Discrepancy in neutral atmospheric delay due to different models for ray path and atmosphere in raytracing

We quantify the discrepancy in neutral atmospheric delay due to different assumptions when raytracing in numerical weather models (NWM). We make the comparisons in a worst-case scenario, in the vicinity of hurricane Charley (August 14, 2004, 12h UTC), as represented by a 15-km (horizontal resolution) NWM. First, we compare the ray path models bended-2d and bended-3d. In the former the ray is confined to a plane of constant azimuth; bending changes the ray direction in elevation angle only. That assumption is embodied in the widely used Bougler's formula, strictly valid only in a spherical atmosphere. In the latter model we solve the original Eikonal equation, making no assumption about the direction of the refraction gradient vector, thus allowing for out-of-plane bending due to horizontal gradients. Employing the 3d NWM, we show that the discrepancy (bended-2d minus bended-3d) at 3-degree elevation reaches at most -10.6 mm, 9.5 mm, and 2.4 mm in geometric, hydrostatic, and non-hydrostatic partial delays, respectively. The discrepancy in total delay is always positive, because the bended-3d model follows more closely Fermat's least time principle. The discrepancy in the combined geometric plus hydrostatic delay is smaller, due to the reversed sign of the components involved. We conclude that the smallness of that discrepancy warrants the use of the simpler bended-2d ray path model with a 15-km 3d atmospheric model. Next, we keep the ray model fixed to bended-2d, and compare different atmospheric models, all derived from the same NWM. Those models are, from simplest to most realistic: spherical concentric, spherical osculating, graded, and 3d. In the spherical models we take a vertical profile for each atmospheric parameter and assume their values constant for different horizontal positions at the same height. The main difference between the two spherical models, concentric and osculating, is in the location of their centers: if it is at the geo-center, we call it spherical concentric; if it is along the ellipsoidal normal passing through the point of interest (e.g., the GPS receiver), we call it spherical osculating. In the graded model we add to the spherical osculating model a vertical profile of horizontal gradient for each atmospheric parameter, whose values are assumed constant for different horizontal positions at the same height. Finally, the 3d model is the original NWM, made available as a grid and then interpolated at each position making up the discretization of the ray path. The figures below are maximum absolute discrepancies w.r.t. spherical osculating model (which is azimuthally symmetric), in non-hydrostatic followed by hydrostatic delay at 3-degree elevation. The spherical concentric atmosphere shows a very large discrepancy (20 cm, 1.3 m) in the North-South direction and zero discrepancy in the East-West direction. That is a simple consequence of the tilting of the spherical horizon with respect to the ellipsoidal horizon. The 3d atmosphere shows discrepancies in non-hydrostatic delay much larger than those in hydrostatic delay (30 cm, 5 cm), as consequence of the higher variability of humidity. The graded atmosphere represents well the main direction of azimuthal asymmetry present in the 3d model, but it is unable to account for secondary directions. Their discrepancy is smallest along that main direction (1 cm, 5 mm), but reaches non-negligible values (15 cm, 2.5 cm) elsewhere. We conclude that, for the purpose of making mapping functions available (not necessarily so in the parametrization for estimation of residual delay), secondary directions of azimuthal symmetry should be considered.