Variational calculation of three-dimensional atmospheric refraction: II. Application to assessment of positioning accuracy

In a previous paper (Berton 2006 J. Opt. A: Pure Appl. Opt. 8 817-30) we described the variational method devised for solving the 3D atmospheric refraction problem when the origin and the end of the refracted beam are given (boundary value problem). A validation was performed by comparison with numerical and analytical models in the case of astronomical refraction and with MODTRAN in the case of atmospheric refraction. Consistency was also checked with the direct method in which the origin, direction of sight and distance are specified (initial value problem). In this second part the method is applied in order to examine the influence of various elements on the positioning of a target in the visible and near-infrared. Ciddor's formula of the refractive index has been adopted here. When the target is on the ground, the separation distance l between the apparent and the real targets is also used as a criterion, beside the refraction angle R. The Earth's oblateness causes a discrepancy of 1% compared to a spherical Earth, while the various geometric configurations show that R can be multiplied by five and the ground distance l by 80 when the distance observer-target d increases from 6 to 45 km. The refraction angle is found to increase quasi-linearly as a function of d, which leads to l increasing as d(2). As regards the impact of the vertical profiles of temperature, pressure and humidity, a maximum difference of 40% is found between the profiles `tropical summer' and `sub-arctic winter'. The `US standard' type, which is a climatic average, yields intermediate refractive effects, closer to the `tropical summer' type. The influence of wavelength in the interval 0.5 - 1.7 mu m leads to a steep decrease of the refraction angle with an amplitude of about 2%; variations have been modelled with a second- degree polynomial of the wavenumber whose coefficients are little dependent on the configurations examined here. Eventually, the optimal sampling step is that one which produces at least 25 sampling points.