Information from a Numerical Weather Model for Improving Atmosphere Delay Estimation in Geodesy

1. Information from a Numerical Weather Model for Improving Atmosphere Delay Estimation in Geodesy Arthur Niell MIT Haystack Observatory Leonid Petrov NVI/GSFC GPS Meteorology Workshop

2. Mapping Function τZ τ(ε) m(ε) = τ(ε)/ τZ GPS Meteorology Workshop

3. Background • Very Long Baseline Interferometry (VLBI) • Preceded GPS • Atmosphere modeling serious limitation • No orbit, multipath, antenna modeling problems below 10 degrees elevation • Use all data down to 3 degrees • Used to evaluate NWM as input for atmosphere model GPS Meteorology Workshop

4. Outline • What is a mapping function? • How can it be parameterized to reflect the real atmosphere? • A new isotropic mapping function • A different way to model the asymmetric parts of the atmosphere • Are the results any better? GPS Meteorology Workshop

5. Summary • Use of NWM improves mapping functions significantly. • Hydrostatic mapping function error is more important than wet for repeatability except in the tropics. • Wet mapping function is more important than hydrostatic for seasonal variation. • A priori hydrostatic gradient allows more accurate wet gradient estimation. GPS Meteorology Workshop

6. Why is the troposphere such a problem for geodesy? Delay observable for ith satellite: where g = geometric delay (antenna position, orbits, Earth parameters) C = clock errors (receiver, satellite) a = atmosphere delay  = elevation angle of observation GPS Meteorology Workshop

7. Troposphere Delay Model  , = elevation,azimuth P = surface pressure hZ = zenith hydrostatic delay (~2 m) wZ = zenith wet delay (~20 cm) LN = north gradient delay (total) LE = east gradient delay (total) mh, mw, mg = mapping functions GPS Meteorology Workshop

8. Analytic mapping function • Determine coefficients a, b, c in terms of atmospheric parameters • e.g. ah,bh,ch as a function of latitude and the geopotential height of the 200 hPa level GPS Meteorology Workshop

9. Numerical Weather Model • Provides global distribution of information • Data every six hours • Grid spacing 2.5° (NCEP) • Geopotential height, specific humidity, temperature GPS Meteorology Workshop

10. Numerical Weather Model • Hydrostatic mapping function parameter • z200 = geopotential height of 200 hPa surface • Physical significance • z200 represents thickness of the troposphere • corresponds to a height near the tropopause • a priorihydrostatic gradient given by (azimuth, zenith angle) of normal to z200 GPS Meteorology Workshop

11. Hydrostatic Gradient gradient ~0.02° 200 hPa surface ~10.05 km ~10 km ~9.95 km ~200 km GPS Meteorology Workshop

12. Numerical Weather Model • Wet mapping function parameter ~mw(3°) GPS Meteorology Workshop

13. Troposphere Delay Model using IMF  ´, = tiltedelevation,azimuth P = surface pressure hZ = zenith hydrostatic delay (~2 m) wZ = zenith wet delay (~20 cm) LNW = north gradient delay (wet) LEW = east gradient delay (wet) mh, mw, mgW = mapping functions GPS Meteorology Workshop

14. IMF Implementation • Obtain NCEP analysis after 6-hour update • geopotential height • temperature • specific humidity • Write out two files on same grid spacing (2.5°) • geopotential height of 200 hPa surface • value of smfw3 calculated at each grid point • Interpolate in time and latitude/longitude • Calculate a, b, and c for hydro and wet • Calculate mh( ´) and mW() GPS Meteorology Workshop

15. Comparison with radiosonde-derived mapping functions GPS Meteorology Workshop

16. Height Error (5° min. elevation) GPS Meteorology Workshop

17. Height Uncertainty(mid-latitude) GPS Meteorology Workshop

18. Evaluation usingVLBI data GPS Meteorology Workshop

19. Baseline Length Repeatability (CONT94) GPS Meteorology Workshop

20. Repeatability Improvement with IMFg (CONT94) GPS Meteorology Workshop

21. Repeatability Improvement with IMFg (1993-2002) GPS Meteorology Workshop

22. Wet Gradient with/withoutapriori Hydrostatic Gradient WVR wtd avg GPS Meteorology Workshop

23. Annual Baseline Length(Westford-Wettzell) GPS Meteorology Workshop

24. Annual Baseline Length(Kashima-Gilcreek) GPS Meteorology Workshop

25. Summary • Use of NWM improves mapping functions significantly. • Hydrostatic mapping function error is more important than wet for repeatability except in the tropics. • Wet mapping function is more important than hydrostatic for seasonal variation. • A priori hydrostatic gradient allows more accurate wet gradient estimation. GPS Meteorology Workshop

26. IMF or YAMF? IsobaricMapping Function or Yet Another Mapping Function Thank you for your attention. GPS Meteorology Workshop