated CTD casts (over 1-2 min), and the upper limit was determined by the minimal interval of the continuous measurements (~2 h).  To assess the role of the ISWs in vertical mixing we used temperature, salinity, and current speed measurements at a 0.5 m vertical grid to calculate the turbulent diffusivity or the diapycnic diffusion coefficient [29]: where 2 = −( 0 ⁄ ) ⁄ is the squared buoyancy frequency (mean over tidal cycle), -the Brunt-Väisälä frequency, and is the dissipation rate of turbulent kinetic energy defined from the current meter data following [30]: where is the dynamic viscosity of seawater, and ⁄ is the vertical shear of horizon- To assess the role of the ISWs in vertical mixing we used temperature, salinity, and current speed measurements at a 0.5 m vertical grid to calculate the turbulent diffusivity or the diapycnic diffusion coefficient [29]: where N 2 = −(g/ρ 0 )∂ρ/∂z is the squared buoyancy frequency (mean over tidal cycle), N-the Brunt-Väisälä frequency, and ε is the dissipation rate of turbulent kinetic energy defined from the current meter data following [30]: where ν is the dynamic viscosity of seawater, and ∂u/∂z is the vertical shear of horizontal velocity. All calculations were performed for the water layer where the ISWs were registered, typically from 5 to 35 m (the actual depths ranged at various polygons) using two time-averaging intervals. In the first case, we used a 2 min interval to keep the effects of the ISWs in the data. In the second case, we applied a 2 h averaging to fully eliminate the effects of the ISWs. Further, the results of both cases were averaged during the tidal cycle to assess the contributions of the short-period processes to the vertical turbulent exchange. For the long-lasting polygons where the ISWs were registered, the calculations were repeated for 2-3 M 2 tidal cycles, and then averaged.

Hot-Spots of the ISWs and the Background Properties
In total, 516 surface signatures of the ISWs were registered in 282 SAR images in May-September of 2007-2013. A seasonal distribution of the number of the available SAR images is shown in Figure 4. Note that the number of the medium-resolution (WSM) SAR images (black bars) is given separately from the higher-resolution SAR data (grey bars). The number of WSM images was nearly similar from May to August, and around half as many in September. The higher resolution SAR data were available only during July-September, with a smaller number of images in September. Despite the relative number of the highresolution images during these months being 2.5 times smaller than that of the WSM images, the number of identified ISW signatures was nearly similar, i.e., 244 ISW signatures in the high-resolution images and 272 in the medium-resolution images.  As the data availability strongly varied from month to month, we used a normalized number of ISW detections (red curve in Figure 4) calculated as a ratio of the total number of ISW detections per month to the number of SAR images available per given month. As seen, the highest number of ISW detections was registered in August, followed by July, i.e., during the months when the vertical stratification conditions were the most suitable for ISW generation in the WS [13]. Figure 5a shows a map with the plotted leading crests of all ISWs detected in the White Sea during the study period. As seen, most waves are concentrated in the northeastern part of the sea, i.e., in the southwestern (SW) part of the Gorlo Strait (GS) and at the outer boundary of the Dvina Bay (DB). Pronounced ISW activity is also seen in the As the data availability strongly varied from month to month, we used a normalized number of ISW detections (red curve in Figure 4) calculated as a ratio of the total number of ISW detections per month to the number of SAR images available per given month. As seen, the highest number of ISW detections was registered in August, followed by July, i.e., during the months when the vertical stratification conditions were the most suitable for ISW generation in the WS [13]. Figure 5a shows a map with the plotted leading crests of all ISWs detected in the White Sea during the study period. As seen, most waves are concentrated in the northeastern part of the sea, i.e., in the southwestern (SW) part of the Gorlo Strait (GS) and at the outer boundary of the Dvina Bay (DB). Pronounced ISW activity is also seen in the eastern part of the Basin, in the straits around the Solovetsky Islands archipelago, and in the northwestern Onega Bay (OB). Apparently, no ISW activity is seen over the deep-sea regions in the Kandalaksha Bay (KB) and the western Basin.     (0.1-0.2) are found at the boundary between the western Basin, the SW GS, and the DB-the major hot-spot of regular ISW generation in the White Sea. Other regions of regular ISW activity are located in the vicinity of the SI, particularly east of it (in the VSSS), where the ISW probability is about 0.08. In the rest of the sea, it does not exceed 0.05 ( Figure 5b). Figure 5c shows a spatial distribution of a mean sea surface temperature (SST) gradient obtained from the daily MODIS Aqua images acquired in May-September 2010. The SST gradient field clearly depicts the main frontal zones of the White Sea, many of which are found in the SW Gorlo Strait, in the VSSS, and in the Onega Bay. An intercomparison of the SST gradient field with that of the ISW probability shows a considerable correspondence between the regions of the high ISW probability and the high SST gradients, suggesting that many of the observed ISWs are generated in the vicinity of strong frontal zones.
To illustrate certain differences of hydrological conditions in the various WS regions, Figure 6 shows the vertical distributions of the Brunt-Väisälä frequency averaged over the tidal period from the field measurements made at polygons 1, 4, and 7 in the summer of 2010 (polygon 1) and 2012 (polygons 4 and 7). correspondence between the regions of the high ISW probability and the high SST gradients, suggesting that many of the observed ISWs are generated in the vicinity of strong frontal zones.
To illustrate certain differences of hydrological conditions in the various WS regions, Figure 6 shows the vertical distributions of the Brunt-Väisälä frequency averaged over the tidal period from the field measurements made at polygons 1, 4, and 7 in the summer of 2010 (polygon 1) and 2012 (polygons 4 and 7). At polygon 1 located on the shallow western shelf (at the boundary of the western Basin and the ZSSS, see Figure 1), the maximal ( ) value ~0.04 s −1 is found at an 8-9 m depth, with the typical thickness of the pycnocline layer being about 5 m (Figure 6a). Polygon 4 is located at the shelf-deep water boundary. The maximal ( ) value here (~0.043 s −1 ) is similar to polygon 1, but it is found deeper, at 15-25 m. The pycnocline layer is about 10 m thick here ( Figure 6b). Polygon 7 is located in the coastal area of the eastern WS where the occurrence of ISWs is highest ( Figure 5b). Here, the buoyancy frequency profile strongly differs from other polygons, due to a strong impact of the Dvina River runoff, described in more detail below. Its main peak is found at about a depth of 5 m, and reaches ~0.06 s −1 . The impact of the riverine water extends down to 20 m, while another minor peak of ~0.025 s −1 at 25-30 m depth is associated with the subsurface water originating from the Basin (Figure 6c).
At all polygons, the water structure corresponds to the so called "Basin type", characterized by well-expressed vertical density stratification. The upper layer, extending to 5-20 m depth, is formed by surface waters warmed during the summer and desalinated by the river runoff and sea ice melt. Subsurface water is saltier, with the temperature gradually decreasing with depth.
The overall analysis of measurements at the different WS polygons shows a significant variability of thermohaline fields in two ranges of periodicity, with a characteristic At polygon 1 located on the shallow western shelf (at the boundary of the western Basin and the ZSSS, see Figure 1), the maximal N(z) value~0.04 s −1 is found at an 8-9 m depth, with the typical thickness of the pycnocline layer being about 5 m (Figure 6a). Polygon 4 is located at the shelf-deep water boundary. The maximal N(z) value here (~0.043 s −1 ) is similar to polygon 1, but it is found deeper, at 15-25 m. The pycnocline layer is about 10 m thick here ( Figure 6b). Polygon 7 is located in the coastal area of the eastern WS where the occurrence of ISWs is highest (Figure 5b). Here, the buoyancy frequency profile strongly differs from other polygons, due to a strong impact of the Dvina River runoff, described in more detail below. Its main peak is found at about a depth of 5 m, and reaches~0.06 s −1 . The impact of the riverine water extends down to 20 m, while another minor peak of~0.025 s −1 at 25-30 m depth is associated with the subsurface water originating from the Basin (Figure 6c).
At all polygons, the water structure corresponds to the so called "Basin type", characterized by well-expressed vertical density stratification. The upper layer, extending to 5-20 m depth, is formed by surface waters warmed during the summer and desalinated by the river runoff and sea ice melt. Subsurface water is saltier, with the temperature gradually decreasing with depth. The overall analysis of measurements at the different WS polygons shows a significant variability of thermohaline fields in two ranges of periodicity, with a characteristic semidiurnal (tidal) period and periods of tens of minutes (associated with ISWs). In different regions characterized by different hydrological and morphometric conditions, it manifests itself in different ways:

Spatial and Kinematic Properties of ISWs from SAR Observations
In this subsection, we present the results addressing the spatial and kinematic properties of ISWs derived from SAR data. Figure 7 shows a map and a histogram of ISW propagation direction. As seen, two main directions prevail-western/southwestern and eastern. While some regions have a single well-defined ISW direction, the others have a mixture of them, due to a local complex bottom emanating the waves in many possible directions.
The wavelength of the leading wave in ISW packets ranges from 0.1 to 2.6 km (Figure 7c  Knowing the crest length and the packet length of ISWs, it is easy to obtain the area of the ISW packets by multiplying the former two. As obtained, the area of about 80% of the detected ISW trains does not exceed 50 km 2 . As seen from Figure 8e, smallest wave trains (A <20 km 2 ) are observed in the SW GS, the OB, and around the SI. The largest ISW packets with the area exceeding 150-200 km 2 are again observed over the deeper (>100 m) parts of the Basin. The overall range of the ISW packet area values spans three orders of magnitude from~0.2 km 2 to~854 km 2 , with a mean value of~30 km 2 (Figure 8f).
During the analysis of SAR images, sequential wave packets having identical patterns and propagation direction were often registered. As has been already mentioned above, and as widely applied in literature [28,31,32], the distance between such sequential wave trains, λ g , can be used to assess the propagation speed of ISW trains, C p (Figure 9).
In this subsection, we present the results addressing the spatial and kinematic prop erties of ISWs derived from SAR data. Figure 7 shows a map and a histogram of ISW propagation direction. As seen, two main directions prevail-western/southwestern and eas ern. While some regions have a single well-defined ISW direction, the others have a mixtu of them, due to a local complex bottom emanating the waves in many possible directions.  Interpacket distances were obtained in 67 cases. As seen from Figure 9a, higher λ g values correspond to higher water depths, and vice versa. The overall range of λ g values is between 0.7 and 46 km, with a mean value of about 7 km (Figure 9b).
Assuming that generation of every new ISW train happens each M 2 tidal cycle (i.e., every 12.4 h), the ISW propagation speed values corresponding to the observed λ g values equal 0.02-1.03 m/s, with a mean value of 0.15 m/s (Figure 9c,d). The values of C p < 0.1 m/s do not seem very convincing, because of the large relative error in measuring the distance between consequent ISW trains (± 150 m). In turn, the range of values of 0.1-1 m/s is rather realistic. In similarity to λ g values, C p increases as the waves propagate from shallow to deep water. The different shallow sea regions have similar C p values of 0.1-0.2 m/s, while the highest propagation speed is attributed to the largest and perhaps most intense ISWs. 0.5 km on average over the shallow regions, and above 1 km in the deeper parts of the sea. The smallest values (0.1-0.3 km) are seen east of the SI, in the OB, and in some parts of the GS. Figure 8 further shows the spatial distribution and histograms of other spatial properties of ISW packets-their crest length, packet length, and area.
(e) (f)  seen over the deeper regions in the northwestern part of the sea. magnitude from ~0.2 km 2 to ~854 km 2 , with a mean value of ~30 km 2 (Figure 8f). During the analysis of SAR images, sequential wave packets having identical patterns and propagation direction were often registered. As has been already mentioned above, and as widely applied in literature [28,31,32], the distance between such sequential wave trains, λg, can be used to assess the propagation speed of ISW trains, (Figure 9). Interpacket distances were obtained in 67 cases. As seen from Figure 9a, higher λg values correspond to higher water depths, and vice versa. The overall range of λg values is between 0.7 and 46 km, with a mean value of about 7 km (Figure 9b).

ISW Generation in the SE Gorlo Strait
As already shown above in Figure 5a,b, the region including the western part of the Basin, the SW GS, and the DB is the main hot spot of ISW generation in the White Sea. It has a very dense and complex ISW pattern. This region is known for intense tides, and the formation of sharp density fronts and complex bottom topography, all resulting in the generation of the large-scale ISWs that are able to cross the entire Basin and dissipate on the western sea shelf [12]. Below, we consider the ISW formation in this region in more detail.
The SST map acquired on 4 August 2010 (Figure 10a) shows a typical picture of SST distribution in the eastern part of the WS, where two very pronounced frontal features permanently exist. One of them, hereinafter the Gorlo Front (GF), is found in the SW GS, where the relatively cold, saline, and mixed Barents Sea water entering the GS from the northeast meets the warmer water of the WS Basin. Another one is formed in the Dvina Bay by the Northern Dvina River discharge. This river plume water, hereinafter the Dvina Front (DF), is a couple of degrees • C warmer than the surrounding water of the Basin, and much warmer (>10 • C) than the GF water. It fills the southern part of the DB, and then spreads northward along the Winter Coast (see Figure 10a for its location).
permanently exist. One of them, hereinafter the Gorlo Front (GF), is found in the SW GS, where the relatively cold, saline, and mixed Barents Sea water entering the GS from the northeast meets the warmer water of the WS Basin. Another one is formed in the Dvina Bay by the Northern Dvina River discharge. This river plume water, hereinafter the Dvina Front (DF), is a couple of degrees °C warmer than the surrounding water of the Basin, and much warmer (>10 °C) than the GF water. It fills the southern part of the DB, and then spreads northward along the Winter Coast (see Figure 10a for its location). To obtain a better understanding of the ISW generation and structure in the SW GS, a 4 day experimental study was carried out in this part of the sea on 29 July-1 August 2012. The experiment included measurements along the section crossing the GS, and fixed-point measurements at polygon 7 (see Figure 10a for their locations), all collocated with the Radarsat-1/-2 overpasses. Figure 10b shows a bathymetry map covering the SW GS, and adjacent regions with overlaid ISW crests detected in the Radarsat-1/-2 data on 29 July-5 August 2012. The overall ISW pattern is rather complex; hence, we show the ISW signatures in different colors depending on their presumed source of origin. Red color denotes ISW signatures most often having circular shapes and presumably originating from the interaction of the DF, with an underwater bank located to the northwest of the Winter Coast (marked by a red cross in Figure 10b). Blue color shows ISW signatures typically directed southwest from the GS toward the deep Basin. These wave trains usually have rather long crests (up to 200 km), and are presumably generated by the complex interaction of tidal currents, the Gorlo Front, and a system of underwater sills (marked by a blue triangle in Figure 10b). The last group of the ISWs shown in black represents the wave trains found in the immediate proximity to the Dvina Front. Below, we consider the overall hydrology and the ISW properties in this region in more detail. Figure 11 shows a vertical distribution of water temperature along the transect crossing the GS made during the ebb and flood tides on 30-31 July 2012. The leftmost part of the transect shows a well-mixed GS water of Barents origin having a temperature of about 7 • C and salinity of about 28 psu (not shown). Stratified water of the northern Basin fills the entire central part of the transect, with the temperature varying from 13.5 • C near the surface to 2 • C near the bottom (the salinity varies from 25.3 to 27.5 psu). In both graphs, a temperature front outcropping to the surface is found at about 10 miles from the Tersky Coast; it marks a cross-strait position of the Gorlo Front. The along-strait position of the GF also depends on the width and intensity of the relatively warm and fresh Dvina Front that is usually attached to the Winter Coast (Figures 10a and 12a). The DF is seen in the rightmost part of the transect during the ebb tide as a warm (>14 • C) 5-7 m thick surface layer (Figure 11a). diate proximity to the Dvina Front. Below, we consider the overall hydrology and the ISW properties in this region in more detail. Figure 11 shows a vertical distribution of water temperature along the transect crossing the GS made during the ebb and flood tides on 30-31 July 2012. The leftmost part of the transect shows a well-mixed GS water of Barents origin having a temperature of about 7 °C and salinity of about 28 psu (not shown). Stratified water of the northern Basin fills the entire central part of the transect, with the temperature varying from 13.5 °C near the surface to 2 °C near the bottom (the salinity varies from 25.3 to 27.5 psu). In both graphs, a temperature front outcropping to the surface is found at about 10 miles from the Tersky Coast; it marks a cross-strait position of the Gorlo Front. The along-strait position of the GF also depends on the width and intensity of the relatively warm and fresh Dvina Front that is usually attached to the Winter Coast (Figures 10a and 12a). The DF is seen in the rightmost part of the transect during the ebb tide as a warm (>14 °C) 5-7 m thick surface layer (Figure 11a). The tidal currents are very strong in the Gorlo Strait, reaching 1.5 m/s [2], and can easily influence the vertical and horizontal location and intensity of frontal zones in the strait ( Figure 11). Tidal currents are directed southwest (northeast) toward the WS Basin (Barents Sea) during the flood (ebb) tide. During the ebb tide, stratified water of the Basin The tidal currents are very strong in the Gorlo Strait, reaching 1.5 m/s [2], and can easily influence the vertical and horizontal location and intensity of frontal zones in the strait ( Figure 11). Tidal currents are directed southwest (northeast) toward the WS Basin (Barents Sea) during the flood (ebb) tide. During the ebb tide, stratified water of the Basin and the DF comes into the strait along the Winter Coast, forming a strong vertical temperature gradient of up to 1 • C/m; the thermocline lies very close to the surface, at 5-12 m depth (Figure 11a). During the flood, less stratified water partly mixed in the strait returns back, the vertical temperature gradient weakens, and the thermocline deepens to about 18-20 m (Figure 11b). Figure 12 shows a time plot of vertical distribution of density anomaly calculated using EOS-80, together with currents and the tidal range at polygon 7. The polygon was occupied during~24 h, starting from 19:30 UTC on 31 July to 19:00 UTC on 1 August 2012.
The total water depth at the polygon was~60 m, but the CTD casts were made down to 40 m to shorten the sampling intervals to 2-3 min. Frequent CTD-sampling resolved the high-frequency oscillations of the upper 40 m quite well, revealing a strong variability of isopycnal depths, both in the pycnocline layer (~5-15 m) and below (Figure 12a-c).
As seen from Figure 12 and the DF comes into the strait along the Winter Coast, forming a strong vertical temperature gradient of up to 1 °C/m; the thermocline lies very close to the surface, at 5-12 m depth ( Figure  11a). During the flood, less stratified water partly mixed in the strait returns back, the vertical temperature gradient weakens, and the thermocline deepens to about 18-20 m (Figure 11b). Figure 12 shows a time plot of vertical distribution of density anomaly calculated using EOS-80, together with currents and the tidal range at polygon 7. The polygon was occupied during ~24 h, starting from 19:30 UTC on 31 July to 19:00 UTC on 1 August 2012. The total water depth at the polygon was ~60 m, but the CTD casts were made down to 40 m to shorten the sampling intervals to 2-3 min. Frequent CTD-sampling resolved Bathymetry contours at a 50 m isobath taken from IBCAO v.3 [16] show the existence of an elongated bank centered at 65.67° N, 39.5° E and oriented along the strait ( Figure  13a). In general, the observed ISW pattern fits well with the noted bathymetry feature, Bathymetry contours at a 50 m isobath taken from IBCAO v.3 [16] show the existence of an elongated bank centered at 65.67 • N, 39.5 • E and oriented along the strait (Figure 13a). In general, the observed ISW pattern fits well with the noted bathymetry feature, assuming its generation via the common lee-wave mechanism [33,34]. Indeed, ISWs were usually registered during the flood, and their locations as observed in the SAR data are found on the lee side of the topographic obstacle, with the waves propagating downslope.
A green box in Figure 13a marks the region of polygon 7 that is captured in two other SAR images of 1 August depicting the ship location and the ISWs nearby (Figure 12c,d). An enlarged crop of the Radarsat-2 image of 29 July shows a system of two pairs of consequent ISW trains traveling west-southwest (WSW, wave trains A, B) and south-southeast (SSE, wave train D), i.e., approximately at right angles to each other (Figure 13b).
On the next Radarsat-1 image of 1 August (04:14 UTC) one can see that the ISW pattern is exactly similar to that in Figure 13b. Note that the locations of wave trains A, B, and D are almost identical (Figure 13c). The time lag between the two images of 29 July and 1 August is equal to 61 h 28 min, i.e., almost exact five M 2 tidal periods, suggesting an M 2 periodicity of ISW arrival to the location of polygon 7. On the same day, a Radarsat-2 image was made at 14:48 UTC, i.e., 10 h 44 min later than the preceding Radarsat-1 image. It shows a similar configuration of the ISW trains (Figure 13d). We presume that the ISW signatures A' and D' denoted in the second image (14:48 UTC) are linked to the wave trains A and D seen in the first image (04:14 UTC). In such a case, their horizontal shifts in space and the time gap (10 h 44 min) between the two sequential observations (SO) can be used to assess their propagation speed (C p ), as is usually performed from such observations [32,35,36].
For simplicity, we consider only the leading waves of each wave train. An estimation of the horizontal shift of the ISW signatures in the SO is made with a 1 km step along each wave crest. Figure 14 shows a resulting map of the propagation speed of four ISW trains present in both images. First, we consider the wave trains A and B. In all fragments of SAR images shown in Figure 12b-d, the interpacket distance (ID or λ g ) between them is about 3.6 km, which, assuming their generation every M 2 period (12.4 h), equals to a propagation speed of 0.08 m/s. An analysis of the SO gives C p equal to 0.087 m/s. The wave train D has a curved shape in both images of 1 August 2012 (Figures 13c and 14). The interpacket distance for D can be estimated only for its southwestern part, i.e., between D and E 1 , and equals 4.5-4.7 km or~0.12 m/s, in terms of C p . From the sequential images, C p is~0.1 m/s for the southwestern part and~0.6 m/s-for the northeastern. For the wave train E, consisting of two parts E 1 and E 2 clearly visible in the first image (04:14 UTC, not shown), the SO-based mean propagation speed is equal to 0.11 m/s for E 1 and 0.13 m/s for E 2 , respectively. The alternative estimate of C p for E can be made from the IDs between wave trains D' and E'. In the vicinity of E 1 and E 2 , the IDs are 4.8-5 km and 6-6.5 km, respectively, yielding C p values of 0.12-0.13 m/s and 0.16-0.17 m/s. In general, the ISW propagation speed estimates obtained from SOs and IDs agree quite well with the ID-based estimates providing somewhat higher values. Some variations in the propagation speed values along the crests of individual ISW trains (e.g., wave trains D and E) are observed, which are most probably linked to differences in sea depth and vertical stratification along their trajectories. Higher C p values are seen over the deeper regions and vice versa, in accordance with the results obtained in Section 3.2 above (Figure 9c) and the results of previous studies [32,37].
For simplicity, we consider only the leading waves of each wave train. An estimation of the horizontal shift of the ISW signatures in the SO is made with a 1 km step along each wave crest. Figure 14 shows a resulting map of the propagation speed of four ISW trains present in both images. First, we consider the wave trains A and B. In all fragments of SAR images shown in Figure 12b-d, the interpacket distance (ID or λg) between them is about 3.6 km, which, assuming their generation every M2 period (12.4 h), equals to a propagation speed of 0.08 m/s. An analysis of the SO gives equal to 0.087 m/s.  Another option to estimate C p is to use a theoretical approach and the vertical CTD measurements made at polygon 7. For this purpose, a convenient option is to use a dispersion relation for the lowest internal mode in a two-layer approximation, often used in similar applications [22,31,38,39]. In this case, the phase speed of the linear internal waves is [40]: where δρ is the density difference between the upper and lower layers, ρ 0 -average density below the pycnocline, g-gravity acceleration, k-wave number defined as k = 2π/λ, where the wavelength λ is taken as a wavelength of the leading waves in ISW trains from SAR observations, d-mean pycnocline depth, and D-full depth. In the case of nonlinear internal solitary waves, the phase speed would be equal to: where η 0 -amplitude of ISWs, and α-coefficient of quadratic nonlinearity, defined as: where h 1 , h 2 -upper-and lower-layer depths, respectively. Using the average over the tidal cycle characteristic values of D = 60 m, d = 8 m, δρ = 2 kg/m 3 , ρ 0 = 1022 kg/m 3 , λ = 250-400 m, and η 0 = 2-8 m, we obtain C = 0.2-0.32 m/s. The theoretical C values are about two times higher than C p obtained directly from the SAR images, ranging from 0.08 to 0.17 m/s. The possible explanation of such a difference could be related to the fact that the two-layer model does not account for background currents that can modulate the effective propagation speed of ISWs. As Figure 14 shows, the surface (and depth-averaged) currents were quite strong (0.5-0.7 m/s) and opposing relative to the ISW travel directions at the moments of the SAR observations. Strong counterclockwise tidal currents superposed with wind drift and the alongshore current of the Dvina Front altogether should modulate the effective ISW propagation speed during the tidal period, explaining the observed difference. In our case, the northward ebb current is stronger than the southward flood current (Figure 12d) possibly explaining the lower SAR-based propagation speed values of southward traveling ISWs, compared to the theoretical ones.

ISW Heights and Associated Vertical Mixing
In situ data collected at 14 polygons enabled some statistics about the ISW properties to be obtained over the different WS regions. Table 2 provides a summary of ISW detection frequency per M 2 cycle, and their periods and heights recorded at polygons.    The data analysis clearly shows the formation of a southward propagating internal bore with a very sheer, 10-14 m high front during the peak flood (episodes 4 and 8 in Figure 15). Before it comes, the water structure has three distinct layers: a 8-12 m thick warm surface layer, a 8-10 m thick thermocline layer, and a nearly homogeneous cold bottom layer. After the bore passing, the upper layers become thinner (about 4-5 m each) and the vertical temperature gradient across the thermocline rises to 2 • C m −1 .
About 2.5 h later (during the ebb), the tidal current slackens and gradually changes direction eastward. At this moment, the ISW trains, consisting of 3-5 strongly nonlinear waves with maximal heights of 14-17 m and periods of 10-20 min, are seen in the record (episodes 1, 5, and 9 in Figure 15), followed by a tail of smaller waves of shorter period (episodes 2 and 6). The propagation of such intense ISW trains observed each tidal cycle is accompanied by the surface signatures in the form of slicks (not shown), commonly observed elsewhere (e.g., [24]).
Notably, the first two waves in the ISW train shown in episode 1 are less clear than those in episode 5, due to possible wave breaking. Indeed, the values of Richardson number R i = N 2 /S 2 , where S 2 = (∂u/∂z) 2 + (∂v/∂z) 2 is the squared current shear, are strongly below 1 at the time interval from 14:41 to 15:06 UTC, indicating favorable conditions for hydrodynamic instability, wave breaking, and enhanced vertical mixing in the water column.
Averaged over the full period of observations (25 h, see Section 2.2 for details), the values of the diapycnic diffusion coefficient K z in the pycnocline layer (8-14 m) are 12.1·10 −4 and 21.5·10 −4 m 2 s −1 when applying 2 h and 2 min time averaging steps, respectively ( Table 3). The difference indicates the contribution of the ISWs to the vertical turbulent exchange. The vertical K z profile obtained in summer 2011 over the same location shows a similar situation (Figure 16a). The K z values resolving high-frequency variability in the water column are 3-4 times higher than the background values of~10 −3 m 2 s −1 obtained with the 2 h averaging. The peak values of 33-37·10 −4 m 2 s −1 are registered in the pycnocline layer at 10-15 m depths.
A summary of the K z estimates obtained at polygons 1-14 using the two timeaveraging steps is given in Table 3. The values of K z vary from 3·10 −4 to 23.5·10 −4 m 2 s −1 . In most cases, the K z values are decreasing with depth ( Figure 16). However, the character of vertical K z variability could differ significantly, depending on the time-averaging interval of the initial data. The pronounced maxima of the K z values immediately below the pycnocline were observed at polygons 1, 3, 7, and 13 for the estimates made with the 2 min step, and absent in the data with the 2 h averaging (see Table 3 and examples in Figure 16a,c).
It is important to note that enhanced K z values in the pycnocline were registered mostly at polygons near the frontal zones where intense ISWs of higher than 5 m were regularly present (Table 3). To the contrary, the regions with absent ISWs activity (polygons 4, 5, 10, and 14) are characterized by low K z values that do not depend on the choice of the averaging interval. This is well illustrated in the vertical K z profiles at polygon 4 (Figure 16b), where both profiles have identical values and average around 10 −3 m 2 s −1 . All these facts allow us to conclude that ISWs strongly influence the hydrology and water mixing in the White Sea, leading to enhanced vertical turbulent exchange in the coastal and strait regions in the vicinity of strong frontal zones.  Figure 15 shows the observations of intense ISW trains made at polygon 1 in August 2010. The polygon was located in the vicinity of an underwater bank Severnaya, with an average depth of 10 m surrounded by regions of 35-50 m depth. Shipborne measurements were completed south of the bank over a 35 m depth during 25 h from 14:00 UTC on 8 August to 15:00 UTC on 9 August 2010. As shown earlier in Figure 6a, the buoyancy frequency profile at polygon 1 has maximal ( ) value (~0.04 s −1 ) at 8-10 m depth. The time variations of sea level and water temperature show distinct semidiurnal variability.
The data analysis clearly shows the formation of a southward propagating internal bore with a very sheer, 10-14 m high front during the peak flood (episodes 4 and 8 in Figure 15). Before it comes, the water structure has three distinct layers: a 8-12 m thick warm surface layer, a 8-10 m thick thermocline layer, and a nearly homogeneous cold bottom layer. After the bore passing, the upper layers become thinner (about 4-5 m each) and the vertical temperature gradient across the thermocline rises to 2 °C m −1 .
About 2.5 h later (during the ebb), the tidal current slackens and gradually changes direction eastward. At this moment, the ISW trains, consisting of 3-5 strongly nonlinear waves with maximal heights of 14-17 m and periods of 10-20 min, are seen in the record (episodes 1, 5, and 9 in Figure 15), followed by a tail of smaller waves of shorter period (episodes 2 and 6). The propagation of such intense ISW trains observed each tidal cycle is accompanied by the surface signatures in the form of slicks (not shown), commonly observed elsewhere (e.g., [24]).
Notably, the first two waves in the ISW train shown in episode 1 are less clear than

Discussion
In this work, we have attempted to build a most detailed picture of ISW properties in the White Sea, based on an analysis of satellite and field observations, including the definition of the main ISW hot-spots, their horizontal (from SAR data) and vertical (from in situ data) properties, the peculiarities of generation and kinematics in the main hot-spot region; and assess a basin-wide influence on the water mixing.
As obtained, the spatial and kinematic properties of the observed ISWs are linked to water depth/distance from the generation regions, with larger wave trains and higher propagation speeds being observed over the deeper regions. The maximal values of ISW propagation speeds attain~1 m/s and correspond to the largest wave trains observed in the deep Basin.
For the summer of 2010, the basin-wide ISW propagation speeds were estimated from the distance between the consequent wave trains seen in a single SAR image, assuming their generation once per M 2 tidal period. Obviously, the true periodicity of ISW generation is not well-known, though it is natural to suppose a semidiurnal periodicity in the region where the M 2 is the dominant tidal component. However, some of the observed ISWs could be generated twice more frequently, e.g., in the transcritical regime during the acceleration and deceleration phases of the ebb tidal current [25,34]. For such waves, the resulting propagation speeds would be two times higher than the obtained values.
Nevertheless, the obtained ISW propagation speeds of 0.1-1 m/s seem to be quite realistic. First, this was because a similar range of values (0.1-0.2 m/s) was derived from sequential SAR observations. Second, because in some regions, the background currents are very strong, up to 0.8-1 m/s. The superposition of the current velocities with the phase speed of ISWs can easily result in the instant propagation speeds of ISW signatures in the order of 1 m/s. A detailed analysis of the ISW field in the SW Gorlo Strait, the major hot spot of ISW generation in the sea, from concurrent satellite and field observations, showed rather complex ISW signatures resulting from multiple generations of sources, due to a local complex bottom. Here, the observed ISW patterns fit the bathymetry features well, assuming their generation via the common lee-wave mechanism. Measurements at a 24 h station revealed pronounced isopycnal depressions of 5-8 m due to passing of high-frequency ISW trains with periods of 10-20 min. The most intense waves were observed during the flood, while some others occurred during the flood/ebb slackening and reversal, similarly as reported in [41].
Unfortunately, concurrent field measurements were made southeast of the large semicircular ISW pattern depicted in Figure 13a. These wave trains have rather strong radar signal contrast [19], and appear to be the intense high-amplitude ISWs. However, historical field campaigns [8,10,[13][14][15] were not able to catch them and prove this, and it remains a subject for future studies.
An analysis of sequential Radarsat-1/-2 images over the SW GS enabled us to directly assess the propagation speeds of consequent ISW trains traveling to different directions. As obtained, estimates derived from the two data sources-sequential images and interpacket distances (from a single image), agreed quite well, with the latter providing somewhat higher values. However, as the literature suggests, sequential observations usually provide more accurate propagation speed values [32,35,37].
Based on well-expressed vertical density stratification at polygon 7 in the SW GS, with a single major peak of buoyancy frequency in the surface layer, we assumed that a two-layer approximation could be satisfactorily applied to theoretically assess the phase speed of the observed ISWs. However, the comparison of SAR-based estimates with those derived from theory showed that the latter were about two times higher than the observed values. Such a difference is presumably related to the fact that the two-layer model does not account for background currents that can effectively modulate the propagation speed of ISWs during the tidal cycle. Thus, SAR-based estimates appear to be more useful for practical applications where the actual propagation speeds of ISWs are needed.

Conclusions
The results of internal wave identification in the satellite SAR data of various spatial resolution clearly show that the latter is important in such studies. The number of identified ISW signatures was nearly similar for medium-(150 m) and high-resolution (6-25 m) SAR data, though the number of the latter was 2.5 times smaller during the same time period.
The major hot-spot of permanent ISW generation in the White Sea characterized by the highest ISW probability is the region in the SW Gorlo Strait, where a superposition of two strong fronts (the Dvina Front and the Gorlo Front), active tidal dynamics, and complex topography takes place. Other regions of pronounced ISW activity are found in straits near the Solovetsky Islands and in the NW Onega Bay, all characterized by strong tides and the presence of frontal zones. An important role of frontal zones in favoring the stratification conditions for ISW generation is also demonstrated from a very good correspondence between the MODIS-based SST gradients and the ISW probability field in the White Sea.
An analysis of field measurements at polygons shows a significant variability of thermohaline fields in two ranges of periodicity-semidiurnal (12.4 h) and high-frequency (tens of minutes). The former is primarily observed in the deep Basin, away from rough topography and frontal zones, while the latter or superposition of the two is predominantly found over the shallow coastal regions and near frontal zones.
Field measurements at polygons reveal that the most intense ISWs are recorded in the vicinity of frontal zones, where their heights often exceed the upper mixed layer thickness. The most intense ISWs were detected on the western sea shelf. Here, packets of strongly nonlinear internal waves with maximal heights of 14-17 m and periods of 10-20 min were repeatedly recorded immediately after the flood-ebb transition, when the tidal current slackened and gradually changed its direction.
An analysis of diapycnic diffusion coefficient values obtained at polygons across the White Sea showed that enhanced K z values in the pycnocline are registered mostly at polygons near frontal zones where intense ISWs (higher than 5 m) are regularly present. This result is in agreement with previous findings from other Arctic regions showing enhanced turbulent kinetic energy dissipation rates associated with the propagation and breaking of nonlinear ISWs [41,42]. In our work, the influence of ISWs on vertical mixing was assessed in a simplified manner, while future studies should definitely address it in a more sophisticated way using contemporary microstructure observations.