## 4 Experimental Results
### Combined C-/X-Band Vertical Deformation Time-Series  
After the SBAS processing of the two independent ASAR-ENVISAT and CSK datasets, the C-/X-band combination technique, described in Section 3.3, was applied to the two (geocoded) vertical displacement time-series.  
For our analyses, we specifically focused on the ocean-reclaimed platforms of Lingang New City (Shanghai), for which a time-dependent geotechnical model of the on-going deformation is available in the literature [40].  
More specifically, the adopted time-dependent model, \(\mathbf{m}\), is provided in [40]:  
\[\mathbf{m}=\mathbf{m}\left(\mathbf{T},S,k,\lambda,\delta\right)=S\frac{\left( \mathbf{T}-\delta\right)^{\lambda}}{k^{\lambda}+\left(\mathbf{T}-\delta \right)^{\lambda}} \tag{5}\]  
where \(\mathbf{T}\) represents the vector of the ordered times of all the available SAR acquisitions. Note that, in Equation (5), \(S\) represents the asymptotic value of vertical deformation (theoretically assumed at time infinite), \(k\) and \(\lambda\) are two parameters that control the shape of a given curve among the family of all possible curves, and \(\delta\) is a time-delay, which takes into account the uncertainty of the knowledge of the exact time when reclamation processes ceased, and the self-weight soil consolidation phase started [6]. The model of Equation (5) is recovered from laboratory tests that simulate, at a reduced scale, real scenarios and the kinematic parameters that can be related to dredger-fill soil characteristics (i.e., thickness, water content, void ratio). For additional information, see also [14; 42; 46]. The combined C-/X-band deformation time-series, spanning the entire time interval covered by the available SAR datasets (from February 2007 to March 2016), were finally retrieved by solving the nonlinear optimization problem in Equation (4) using Equation (5). The problem was efficiently solved through the (iterative) Levenberg-Marquadt least squares (LS) minimization technique [65; 66], as provided in the implementation of the MPFIT module, which is available in several programming languages. In particular, for our experiments, we used the code implemented in the MPFIT module, available in the Interactive Data Language (IDL) language environment [67].  
As a result, we obtained the combined (vertical) displacement time-series for all the coherent pixels common to both C- and X-band SAR datasets. Figure 5a shows a zoomed view of the map, reporting the mean displacement rate of the vertical deformation in the Lingang New City area, as retrieved by combining ASAR/ENVISAT and CSK data.  
Figure 5: (**a**) Geocoded map of the mean (vertical) deformation velocity during the 2007–2016 time-interval over Lingang New City, as retrieved by combining ENVISAT and CSK LOS displacement time-series; and (**b**) map of the root mean square error (RMSE) values of the difference between the computed best-fit models and the combined ASAR/ENVISAT and CSK (vertical) deformation time-series. The plots of the ENVISAT/CSK combined (vertical) deformation time-series, calculated in correspondence with the four pixels, labeled as P\({}_{1}\), P\({}_{2}\), P\({}_{3}\), and P\({}_{4}\), are also shown. Combined time-series are plotted in **black** (ASAR/ENVISAT) and **red** (CSK) triangles, whereas the corresponding best-fit models are plotted by continuous **black** lines.