1. GPS / RO for atmospheric studies Dept. of Physics and Astronomy GPS / RO for atmospheric studies Panagiotis Vergados Dept. 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) high vertical and horizontal resolution  There is an increased interest in high vertical and horizontal resolution global – scale coverage observations and global – scale coverage of temperature and water vapour Global Positioning System  Yunck et al. (1988) suggested that the Global Positioning System (GPS) (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 April 3 rd 1995 with the GPS Meteorology (GPS/MET) experiment on April 3 rd 1995 [Ware et al., 1996; Kursinski et al., 1996, 1997]

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

6. Introduction (3) Able Inversion Transform Standard method to calculate refractivity profiles: Able Inversion Transform of bending angle profiles 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: Problems: Diffraction and Multi-path effect.

7. strong gradients of water vapour diffraction and multi-path  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 Description of the techniques (1)

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

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

10. Radio-holography (1) Approximations:   Account for a reference electric field, E m (t) = exp(i φ(t))  Construct a radio-hologram, ΔE(t) = E(t) / E m (t)  Assume the radio-hologram is consisted of complex sine-waves Governing equations: Governing equations:    m   (the bending angle) p   p m +  p  (the impact parameter)

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

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) Vertical temperature profile of a terrestrial atmosphere (Karayel et al., 1997) Error estimates: range: 0.2 o K to 2 o K Vertical resolution: Around 250 m (terrestrial atmosphere) Around 40 m (Martian atmosphere)

14. Atmospheric parameters After the refractive index profile has been constructed, atmospheric parameters can be calculated through: N = a 1 ∙P / T + a 2 ∙P w / T 2 where P and P w are the atmospheric and water vapour pressure, T is the temperature at the respective pressure level and a 1 and a 2 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)