**Appendix G. Estimation of APS Amplitude using Modeled Atmospheric PWV Contents Obtained from GDAS1 Soundings**

The atmospheric phase contributions in our coarsely corrected DInSAR maps (Figure 5b) are mainly caused by the presence of water vapor. Amplitudes of the atmospheric contribution to total DInSAR phase thus to a certain extent may be predicted using the modeled atmospheric PWV contents that were obtained from GDAS1 soundings for the summit region of Láscar volcano (Figure 7b and Table 2, columns 6 and 11).

In order to assess how well these modeled PWV values are suited to reproduce the APS amplitudes we therefore utilized the calculations described in Section 3.4 to determine the differential slant wet delays (dSWDs) that the PWV contents would produce in respective DInSARs, and compared their absolute values to the measured amplitudes of associated phase delays in each of the corresponding DInSAR maps (Figure 5b).

As a first step, we compared these predicted dSWDs (Table A1, column 4) to visually determined estimates of the mean APS amplitude in each of the DInSARs (Table A1, column 5). Using the scale bar ranges of the DInSAR maps in Figure 5 as reference, the mean APS amplitudes in five of the DInSARs (DInSARs 1-3, 5 and 6) were estimated to roughly amount to half of the scales, because a majority of the APS amplitudes does not exceed half of the associated scale, while they rather span 2/3rds of the scale bar in DInSAR 4, and only about 1/4 in DInSAR 7. Comparing the absolute values of the predicted dSWDs with our estimates of the mean APS amplitudes measured in corresponding DInSARs reveals that the latter are surprisingly well represented by the modeled dSWDs (R2 = 0.96; Figure A5a), which at average are offset from measured APS amplitudes by merely 2.1 mm.

In order to obtain more representative values for the measured amplitudes of the atmospheric delays in the DInSAR maps (Figure 5b) we further determined the root-mean-square-deviation (RMSD) of the phase delay amplitudes in each DInSAR map (Table A1, column 6) and compared it to the absolute values of the dSWDs, which the GDAS1 soundings predicted for the acquisition times of corresponding DInSARs. The comparison revealed that the absolute values of the predicted dSWDs are in good agreement with the RMSDs of DInSAR amplitudes (R2 = 0.70; Figure A5b).


**Table A1.** Absolute values of predicted dSWDs, obtained from GDAS1 soundings, along with estimates of the mean measured APS amplitudes (= scale bar fractions of DInSARs) and RMSDs of phase delay amplitudes in DInSARs.

**Figure A5.** Comparison of the absolute values of the predicted dSWDs with (**a**) estimates of the mean measured APS amplitudes, and with (**b**) RMSDs of phase delay amplitudes in DInSARs. Best fitting linear regression lines (*thick black lines*) are depicted along with their corresponding equations and R-squared values. Additionally, to guide the eye, linear regression lines that are forced through zero (*thin dashed lines*) are given as reference.

#### **Appendix H. Gas Plume Related Phase Delays of DInSAR Time Series Subsets 01 and 02**

Interferograms of DInSAR time series *subsets 01* and *02* were decomposed, in order to separately examine the associated gas plume related phase delays. Estimates of gas plume related phase delays were computed for each of the two disjoint time series subsets, i.e., using a limited number of three (*subset 01*), and respectively four temporally interconnected interferograms (*subset 02*). Presented are the results obtained from the WBDD run, that was conducted omitting surface temperature and pressure *priors*, i.e., the phase delays associated to refractivity changes caused by atmospheric pressure and temperature variations were not prevented from leaking into the phase delay estimates obtained for the gas plume. Gas plume estimates of both subsets show a fan-shaped interferometric pattern indicating lengthening of the radar path over the south-eastern flank of Láscar volcano (depicted by yellow to orange colors in Figure A6a,b), which is in good agreement with the common direction of plume transport (see supplementary Figure A1c,d, Figures A2 and A3 in Appendix D, where a detailed description of the wind field is given). Furthermore, this delay lengthening is coherent regarding the expected effect (Equation (1) in Smith and Weintraub, [66]), because the enhanced water vapor content

of the volcanic gas plume is expected to increase the refractivity with respect to its surroundings. Negatively correlated phase delay patterns (depicted by cyan to blue colors in Figure A6a,b), which are distributed over the western flanks of Láscar and Aguas Calientes volcanoes, in contrast are incoherent in terms of the expected sign of the phase delay (Equation (1) in Smith and Weintraub, [66]) and thus cannot be attributed to the gas plume. They rather indicate the contribution of another process (or other processes), which was (were) not mitigated from the gas plume estimate. *Subset 02* was additionally processed without the SAR acquisition of 3 January 2014, in order to display the resulting reduction of the phase delay amplitude in the repeating plume related signal (Figure A6c). PWV contents inside the plume and their respective differences were larger for SAR observations of *subset 01*, than they were for observations of *subset 02* (Table 2), suggesting a stronger influence on the gas plume related phase delay signal of *subset 01* (Figure A6a), if compared to *subset 02* (Figure A6b,c). The amplitudes of the estimated phase delays displayed in Figure A6a–c are thus consistent with their respective input dSWD values (Table 3, column 4), and are also in accordance with humidity contrast between plume and atmosphere (Table 2).

**Figure A6.** Delay correlation maps depicting estimated interferometric gas plume patterns from (**a**) *subset 01* and (**b**) *subset 02*. (**c**) Estimated interferometric pattern from *subset 02*, where the SAR observation of 03 Januray 2014 was omitted. All three estimates contain phase contributions of the temperature and pressure related phase screens (TPS & PPS not removed). Scales correspond to estimated delay (mm) per theoretical delay (mm). Upper and lower bounds of the scale bar are equal to unity in *subset 01*, but not in *subset 02*, indicating that the estimated delay in *subset 02* was by a factor 2 larger than the theoretical delay.
