Horizontal gradients

Very little is known up to now on the error incurred in the refraction correction in terms of horizontal pressure gradients. GARDNER [Gardner (1977)] estimated an error on the order of 2cm at 10 degrees elevation in the refraction correction by raytracing through radiosonde profiles taken at locations in the vincinity (20 km) around the site for which the correction should be derived. As the error lies within the accuracy of the MARINI-MURRAY mapping function itself, it might not be easy to show it up in residuals of SLR data.
As a first approach to include horizontal pressure gradients into the refraction correction formula, it is proposed to input an effective pressure value into the correction formula. The effective pressure can be obtained by use of the atmospheric scale height

$$H_s=\frac{T(0) \cal{R}}{g(\phi,H)\bar{g}M_d}$$ (17)

and by averaging the pressure gradient $\Delta P$ over the ground footprint path encompassed by the line of sight up to the atmospheric scale height.

$$P_{eff}(\theta_w,\alpha,\Delta P,\alpha_P)=P(0)+\cos(\alpha-\alpha_P) \frac{\Delta P H_s}{2 \tan(\theta_w)}.$$ (18)

Here $\alpha$ denotes the azimuth of the satellite and $\alpha_P$ the azimuthal direction of the pressure gradient.
Remaining questions in the modeling of horizontal gradients are:

• How do we provide horizontal gradients?
• Is it useful to use tabulated meteorological data from the weather forecast?
• Can GPS arrays around a tracking station be used for atmospheric tomography or provide ground meteorological data?