1. Climate Monitoring with Radio Occultation Data Systematic Error Sources C. Rocken, S. Sokolovskiy, B. Schreiner, D. Hunt, B. Ho, B. Kuo, U. Foelsche

2. Radio Occultation Claims “Most stable Global Thermometer” “Mission independent - any satellite will give the same results” “Observations are traceable to most stable atomic clocks” …… these statements need to be put to the test and quantified

3. Purpose of this Presentation Identify potential sources of error that may affect the RO climate record We distinguish between two Error types –(1) Observational Errors Errors in RO phase observation Errors in RO atmospheric excess phase –(2) Inversion Errors Errors in RO inversion products: bending, refractivity, geopotential height, pressure temperature humidity profiles

4. Radio Occultation

5. Observational Errors that can Affect the RO Climate record Rate errors that accumulate over the duration (1-2 minutes) of the occultation Rate errors that are not zero mean when averaged over many RO soundings Rate errors that accumulate at a different rate today and several years from now Rate errors that accumulate at a different rate for different LEO satellites

6. Example Observational Errors We will specify observational errors in terms of a velocity in units of mm / sec Velocity error is obvious for a satellite orbit determination error Clock can also be converted to mm/sec - i.e if the clock of a GPS satellite drifts 10^-12 sec / sec this is equivalent to a velocity error of 0.3 mm / sec

7. RO Steps (1) Observation (2) Excess Phase Computation - determine the signal delay caused by the atmosphere compared to a vacuum signal (3) Process the Excess Phase to determine atmospheric profiles (bending, refractivity, geopotential height, pressure temperature humidity)

8. Simplified GPS Observation Principle GPS satellites transmit two carriers (L1 & L2) GPS receivers generate internal replicas of the L1 and L2 carriers The phase of the beat frequency between the doppler-shifted incoming signal and the signal replica is measured for L1 and L2. This is the phase observation based on which all subsequent analysis is based. Amplitude ignored - no influence on RO climate

9. The GPS Observation Equation

10. From Phase to Bending Bending is computed from Excess Doppler Because Doppler is the time derivative of “Excess Phase” RO occultation is insensitive to constant errors in “Excess Phase” Phase Observations Excess Phase Observations Doppler Bending Angle  We are insensitive to position errors & time errors etc. that remain constant during the occultation  We are sensitive to velocity, clock frequency, and other errors that change during the 2-minute occultation

11. From Phase to Excess Phase RO phase observation RO excess phase observation

12. IGS Clock Estimation Network Hydrogen masers (57) are indicated in brown, cesiums (32) in green, and rubidiums (30) in blue. Stars indicate clocks at BIPM timing laboratories (includes,standard labs at NIST, Paris, Braunschweig, ….) The quality of the clocks in this GPS tracking network (some as good as 1e-15 sec/sec or 0.0003 mm/sec) ensures time and frequency synchronization of the GPS satellite clocks.

13. Eliminating Clock Errors Double Difference –Advantage: Station clock errors removed, satellite clock errors mostly removed (differential light time creates different transmit times), general and special relativistic effects mostly removed –Problem: Fid. site MP, atmos. noise, thermal noise Single Difference –LEO clock errors removed –use solved-for GPS clocks –Main advantage: Minimizes double difference errors

14. From Phase to Excess Phase RO phase observation RO excess phase observation

15. Multipath Reflection from COSMIC Solar panel

16. Multipath - Induced Equivalent Excess Doppler Error Multipath can be a significant and systematic error source Can be larger than 2 mm /sec for large satellites For COSMIC it is smaller than 0.05 mm / sec COSMIC MP effect

17. From Phase to Excess Phase RO phase observation RO excess phase observation

18. Orbit Determination LEO satellite orbits can be determined to < 10 cm rms Velocity error due to LEO POD < 0.03 mm/ sec COSMIC is affected by additional attitude error This POD/attitude error is NOT systematic Systematic velocity error due to GPS POD is negligible …. except Error due to surveying occultation antenna relative to satellite center of mass or due to systematic attitude error: 1 cm radial error gives 0.01 mm/sec velocity error - thus this error is minimized by using small satellites (i.e for COSMIC < 0.01 mm/sec)

19. From Phase to Excess Phase RO phase observation RO excess phase observation

20. Summary Excess Phase Systematic errors affecting the excess phase Doppler are: Multipath error: < 0.05 mm/sec (good small satellite design needed but no attempt is made to correct for this error ) Orbit determination error: < 0.01 mm / sec (with reasonable survey of GPS antenna placements and antenna specification) These errors are spacecraft / mission dependent

21. Impact of Systematic Observation Errors on RO Refractivity A systematic obs. error of 0.05 mm/sec results in a systematic refractivity error of 0.01% and a temperature error of 0.06 degK at 25 km and decreases exponentially towards the surface.

22. Processing of real GPS RO signals includes several steps. Lay-out of inversion of GPS RO signals at Cosmic Data Analysis and Archive Center (CDAAC)

23. Processing of real GPS RO signals includes a number of steps. Lay-out of inversion of GPS RO signals at Cosmic Data Analysis and Archive Center (CDAAC)

24. Processing of real GPS RO signals includes a number of steps. Lay-out of inversion of GPS RO signals at Cosmic Data Analysis and Archive Center (CDAAC)

25. Processing of real GPS RO signals includes a number of steps. Lay-out of inversion of GPS RO signals at Cosmic Data Analysis and Archive Center (CDAAC)

26. Processing of real GPS RO signals includes a number of steps. Lay-out of inversion of GPS RO signals at Cosmic Data Analysis and Archive Center (CDAAC) This processing step assumes spherical symmetry in refractivity. A systematic error may be introduced because “surfaces of equal refractivity” will, on average, have a slight angle relative to surfaces of equal gravitational potential. The size of this error is not known - but believed to be (a) small (b) nearly constant in time. Needs to be quantified.

27. Processing of real GPS RO signals includes a number of steps. Lay-out of inversion of GPS RO signals at Cosmic Data Analysis and Archive Center (CDAAC) This processing step assumes spherical symmetry in refractivity. Important error source in the lower troposphere (below 5km height). The bias / long term change of this error is not known. This error is still under investigation.

28. Processing of real GPS RO signals includes a number of steps. Lay-out of inversion of GPS RO signals at Cosmic Data Analysis and Archive Center (CDAAC)

29. Processing of real GPS RO signals includes a number of steps. Lay-out of inversion of GPS RO signals at Cosmic Data Analysis and Archive Center (CDAAC)

30. Ionospheric Calibration We estimate systematic ionospheric error by computing the “mean of the iono-free bending angle minus neutral bending angle (from climatology) in the 60-80 km height bin”. We compare this quantity “smean” for daytime vs. nighttime soundings. COSMIC Days 0-120, 2007 -20 < Lat. < 20 DAY (11<LT<15) smean= -1.19 e-7 rad NIGHT (2<LT<6) smean=-0.37e-7 rad Because we can see the day vs. night iono bias change we expect that we can monitor the change of this bias to better than 0.5e-7 rad during the 11-year solar cycle.

31. Climate change effect on Temperature and Bending Angles Temperature change due to 2xCO2 Bending Angle change due to 2xCO2 Bending angle signal over 80 years (from model) is ~ 7e-5 rad Bending angle iono. bias can be calibrated to better than 5e-8 rad Thus the ratio of climate signal to measurement bias is almost 1000 !

32. Processing of real GPS RO signals includes a number of steps. Lay-out of inversion of GPS RO signals at Cosmic Data Analysis and Archive Center (CDAAC)

33. Statistical Optimization Error in climatology introduces errors in temperature profile at greater altitude. This error depends on (a) climatology and (b) noise level of data. “Small” below 30 km.

34. Processing of real GPS RO signals includes a number of steps. Lay-out of inversion of GPS RO signals at Cosmic Data Analysis and Archive Center (CDAAC) Systematic lower troposphere errors could be large due to horizontal refractivity gradients, tracking errors, super refraction - their change in time is not well understood. Refractivity in the lowest 5 km may have systematic errors that are not yet well defined.

35. Processing of real GPS RO signals includes a number of steps. Lay-out of inversion of GPS RO signals at Cosmic Data Analysis and Archive Center (CDAAC) Integration of hydrostat. eqn. starts at 150km assuming P=T=0. Above water vapor no new systematic errors introduced. Water vapor retrieval requires additional external information. This can introduce an additional systematic error.

36. Summary Observational systematic error is < 0.05 mm/sec –At 25 km this corresponds to a refractivity / temperature error of 0.01 % / 0.06 degK –This error is mission dependent. Caused by multipath and antenna position error. To minimize this error: use micro satellites for climate missions! The main inversion errors are: –Ionosphere bias can be monitored better than 5e-8 rad corresponding to ~0.1 mm/sec (0.02 % / 0.12 degK at 25 km) –These errors decrease exponentially towards the surface –Method of initialization of bending angle can have significant impact on these numbers - will be discussed in next talk For climates studies we can quantify errors of raw BA: 40 to ~5 km, N: 20 to ~5 km, T: 20 to 5-10 km height range

38. Is there an error in the ionospheric calibration? Idea: Looks at “raw ionosphere - free” bending angle at ~65-70 km and see if: a)Is bending angle “~0” as it should be? b)Is there a difference between local time noon and night time bending angles?

39. CHAMP RO Data LT Sampling for 30S-30N in 2004

41. Difference between day and night bending angles for CHAMP at ~ 65 km height in 2004 is less than 1-e7 radians This is small - but study is preliminary and needs to be repeated as we approach solar max.

42. Orbits A velocity bias could be caused by: 1)Scale error in the reference frame - future changes in reference frame will be smaller than 1 ppb - (0.03 - 0.1 mm/sec ) 2)Center of Mass systematic error (10 cm radial error will produce a velocity error 0.11 mm/sec at 500 km according to Mannucci et al. ‘06) 3)Other … ????

43. If we would not correct for this pattern 0.01 - 0.03 mm/sec effect. Small! Phase Pattern Effect

44. Previous error analysis …. for climate studies we need to separate systematic and random error components Kursinski et al, 1997

45. Double/Single-Difference Processing Description Neglecting ambiguities, multipath, and thermal noise, the observed occulting-link L1 phase path and the non- occulting L3 (ionosphere-free) phase paths can be written as where and are the combined oscillator effects of general and special relativity at the ground station (constant) and LEO receiver, respectively, and is the geometric distance and is the signal travel time. The desired L1 excess phase path is shown in GREEN, and quantities computed from previous POD and ZTD estimates are shown in BLUE. Forming the Double-Difference and subtracting known quantities leaves the desired excess phase path and an error term of small magnitude due to incomplete cancellation of the GPS satellite clocks because each observation has a slightly different signal transmission time. Forming the Single-Difference and subtracting known quantities, including the GPS solved-for clocks at transmit time leaves the desired excess phase. The GPS clocks are not solved for perfectly and contribute some residual errors.

46. Effects of CO2 increase on climate change simulated by NCAR Climate System Model (CSM)

47. Climate Change and Geopotential Heights

48. Effect of 2xCO2 on Temperature and GPH