Conclusion

As foreseen by charter item 1 the accuracy of the standard model of MARINI and MURRAY for applying propagation delay corrections has been assessed at the 1mm level.
The MARINI-MURRAY model was compared to the results of a raytracing algorithm for the wavelengths 355nm, 425nm, 532nm, 694.3nm and 850nm. Due to the unavailability of procedures calculating the effects of anomalous dispersion the comparison for the wavelengths 1064nm and 1570nm has been left for future investigations. The maximum error mainly incurred by the inadequate dispersion model of the MARINI-MURRAY mapping function was found to be 3cm at 15 degrees elevation at a laser wavelength of 355nm. The proposed goal of reaching 1mm accuracy at 15 degrees elevation seems to be unrealistic, since it corresponds to a zenith path delay of roughly 200 micrometers and a refractive index accuracy of $10^{-8}$, which is at the physical limit and would require atmospheric sounding in realtime. Moreover one has to keep in mind that the path delay jitter due to atmospheric turbulence is estimated at the millimeter level.
The mapping function derived by GARDNER modified in terms of the dispersion model was found to perform best with deviations smaller than 4mm at 15 degrees elevation and smaller than 2mm at 20 degrees elevation for all wavelengths under consideration.
The remaining action items are:

• Experimental verification of the new mapping function
• Modeling of anomalous dispersion for the wavelengths 850nm, 1064nm and 1570nm
• Inclusion of horizontal gradients