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Looking for the primary rainbow in starlight that is reflected by exoplanetsappears to be a promising method to search for liquid water clouds inexoplanetary atmospheres. Ice water clouds, that consist of water crystalsinstead of water droplets, could potentially mask the rainbow feature in theplanetary signal by covering liquid water clouds. Here, we investigate thestrength of the rainbow feature for exoplanets that have liquid and icy waterclouds in their atmosphere, and calculate the rainbow feature for a realisticcloud coverage of Earth. We calculate flux and polarization signals ofstarlight that is reflected by horizontally and vertically inhomogeneousEarth--like exoplanets, covered by patchy clouds consisting of liquid waterdroplets or water ice crystals. The planetary surfaces are black. On a planetwith a significant coverage of liquid water clouds only, the total flux signalshows a weak rainbow feature. Any coverage of the liquid water clouds by iceclouds, however, dampens the rainbow feature in the total flux, and thus thediscovery of liquid water in the atmosphere. On the other hand, detecting theprimary rainbow in the polarization signal of exoplanets appears to be apowerful tool for detecting liquid water in exoplanetary atmospheres, even whenthese clouds are partially covered by ice clouds. In particular, liquid waterclouds covering as little as 10%-20% of the planetary surface, with more thanhalf of these covered by ice clouds, still create a polarized rainbow featurein the planetary signal. Indeed, calculations of flux and polarization signalsof an exoplanet with a realistic Earth--like cloud coverage, show a strongpolarized rainbow feature.

Looking for the rainbow on exoplanets covered by liquid and icy water clouds