12.540 Principles of the global Positioning System Lecture 15 Prof. Thomas Herring 0409/03 12540Lec15 Propagation Medium: Neutral atmosphere Summary Basic structure of the atmosphere: Here we exclude the effects of electrons in the ionosphere(covered next lecture) Refractivity of constituents in the atmosphere Separation of atmospheric delay into "hydrostatic and wet components Elevation angle dependence Azimuthally symmetric mapping functions Gradient formulations Effects of atmospheric delays on position estimates 12540Lec15
04/09/03 12.540 Lec 15 1 12.540 Principles of the Global Positioning System Lecture 15 Prof. Thomas Herring Propagation Medium: Neutral atmosphere • Summary – Basic structure of the atmosphere: Here we exclude the effects of electrons in the ionosphere (covered next lecture). – Refractivity of constituents in the atmosphere – Separation of atmospheric delay into “hydrostatic” and wet components. – Elevation angle dependence: • Azimuthally symmetric mapping functions • Gradient formulations – Effects of atmospheric delays on position estimates 04/09/03 12.540 Lec 15 2 1
Basic atmospheric structure mosphere Troposphere is 2 100 where the temperature stops decreasing in the tmosphere(10 km altitude) 0409/03 12540Lec15 Troposphere Lots of examples of web-based documents about the mosphere: See for example Tropopause is where temperature stops decreasing Generally at pressure levels of about 300 mbar but can be as low as 500 mbar Sometimes term"tropospheric delay used but this only about 70%of delay Generally by height of 50-100km all of atmospheric delay accounted for Troposphere is where weather systems occur and aircraft fly on the tropopause 12540Lec15
04/09/03 12.540 Lec 15 3 Basic atmospheric structure Troposphere is where the temperature stops decreasing in the atmosphere. (~10 km altitude) 04/09/03 12.540 Lec 15 4 Troposphere • Lots of examples of web-based documents about the atmosphere: See for example. http://www-das.uwyo.edu/~geerts/cwx/notes/chap01/tropo.html • Tropopause is where temperature stops decreasing. Generally at pressure levels of about 300 mbar but can be as low as 500 mbar. • only about 70% of delay. • Generally by height of 50-100km all of atmospheric delay accounted for. • Troposphere is where weather systems occur and aircraft fly on the tropopause. Sometimes term “tropospheric delay” used but this is 2
Refractivity of air Air is made up of specific combination of gases, the most important ones being oxygen and nitrogen Each gas has its own refractive index that depends on re and temp For the main air constituents, the mixing ratio of the constituents is constant and so the refractivity of a packet of air at a specific pressure and temperature The one exception to this is water vapor which has a very variable mixing ratio Water vapor refractivity also depends on density/temperature due to dipole component 0409/03 12540Lec15 Refractivity of air The refractivity of moist air is given by N=k tk k1=77.60±0.05K/mbar k,=70.4±22 k2=(3.730±0.012)×105K2/mba For most constituents, refractivity depends on density (ie, number of air molecules ). Water vapor dipole terms depends on temperature as well as density 12540Lec15
Refractivity of air • Air is made up of specific combination of gases, the most important ones being oxygen and nitrogen. • Each gas has its own refractive index that depends on pressure and temperature. • For the main air constituents, the mixing ratio of the constituents is constant and so the refractivity of a packet of air at a specific pressure and temperature can be defined. • The one exception to this is water vapor which has a very variable mixing ratio. • Water vapor refractivity also depends on density/temperature due to dipole component. 04/09/03 12.540 Lec 15 5 04/09/03 12.540 Lec 15 6 Refractivity of air • The refractivity of moist air is given by: • For most constituents, refractivity depends on density (ie., number of air molecules). Water vapor dipole terms depends on temperature as well as density N = k1 Pd T Zd -1 Density of dry air + k2 Pw T Zd -1 Density of water vapor + k3 Pw T2 Zd -1 Dipole compoent of water vapor r/T k1 = 77.60 ± 0.05 k2 = 70.4 ± 2.2 k3 = (3.730 ± 0.012) ¥105 K2 123 123 123 K/mbar K/mbar /mbar 3
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 12540Lec15
04/09/03 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
Zenith delay The zenith delay is determined by the integration of refractivity vertically The atmospheric is very close to hydrostatic equilibrium meaning that surface pressure is given by the vertical integration of density. Since the first term in refractivity depends only on density, its vertical integration will depend only on surface pressure. This integral is called the "zenith hydrostatic delay(zHD) Often referred to as "dry delay "but this is incorrect because has water vapor contribution 04/09/03 12540Lec15 Zenith hydrostatic delay The Zenith hydrostatic delay is given by ZHD=10k.8m Ps =0.00228 m/mbar Where gm is mean value of gravity in column of air (Davis et al. 1991) gm=98062(1000265c0s(2中)3.1×107(0.92+7300)ms2 Ps is total surface pressure(again water vapor contribution included Since Ps is 1013 mbar at mean sea level; typical ZHD =2. 3 meters 04903 12540Lec15
Zenith delay • The zenith delay is determined by the integration of refractivity vertically. • The atmospheric is very close to hydrostatic equilibrium meaning that surface pressure is given by the vertical integration of density. Since the first term in refractivity depends only on density, its vertical integration will depend only on surface pressure. This integral is called the “zenith hydrostatic delay (ZHD)”. (Often referred to as “dry delay” but this is incorrect because has water vapor contribution). 04/09/03 12.540 Lec 15 9 Zenith hydrostatic delay • The Zenith hydrostatic delay is given by: ZHD =10-6 k1 M R d gm -1 P ª 0.00228 m/mbar s • Where gm is mean value of gravity in column of air (Davis et al. 1991) gm=9.8062(1-0.00265cos(2f)-3.1x10-7(0.9Z+7300)) ms-2 • Ps is total surface pressure (again water vapor contribution included) • Since Ps is 1013 mbar at mean sea level; typical ZHD =2.3 meters 04/09/03 12.540 Lec 15 10 5