Short surface waves in the Canadian Arctic in 2007 and 2008

Abstract

AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract [1] We have collected time series data of short oceanic waves as a part of the International Polar Year (IPY) 2007–2008. Using a shipboard laser wave slope (LAWAS) system operating at 900 nm, we have obtained wave slopes measurements up to 60 rad m−1 wave number. We have compared our in situ wave slopes with collocated and concurrent high-resolution upwind Normalized Radar Cross Sections (NRCS) collected by QuikSCAT. The LAWAS measured wave slope spectra were consistent with local wind speeds and QuikSCAT measured NRCS. Our measured short wave mean slopes indicate their enhancement by long waves (0–1 rad m−1) at small values of long-wave slope. Concurrent with wave slope measurements, the strength of the reflected LAWAS light beam was analyzed in terms of the light attenuation coefficient at 900 nm. We have observed a correlation between surface elevation and light attenuation. The mechanism of wave modulated beam attenuation was found to be related to the instantaneous long wave skewness. Key Points Short wave slopes Inhibiting effect of long waves Normalized Radar Cross Sections 1. Introduction [2] Our work is focused on field measurements of short oceanic wave slopes. The importance of the short-wave slopes lies in the fact that they are a good proxy for quantifying measurement of how efficiently the ocean exchanges CO2 with the overlying air. Gas is transferred across the air-water boundary when the diffusive sublayer, the thin layer where molecular diffusivity is the dominant process, is disrupted. Experimental studies reveal that the most important process mediating gas transfer at moderate wind speeds is microscale breaking of short wind waves, i.e., those with wavelengths of 0.03–0.1 m [Zappa et al., 2002; Bock et al., 1999; Peirson and Banner, 2003]. The oceanic observations of Frew et al. [2004] suggest that the short wave slopes corresponding to waves between 40 and 800 rad m−1 are linearly related to gas transfer flux with a correlation coefficient of at least 89%—i.e., the linear fit accounts for at least 89% of the observed variance. Unfortunately, the dynamics of short oceanic waves remain both poorly quantified and understood. Some short wave dynamics can be gleaned from a few field experiments (e.g., Gasex2001) [McGillis et al., 2004; Jackson et al., 2012] or inferred based on the strength of the microwave backscatter off the oceanic surface. For example, the QuikSCAT Ku-band radar (13.46 GHz) signal is particularly sensitive to the approximately 1.45 cm long surface waves which dominate the return signal via Bragg scattering. Furthermore, satellite scatterometers such as QuikSCAT (or future Ocean Vector Winds missions) are capable of obtaining a wide snapshot of the oceanic wave field for waves between 360 and 510 rad m−1 [Bogucki et al., 2010]. Unfortunately, there are very few oceanic in situ wave measurements collocated with satellite scatterometer overpasses to verify the accuracy of microwave wave measurements. Our research aims to bridge that gap by directly measuring the short wave spectra and relating them to satellite scatterometer ocean wave observations. As a part of the International Polar Year (IPY), we have experimentally investigated the variability of short oceanic surface waves with the ultimate goal of relating them to the local carbon dioxide fluxes as described in Bogucki et al. [2010]. [3] The circumpolar flaw lead (CFL) system study was a Canadian-led IPY initiative with over 350 participants from 27 countries. The CFL study was 293 days in duration and involved the overwintering of the research icebreaker—Canadian Coast Guard Ship “Amundsen” in the Cape Bathurst flaw lead throughout the annual sea-ice cycle of 2007–2008. The CFL experiment was organized around a variety of objectives, many aimed at understanding basic physical and biogeochemical processes in the changing Arctic. For example, Else et al. [2012] reports new findings on the annual cycle of pCO2 and air-sea CO2 exchange in Arctic waters. Extensive valuable information can be found in the IPY-CFL special section of the Journal of Geophysical Research. [4] The paper begins with description of the experimental system and the experiment site, followed by description of the processing methods. Next, we present results including the observed wave spectra, along with the surface roughness measured during the coinciding overpasses of QuikSCAT. We finish with a discussion of the results. LAWAS Wave Measurements [5] We have designed and built the laser wave slope (LAWAS) system to measure the short surface waves and deployed it from the CCGS “Amundsen” in Baffin Bay and the Beaufort Sea, see Figure 1. In all, 15 weeks of wave time series were collected, with special attention paid to collecting time series that are concurrent and collocated with QuikSCAT overpasses. Out of over 60 observation stations, after quality control, we have selected five representative LAWAS deployments, see Figure 1 and Table 1. Figure 1Open in figure viewerPowerPoint The location of LAWAS deployments described in this paper, see Table 1 for more detail. (Image© 2012 TerraMetrics ©2012 Google Data SIO, NOAA, U.S. Navy, NGA GEBCO.) Table 1. LAWAS Measurement Stations and Description of Concurrent QuikSCAT (QS) Overpasses Date File Name Latitude N (deg, min) Longitude W (deg, min) LAWAS Data (UTC) QS Pass (UTC) QS Rev # QS Wind Speed (ms−1) 20 Oct. 2007 Oct20 71, 47 126, 33 4.5–5.1 (21 October) 19 Jul. 2008 Jul19_S2 70, 05.94 120, 02.52 4.88–5.72 4:47 47,298 4.7 22 Jul. 2008 Jul22_S1 71, 42.27 126, 32.76 4.27–5.37 3:28 47,340 5.6 22 Jul. 2008 Jul22_S1 71, 42.27 126, 32.76 4.27–5.37 5:09 47,341 4.7 31 Jul. 2008 Jul31_S1 71, 10.80 133, 33.94 11.92–12.55 11:45 47,459 4.9 1 Aug. 2008 Aug1 71, 18.189 126, 16.376 4.1–4.68 4:09 47,483 9.1 [6] The surface wave slope data were collected during four daytime LAWAS deployments in July and August 2008. The data from the LAWAS 20 October 2007 nighttime station were used to analyze the laser beam attenuation coefficient. This nighttime deployment was carefully selected so as to minimize ambient light contamination. All stations were ice free and characterized by 0.2–1.5 m root mean square (rms) wave amplitude. For a more detailed station description and QuikSCAT measured wind speeds averaged within 30 km from the station location, see Table 1. [7] The LAWAS system (Figure 2) consisted of four Riegl LD-90 laser range finders (or LIDAR) operating at 900 nm wavelength. Each optical transmitter/receiver assembly (or “laser head”) was made up of a laser and receiving telescope optics. Optical heads were placed at the corners of a square of aluminum plate measuring 0.6 m on each side and were pointed toward the sea surface, perpendicular to the square metal plate holding the optical heads. The metal square plate also housed a full tri-axis motion pack (Systron Donner BEI MotionPak). Figure 2Open in figure viewerPowerPoint LAWAS, four Riegl laser range finders operating at 900 nm, mounted 60 cm apart at the corners of a square and attached to an extendable aluminum beam. The mean distance to the sea surface is around 8 m. Inset: The CCGS Amundsen where LAWAS was installed during 2007 and 2008 experiments. [8] The square metal plate with laser heads was attached to an extendable 12 cm × 12 cm × 7 m aluminum beam. During measurement collection, the beam was extended from the upwind side of the ship. Four receiving units collected data from each Riegl rangefinder and tagged it with a time stamp. Data were then sent over a gigabit ethernet cable to a LabView-based data acquisition system. Concurrently with optical data, an additional acquisition system collected motion data from the MotionPak. [9] Every second, each of the four range finders (independently of each other) sent 2000 short light pulses toward the sea surface. The gated light reflections from the sea surface were binned and averaged in groups of 30 returns, thus yielding the average distance to the sea surface every 30/2000 s. This corresponds to acquisition frequency with an ensemble accuracy of better than 1 mm. We have verified that accuracy in the lab using a variety of reflecting surfaces. For discussion, we have selected sets of 30 valid returns thus eliminating returns from rain particles or small snow flakes suspended in the air. [10] The laser telescopes were mounted so that each laser head and its spot on the ocean surface created a square with a side of 0.6 m in length, see Figure 3 (top). The nominal distance between the laser telescopes and sea surface was less than 8 m and each of the laser spots on the ocean surface was typically 2 cm in diameter. Collocated with each laser (and mounted within the same laser head) was a receiving telescope with a field of view (FOV) partially overlapping the laser spot as seen in Figure 3 (bottom). The overlap area was smaller than either the laser spot or the receiving telescope FOV yielding an effective spot smaller than 1 cm wide, as shown in Figure 3 (bottom). Figure 3Open in figure viewerPowerPoint (top) The image of the LAWAS laser generated spots at 8 m away from the laser heads. (bottom) Close up of LAWAS laser spots. Partially overlapping with the laser spot is the spot corresponding to the receiving telescope field of view. Note the overlap region between telescope field of view and the laser spot. Each of the spots is approximately 2 cm wide. The overlap region, the source of the received light pulse, is less than 1 cm long. [11] The overlap length effectively sets up the shortest resolvable surface wave—less than 2 cm in our configuration. To be able to interpret the results of our measurement, we need to develop a model of laser pulse reflection from the sea surface. 3. Model of Laser Pulse Reflection From the Sea Surface [12] The 66.7 Hz LAWAS data stream contains time series of distance from the surface and the reflected signal strength. The returned signal strength is measured in 256 increments such that zero is the weakest and 255 is the strongest signal. [13] Light attenuation and surface reflection coefficients were the two main factors affecting the LAWAS returned signal strength. The LAWAS light pulse after leaving the laser and before making its way to the receiver, undergoes attenuation in air, reflection from the water surface and then attenuation in air again. [14] To the first order, the light beam reflection off the sea surface depends on the value of its Fresnel reflection coefficients and the statistics of the wave facets linking the laser with the detector. For a clean water surface undisturbed by a background swell, the Fresnel reflection coefficients are relatively insensitive to the wind speed up to 12 ms−1 and are relatively constant with an incidence angle up to 45° [Haltrin et al., 2000], which is much larger than any encountered wave. Hence, the reflectance of the pure water surface is relatively constant with reflectance (Rs) values between 0.02 and 0.03 for most of the waves and wind conditions encountered in our experiment. [15] In the case of a water surface covered by foam or whitecaps, the surface reflectance becomes drastically different. The optical properties of white caps at 900 nm are characterized by little absorption and strong reflectance Rs of around 0.4–0.6 [Koepke, 1984]. We have used the white caps' large light reflectance and their relative insensitivity to environmental conditions as a means to calibrate Riegl returns and ultimately to calculate the light attenuation between ocean surface and Riegl receiver. Typically with no wind, background whitecaps have been observed to cover less than 0.01% of the sea surface [Goddijn-Murphy et al., 2011]. During the deployment on 20 October 2007, the wind speed was around 8 m s−1, corresponding to the whitecap coverage of around 0.2%, equivalent to few seconds long-time interval containing whitecaps over a 30 min long deployment. [16] The light beam reflection coefficient of a clean ocean surface is further complicated by effects of the time varying curvature of the ocean surface. The surface curvature created by long waves results in reflection at wave troughs being somewhat larger then at wave crests [Srokosz, 1986]. The difference between reflection at the wave trough and the wave peak is linked to nonGaussian wave slope statistics. [17] As the LIDAR works by specular reflection, it senses the elevation of wave facets with zero slope relative to the incoming light beam. For realistic wave slopes, to the leading order, the zero-slope wave statistics, as a function of wave displacement, is a Gaussian function multiplied by an odd (third) order polynomial [Srokosz, 1986; Jackson, 1979]. The presence of the odd third-order polynomial mathematically implies different light beam reflectance at wave troughs and peaks. The peak/trough reflectance difference in turn, depends on the skewness of the sea surface elevation distribution [Srokosz, 1986]. Physically, this is related to the peakier crests and flatter troughs of nonlinear waves and is a measure of the nonlinearity. [18] We illustrate the effect of these processes on a LIDAR beam in terms of beam attenuation—a quantity independent of the LIDAR radiated power. 4. Measured Light Beam Attenuation at 900 nm [19] In general, we can express the received pulse intensity reflected off the water surface with beam reflectance Rs and attenuated in air as: (1)where z is the distance to the ocean surface, I0 is the LAWAS initial pulse strength, α(z) is the distance-dependent absorption in air, and is the mean absorption, in the integral sense, over distance z, i.e., . [20] When the beam reflects from a bright target such as a white cap, then equation 1 can be rewritten as: (2)where indices ()max correspond to the target distance, water reflectance, and air attenuation when observing the reflective target. [21] Combining equations 1 and 2 yield the expression for the mean attenuation as: (3)where the constant A is estimated to be based on laser 1 measurements carried out on 20 October 2007. Note that the presence of any obstruction on the water surface such as foam, whitecaps, and so on results in lowering of the mean absorption , as the clean water surface is a very weakly reflective target. [22] In the air, the main source of pulse absorption at 900 nm is the presence of the water vapor [Walker, 1994]. The pure water absorption coefficient at 900 nm is 7 m−1 [Mobley, 1994], which results in the light beam losing 72% of its energy over a distance of 14 cm when propagating in liquid water. [23] We have used the 20 October 2007 LAWAS data set collected during Arctic night. The data spans 30 min and are the laser 1 measurements. A subset of the full record, a 30 s time series of attenuation is presented in Figure 4a. The black dots are the instantaneous surface elevation (the mean elevation is zero), while the connected red dots represent the calculated (equation 3) beam attenuation at 900 nm. In the time interval 1570–1600 s, see Figure 4a, the measured attenuation varies between 0.02 and 0.16 m−1 and the surface elevation about the mean varies between −2.5 and 2.5 m. At the first wave peak (t = 1573 s), the laser 1 maximum sensed attenuation lags slightly behind the wave peak, while the last wave peak coincides with the maximum air attenuation (t = 1595 s). Note that the presence on the surface of any features (foam, etc.) or reflection from a passing snowflake should decrease the measured attenuation. Figure 4Open in figure viewerPowerPoint (a) Long-time series (30 s) of LAWAS, laser 1 attenuation as estimated from equation 3. The red connected dots: The light pulse attenuation the black dotes denote the ocean surface location (the mean surface location is at z = 0 m). (b) Scatter plot (20 October 2007) of measured light attenuation, equation 3 versus the surface displacement from the mean. (c) The scatterplot of skewness of the long-wave component versus observed attenuation for waves larger that 2.5 m amplitude. [24] We have observed several instances when the wave peak is associated with observed increased mean absorption, see Figure 4b. The scatterplot of all measured absorption values as a function of the surface elevation for the nighttime deployment of 20 October clearly shows the correlation. Note the asymmetry of the scatterplot with enhanced absorption when the surface displacement exceeds 2.5 m. [25] Light attenuation when plotted as a function of the long and large wave's skewness is presented in Figure 4c. The long-wave component was obtained by filtering the surface displacement record by a 1 Hz low pass filter and retaining only waves of 2.5 m or larger, Figure 4c. [26] The skewness of the long-wave component is related to observed light beam attenuation such that only waves with increasingly negative skewness (i.e., “forward leaning” waves) are associated with increased attenuation, Figure 4c. This is consistent with the wave trough/peak reflectance asymmetry as discussed earlier, albeit the insensitivity of the absorption to large and positive wave's skewness is puzzling. A possible explanation for that could be paucity of data with larger wave displacement. 5. LAWAS Measured Surface Displacement [27] Each Riegl unit is a range finder (LIDAR) which senses the distance to the water surface by converting the transmitted short light pulse from the time of flight to the distance from the obstacle, i.e., the water surface. The distance to the water surface is then calculated as the time taken for the reflected light to return to the laser head. The LAWAS had the lowest amount of dropouts when the water surface was populated with strongly scattering capillary waves with wavelengths smaller than 1 cm—typically encountered when the wind speed exceeds 5 m s−1 [Zhang, 1995]. [28] During the experiment, we discovered that each Riegl unit with its acquisition system had a significant time drift, i.e., the time stamps of measured distances had some variation when compared to the other Riegl units. The first stage of processing was then to align the readings from all four Riegl units in time. We have accomplished this by correlating readings of a selected Riegl unit (laser 1) with the remaining three units. For the cross correlation, we used a 1 min long time series subset (typically containing 5–10 waves). The largest observed time lag was around 20 s at the end of a 30 min long data set. [29] An example of a surface elevation time series for a selected Riegl unit is presented in Figure 5. Each of the Riegl units acquired 66.7 samples per second with corresponding Nyquist frequency 33.35 Hz. Some of the RIEGEL LIDAR returns have dropped out and these missing data points were obtained by linear interpolation from nearest neighbors. The time series all Riegl units were then resampled on a common time series with a fixed interval . Figure 5Open in figure viewerPowerPoint (top) A 30 s subset of 1 August 2008 time series of LAWAS measured surface elevation (Laser 1). (bottom) The high frequency (>1 Hz) part of the above elevation time series. Note the effect of the linear interpolation between missing data points. [30] In the last step, each of the Riegl unit elevation timer series was split into 10 min long segments and then analyzed for number of dropouts and spikes. For the final analysis, we have only retained the segments with minimal number of dropouts. This approach resulted in reducing by a factor of two the number of good segments available for analysis. [31] The subsequent statistical spectral analysis was then carried out on an ensemble average of four Riegl units within a 10 min long window. 6. Spatial Omnidirectional Wave Slope Spectra [32] The Bragg scattering of QuikSCAT microwave signal by the ocean surface depends on waves from a specific wave number range for a given incidence angle. For QuikSCAT, the range encompasses waves of wave numbers between 360 and 510 rad m−1. In order to convert our LAWAS frequency-based wave surface elevation observations to the spatial domain, we need to assume a relationship between wave parameters such as wave number and frequency. Such a connection is provided in the form of the wave dispersion relation. For deep water, small amplitude, gravity waves (i.e., “linear” surface waves), the dispersion relation between the magnitude of the wave number k and the frequency ω can be expressed as: ω2 = gk, where g is the gravitational acceleration. Laboratory and field observations demonstrate that as we approach the short gravity waves limit, the observed dispersion relation begins to differ from the linear dispersion relation. Following observations of Wang and Hwang [2004], we assume that the linear dispersion relation for frequency-based measurements is exactly valid up to a wave number of 15 rad m−1. For larger wave numbers, the linear dispersion relation becomes a like relationship, see Figure 7 of Wang and Hwang [2004] for frequency-based measurements. Wang and Hwang [2004] also document that the linear dispersion relation is valid up to 60 rad m−1 when based on spatial surface wave measurements. [33] Following Phillips [1977] and Hwang et al. [2000] for a stationary observer, the omnidirectional surface displacement spectrum Φ(ω) (see Appendix Appendix A), can be converted to omnidirectional wave number wave slope spectrum S(k) using the following relationship [Phillips, 1977]: (4) [34] This relationship is valid as long as the observer remains stationary with respect to the water surface which is the case for the analyzed data sets. In the presence of slow ship motion with the speed U, the dispersion relation is modified to become: (ω and ωd are, respectively, the real and the Doppler shifted angular frequencies, θ represents the ship angle in respect to the waves, which is assumed to be zero) [Drennan et al., 1994]. [35] The relative accuracy of the wave number estimated from frequency measurements becomes then: , when determined from a Doppler shifted wave frequency. Our estimated accuracy of ship drift is implying that the maximum relative wave number error is at k = 60 rad m−1, which also is the upper domain limit for S(k) spectra in Figure 6. Figure 6Open in figure viewerPowerPoint Frequency Φ(f) and slope wave number spectra S(k) acquired during 30 min long LAWAS deployment on 1 August 2008 (Table 1). (top) The frequency displacement spectra. The blue line corresponds to f−4 spectral dependence. (bottom) The spatial slope spectra. The f−4 in the frequency domain corresponds to k−1/2 dependence in the wave number domain. Note slight leveling of the frequency spectra for f > 2 Hz and corresponding S(k) change at k > 10 rad m−1 m. The red line represents the averaged spectra. Figure 7Open in figure viewerPowerPoint The high-resolution QuikSCAT data: (a) The wind direction in degrees from north, (b) sigma-0, and (d) wind speed distribution. The data presented here are acquired on 1 August 2008 concurrently with LAWAS measurements. The LAWAS measurements location is denoted by a dot in the Amundsen Gulf. (c)The ice distribution on 1 August 2008 (http://www.ec.gc.ca/). The light blue denotes open water, white denotes the ice free waters, and brown denotes the old ice. The arrow points North. [36] The observed surface elevation spectra Φ(f) shown in Figure 6 exhibit the expected f−4 or equivalent of k−1/2 for the wave slope spectra, S(k), down to the wave number of k = 2.5 rad m−1, within the equilibrium subrange. Note some leveling of the frequency spectra for f > 2 Hz and corresponding S(k) change at k > 10 rad m−1. The S(k) slope change at around k > 10 rad m−1 reflects the dynamics of observed surface waves [Hwang, 2005] and also is partially an artifact of linear interpolation of missing points as in Figure 5. [37] This last point can be understood when considering the effect of linear interpolation on missing LAWAS data points in Fourier space. The linear interpolation corresponds in physical space [Vaseghi, 1996] to convolving the “real” surface elevation spectra Φ(f) with a filter function, sin (f/f0)/f, with f0 being the effective filter width. This convolution in the case of monotonically decreasing surface elevation spectra Φ(f) effectively results in transferring the low-frequency spectral components to higher frequencies. [38] The additional factor affecting the variability of S(k) spectra is the apparent change of the dispersion relation (from ω2 = gk to , Figure 7 of Wang and Hwang [2004]) for k > 15 rad m−1, when the wave slopes are obtained from frequency measurements. Our estimate of this effect on the S(k) spectra is around a factor of 0.2 at k = 60 rad m−1. For consistency with other researchers, we use the linear dispersion relation throughout this paper, keeping in mind that it may contribute up to 20% to overall spectral S(k) error at 60 rad m−1 and less than 10% when considering the S(k) integral in the 20–60 rad m−1 range. The effect of missing LAWAS data points and their subsequent linear interpolation for k > 10 rad m−1 permits only qualitative evaluation of the wave contribution to mean square slopes (mss) in the 20–60 rad m−1 range. [39] We have minimized the effect of missing data interpolation, which results in spectral transfer of S(k) from shorter wave numbers to longer wave numbers, by constructing a new spectral slope estimator, defined as: for k > 20 rad m−1. Normalizing the slope spectra S(k) to a fixed value at k = 20 rad m−1 effectively removes the effects of short wave numbers aliased to longer wave numbers, but precludes us from using the spectra to obtain the absolute values of the mss in the 20–60 rad m−1 range. [40] In the final step, we compare our wave slope measurements to high resolution concurrent QuikSCAT observations. 7. High Resolution QuikSCAT Observations [41] In our presentation, we use two quantities derived from QuikSCAT measurements. The upwind Normalized Radar Cross Section (NRCS, also referred to as σ0 or sigma-0) and the estimates of wind speeds and directions under the QuikSCAT swath. The QuikSCAT Ku-band radar (13.46 GHz) signal is particularly sensitive to the surface waves which dominate the signal via Bragg scattering. QuikSCAT measures both vertically and horizontally polarized NRCS, i.e., v-pol and h-pol, respectively [Spencer et al., 2000]. [42] The QuikSCAT instrument design allows for the collection of spatially overlapping measurements of sigma-0 on a fine but irregular spatial grid. The nominal resolution of individual “slice” sigma-0 measurements is 6 km × 25 km. However, the spatial overlap in the measurements can be exploited to reconstruct the surface sigma-0 at a higher resolution using signal processing techniques [Early and Long, 2001]. This enables retrieval of winds on a much finer (i.e., 2.5 km) grid [Long et al., 2003; Williams et al., 2009]. Though noisier than the standard 25 km QuikSCAT wind products, the high-resolution winds reveal mesoscale wind features [Williams et al., 2009; Plagge et al., 2009] and can be used closer to the coast [Owen and Long, 2011]. For the details of QuikSCAT data collected simultaneously with LAWAS data, see Table 1. [43] Figure 7 shows the spatial distribution of sigma-0 wind speed and wind direction concurrently collected with LAWAS observations on 1 August 2008. The data is presented along the QuikSCAT swath, each pixel is 2.5 km wide. The swath (see Figure 7) is oriented approximately the same as the map in Figure 1, with the dark blue color corresponding to approximate land locations. [44] We can observe in Figures 7b and 7d that the main features of sigma-0 and QuikSCAT estimated wind speed are roughly similar as the wind speed is inferred from the sigma-0 data. Note in Figure 7a that the wind over the LAWAS site is approximately directed toward the North (denoted by red), while the wind on the Western side of the Amundsen Gulf has a predominant Eastward (blue) component, over open water as presented in Figure 7a. 8. The Comparison of Concurrent and Collocated QuikSCAT Observations With LAWAS Data-Long-Wave Effects [45] Our data set gives insight into complicated interaction of surface wave components. Unfortunately, the paucity of our ship's data set and lack of directionality of wave spectra allows only for simple correlation between wave slope components and preclude us from drawing more advanced conclusions about the evolving wave field. [46] The times series of wind data measured on the ship is unfortunately incomplete during the LAWAS measurement periods. We have compared available time series of wind speed with QuikSCAT spatial wind distribution and found that mean wind speed relative difference were within 10%. [47] Here, we have compared spatial sigma-0 fields and temporal wave slope data from LAWAS. All observations are concurrent and collocated, see Table 1. To get a handle on their variability, we have averaged them either in time—over the 30 min for LAWAS time series—or over a 15 km radius around the LAWAS deployment site, in case of QuikSCAT data. The radius of 15 km corresponds to approximately 1/2 h time span of sigma-0 when considering local winds. [48] The error bar length (see Figure 8) is equal to a standar