3.2.1. SAR Data Set and Amplitude Images

SAR systems emit electromagnetic pulses to the Earth's surface. Based on the backscattered intensity (amplitude) and the time delay, the amplitude images are obtained from the illuminated surface independent of daytime and weather conditions [11]. Earlier applications have used SAR amplitude imagery to monitor and comprehend the evolution of dome building [14–16,44] and other volcanic processes [45–47]. At Bezymianny, we employ 39 descending (track 11) spotlight [48] TerraSAR-X satellite (TSX, wavelength = 31 mm) amplitude images that have been acquired between January 2016 and August 2017, with a recurrence time of mostly 11 days (Figure 2a and Figure S2, Table S1). The images were recorded with an incidence angle of 38.7◦, and have a resolution cell (pixel) spacing of 0.9 × 1.25 m in slant-range and azimuth direction, respectively. We also studied eight ascending (track 64) (Figures S9, S10 and Table S2) spotlight-mode TSX images (incidence angle = 49◦; 0.9 × 1.20 m in slant-range x azimuth, respectively). The backscattered radar signal is confined by the acquisition geometry, as well as the roughness and dielectric properties of the illuminated surface [11]. Thus, rougher and smoother surfaces correspond to brighter and darker pixels in the amplitude image (Figure 2d,e), respectively. To visualise the reflectivity changes between amplitude images, we created change difference maps [15] that show regions of unchanged, decreased, and increased reflectivity values with yellow, magenta, and green colours, respectively. We note that the amplitude information is strongly influenced by steep topography and the oblique radar acquisition geometry, which causes distortions, such as the foreshortening of Bezymianny's eastern flank or shadowing at the summit crater floor (both track 11; Figure 2e). We mainly focus on track 11, as the viewing geometry of track 64 creates pronounced foreshortening and shadowing of the western and eastern flanks. However, although distortions in track 11 prohibit comprehensive observations of Bezymianny, the TSX amplitude data set provides unique information to determine exogenous and endogenous dome growth processes during the 2016–2017 eruptive sequence.

### 3.2.2. SAR Co-registration and Pixel Offset Measurements

Tracking pixel offsets of the co-registered SAR amplitude images may provide unambiguous range and azimuth quantification of surface displacements, where InSAR measurements become decorrelated [11,49]. Here, we co-registered all of the descending scenes with respect to the reference image (master) from 25 January 2016 with the Gamma remote sensing software (Gamma) [50] (Figure S3). We used a Pléiades digital elevation model (DEM) with a grid size of 2 m for real to SAR coordinate conversion. Look-up tables were calculated for the first scene (sub-master) of individual amplitude pairs, which subtracts topographic effects in the sub-master scene from range and azimuth pixel offsets. Moreover, to retain the deformation signal, orbital related offsets were subtracted via application of a cross-correlation based offset estimation, which determines a linear fit all over the offset tracking image pairs. Lastly, the TSX spotlight SAR scenes were deramped to remove azimuth ramps in the Doppler frequency. Subsequently, we employed an iterative image offset tracking algorithm with Gamma on the amplitude data with maximum resolution (i.e., no multilooking). Initially, we used a large tracking patch of 256 × 256 pixels (step-size = 4 pixels) to estimate the large pixel offsets. Then, we refined the offset estimation in a subsequent step with smaller patches that varied from 160 × 160 to 32 × 32 pixels to identify smaller displacements. To avoid aliasing of the spectrum, we oversampled the data by a factor of two. Appendix A details the error estimation.

#### **4. Results**

#### *4.1. Precursory Ground Movement*

#### 4.1.1. Precursory TSX Observations

Analysis of 26 TSX amplitude images that were acquired between January and November 2016 provides detailed evolution of surface motion at Bezymianny before the first documented effusive eruption in December 2016. For this episode, we calculated range offset maps based on three cross-correlation patches (32, 64, 96 pixels), and derived mean range offset rates under consideration of the TSX recurrence time (Table S1) for a selected region within the summit crater (Figure 3h).

Initial ground motion (0–0.08 m d<sup>−</sup>1) is observed between January–April 2016, while the amplitude images do not show clear changes in reflectivity (Figure 3a,e). Simultaneously, only few seismic events occurred between February–March 2016. In May 2016, a new radar shadow area appears at the western portion of the crater floor, which gradually increases in size until August 2016 (Figure 3b). During this time, the crater floor moves at increased, but near constant, rates of 0.07–0.13 m d−<sup>1</sup> towards the satellite (Figure 3i). By the beginning of September 2016, the shadow area considerably increased, but it started to diverge with brighter pixels in-between at its western portion (Figure 3c). Moreover, new radar shadows appeared at the north-eastern summit rim. Concurrent range pixel offsets within the summit crater show a stepwise increase from 0.16 to 0.23–0.25 m d−<sup>1</sup> during October (Figure 3g,i). At the same time, and after five months of quiescence, seismic events were recorded again, and seismicity continued throughout November 2016. Simultaneously, the summit floor radar shadow considerably increased eastwards, and the ground motion is marked by the most significant stepwise increase from 0.43 m d−<sup>1</sup> to 0.63 m d−<sup>1</sup> (Figure 3d,i). Eventually, the total detected ground displacement at the summit crater floor amounts to approximately 39 m towards the satellite (Figure 3h).

**Figure 3.** Eruption precursory deformation at Bezymianny between January and November 2017 determined in radar amplitude imagery change difference maps (**a**–**d**). Close-ups of these maps show the gradual emergence of a rigid body that produces a successively larger radar shadow at the summit crater floor displayed by magenta colours.

Contemporaneously, new shadows appear at the northern summit rim. Displayed cumulative range offset maps of consecutive amplitude images (**e**–**h**) are calculated with a cross-correlation patch of 64 pixels. Red and blue pixel displacements reflect motion away or towards the satellite, respectively. (**i**) The lower row shows the temporal evolution of ground movement calculated for a 10 × 10 pixels area located within the crater (red box in (**h**)). Error bars correspond to offset deviations in selected stable regions (cf. Figure S4). See text for details.

#### 4.1.2. Precursory Webcam Observations

To visually confirm the overall detected precursory TSX ground motion, we created a Mimatsu-diagram based on five clear webcam images acquired between May and December 2016 (Figure 4a,b). The camera images reveal slight growth of the summit between May–September 2016, whereas other images of the same period show intermittent translucent degassing and white steaming (Figure S7). First clearly distinguishable topographic changes are discernable in October 2016, where the eastern summit uplifts by 9–22 m, and elevations at the southern summit changes by 15 m in FOV. This topographic growth occurs at approximately the same time as the first significant rise of TSX range offsets (see above) and the onset of seismic activity in October 2016. Between September and beginning of December 2016, summit degassing significantly enhanced (Figure S7), and the 7 December 2016 Mimatsu image reveals a striking topographic uplift of 9–37 m of the eastern summit. The latter observations concurrently occurred with the gradual increase of detected seismic events as well as with the most significant increase of radar-derived ground motion detected in November 2016 (Figure 3).

**Figure 4.** Mimatsu diagrams depicting Bezymianny's summit: (**a**) before onset of the eruption sequence, (**b**,**c**) during the 5 December 2016 and 28 March 2017 eruption, (**d**,**e**) after the first (9 March 2017) and second (16 June 2017) explosive eruptions, respectively. Coloured bold lines correspond to the elevation change of the summit with respect to the previous camera image.

#### *4.2. Co-eruptive Ground Movement Observations*
