Pre-processing. The pre-processing is mainly performed by exploiting existing tools in the free and open-source software SNAP (Sentinel Application Platform). It is based on well-known techniques such as co-registration (Sansosti et al., 2006) and debursting (De Zan, Xxxxx Xxxxxxxxx, 2006). The topographic contribution to the interferogram phases is compensated by using precise orbit information and a DEM of the scene. The ionospheric contribution is estimated and then compensated by a novel method based on the split spectrum technique (Xxxxx et al., 2016). The estimation is performed jointly over the whole stack of images, reaching in this way a better accuracy. The processing phase includes both the interferometric technique and all the steps required to obtain absolute ZTD maps. The estimation of differential ZTD maps is usually performed using techniques that exploit the Permanent Scatterers (PS). The drawback of these approaches is that PS density is usually low in rural areas. Thus, the final water vapor products cannot be as dense as required. Our procedure implements the phase linking method (Xxxxxxxxx, Xxxxxxxxx, 2008) to extract differential ZTD dense maps by exploiting both PS and Distributed Scatterers (DS). Given a stack of N coregistered SAR images, the phase linking technique generates all the possible N(N-1)/2 interferograms. The procedure iterates by minimizing, in each small window centered on the kth target, the following cost function: 𝜙�𝑛(𝑃𝑘 ) = arg min 𝑅𝑒(∑𝑚 ∑𝑛 ∑𝑘 𝐼(𝑃𝑘−𝑚,𝑘−𝑛) ⋅ 𝑒𝑗𝑗(𝜙�𝑛−𝜙�𝑚)), (1) where 𝜙�𝑛(𝑃𝑘 ) = estimated phase I = interferogram 𝑃𝑘 = k-th target Notice that the cost function involves only phase differences. Therefore, a constant can be added to all the terms 𝜙�𝑛(𝑃) without changing the solution. In other words, for each pixel Pk, all the phases can be estimated but for a constant phase offset. After applying the unwrapping technique (Ghiglia, Pritt, 1998), the estimated differential ZTD products need to be further enhanced. Due to the lack of millimetric accuracy in the satellite orbit determination, the pre-processing phase cannot completely remove the topographic contribution. The joint exploitation of SAR data and GNSS atmospheric products allows for the correction of this error. It is worth noting that the synergic use of satellites (SAR) and in-situ (GNSS) observations is one of the significant innovations in TWIGA paradigm. The orbital parameters are estimated by matching the SAR phases evaluated...
