## 3 Results
### Echo Fit Examples  
Here we give details on the fitting of the idealised waveforms to the SAR and LRM echoes. When looking at the matched waves in detail, Figure 1, the semi-analytical echoes make a close match to the 1 Hz downsampled echos. Matching all three parameters \((A,\sigma_{s},t_{0})\) makes a closer fit than when matching \(\sigma_{s}\) alone. Comparing the down-sampled pLRM to the coincident SAR in Figure 1a,b, there is a similar waveform fit, with a close match in retrieved SWH except for the red example. This is the case for the all the SWH retrieved from this track, see Figure 2, with a mean fit error of 5.7 \(\times\) 10\({}^{-3}\) for pLRM 2.7 \(\times\) 10\({}^{-4}\) for SAR and 6.7 \(\times\) 10\({}^{-4}\) for LRM.  
For the example SAR echos (Figure 1) increasing from fitting \(\sigma_{s}\)only, to fitting all of \((\sigma_{s},A,t_{0})\) greatly reduces the fit error from order 10\({}^{-3}\) to 10\({}^{-4}\) (Figure 3) greatly improving the reliability of the retrieved SWH. For comparison Figure 3 also contains the three parameter fit of every individual 20 Hz echo power waveform. The 1 Hz three parameter fit has a lower error than the 20 Hz waveforms throughout Figure 3 with the 1 Hz retrieved values for \((A,\sigma_{s},t_{0})\) at the centre of spread of 20 Hz retrieved values. In order to produce a full and usable SWH data set covering 2011-2019 the data retrievals from CryoSat2 had to be downsampled from the level 1-B 20 Hz record. Data at this frequency would have resulted in a dataset that was far too fine for use. We tested both 1 Hz and 20 Hz waveforms with Figure 3 showing how the 1 Hz waveform gets a more stable inversion. In particular we found that noise about the 20 Hz waveform peak caused the greatest variation in retrieved parameters. At present we are not confident that the inversion scheme is robust at 20 Hz and before further investigation resolves this, we therefore chose to restrict our analysis and inversions to 1 Hz averages.  
The fit error is low for the one and two parameter fit for waveforms numbered 2300 to 3200 with a similar SWH for all. We attribute this similarity to the similar wave power scale \(A\) to the default value of \(A=1.0\) for these waves, while the retrieved leading edge \(t_{0}\) is variable about the default value associated with wave bin number \(t_{0}=28.0\).  
Figure 1: Example power waveform fit for (**a**) pseudo-LRM echoes (**b**) coincident 1 Hz down samples SAR echoes and (**c**) 1 Hz downsamples LRM echoes. Note that plots a and b originate from the same level 1 SAR retrievals. Each waveform (solid line) is plotted alongside an optimised 3 parameter fitted semi-analytic wave (dashed line) with the associated SWH listed. All waves are normalised by peak power and plotted at increasing height for clarity. The bottom most wave also has a 1 parameter (SWH only) matched wave plotted alongside (dotted line). The location of each wave is plotted in the same colors in Figure 2.  
Figure 2: Significant wave height and ice concentration 6 September 2014 12:11. To the left is the map of the Arctic with NSIDC ice concentration contours of 15%, 50% and 85%. We plot our retrieved SWH from SAR and LRM modes, with the transition indicated by the black line. The coloured crosses correspond to the location of the echoes plotted in Figure 1. To the the right is the detailed SWH for the track from our new data (SAR and LRM modes), RADS (pseudo-LRM and LRM modes), SAMOSA (SAR mode) and the WaveWatch 3 and ECMWF wave models.