## 3 Methods
### Basic Processing of SAR Data for Multi-Temporal Analysis  
A fully automated processing chain was developed to convert the multi-temporal space-borne SAR SLC data into terrain-geocoded \(\sigma^{\circ}\) values. The processing chain is a module within the MAPscape-RICE software [25]. The basic processing chain includes the following steps:  
1. Strip mosaicking: To facilitate the overall data processing and data handling, single frames of the same orbit and acquisition date were mosaicked along their azimuth, generating long strips in slant range geometry. This step is performed exclusively when the SAR data are zero-Doppler focused. 2. Co-registration: Images acquired with the same observation geometry and mode were co-registered in slant range geometry. The co-registration was performed in three steps: (i) a gross shift estimation based on the orbital data; (ii) a set of subwindows was automatically identified based on a reference image and on the images to be co-registered, and subsequently, the shifts between pixels of corresponding subwindows were calculated, including elevation by means of cross-correlation; (iii) finally, the shifts to be applied in the azimuth direction and range direction were calculated by a polynomial function depending on the pixel position, respectively, in the azimuth and range. 3. Time-series speckle filtering: Within the multi-temporal filtering, an optimum weighting filter was applied to balance differences in reflectivity between images at different times [28]. Multi-temporal filtering is based on the assumption that the same resolution element on the ground is illuminated by the radar beam in the same way and corresponds to the same slant range coordinates in all images of the time series. The reflectivity can change from one time to the next because of a change in the dielectric and geometrical properties of the elementary scatters, but should not change because of a different position of the resolution element with respect to the radar. 4. Terrain geocoding, radiometric calibration and normalization: A backward solution by considering a digital elevation model (DEM) was used to convert the positions of the \(\sigma^{\circ}\) elements into slant range image coordinates. A range-Doppler approach was applied to convert the two-dimensional row and column coordinates of the slant range image into three-dimensional object coordinates in a given cartographic reference system. During this step, the radiometric calibration was performed by means of the radar equation, in which scattering area, antenna gain patterns and range spread loss were considered. Finally, in order to compensate for the range dependency, \(\sigma^{\circ}\) was normalized according to the cosine law of the incidence angle. 5. Anisotropic non-linear diffusion (ANLD) filtering: This filter significantly smoothes homogeneous targets, while also enhancing the difference between neighboring areas. The filter uses the diffusion equation, in which the diffusion coefficient, instead of being a constant scalar, is a function of image position and assumes a tensor value [29]. In this way, it is locally adapted to be anisotropic close to linear structures, such as edges or lines. 6. Removal of atmospheric attenuation: Although microwave signals have the ability to penetrate clouds, it is possible that \(\sigma^{\circ}\) from shorter wavelengths (X- and C-band) can be locally attenuated by water vapor in the range of several dB, because of severe (tropical) storms. The temporal signature of \(\sigma^{\circ}\) can be affected by these events in two ways: (i) the thick layer of water vapor generates a strong decrease in \(\sigma^{\circ}\) during the event, followed by a strong increase after the event; (ii) the intense rainfall generates a strong increase in \(\sigma^{\circ}\) during the event, followed by a strong decrease after the event.