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GPS / RO for atmospheric studies Panagiotis Vergados Dept. of Physics and Astronomy

GPS / RO for atmospheric studies Panagiotis Vergados Dept. of Physics and Astronomy. Outline. Objectives Introduction Description of the techniques Fresnel diffraction theory Radio-holography Back-propagation theory

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GPS / RO for atmospheric studies Panagiotis Vergados Dept. of Physics and Astronomy

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  1. GPS / RO for atmospheric studiesPanagiotis VergadosDept. of Physics and Astronomy

  2. Outline • Objectives • Introduction • Description of the techniques Fresnel diffraction theory Radio-holography Back-propagation theory • Atmospheric parameters retrieval • Remarks • Work in progress & future work

  3. Objectives • Develop knowledge and expertise in GPS / RO studies • Review and understand currently used methods and models • Choose and improve the method which gives the best vertical resolution of refractive index profiles • retrieve atmospheric parameters (such as temperature and water vapour) from refractive index profiles

  4. Introduction (1) • There is an increased interest in high vertical and horizontal resolution observations and global – scale coverage of temperature and water vapour • Yunck et al. (1988) suggested that the Global Positioning System (GPS) be used to make Radio Occultation (RO) observations of the Earth’s atmosphere • The era for GPS RO observations of the Earth’s atmosphere began with the GPS Meteorology (GPS/MET) experiment on April 3rd 1995 [Ware et al., 1996; Kursinski et al., 1996, 1997]

  5. Introduction (2) The RO technique • Bending angle, α • Impact parameter, a • Spacecraft distance, D Radio occultation (RO) experiment geometry

  6. Introduction (3) Standard method to calculate refractivity profiles: Able Inversion Transform of bending angle profiles HOW do you calculate bending angle profiles? Through measurements of the Doppler-shifted phase of the received electric field and observation geometry of the experiment Problems:Diffraction and Multi-path effect.

  7. Description of the techniques (1) • FACT #1: strong gradients of water vapour in the lower troposphere cause diffraction and multi-path, which limit the vertical resolution of the measurements • FACT #2: First-order ionospheric correction not sufficient (L1 and L2 follow two different paths) • Various methods have been introduced in order to overcome these limitations: Fresnel diffraction theory Radio-holography Back-propagation theory

  8. Fresnel Diffraction (1) Approximations: • Thin screen [Melbourne et al., 1994; Mortensen and Hoeg, 1998] and • Spherical symmetry • Advantages: • Introduction of a weighting function • Vertical resolution is not diffraction limited • Multi-path effects can be reduced

  9. Fresnel Diffraction (cont’d) • Error estimates: • ± 2oC (between 5 and 25 km) • > 2oC (below 5 km) Vertical resolution: • Few hundreds of m to 1 km 20 15 10 5 a b Vertical temperature difference profiles: a) f=52o N b) f=70o N (Mortensen et al., 1998)

  10. Radio-holography (1) • Approximations: • Account for a reference electric field, Em(t) = exp(iφ(t)) • Construct a radio-hologram, ΔE(t) = E(t) / Em (t) • Assume the radio-hologram is consisted of complex sine-waves Governing equations:ak = am + Dak(the bending angle) pk = pm + Dpk(the impact parameter)

  11. Radio-holography (cont’d) • Error Estimates: • ± 1.7 – 3.3 oK (between 5 and 25 km) • ± 5 oK (below 5 km) Vertical temperature difference profiles: a) 28o, b) 36o and c) 48oN (Hocke et al., 1999)

  12. Back propagation (1) • Approximations: • Multiple Phase Screen (MPS) [Karayel et al., 1997] • Spherically symmetric atmosphere • Advantages: • Diffraction and multi-path effects are mostly removed • Much better vertical resolution, below the sub-Fresnel scale • Back-propagation of the electric field rays to an auxiliary plane

  13. Back-propagation (cont’d) • Error estimates: • range: 0.2 oK to 2 oK Vertical resolution: • Around 250 m (terrestrial atmosphere) • Around 40 m (Martian atmosphere) Vertical temperature profile of a terrestrial atmosphere (Karayel et al., 1997)

  14. Atmospheric parameters After the refractive index profile has been constructed, atmospheric parameters can be calculated through: N = a1∙P / T + a2∙Pw / T2 where P and Pw are the atmospheric and water vapour pressure, T is the temperature at the respective pressure level and a1 and a2 are constants Known: Refractive index profile and either P or T

  15. Remarks • Fresnel Diffraction Theory, Radio-holography and Back-propagation remove mostly the diffraction and multi-path effects • The vertical resolution achieved from all three methods ranges approximately from a few hundred meters to 1 km • The back-propagation method is capable of achieving vertical resolution at sub-Fresnel scales (< 250 m) • The error estimates of the retrieved temperature profiles with the back-propagation method range between 0.2 and 2 K, and of the refractive index profile between 4·10-6 and 1.4·10-5

  16. Work in progress and future work • Second and third order ionospheric correction in the calculation of bending angle profiles • Abel inversion investigation and possible improvement • Modification and/or development of software for ionospheric correction and Abel inversion transform • Investigation of the non-spherical symmetry and how it affects the refractive index profile • Investigation of other possible methods and development of an improved model for the retrieval of atmospheric parameters from refractive index profiles (e.g. 1D-VAR method)

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