## 2 Materials and Methods
### Interferometric Coherence  
Let \(S_{1}\) and \(S_{2}\) be two SAR images acquired with a given spatial and temporal baseline, see Figure 1, at a given polarization assumed to be the same for both images [6; 15; 38]. The interferometric coherence \(\gamma_{12}\) is defined as  
\[\gamma_{12}=\frac{\langle S_{1}S_{2}^{*}\rangle}{\sqrt{\langle|S_{1}|^{2}\rangle \langle|S_{2}|^{2}\rangle}} \tag{5}\]  
where \(\langle\cdot\rangle\) represents the speckle filtering [39], \(\gamma_{12}\) is a complex magnitude, whose modulus \(|\gamma_{12}|\) indicates the correlation between the images and its angle \(arg(\gamma_{12})\) denotes the interferometric phase. This work focuses on \(|\gamma_{12}|\), as it is a good indicator of how different decorrelation sources affect the coherence. Due to the polarimetric capabilities of SAOCOM-1 and Sentinel-1, \(\gamma_{HH}\), \(\gamma_{VV}\), \(\gamma_{HV}\), \(\gamma_{VH}\) will refer to the InSAR coherences at the different polarization combinations for transmission and reception, where \(H\) and \(V\) denote the linear horizontal and vertical wave polarization states, respectively. The coherence \(\gamma_{12}\) suffers from different decorrelation processes, and according to [15; 40] it can be written as  
\[\gamma_{12}=\gamma_{vol}\gamma_{sys}\gamma_{tmp}. \tag{6}\]  
For volumetric scatterers such as trees, \(\gamma_{vol}\) appears due to the different scattering processes that occur at different heights within a resolution cell [6]. It is a term that has a high dependence on frequency, as a variation in the wavelength implies different interactions with the scatterers. However, it does also depend on \(B_{\perp}\). For forested targets, if an exponential decrease of the scattering power is assumed within the canopy, \(\gamma_{vol}\) can be modeled as [18; 19]  
\[\gamma_{vol}=\frac{\alpha}{\alpha-j\kappa_{z}}\cdot\frac{e^{-j\kappa_{z}h}-e^ {-\alpha h}}{1-e^{-\alpha h}} \tag{7}\]  
where \(h\) is the volume height, and \(\alpha\) is the attenuation coefficient, which is normally expressed in dB/m and is also known as the extinction parameter in the PolInSAR literature. An important outcome of Equation (7) is that \(B_{\perp}\) plays a relevant role on the value of \(|\gamma_{vol}|\). Indeed, with higher values of \(B_{\perp}\) and \(\kappa_{z}\), see Equation (3), \(|\gamma_{vol}|\) will decrease more rapidly with an increase in the volume height. Satellite constellations such as Sentinel-1 have stringent orbit control. Orbit positioning control is defined using an orbital Earth fixed tube which is approximately 50 m wide in radius around the nominal operation path. Therefore,  
Figure 1: InSAR acquisition geometry (Source: [5]). \(B_{\perp}\) values for Sentinel-1 are normally within a range of \(-200\) to \(200\) m, which mitigates the potential effect of volume decorrelation [41]. \(\gamma_{sys}\) comprises a wide range of decorrelation effects caused by the SAR system configuration and processing aspects, that include contributions induced by additive noise, range and azimuth ambiguities, quantization, and other effects [15]. One of the most important components is the geometric term \(\gamma_{geom}\), which is function of \(B_{\perp}\) and \(B_{\perp,crit}\)[42]  
\[\gamma_{geom}=\left\{ \begin{array}{ll}\frac{B_{\perp,crit}-B_{\perp}}{B_{ \perp,crit}}&,|B_{\perp}|\leq B_{\perp,crit}\\ 0&,|B_{\perp}|>B_{\perp,crit}.\end{array} \right. \tag{8}\]  
Hence, if \(|B_{\perp}|>B_{\perp,crit}\), \(\gamma_{12}\) becomes 0, causing a total loss of correlation. Finally, \(\gamma_{tmp}\) represents the temporal decorrelation, and it is originated by geometric and/or dielectric changes in the scatterers within the temporal window that separates SAR acquisitions. Generally, the larger the temporal baseline, the lower the \(\gamma_{tmp}\). This term is critical when working with repeat-pass InSAR, and it is present even when working with almost-zero temporal separation between the images [16].