# Is Sentinel able to obtain wave spectrum by interferometric Data?

I have recently read many articles on recovering wave spectrum from the AT-INSAR image spectrum (through interferometric images). However, it is not clear to me whether Sentinel is a viable option, although it is theoretically feasible. I know it is possible with satellites of two antennas, and these antennas are used to calculate the phase difference of the waves. But since the sentinel has only one antenna, it uses the technique of interferometry using two distinct orbits to calculate this phase difference.

A non linear transform from the article "On the nonlinear integral transform of an ocean wave spectrum into an along-track interferometric synthetic aperture radar image spectrum"

$$\begin{multline}\label{eq:tfasecomplete} P^S_P (\mathbf{k})= \left(\frac{k_xB}{\pi V}\right)^2\int d\mathbf{r} \exp(-j\mathbf{k}\cdot \mathbf{r}) \exp\left[\left(\frac{k_xR}{ V}\right)^2(f^u(\mathbf{r})-f^u(\mathbf{0}))\right] \\ \times\left[f^u(\mathbf{r})+\left(\frac{k_xR}{ V}\right)^2(f^u(\mathbf{r})-f^u(\mathbf{0}))^2\right] \left(1-\frac{\partial^2 f^u(\mathbf{r})}{\partial\mathbf{r}^2}\right)\left(\frac{k_xR}{V}\right)^2+2j\left(\frac{k_xR^2}{ V^2}\right) \\ \times \left(\frac{R}{V}\right)^2\left(\frac{\partial f^u(\mathbf{r})}{\partial\mathbf{r}}\right)^2 \left(\frac{\partial f^u(\mathbf{r})}{\partial\mathbf{r}}\right)\left[2f^u(\mathbf{r})-f^u(\mathbf{0})+(\frac{k_xR}{V})^2(f^u(\mathbf{r})-f^u(\mathbf{0})^2)\right]\\ - \left[1+\left(\frac{k_xR}{V}\right)^2 (3f^u(\mathbf{r}) -2f^u(\mathbf{0}))+(f^u(\mathbf{r})-f^u(\mathbf{0}^2)\left(\frac{k_xR}{V}\right)^4\right]. \end{multline}$$

Acctually, i want to know if a can use this transform for sentinel's interfometric data.

Thanks any help

In the paper you reference, the authors are using along-track interferometric synthetic aperture radar (AT-INSAR) over the ocean to retrieve the wave spectrum of gravity waves on the surface; moreover, they are using phase information, not amplitude information to do this.

Amplitude is not a great variable because the scattering angle dependence is large and not well understood, as it depends on smaller capillary waves on the surface of the gravity waves, and that is wind dependent and so on.

So they use phase. With 2 antenna on the same platform, offset in the direction of motion, you are basically taking 2 snaps shots of the surface (with phase info), and then you can compare those and see how much the surface shifted in the brief interval between image formation, leading to an ocean wave power spectrum vs the wavenumber $$k$$.

They key is brief: If you wait too long, the ocean surface decorrelates and the phase information is random noise.

If Sentinel is a repeat pass system, which needs at least 1 orbit, there will be no information about wave spectra available.

• Thanks for your response. However, I did not quite understand a few things. Yes, Sentinel is a repeat pass system, but with an 1 orbit, i believe it's impossible to create the image phase spectrum, since the Sentinel only has one antenna. this part about the surface decorrelation I agree, according to some calculations, it takes about an hour and a half for a full orbit. Is this time enough for the ocean surface to be decorrelation? Jul 19, 2019 at 11:36
• Repeat pass interferometry uses phase information over long periods, for example, before and after an earthquake (sciencealert.com/…). For C band (6-cm wavelength), the ocean surface needs to be scrambled by 1/4 of that over an image pixel (5m x 5m), which happens in factions of a second in high sea states. SRTM had antenna offset along track, with a 7ms time difference, and any AT-INSAR satellite is probably smaller than a space shuttle.
– JEB
Jul 19, 2019 at 13:50