Refractivity in terms of density We can write the refractivity in terms of density R N=k k',=k,-kM、/M,=22.1±2.2 K/mbar Density p is the density of the air parcel including water vapor. R is universal gas constant, Md and M are molecular weights. Zw is compressibility(deviation from ideal gas law) See Davis, J L, T AHerring, and L. baseline vectors from VLBl, J Geophys. Res, 96, 643-650, 199of Shapiro, Effects of atmospheric modeling errors on determinatio 04/09/03 12540Lec15 Integration of Refractivity To model the atmospheric delay, we express the atmospheric delay as D=Jn(sd-∫dm(e)J2(m()-d-m(JN(2)×10 Where the atm path is along the curved propagation ath vac is straight path, z is height for station height Z and m(e) is a mapping function Extended later for non-azimuthally symmetric atmosphere) The final integral is referred to as the"zenith delay 12540Lec1504/09/03 12.540 Lec 15 7 Refractivity in terms of density • We can write the refractivity in terms of density: • Density r is the density of the air parcel including water vapor. R is universal gas constant, Md and Mw w from ideal gas law) See Davis, J. L., T. A. Herring, and I.I. Shapiro, Effects of atmospheric modeling errors on determinations of baseline vectors from VLBI, N = k1 R Md r + k' 2 T + k3 T2 Ê Ë Á ˆ ¯ ˜PwZw -1 k' 2 = k2 - k1Mw /Md = 22.1± 2.2 K/mbar are molecular weights. Z is compressibility (deviation J. Geophys. Res., 96, 643–650, 1991. 04/09/03 12.540 Lec 15 8 Integration of Refractivity • To model the atmospheric delay, we express the atmospheric delay as: • Where the atm path; vac is straight vacuum path, z is height for station height Z and m(e) is a mapping function. (Extended later for non-azimuthally symmetric atmosphere) • D = n(s)ds - ds vac Ú atm Ú ª m(e) (n(z) -1)dz = Z • Ú m(e) N(z) ¥10-6 dz Z • Ú path is along the curved propagation The final integral is referred to as the ”zenith delay” 4