We use three different methods to determine the AMEC altitude:
 Analysis of shadows and illumination conditions.
 Visibility of the cloud tops during twilight (Hernández-Bernal et al., 2018).
 Direct measurement from images of the AMEC phenomenon at the limb of Mars.
The observations used in the analysis of the cloud altitude in MY34 are presented in Figure 10. All altitudes in this section are relative to the Martian areoid as defined by MOLA data. The accuracy of these measurements is highly dependant on how sharp the border of the clouds is, as detailed in supporting material text S4.

Figures 10a and 10f show the shadow projected by the cloud in two different stages of the phenomenon and with different illumination conditions. Figure 10a shows the cloud and its shadow as seen in high resolution by HRSC. We studied this shadow in three dimensions, taking into account the parallax effect due to the high altitude of the cloud, the position of the observer, and the local topography. We found that the tail of the cloud was around 40-50 km in altitude. The profile of heights along the tail is indicated by the blue line in Figure 10g. The uncertainty of these measurements is mostly due to the difficulty of determining the limits of the cloud and the shadow, because of the presence of surrounding hazes. It is interesting to note that, within measurement uncertainties, the head of the cloud is higher than the tail, and the farthest extreme of the tail is at a lower altitude.

[Figure: Figure 10f is a low-resolution image acquired by VMC taken on a sol when the expansion of the cloud was delayed with respect to the trend established in section 4 (an early anomaly). Local time at Arsia Mons is 6.8 LTST and the low solar elevation angle (~15º) results in a long shadow that extends to the terminator. Simple geometry calculations indicate a minimum altitude of 45 km for the cloud tops and a vertical extension of the cloud of at least 5-10 km. The extension and altitude of this cloud is represented by the green area in Figure 10g.]

Figures 10b and 10c shows images obtained with VMC of the AMEC cloud at the limb of Mars.  The curves corresponding to the limb in these images are shown with white lines in Figure 10d. The limb observation shows aerosols around Arsia Mons and in its eastern side. Note that this observation was performed at Ls 281º, a season where hazes are also commonly observed in nadir observations of the region (section 5.3). On the eastern side of Arsia Mons (yellow arrows in Fig. 10c), optically thick aerosols are present up to an altitude of 35±10 km, and an optically thinner detached layer is present at altitudes of 45±10 km. On the western side of the volcano (cyan arrows in Fig. 10c), the head appears at a slightly higher altitude next to Arsia Mons (~50 ±10 km) in agreement with measurements of the shadow in the HRSC image (see Fig 10g for comparison).

[Figure: Figure 10e is a good example of a twilight observation by VMC. From an analysis of image sequences like this one, we constrained the top altitude of the cloud to be 30±5 km.]

Finally, figure 10g summarizes the results of our altitude measurements. Our results suggest that the cloud head raises during twilight, when we measure lower heights for the head cloud tops than at the start of expansion.

[Figure: Figure 10. Altitude of the AMEC relative to the areoid from different observations. (a) Shadow of the cloud at high resolution as observed by HRSC. This image has been enhanced to improve shadow visibility, for the equivalent color image refer to Fig. 3d. Acquired on  2018-09-21, Ls 254º, LTST 8.5, (orbit 18627). (b,c) AMEC cloud seen at the limb, clearly visible on the western flank (left of the volcano position, indicatedwith dark blue arrows), with hazes and a]