*E.1. Single Event APS Estimates*

Delay maps of *single event APSs* were generated to mitigate non-repeating atmospheric disturbances from the gas plume estimate, and were used to infer the meteorological conditions during each SAR observation (Figure A4). These APS estimates are presented in the form of simple phase delay maps, where the scale indicates lengthening or shortening of the radar delay in units of millimeters. Such phase delay maps are snapshots of the meteorological situation, reflecting the spatial distribution of water vapor fields at the times of SAR acquisitions. Atmospheric disturbances aloft volcanoes are generally more pronounced and show more complex flow patterns on the lee side of the volcanic edifice [18]. This anisotropic distribution of turbulent atmospheric patterns can be attributed to the presence of volcanic gas plumes on the one hand, but also to orographic effects that govern the transport of moist air over mountainous terrain [17,20]. Orographic effects comprise diabatic heating of air masses over insolated mountain flanks and orographic lifting of air masses that are pushed by the wind, causing upslope advection of moist air that is forced to rise following the steep topography, and to cool adiabatically causing an increase of the relative humidity.

**Figure A4.** *Single event APS estimates* superimposed by surface wind fields obtained from the lowest eta level of WRF (*thin white arrows*). Scales indicate range change in millimeters, and are unique to each image, in order to enhance contrast by depicting the full range of each image. Katabatic (downslope) mountain winds prevail at the time of SAR acquisitions recorded during the early morning hours (10:04 a.m. GMT, local time is offset −3 h). *Wind barbs* indicate wind directions and wind speeds above the summit of Láscar volcano, which were obtained from GFS hindcasts at the times of SAR acquisitions. The *barbs* are displaced upstream in order not to cover the delay signatures of the summit area. The individual lines of the *barbs* represent the wind speeds in units of knots (half strokes correspond to 5 knots and full strokes correspond to 10 knots). Wind directions (clockwise degrees from North), wind speed (m·sec<sup>−</sup>1) and estimated average PWV contents (mm) are additionally indicated in the upper right corner of each image.

APS delay patterns were compared to wind directions and atmospheric PWV contents estimated for the times of SAR acquisitions to assure that the modeled and measured wind directions and PWV estimates are consistent with the location and strength of associated phase delay patterns. Wind directions determined for the summit region of Láscar were prevailing westerly during the early morning hours of the "dry season", whereas wind directions of the "wet season" were predominantly easterly (see Figure A1c,d, Figures A2 and A3). This is reflected by the spatial distribution of cloud shaped signatures, which are confined to the plateau east of the volcano during the "dry season", while pronounced cloud shaped signatures are mainly confined to the western flank of the volcano during early summer, indicating that moist air has been transported at low-altitude by easterly winds towards the edge of the plateau during the "wet season" (period comprising SAR acquisitions of 23 December 2013 to 14 January 2014). Wind directions are thus consistent with the spatial distribution of observed phase delay patterns and PWV estimates agree with the strength of these patterns. Enhanced humidity variations encountered during SAR acquisitions of early summer can further be ascribed to the SAR acquisition strategy. Space based SARs typically repeat their observations at the same local time, causing SAR observations of early summer to be more affected by atmospheric disturbances, since they are recorded later with respect to sunrise, due to variations in the length of the day (Figure 2b). At Láscar volcano this effect is additionally enforced by more humid conditions that generally occur during that period.

#### *E.2. Repeating Atmospheric Phase Delays*

The phase delay estimates obtained for air temperature, air pressure and relative humidity *priors* comprise refractivity related phase contributions, which repeatedly occurred in all DInSARs of the time series and thus were not captured by the *single event APS estimates*. Such phase contributions therefore may contain residues of the stratification, which have not yet been removed through the coarse atmospheric correction that was performed prior to WBDD analysis utilizing the phase delay simulations obtained from the WRF, as well as repeating orographic effects, which may occur in multiple interferograms due to similar weather conditions.

Phase delay patterns in the air temperature dependent phase screen (Figure 6e) are asymmetrically distributed with respect to topography of the volcanic edifice, which can be ascribed to the distinct exposure of mountain flanks to sunlight. All SAR observations used in this study were made around sunrise, thus the western flank commonly lies in the shadow of the volcanic edifice, resulting in cooler air masses with a higher refractivity aloft the western flank, which produces a lengthening of the propagation path delay, whereas the air masses above the flat plain southeast of the volcano, the summit region, and the eastern flanks are subjected to diabatic heating due to a more pronounced insolation, which causes refractivity in the overlying air mass to be smaller due to higher air temperature.

Phase delay patterns of the pressure related phase screen (Figure 6f) indicate a lengthening of the delay over several confined steep-sloped areas, which are particularly exposed to westerly winds. The phase delay patterns of the temperature and pressure phase screens (Figure 6e,f) thus have the opposite direction, if compared to the phase delay patterns of the gas plume estimates (Figure 6c,d), resulting in a partial cancellation of the plume related phase delay (Figure 6b). Cancellation of the opposing phase screens hence reflect the negative dependence of volcanic gas emissions on barometric pressure and ambient temperature [77,78]. This is further supported by the spatial distribution of phase delay patterns in the relative humidity related phase screen (Figure 6g), which indicate enhanced relative humidity over exactly the same areas, which show a decreased temperature in the temperature phase screen (Figure 6e).

#### **Appendix F. DEM Error Related Phase Delays**

The SRTM-1 DEM that we used as a reference surface for our DInSAR observations is based on data which have been recorded in February 11–22, 2000. Since then several explosive eruptions occurred at Láscar volcano (July 2000, October 2002, December 2005, April 2006, and April 2013), which locally may have resulted in substantial changes in surface altitude that occurred previous to the period considered here. This in turn may have given rise to phase differences in our SAR interferograms, where the ground surface geometries measured by SAR observations and modeled digital elevation are different. The amplitude of such topographical artifacts is largely controlled by the measurement geometry of the DInSAR measurement, and generally increases proportionally to the length of the spatial baseline. As these phase differences can become exceedingly large in interferograms with a long spatial baseline, we instead used very small baseline interferograms for our DInSAR decomposition analysis.

The patterns in the phase delay estimate that we obtained for the spatial baseline *prior* are indeed intimately linked to topographic features (Figure 6h), and thus very likely reflect the development of the land surface during the period following the SRT Mission. The most prominent feature of this phase delay estimate is a pronounced shortening of the phase delay in the summit region of Láscar and on the SW flank of Aguas Calientes, which may be attributed to the deposition of erupted material. Furthermore, a lengthening of the phase delay occurs along morphological depressions, which follow the steep southeastern flank of Láscar and the base of Aguas Calientes, and therefore may be a result of removal or compaction of sedimentary deposits.
