**4. Results**

Figures 11 and 12 show inverted surface current speed and direction, wind direction and significant waveheight and spectral peak direction maps for the model cases in Table 1 for the monostatic and bistatic configurations. For the bimodal case 2, Figure 13 shows the long (swell, here defined as waves in 0.05-0.1Hz band) and short (wind–wave, 0.1–0.2Hz) contributions separately to confirm that the latter are aligned with the wind. Figures 14–17 show current, wind and wave maps for the buoy cases. Figures 18–21 show sample directional spectra compared with those measured by the buoy and used in the simulations to provide a qualitative validation of the radar measured spectra. They are from 4 selected locations to cover the key parameter ranges expected to be important in the accuracy of the inversion. The key parameters are the bistatic angles and the difference in angle between the two Bragg directions (a minimum of 30◦ is required for monostatic processing [38]) and are presented in Table 2. Note that for some of the locations the Bragg angle difference is below the suggested monostatic threshold. Cell 1664 is the one on the left of the top row in the maps, cells 3116, 3128 and 3140 are the lower three going south along the column to the east of −5◦36 .

There is generally good agreement both for both the standard monostatic and the bistatic case. Differences will be discussed further in the next section.


**Table 2.** Configuration parameters at selected cells.

**Figure 11.** Inverted data for case 1. (**a**) monostatic (**b**) 1 bistatic. Current speed and direction on left, shortwave directional spreading and wind direction, centre, significant waveheight and peak direction, right.

**Figure 12.** Inverted data for case 2. (**a**) monostatic (**b**) 1 bistatic.

**Figure 13.** Inverted swell and wind wave components for case 2 (**a**) monostatic (**b**) 1 bistatic.

**Figure 14.** Inverted data for case 3. (**a**) monostatic (**b**) 1 bistatic.

**Figure 15.** Inverted data for case 4. (**a**) monostatic (**b**) 1 bistatic.

**Figure 16.** Inverted data for case 5. (**a**) monostatic (**b**) 1 bistatic.

**Figure 17.** Inverted data for case 6. (**a**) monostatic (**b**) 1 bistatic.

**Figure 18.** Inverted spectra for case 3. (**a**) monostatic (**b**) 1 bistatic.

**Figure 19.** Inverted spectra for case 4. (**a**) monostatic (**b**) 1 bistatic.

**Figure 20.** Inverted spectra for case 5. (**a**) monostatic (**b**) 1 bistatic.

**Figure 21.** Inverted spectra for case 6. (**a**) monostatic (**b**) 1 bistatic.

Scatter plots and statistics of the comparisons for currents are presented in Figure 22 and for waves in Figure 23. The data are colour-coded according to the bistatic angle with red being the largest bistatic angle. There is some dependence of the accuracy of the wave measurements on this parameter as can be seen in the right hand column of Figure 23. Most of the larger differences in peak period and peak direction are associated with the bimodal model case where the swell and wind–waves peaks were of similar magnitude and small differences in these magnitudes can lead to differences in peak identification. This is also evident when comparing Figure 12 with Figure 13.

**Figure 22.** Scatter plots and statistics of the current measurements. These are colour-coded with the bistatic angle.

**Figure 23.** Scatter plots and statistics of the wave parameter measurements, colour-coded with the bistatic angle.

#### **5. Discussion**

Monostatic and bistatic radar data have been simulated using the backscatter cross-section formulations developed in Section 2. The Seaview software package has been modified to include bistatic configurations and inverted to provide current, wind direction and wave measurements.

Currents have been obtained with good accuracy and consistency over many different bistatic and Bragg angles as evidenced in the scatter plots, Figure 22, and maps.

Wind directions are consistent with modelling except for the case shown in Figure 17. Note that the colour-coding in the wind plots is the derived directional spreading of the short waves which we haven't attempted to validate at this point. In Figure 17 this goes beyond the expected maximum (80◦) for this parameter. The reason is that the simulation used a wind direction that was roughly aligned with the Bragg direction and the smaller Bragg peak was mostly lost in the simulated noise level. The Seaview algorithm has difficulty estimating a wind direction accurately in these circumstances which, in our experience, rarely occur in measured data. It is interesting to note that waves are still measurable in these conditions confirming that the inversion result is independent of the initial guess which uses the wind direction.

The wave inversions are not as uniform as those for currents and winds. The significant waveheights are in reasonable agreement, Figure 23, although there is some evidence of overestimation at the highest simulated waveheight. That figure also shows that waveheight is underestimated for the largest bistatic angles of 64◦. More work is needed to determine a bistatic angle threshold for accurate wave measurement. Case 5 shows particularly noisy peak wave directions, Figure 16, including at the selected cells for which directional spectra are shown in Figure 20. While the frequency spectra (top left in each case) show good agreement, the low frequency part of the mean directions as a function of frequency (bottom left in each case) are not good at the low frequency peaks for three of these cases particuarly for the bistatic case. The inversion seems to be oversensitive to noise at these frequencies, which correspond with Doppler frequencies near the first order peak, and this needs further work as has been noted in many other applications of this method ([34,39]). Although some locations, including cell 1664, have Bragg angle differences in the bistatic case that are below the suggested monostatic angle threshold, there is no evidence that the results are worse there. This aspect also needs further work.

The directional spectra in Figures 18–21 use log scales for both the frequency spectra (top left) and the directional spectra (right column) so that differences at both high and low amplitudes can be identified. Apart from the low frequency issue referred to above, the shape of the spectra are in good agreement in all cases. As mentioned above, the maximum frequency for the radar measurements is variable and depends on geometrical factors such as Bragg direction relative to wind direction. At the frequency (12.355 MHz) of the examples presented her, the monostatic cases have maximum frequencies in the range of 0.22–0.283 Hz and the bistatic in the range of 0.187–0.277 Hz.

#### **6. Conclusions**

In this paper, the theory for the interpretation of bistatic radar Doppler spectra in terms of currents, winds and waves has been reviewed and methods to simulate and then invert such data have been developed. As far as the authors are aware this is the first time that ocean wave directional spectra, to a maximum frequency that depends on the geometrical parameters and without any prior assumptions about the shape of those spectra, have been obtained from bistatic, albeit only simulated, data. The next step will be to apply the method to measured radar data.

Current, wind and wave measurements from bistatic radar data have been obtained with reasonable accuracy. The statistics for the bistatic cases are not quite as good as the monostatic cases, although they are biased by the large bistatic angle cases. The exact limits on bistatic angle and angle between Braggs still need to be determined but are expected to be about 60◦ and <≈ 30◦ respectively.

The results in this paper compare a monostatic configuration with a combined monostatic and bistatic configuration with one transmitter at one of the receive sites. Work on a configuration involving two bistatic radars with one transmitter located between the two sites is in progress. This will help to determine suitable configurations for bistatic radar installations for oceanographic measurements.

**Author Contributions:** Conceptualization, R.L.H., L.R.W.; methodology, R.L.H., L.R.W.; software, C.C.E., L.R.W., R.L.H.; validation, R.L.H., L.R.W.; formal analysis, R.L.H., L.R.W.; investigation, R.L.H., L.R.W.; resources, R.L.H., L.R.W.; data curation, R.L.H., L.R.W.; writing–original draft preparation, R.L.H., L.R.W.; writing–review and editing, L.R.W.; visualization, R.L.H., L.R.W.; supervision, L.R.W.; project administration, L.R.W.; funding acquisition, R.L.H., L.R.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was partly funded by the UK Engineering and Physical Sciences Research Council (grant number: X/008627-14). The contributions of L.R.W. and C.C.E. were funded by The University of Sheffield and the APC by the UKRI block grant administered by UoS.

**Conflicts of Interest:** R.L.H. and C.C.E. declare no conflict of interest. L.R.W. is the Technical Director of Seaview Sensing Ltd but her role in this paper is as a University of Sheffield Professor and, as such, makes only scientific inputs and judgements on the work. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
