  Images of Europa's surface taken by the Galileo Solid State Imager (SSI) show
smooth features measuring a few kilometers, potentially resulting from
eruptions of low-viscosity material such as liquid cryomagma. We estimated the
volume of four of these smooth features by producing digital elevation models
(DEMs) of four Galileo/SSI images. We used the shape-from-shading technique
with special care to estimate the uncertainties on the produced DEMs and
estimated feature volumes to be between ($5.7*10^{7}$ m$^{3}$ and ($2.7*10^{8}$
m$^{3}$. We discussed the implications for putative sub-surface liquid
reservoir dimensions in the case of eruptions induced from freezing reservoirs.
Our previous cryovolcanic eruption model was improved by considering a cycle of
cryomagma freezing and effusion and by estimating the vaporized cryolava
fraction once cryolava spreads onto Europa's surface. Our results show that the
cryomagma reservoirs would have to be relatively large to generate these smooth
features (1 to 100 km$^{3}$ if the flow features result from a single eruption,
and 0.4 to 60 km$^{3}$ for the full lifetime of a reservoir generating cyclic
eruptions). The two future missions JUICE (ESA) and Europa Clipper (NASA)
should reach Europa during the late 2020s. They shall give more information on
those putative cryovolcanic regions which appear as interesting targets that
could provide a better understanding of the material exchanges between the
surface, sub-surface and ocean of Europa.
