3D representation of the CR(E₀, θ) modeled relationship for the case of a mono-energetic distribution (left panel) and for the case of a kappa distribution (right panel). Both relationships are calculated for the north pole (i.e., for ψ = 65.7°). The green grid lines represent the fit of the modeled CR(E₀, θ) relationship. The colored surface (color bar from blue to red) represents the absolute difference between the modeled surface and the fit surface, with an average CR uncertainty of around 0.6 for the case of the mono-energetic distribution and an uncertainty of around 0.5 for the case of the kappa distribution.