*The Seaview Inversion Method*

The method used makes the assumption that the first order Bragg wave, *k* - *<sup>B</sup>*, is generated by the local wind and that, by limiting the Doppler frequency range used in the inversion, the waves contributing to the second order scatter can be separated into long waves *k* -<sup>1</sup> and short waves *k* -<sup>2</sup> the latter also being locally wind-driven. These short wind waves are then modelled with a Pierson–Moskowitz spectrum [31], using an initial waveheight estimate obtained using an empirical method [32], and a sech<sup>2</sup> directional distribution [33] the parameters of which are determined using a wind direction estimation model [4].

The method is iterative and is initialised assuming the wind–wave model applies at all wavenumbers. The ratio of the Equations (1) and (3), *<sup>σ</sup>*2(*ω*) *<sup>σ</sup>*1(*ω*), is then integrated to provide a simulated Doppler spectrum ratio which is compared with the measured Doppler spectrum ratio to obtain the difference between them at each Doppler frequency. The wave spectrum is then updated taking into account the calculated Doppler spectrum ratio difference and the value of the coupling coefficient at the long wave vector wavenumber, *k* -<sup>1</sup> relative to the maximum along the Doppler frequency contour. The iteration continues until convergence is achieved or a specified number of iterations, usually 100, has been reached. The quality of the convergence is measured by a quantity that reflects the difference between the measured and simulated ratio. The solution can be very different from the initialising spectrum and often shows bimodality in frequency or direction or both due to the presence of swell or changing wind conditions. More details of the method can be found in Wyatt [10], and Green and Wyatt [11]. The maximum frequency (or equivalently wavenumber) of the long waves that can be measured is dependant on the radio frequency [5,34]. The minimum frequency depends on the quality of the radar data which impacts on the ability to clearly separate first and second order parts of the measured Doppler spectrum. An independent validation of the method applied to monostatic data is presented in [35].

The inversion software, providing surface current, wind direction and wave information, was written for monostatic radar configurations only. This has been extended to bistatic configurations using the analysis in Sections 2.1 and 2.2 above with some modifications to account for a difference in the coordinate system used in the Seaview software. The bistatic extension is not yet part of the commercial package. It has been tested using simulated data, using the methods given in Section 2.2, of two types: (a) two monostatic radars (in order to check that the bistatic extension to the Seaview package provides the same results for zero bistatic angle as the original monostatic package); (b) one monostatic and one bistatic radar sharing a transmitter at the monostatic site. Tests using two bistatic radars with a transmitter between the two sites are in progress but the results are not ready to be reported on at this time. The two receiver sites are those of the University of Plymouth wavehub WERA radar [36,37] and a limited number of cells from the coverage grid for that radar have been used to provide different bistatic angles for the simulations. Using an existing configuration made it easier to provide data for the inversions in standard Seaview formats. The wave parameters used in each simulation are the same at all cells and propagations losses and any antenna effects are not included so the only differences at each cell are the bistatic angle and the Bragg wave bearing relative to wave,wind and current directions.

The wave parameters for the different simulations are described in Table 1. They include modelled and buoy-measured wave spectra.


**Table 1.** Wave, wind and current parameters used for the Doppler spectra simulations. The buoy data are not separated into wind–waves and swell but their peak period and direction are included in the swell columns.
