Revised Refractive Index Formulae and Their Effect in Zenith Delay Prediction and Estimation

Tamanho: px

Começar a partir da página:

Download "Revised Refractive Index Formulae and Their Effect in Zenith Delay Prediction and Estimation"

Felipe de Sintra Conceição
6 Há anos
Visualizações:

1 Revised Refractive Index Formulae and Their Effect in Zenith Delay Prediction and Estimation Virgílio B. Mendes (1) and Richard B. Langley (2) (1) LATTEX and Departamento de Matemática Faculdade de Ciências da Universidade de Lisboa, Portugal (2) Geodetic Research Laboratory Department of Geodesy and Geomatics Engineering, University of New Brunswick Fredericton, N.B., Canada Position Location and Navigation Symposium 2002 Palm Springs April 2002

2 Outline Atmospheric refraction Refractivity Zenith atmospheric propagation delay Impact of refractivity computation Impact of saturation vapour pressure computation Conclusions

3 Atmospheric Refraction Thermosphere Ionosphere Mesosphere 80 km S S 50 km Stratosphere Tropopause Troposphere 9-16 km 0 km τ= 1 v ds S

4 Refractive Index Refractive Index (n) ratio of the speed of propagation of an EM wave in a vacuum (c) to the phase speed of propagation in a given medium (v) v less than c excess path delay n variable throughout the atmosphere ray bending Refractivity (N): N = ( n 1) 10 6

5 Refractivity - I P e e P N= K + K + K + K T T T T * ' d c K i refractivity constants (determined in a laboratory) P * d partial pressure due to dry air (CO 2 -free) P d partial pressure due to dry air (including CO 2 ) e partial pressure due to water vapour P c partial pressure due to CO 2 T temperature P e e N= K + K + K T T T d

6 Refractivity - II P e e N = K Z + K + K Z T T T d d w dry wet e e N= K R ρ+ K + K Z T T ' 1 1 d w hydrostatic non-hydrostatic ( wet )

7 Refractivity - III 1 Z d inverse compressibility factor for dry air 1 Z w inverse compressibility factor for water vapor R = ' d K2 K2 K1 R w R d specific gas constant for dry air (R d = ± J kg -1 K -1 ) R w specific gas constant for water vapor (R w = ± J kg -1 K -1 ) ρ density for dry air

8 Neutral Atmosphere Delay d na = d z h m h ( ε) + d z nh m nh ( ε) Hydrostatic mapping function Non-hydrostatic ( wet ) mapping function Zenith hydrostatic delay Zenith non-hydrostatic ( wet ) delay

9 Zenith Propagation Delay r z a d ( ) na = n 1 dz rs z 6 a dna = 10 N dz rs r r r z 6 e dna = 1 ρ + + T a 6 a ' 1 0 K1R r d dz 10 K2 K3 Z 2 w dz s r s e T zenith hydrostatic delay (ZHD) zenith non-hydrostatic delay (ZNhD)

10 Zenith Hydrostatic Delay r z 6 a dh = 10 K r 1Rdρ dz s r r 0 s a dp ρ dz = = Ps g P P d = 10 K R =ζ g f,h z 6 s s h 1 d m φ ( ) ZHD can be determined accurately if surface pressure measurements are available ZHD depends on the choice of K 1 and g m P g s m

11 ZHD Changes for K 1 = 0.1 K hpa -1

12 Zenith Non-hydrostatic Delay r e T e T z 6 a ' 1 dnh = 10 r K2 + K3 Z 2 w dz s e is variable in space and time Distribution of water vapour with altitude is not known There is no closed solution for the ZNhD Effect of changes in refractivity constants can be analyzed by raytracing profiles of e and T obtained by radiosondes

13 Refractivity Constants Formula K 1 (K hpa -1 ) K 2 (K hpa -1 ) K 3 (K 2 hpa -1 ) ' K 2 (K hpa -1 ) ζ (m hpa -1 ) BOUD (±0.075) (±10.5) (±3000) 23.7 (±10.5) (± ) IAG (-) (-) (-) 16.4 (-) (-) LIEB (±0.023) (-) (-) 23.3 (-) (-) LIEB (±0.023) 71.7 (-) (-) 23.4 (-) (-) BNB300 (300 ppm CO2) (±0.013) (±10.5) (±3000) 23.6 (±10.5) (± ) RUEG375 (375 ppm CO2) (±0.0094) (±1.3) (±760) 23.0 (±1.3) (± )

14 Radiosonde Locations

15 ZNhD: IAG63 minus LIEB77 Cocos Island

16 ZNhD: IAG63 minus LIEB77 Tateno

17 ZNhD: IAG63 minus LIEB77 Lhasa

18 ZNhD: IAG63 minus LIEB77 Uccle

19 ZNhD: IAG63 minus LIEB77 St. John s

20 ZNhD: IAG63 minus LIEB77 San Diego

21 Saturation Vapour Pressure Water vapour pressure is computed from RH (or dew point) and saturation vapour pressure (e sw ) Different formulae for saturation vapour pressure available (Berry, Goff-Gratch, Wexler, Davis, etc.) Differences can amount to a few mm in ZNhD computation e sw of moist air e sw of pure water Use of enhancement factor (differences < 1 mm)

22 e sw Computation Cocos Island

23 e sw Computation Tateno

24 e sw Computation St. John s

25 e sw Computation San Diego

26 Concluding Remarks A new formula for refractivity computation will have impact in modeling the neutral-atmosphere propagation delay in high-precision applications Models for ZHD prediction, such as Saastamoinen, can be easily reformulated to reflect any future recommendation Effects in existing models for ZNhD prediction are not significant (below the prediction accuracy) A recommendation for the computation of saturation vapour pressure is highly desirable

Documentos relacionados

Radio Ocultação GPS. João Francisco Galera Monico Junho 2016

Radio Ocultação GPS. João Francisco Galera Monico Junho 2016 Radio Ocultação GPS João Francisco Galera Monico Junho 2016 Aspectos básicos de física Índice de refração: velocidade da onda eletromagnética no vácuo dividida pela velocidade no meio. Lei de Snell Law