1. 1 Experimental Study of the Microwave Radar Doppler Spectrum Backscattered from the Sea Surface at Small Incidence Angles Titchenko Yu. A., Karaev V. Yu., Panfilova M. A., Zuykova E. M., Meshkov E. M. Institute of Applied Physics, Russian Academy of Sciences e-mail: yuriy@hydro.appl.sci-nnov.ru Osipov M. V., Khlusov V. A. Micran, Research & Production Company

2. 2 Abstract This report focuses on the comparison of the measured characteristics of radar backscattering by the water surface with the theoretical model which includes the scattering model and the surface model. In the experiment, the backscattered signal at small incidence angles was studied at the different azimuth angle of antenna rotation. Comparison of the experimental data with the model confirmed the accuracy of the sea wave spectrum model and the electromagnetic scattering model. It is shown that in the analysis of the reflected signal is necessary to take into account the parameters of the surface rather than wind speed as it usually done.

3. 3 1. Introduction Radars successfully used to obtain information about the sea surface and the near surface layer of the oceans. Further development of remote sensing methods of the sea surface is directed to the creation of new algorithms to increase the number and accuracy of the measured parameters. Creation of new algorithms requires a precise scattering model of the sea surface. Recently a lot of models have been proposed that allow a qualitative description of the observed phenomena. However, a quantitative comparison of the models is complicated by the lack of experimental data. Usually characteristics of the scattered signal are analyzed with respect to wind speed changes that cannot be interpreted unambiguously. But in fact, the electromagnetic wave scattered by the sea surface and not by the wind. Therefore the sea surface parameters completely determine the characteristics of the reflected signal. Doppler spectrum is used to analyze the reflected radar signal. Because a Doppler spectrum contains more information than the backscattering cross section which usually used. Our group have been studying the Doppler spectrum of the reflected radar and acoustic signal for a long time. We actively promote the use of the Doppler spectrum for remote sensing of the sea surface.

4. 2. Doppler radar Measurements using a Ka-band Doppler radar with knife-beam antenna pattern (AP) were performed to study the backscattering. It is based on the 9 mm frequency modulated continuous wave marine radar, without determining the Doppler frequencies created by Micran. Parameters of the radar are shown in Table 1. Radar allows determining the exact distance to reflective objects. In the IAP RAS the radar was upgraded for another problem. In low range resolution, to determine the Doppler frequencies with sign in a band of tens of kHz. Low range resolution required to receive signals from all angles of antenna beamwidths. 4 Receiving tract input frequency range, GHz 33.4 – 34.2 Receiving tract output frequency range, MHz 0.0 – 1.4 The transmission coefficient of the receiving tract, dB > 25 The noise factor of the receiving tract, dB < 5 Transmitting tract input frequency range, MHz 4.175 – 4.275 Transmitting tract maximum output power, dBm > 16 The reflection coefficient of transmitting tract for the input, dB < -10 Currents on supply circuits, mA, - Plus 5 V - Minus 5 V 800 200 Table 1. Micran radar

5. 5 3. Place of measurements Measurements were made at nadir in the marine environment from an offshore platform of experimental branch of the Marine Hydrophysical Institute near the Katsiveli settlement. Platform 25 x 25 m located approximately 500 m to the south from the shore at a depth of 28 m in the open sea. The speed and direction of the wind at the height of 12 m are measured continuously on the platform. For the joint analysis of radar measurements, we used data about the sea surface from the string wave gauge fixed on the platform. Fig. 1. Ka-band Doppler radar with knife-beam antenna pattern Fig. 2. Offshore platform near the Katsively settlement

6. 6 The two-scale surface model is used to describe electromagnetic wave scattering by the water surface. In the quasi-specular region (the incidence angle is less than 10 – 15°), scattering occurs on the facets perpendicular to incident radiation. Motion of the "reflecting" surface segments gives rise to the Doppler shift and broadening of the Doppler spectrum (DS) of the signal reflected from the water surface. As a result, the DS parameters for fixed radar are completely determined by the large-scale surface characteristics. Consider the statement of the problem. Doppler radar with transmitting and receiving antennas with a knife-beam antenna pattern is employed to measure the DS. The aperture width of the AP is 1 x 30 deg. 4. E LECTROMAGNETIC W AVE S CATTERING BY A WATER SURFACE AT LOW INCIDENCE ANGLES RADAR Fig. 3. Measurement scheme Radar fixed at a height of 10 m. The aperture of knife- beam antenna pattern oriented vertically downward at an angle of incidence to the vertical, which is expected to be small enough that the mechanism of backscatter stayed quasispecular and do not need to take into account the Bragg component.

7. 7 Doppler radar measures the backscatter intensity and the DS of the reflected signal. This work does not use the backscatter intensity but focuses on the DS analysis. The Kirchhoff approximation method is used to obtain the formula for the DS width at -10 dB relative to the maximum: 4. E LECTROMAGNETIC W AVE S CATTERING BY A WATER SURFACE AT LOW INCIDENCE ANGLES where - radar wavelength, is the variance of the vertical orbital velocity component,, are the variances of slopes along and across the wave travel direction, respectively;, are the correlations between slopes and the vertical orbital velocity component; is the correlation between slopes in two direction.

8. 8 In the specified measurement scheme ( near 0°), the DS shape of the reflected signal is Gaussian and can be represented as follows Parameters of large-scale surface calculated using wave spectrum model. In the model, all parameters are determined by speed and direction of wind and the non-dimensional wind fetch. A fetch of 20170 is corresponds to fully developed waves, fetches of 5000 and 10000 are correspond to developing waves. Fig. 4 shows that the wind speed variation (for fully developed waves) on 1 m/s corresponds to a change in DS width on approximately 60 Hz. 4. E LECTROMAGNETIC W AVE S CATTERING BY A WATER SURFACE AT LOW INCIDENCE ANGLES Fig. 4. DS width as a function of wind speed at different non dimensional wind fetch.

9. 3. A CCOMPANYING MEASUREMENTS 9 To control radar measurements, we keep a record of speed and direction of wind using a weather station located at a height of 12 m. To demonstration of the variability of the measured wind speed consider one interval which is shown in Fig. 5. The figure shows a rapid variability of the wind speed. For further analysis, we selected 6 intervals where the average wind speed differed by no more than 0.5 m / s (less than 5% of the 11 m/s) and the mean direction differed by no more than 10 degrees (less than 5% of the 71°). During all 6 intervals a synchronous recording by the string wave gauge was conducted. According to Fig. 5 the orbital velocity variance obtained by a string wave gauge for given interval varies stronger than the wind speed and decreases with increasing of the average wind speed. This confirms the fact that the parameters of the surface are not related with the wind speed. This is due to the fact that the formation of the surface requires time. Thus the actual surface depends on the previous wind. Fig. 5. Measured wind speed (black) and orbital velocity variance (red) during 450 s. Black line – wind speed record. Black stars - average values of wind speed for 150 s. Red circles - average values of orbital velocity variance for 150 s.

10. 2. Numerical simulation 10 Fig. 6. Comparison of elevation spectra. Black line – obtained by measurements. Red line - model spectrum obtained by selection of the model parameters. String wave gauge records the change in height of the surface on time at the point. Surface characteristics and frequency spectra of surface waves are calculated by recording of single-channel string wave gauge. The spectrum of our work is called the power spectral density of the process, which is calculated by definition through the Fourier transform of the autocorrelation function of the process. String wave gauge records elevation at 4 Hz, which is enough to calculate the elevation variance and orbital velocity variance, but not enough to calculate the slopes variance and other parameters necessary for the analysis of radar scattering. For the analysis of radar data, we use the wave spectrum model for which it is possible to calculate all the parameters affecting on the scattering of microwaves from the water surface. The red curve in Fig. 6 was obtained as a result of selection parameters (wind fetch and wind speed) of wave spectrum model. In this case the lowest mean square error of spectrum model obtained at a wind speed of 5.4 m/s and the non-dimensional wind fetch of 19000. Further, these parameters will be used to simulate the radar reflection signal.

11. 2. Numerical simulation 11 In each of the 6 intervals at stable wind, radar measurements were performed at different azimuthal angles of the antenna rotation. In Fig. 7, the black line shows the measured Doppler spectrum averaged over 150 s at an azimuthal angle = 90°. The red line in the figure shows the simulation DS for the wave parameters selected for the best match with the simultaneous measurement of string wave gauge. Figure shows good agreement between the model of the DS based on the string wave gauge data improved by wave spectrum model with measured DS. Fig. 7. DS Comparison. Black line - the measured spectrum. Red line - DS obtained by the model based on the string wave gauge data. The amplitude was selected for easy comparison of the spectrum shape.

12. 3. Results 12 Comparison of the measured width of DS with the calculated DS width based on string wave gauge measurements for all 6 intervals shown in Fig. 8. Total number of points for comparison is 21. The error in DS width calculation is related to the uncertainty of the sea surface parameters obtained by the spectrum parameters selection. However Fig. 8 shows good agreement between the model of the DS width based on the string wave gauge data improved by wave spectrum model with measured DS. The standard deviation of the measured values is 19 Hz which is achieved quite a small change in the parameters of the model, less than 0.3 m/s. If we used the wind speed data from the weather station we would have a DS width of more than 2 times greater than measured. Fig. 8. Measured and calculated DS width comparison. In the figure the different colors correspond to different azimuthal angles in the experiment. Blue - 0°, Red - 90°, Black - 180°, Orange - 210°, Cyan - 240°, Green - 270°.

13. 13 Conclusions To estimate the reflected radar signal is necessary to know the parameters of the water surface instead of the wind speed. The results indicate that the used of our wave spectrum model and the scattering model well corresponds to the processes occurring in the backscattering of electromagnetic waves by water surface. Further efforts will be made to compare existing scattering models using surface characteristics data. Due to this it will be possible to choose the best scattering model based on data completely and uniquely determine the parameters of the scattered signal. This will allow in the future to solving the inverse problem of water surface parameters retrieval. The reported study was supported by RFBR, research project No. 13-05-00852 a and 14-05-31517 mol_a.

14. 14 Thank you! Yuriy Titchenko, PhD student, IAP RAS e-mail: yuriy@hydro.appl.sci-nnov.ru