Numerical solutions of equation (1.2) for the e-vector orientation, ψ, presented in the viewing (sensor) zenith angle (VZA = θp) and the sun-viewing azimuthal difference (Δϕ = ϕs − ϕp) plane. The colour bar represents the calculated e-vector orientation, in the range of ±90° relative to the horizon. (a,d) angle of refraction into the water θr = 48.4° (solar zenith angle θs = 90°), (b) θr = 31.9° (θs = 45°) and (c) θr = 7.5° (θs = 10°). Pixels for which θr − δ < ψ <θr + δ, where δ is the detection resolution, are coloured in white. (a–c) δ = 0.1°, (d) δ = 1°. All cases assume a water refractive index of 1.337 at wavelength λ = 450 nm. Black pixels indicate convergence or discontinuity of ψ (e.g. values of −90° or 90°). Owing to the symmetry of the solution, Δϕ is presented in the range 0–180° only.