1. January 14, 2003GPS Meteorology Workshop1 Information from a Numerical Weather Model for Improving Atmosphere Delay Estimation in Geodesy Arthur Niell MIT Haystack Observatory Leonid Petrov NVI/GSFC

2. January 14, 2003GPS Meteorology Workshop2 Mapping Function τZτZ τ(ε)τ(ε) m(ε) = τ(ε)/ τ Z

3. January 14, 2003GPS Meteorology Workshop3 Background n Very Long Baseline Interferometry (VLBI) u Preceded GPS u Atmosphere modeling serious limitation u No orbit, multipath, antenna modeling problems below 10 degrees elevation u Use all data down to 3 degrees n Used to evaluate NWM as input for atmosphere model

4. January 14, 2003GPS Meteorology Workshop4 Outline n What is a mapping function? n How can it be parameterized to reflect the real atmosphere? n A new isotropic mapping function n A different way to model the asymmetric parts of the atmosphere n Are the results any better?

5. January 14, 2003GPS Meteorology Workshop5 Summary n Use of NWM improves mapping functions significantly. n Hydrostatic mapping function error is more important than wet for repeatability except in the tropics. n Wet mapping function is more important than hydrostatic for seasonal variation. n A priori hydrostatic gradient allows more accurate wet gradient estimation.

6. January 14, 2003GPS Meteorology Workshop6 Why is the troposphere such a problem for geodesy? Delay observable for i th satellite: where  g = geometric delay (antenna position, orbits, Earth parameters)  C = clock errors (receiver, satellite)  a = atmosphere delay  =elevation angle of observation

7. January 14, 2003GPS Meteorology Workshop7 Troposphere Delay Model ,  = elevation, azimuth P = surface pressure  h Z = zenith hydrostatic delay (~2 m)  w Z = zenith wet delay (~20 cm) L N = north gradient delay (total) L E = east gradient delay (total) m h, m w, m g = mapping functions

8. January 14, 2003GPS Meteorology Workshop8 Analytic mapping function n Determine coefficients a, b, c in terms of atmospheric parameters n e.g. a h, b h, c h as a function of latitude and the geopotential height of the 200 hPa level

9. January 14, 2003GPS Meteorology Workshop9 Numerical Weather Model n Provides global distribution of information u Data every six hours  Grid spacing 2.5 ° (NCEP) u Geopotential height, specific humidity, temperature

10. January 14, 2003GPS Meteorology Workshop10 Numerical Weather Model n Hydrostatic mapping function parameter u z200 = geopotential height of 200 hPa surface u Physical significance F z200 represents thickness of the troposphere F corresponds to a height near the tropopause n a priori hydrostatic gradient given by (azimuth, zenith angle) of normal to z200

11. January 14, 2003GPS Meteorology Workshop11 Hydrostatic Gradient gradient ~0.02° ~10 km~9.95 km~10.05 km ~200 km 200 hPa surface

12. January 14, 2003GPS Meteorology Workshop12 Numerical Weather Model Wet mapping function parameter ~m w (3 ° )

13. January 14, 2003GPS Meteorology Workshop13 Troposphere Delay Model using IMF  ´,  = tilted elevation, azimuth P = surface pressure  h Z = zenith hydrostatic delay (~2 m)  w Z = zenith wet delay (~20 cm) L N W = north gradient delay (wet) L E W = east gradient delay (wet) m h, m w, m g W = mapping functions

14. January 14, 2003GPS Meteorology Workshop14 IMF Implementation n Obtain NCEP analysis after 6-hour update u geopotential height u temperature u specific humidity Write out two files on same grid spacing (2.5 ° ) u geopotential height of 200 hPa surface u value of smfw3 calculated at each grid point n Interpolate in time and latitude/longitude n Calculate a, b, and c for hydro and wet n Calculate m h (  ´) and m W (  )

15. January 14, 2003GPS Meteorology Workshop15 Comparison with radiosonde-derived mapping functions

16. January 14, 2003GPS Meteorology Workshop16 Height Error (5° min. elevation)

17. January 14, 2003GPS Meteorology Workshop17 Height Uncertainty (mid-latitude)

18. January 14, 2003GPS Meteorology Workshop18 Evaluation using VLBI data

19. January 14, 2003GPS Meteorology Workshop19 Baseline Length Repeatability (CONT94)

20. January 14, 2003GPS Meteorology Workshop20 Repeatability Improvement with IMFg (CONT94)

21. January 14, 2003GPS Meteorology Workshop21 Repeatability Improvement with IMFg (1993-2002)

22. January 14, 2003GPS Meteorology Workshop22 Wet Gradient with/without apriori Hydrostatic Gradient WVR wtd avg

23. January 14, 2003GPS Meteorology Workshop23 Annual Baseline Length (Westford-Wettzell)

24. January 14, 2003GPS Meteorology Workshop24 Annual Baseline Length (Kashima-Gilcreek)

25. January 14, 2003GPS Meteorology Workshop25 Summary n Use of NWM improves mapping functions significantly. n Hydrostatic mapping function error is more important than wet for repeatability except in the tropics. n Wet mapping function is more important than hydrostatic for seasonal variation. n A priori hydrostatic gradient allows more accurate wet gradient estimation.

26. January 14, 2003GPS Meteorology Workshop26 IMF or YAMF? Isobaric Mapping Function or Yet Another Mapping Function Thank you for your attention.