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## Summary

#### First order signal-to-noise (dB)

The ratio of first-order signal (the Bragg peak) to noise. Higher values of the threshold remove cells with Doppler spectra where noise predominates. Applied to all parameters.

#### Second order signal-to-noise (dB)

The ratio of second-order signal to noise. The paper [3] discusses signal-to-noise as an HF-radar quality metric. Applied to wind and wave parameters.

#### Ratio of first-order to second-order signals (dB)

Higher values of the threshold remove cells affected by current shear and sidelobes. Applied to wind and wave parameters.

#### Wind driven

There are two thresholds in this category. The one set to a lower value removes cells where Bragg waves are not wind driven, so the first-order signal could be from swell waves. Applied to wind and wave parameters.

The higher value threshold removes cells where short waves modelled in the inversion process are not wind-driven. Applied to wave spectral parameters, period and direction.

#### Inversion residual

The computed wave-spectrum is the result of an iteration driven by the difference between the Doppler-spectrum calculated from the Barrick-Weber relation, and as measured. A smaller value of this residual indicates a better inversion, see [2] for details. Applied to wave parameters.

#### Ratio of inverted and combined Hs

Smaller values remove cells with Doppler spectra with sidelobe problems, but use with care. Available for wave parameters, but not applied by default.

#### Ratio of model Hs to Tm squared (m/s2)

The significant-waveheight and mean-frequency of real ocean waves are constrained by the physics. When the height is too large for the period, waves will break, and empirical results [1] suggests that this limit is given by $$H_s / T_ m^2 < 1 / 13.$$ Larger values of the threshold rejects cells with these infeasible wave-slopes. Available for wind and wave parameters, but not applied by default.

#### Current angular geometric error (°)

The current vector is estimated from the spectral shifts along with an estimate of error. In the vector-combination of these, the error is combined similarly, forming an error parallelogram. Decreasing this threshold removes cells where this geometric error estimate is large. Applied to the current parameter.

#### Current (m/s)

Simply removes cells where the current is larger than the threshold level. This is sometime needed in regions where extreme currents could lead to aliasing of the Bragg peaks in the Doppler spectrum. Applied to the current parameter.

## Doppler spectra

The ocean data displayed by SVDV is derived from the Doppler spectra of radar backscatter, i.e., the power spectrum of the radar signal after demodulation and range-resolution.

The physics of the relation between a Doppler spectrum and wave-state is symmetric about the radar boresight, so two Doppler spectra are needed to resolve asymmetric features, in particular the directional wave-spectrum.

#### First-order peaks

Doppler spectra typically have two obvious peaks at Doppler frequencies $\pm\omega_\text{B}$ where the Bragg frequency is $$\omega_\text{B} = \sqrt{2 g k_0 \mathrm{tanh}(k_0 d) }$$ for radar wavenumber $k_0$, acceleration due to gravity $g$ and depth $d$: this relation being determined by the first-order theory, hence first-order peaks.

The first-order peaks are shown in red in Figure 1.

#### Second-order sidebands

The regions around each first-order peak will usually have features resulting from second-order interaction of radar and ocean waves. It is the inversion of this relation which allows one to determine the full directional wave-spectrum from a pair of Doppler spectra of sufficient quality.

The second-order sidebands are shown in blue in Figure 1.

#### Noise

Measured Doppler spectra are contaminated by noise, and the level of this noise quantifies spectrum quality. We take the level to be the 5th percentile rather than the value in a particular region of the spectrum; the latter is susceptible to aliasing effects and marine traffic noise.

Figure 2 illustrates the noise, the first- and second-order signal levels for a typical Doppler spectrum.

#### Spectral shift

The effect of current on the Doppler spectrum is a rigid shift, in particular the first-order spectral peaks are shifted from their current-free positions at Doppler frequencies $\pm\omega_\text{B}$ (shown red in Figure 3). This allows one to determine the component of the current vector in the direction of the radar (so with two spectra, one can recover the current vector).

References

[1] Tucker, M. J.: Waves in Ocean Engineering Measurement, Analysis, Interpretation. Ellis Horwood (1991)

[2] Wyatt, L. R.: Limits to the inversion of HF radar backscatter for ocean wave measurement. Journal of Atmospheric and Oceanic Technology 17, 1651–1666 (2000)

[3] Wyatt, L. R., Green, J. J., Middleditch, A.: HF radar data quality requirements for wave measurement. Coastal Engineering 58, 327–336 (2011)