*3.1. Sigma S6 WaMoS*® *II*

The MR-based measurements were carried out by the *sigma* S6 WaMoS® II system. This standard commercial, off-the-shelf system consists of a high-speed video digitizing and storage device, which can be interfaced to most conventional analog and digital navigational X-Band radars. The *sigma* S6 system technology can be supplied with different software packages for various real-time applications like small target detection, oil spill detection and ice navigation and monitoring, as well as real-time sea state and current measurements (WaMoS® II).

The WaMoS® II system can be operated from fixed platforms and coastal sites, as well as from moving vessels. For the latter application, the horizontal vessel motion needs to be compensated. The large vertical beam width of MRs, the range of which is normally between 20◦ and 25◦, depending on the used radar type, ensures the ability to scan the sea surface even when the ship is pitching and rolling [19]. Hence, we assume that vessel motions like pitch, roll and heave have no critical influence on the WaMoS measurements.

The horizontal vessel movement can be removed during data processing, either in the space-time or in the wave number-frequency domain. The compensation in the wave number-frequency domain requires that the vessel movement over ground is constant (no variation in speed or course) during radar data acquisition given by number of individual radar images times radar repetition rate. In this case, the vessel movement is related to a fixed Doppler shift (<sup>→</sup> *k* → *Vship*), and can be separated from the Doppler shift related to the surface current (<sup>→</sup> *k* → *Ucurrent*), where <sup>→</sup> *k* is the wave number vector. The motion compensation in the space-time domain is performed by georeferencing [15,20]. Using GPS ship position and heading (gyro), orientation and position are estimated for every radar pulse. When transforming the sea clutter information from polar coordinates to Cartesian image sequences, each point of the resulting analysis area corresponds to a fixed position relative to the earth, independent of how the vessel is moving during the acquisition time. This method requires more computing time and limits the area available for analysis, but is independent of the ship movement. However, in cases when the vessel is moving very fast (>20 kn), this method might fail, and this occurs when the analysis area moves out of the radar view field. In both cases, very precise vessel heading is required as the error due to misalignment is amplified by the vessel speed [10]. For this application, WaMoS® II processing was set to *georeferencing* mode, as the vessel speed of *Polarstern* was <12 kn, in general. With the sampling strategy of 64 images per individual WaMoS® II measurement and a radar rotation time of 2.5 s, the maximum expected offset during data acquisition is about 1 km, and this is acceptably small compared to the WaMoS® II radar view range of 3 km.

The WaMoS® II system onboard *Polarstern* is connected to an analog SAM Radarpilot 1100 (9.4 GHz), with a rotation rate of *RPT* = 2.5 s. This radar is dedicated to the WaMoS® II application (in the following, this is referred to as the WaMoS® II radar). The mounted 5 ft antenna provides 1.5◦ angular resolution. Running in short pulse mode, with a pulse length of 80 nsec, the transceiver delivers data with 12 m range resolution. By oversampling of the radar raw data in direction and range, the *sigma* S6 digitizer delivers radar information with an angular resolution of 0.35◦ and 5.62 m in range (26.7 MHz). The WaMoS® II radar view field covers a range for 0.303–2.356 km from the antenna, with the second quadrant sector blanked due to the mast construction (Figure 1).

For one individual WaMoS® II measurement on board *Polarstern*, 64 consecutive radar images were analyzed, so that the WaMoS® II results represent temporal means of 2.67 min (64 <sup>×</sup> 2.5 s). To overcome the effects of the directional dependency of the wave imaging in radar images from radar look direction relative to wave and wind direction [10], the WaMoS® II analysis areas were placed all around the vessel. Figure 1 shows a vessel-oriented radar image, which was obtained by *sigma* S6 WaMoS® II on 12 May 2018, 12:00 UTC. At that time *Polarstern* was sailing northeastwards (42◦) at 12 kn (6.2 m/s), while the wind was blowing from 271◦, at about 14.4 m/s. The color refers to the measured radar return: black meaning no return level, and white indicating the maximum level. The radar return is digitized to 12 bits, which allows a signal strength ranging from 0–4095. To ensure no information is lost due to clipping at the lower limits, the digitizer is set below the noise level of the system. For the *Polarstern* system, a mean noise level of 500 was determined during system installation. To avoid reflections from the vessel superstructure in the near range, the system starts sampling after a dead range of 300 m. The analysis areas are the three grey rectangles indicating size (128×256 pixels) and alignment (35◦, 255◦, 325◦ relative to vessel heading) of the *sigma* S6 WaMoS® II (Figure 1). To overcome the directional dependency of the wave imaging in the radar images, the individual wave spectra of each analysis area are averaged. From the resulting spatially averaged spectrum, statistical wave parameters such as significant wave height (*Hs*), peak wave period (*Tp*), peak wave direction

(θ*p*), etc., are derived. The WaMoS® II update rate onboard *Polarstern* is approximately 3 min, given by the time taken for 64 images to be acquired, multiplied by the radar repetition rate of 2.5 s.

**Figure 1.** Vessel head-oriented WaMoS® II radar image acquired onboard the *Polarstern* on 12 May 2018, 12:00 UTC. The color scale refers to strength of the received radar return. The highlighted boxes indicate size and alignment of the three WaMoS® II wave analysis areas relative to the radar view field. The arrow in the center indicates the orientation of the *Polarstern*, which was moving at 12 kn and a course of 43◦ during data acquisition, and north is indicated by the arrow in the top right.

From the measurements of the phase speed (*c*) of the captured surface waves, the underlying ocean surface currents (<sup>→</sup> *Us*) are derived by identifying deviations from the known dispersion relations of surface waves. Assuming that <sup>→</sup> *Us* is small compared to *c*, the depth-weighted effective surface current is given by:

$$
\overrightarrow{\mathcal{U}}\_{s}(k) = 2k \int\_{0}^{H} \overrightarrow{\mathcal{U}}(z) \exp(-2kz) dz \tag{6}
$$

where <sup>→</sup> *U*(*z*) is the vertical current profile, with z being positive downwards and *H* being the water depth. As the influence decays exponentially with depth, the resulting current <sup>→</sup> *Us* represents a vertical average of the ocean currents within the wave-influenced surface layer *DW* [21]. *DW* varies depending on the wavelength (λ = 2π/*k*) and height of the captured waves. On average, *DW* is assumed to range between 3 and 10 m depending on the predominant wave length, and this will be shallower for short wind sea waves than for long swell waves [15].

### *3.2. ADCP*

As a reference, data from a vessel-mounted acoustic Doppler current profiler (ADCP) type Ocean Surveyor from Teledyne RD instruments [22] were used. Its transducers/receivers, operating at a nominal frequency of 150 kHz, are mounted in the hull of *Polarstern*, about 11 m below the water line. It was working in long-range mode with a vertical cell size of 4 m, a blanking distance of 4 m, and a maximum range of ~320 m. Heading, pitch, and roll from the ship's inertial navigation system (GPS and magnetically constrained "gyro") were used to convert the ADCP velocities to earth coordinates. The accuracy of the ADCP velocities mainly depends on the quality of the position fixes and the ship's heading data. Further errors stem from a misalignment of the transducer with the ship's centerline. The ADCP data were processed using the Ocean Surveyor Sputum Interpreter (OSSI) developed by GEOMAR, Helmholtz Centre for Ocean Research, Kiel ([22]), which corrects for a possible misalignment between the ADCP transducer orientation and the ship's forward direction.

To avoid interference with vessel-induced currents, the ADCP measurements are averaged over the 20–50 m depth range. For the data comparison, quality controlled ADCP current data with averages over 2 min were used. The quality filter is based on the statistical analysis, where data outliers exceeding the range of mean value and standard deviation of surface velocity are neglected. The ideal-theoretical precision σ*ADCP*(*ideal*) of the ADCP measurements can be estimated from the single ping/bin standard deviation of σ*ADCP*(*SP*) = 0.3 m/s, given by the ADCP manufacturer. Neglecting natural variability and assuming vertical and temporal homogeneity and independence over 20–50 m (7 depth bins) and 2 min (100 pings), results in σ*ADCP*(*ideal*) = σ*ADCP*(*SP*)/ √ *N* = 0.0113 m/s.
