Reflection-polarization patterns at flat water surfaces and their relevance for insect polarization vision

It has recently been shown that horizontally polarized ultraviolet light reflected from the surface of water is the main optical cue for habitat finding by insects living in, on, or near water. What are the polarization properties that make the skylight reflected by water attractive to flying water insects in nature? In this paper, as an approach to this problem, the patterns of the degree and direction of polarization of skylight visible over a flat water surface are computed for unpolarized light from an overcast sky and for partially polarized skylight as a function of the zenith distance of the sun. These patterns are compared with the corresponding celestial polarization patterns. The effect of depolarizing clouds on these reflection-polarization patterns is demonstrated. Reflectivity patterns of a flat water surface are also calculated for clear and overcast skies. The polarization of the blue sky is described by the semi-empirical Rayleigh model. It is assumed that the reflection polarization of skylight at the water surface is governed by the Fresnel formulae. The effect of some modifying factors on the reflection-polarization field is briefly discussed. The adaptations of the visual system of insects living in, on, or near water to reflection-polarization patterns at water surfaces are briefly reviewed and discussed by means of three representative species: the waterstrider (Gerris lacustris), the backswimmer (Notonecta glauca), and the dragonfly (Hemicordulia tau).