Certain terrestrial animals use sky polarization for navigation. Certain aquatic species have also been shown to orient according to a polarization stimulus, but the correlation between underwater polarization and Sun position and hence the ability to use underwater polarization as a compass for navigation is still under debate. To examine this issue, we use theoretical equations for per cent polarization and electric vector (e-vector) orientation that account for the position of the Sun, refraction at the air-water interface and Rayleigh single scattering. The polarization patterns predicted by these theoretical equations are compared with measurements conducted in clear and semi-turbid coastal sea waters at 2 m and 5 m depth over sea floors of 6 m and 28 m depth. We find that the per cent polarization is correlated with the Sun's elevation only in clear waters. We furthermore find that the maximum value of the e-vector orientation angle equals the angle of refraction only in clear waters, in the horizontal viewing direction, over the deeper sea floor. We conclude that navigation by use of underwater polarization is possible under restricted conditions, i.e. in clear waters, primarily near the horizontal viewing direction, and in locations where the sea floor has limited effects on the light's polarization.