Recent developments for a forward operator for GPS RO

1. Recent developments for a forward operator for GPS RO Lidia Cucurull NOAA GPS RO Program Scientist NOAA/NWS/NCEP/EMC NCU, Taiwan, 16 August 2010

2. Outline • Introduction • 3-term Refractivity expression • Bending angle • Effects of including compressibility factors (Yu-Chun Chen) • Summary and future work

3. Occulting GPS Ionosphere Neutral atmosphere LEO Earth Radio Occultation concept • An occultation occurs when a GPS (GNSS) satellite rises or sets across the limb wrt to a LEO satellite • A ray passing through the atmosphere is refracted due to the vertical gradient of refractivity (density) • During an occultation (~ 3min) the ray path slices through the atmosphere Raw measurement: change of the delay (phase) of the signal path between the GPS and LEO during the occultation. (It includes the effect of the atmosphere) GPS transmits at two different frequencies: ~1.6 GHz (L1) and ~1.3 GHz (L2).

4. choice of ‘observations’ Raw measurements of phase of the two signals (L1 and L2) s1, s2, Bending angles of L1 and L2 a1, a2 (neutral) bending angle Clocks correction, orbits determination, geometric delay Refractivity a Atmospheric products Ionospheric correction N Abel transfrom T, Pw, P Hydrostatic equilibrium, eq of state, apriori information

5. Choice of observation operators L1, L2 phase L1, L2 bending angle Neutral atmosphere bending angle (ray-tracing) Linearized nonlocal observation operator (distribution around TP) Local refractivity, Local bending angle (single value at TP) Retrieved T, q, and P Not practical Possible choices Complexity Not good enough

6. Introduction • At microwave wavelengths (GPS), the dependence of N on atmospheric variables can be expressed as: Ionosphere f is the frequency (Hz) ne electron density(m-3) Hydrostatic balance P is the total pressure (mb) T is the temperature (K) Scattering terms Ww and Wi are the liquid water and ice content (gr/m3) Moisture Pw is the water vapor pressure (mb) • important in the troposphere for T> 240K • can contribute up to 30% of the total N in the tropical LT. • candominate the bending in the LT. Contributions from liquid water & ice to N are very small and the scattering terms can be neglected RO technology is almost insensitive to clouds.

7. Forward Model for refractivity • (1) Geometric height of observation is converted to geopotential height. • (2) Observation is located between two model levels. • (3) Model variables of pressure, (virtual) temperature and specific humidity are interpolated to observation location. • (4) Model refractivity is computed from the interpolated values. • The assimilation algorithm produces increments of • surface pressure • water vapor of levels surrounding the observation • (virtual) temperature of levels surrounding the observation and all levels below the observation (ie. an observation is allowed to modify its position in the vertical) • Each observation is treated independently and we account for the drift of the tangent point within a profile

8. k2 obs k1 k1-1 k1-2 surface

9. Pre-operational implementation run • PRYnc (assimilation of operational obs ), • PRYc (PRYnc + COSMIC refractivity) • We assimilated around 1,000 COSMIC profiles per day rms error (wind) Anomaly correlation as a function of forecast day (geopotential height)

10. Pre-operational implementation run (cont’d) • Dashed lines: PRYnc • Solid lines: PRYc (with COSMIC) • Red: 6-hour forecast • Black: analysis

11. Improved algorithms for N • More accurate forward operator for refractivity • Three term expression • Analysis of different sets of refractive indexes • Update of the quality control procedures • More observations (in particular in tropical latitudes) • Optimal observation error characterization (Desroziers 2005) • Smoother normalized differences • No empirical tuning • Changes resulted in an improvement in model skill in SH (mass fields) and reduction of the low- and high-level tropical wind errors • These changes were implemented operationally at NCEP in Dec 2009 • Detailed description of the changes and results can be found in Cucurull 2010, WAF, 25,2,769-787

12. 3-term Forward Operator for refractivity • (1) Geometric height of observation is converted to geopotential height. • (2) Observation is located between two model levels. • (3) Model variables of pressure, (virtual) temperature and specific humidity are interpolated to observation location. • (4) Model refractivity is computed from the interpolated values. • The assimilation algorithm produces increments of • surface pressure • water vapor of levels surrounding the observation • (virtual) temperature of levels surrounding the observation and all levels below the observation (ie. an observation is allowed to modify its position in the vertical) • Each observation is treated independently and we account for the drift of the tangent point within a profile

14. (O-B)/O_err original (ops) QC & error modified QC & error NH TR Many more Observations !! Very few observations Errors too small SH

15. Impact with COSMIC • AC scores (the higher the better) as a function of the forecast day for the 500 mb gph in Southern Hemisphere • 40-day experiments: • expx (NO COSMIC) • cnt (old RO assimilation code - with COSMIC) • exp (ops • - with COSMIC) COSMIC provides 8 hours of gain in model forecast skill starting at day 4 !!! Cucurull 2010 (WAF)

16. Forward Model for bending angle • Make-up of the integral: • Change of variable to avoid the singularity • Choose an equally spaced grid to evaluate the integral by applying the trapezoid rule

17. Forward Model for bending angle (cont’d) • Compute model geopotential heights and refractivities at the location of the observation • Convert geopotential heights to geometric heights • Add radius of curvature to the geometric heights to get the radius: r • Convert refractivity to index of refraction: n • Get refractional radius (x=nr) and dln(n)/dx at model levels and evaluate them in the new grid. We make use of the smoothed Lagrange-polynomial interpolators to assure the continuity of the FM wrt perturbations in model variables. • Evaluate the integral in the new grid. • Each observation is treated independently and we account for the drift of the tangent point within a profile

18. QC NH NH TR TR SH SH

19. QC (model level) NH NH TR TR SH SH

20. N vs BA (single case, T62L64) N BA

21. N BA

22. N BA

23. Assimilation algorithm Counts J J/counts 0:gps 49970 7.7231250467998078E+04 1.546
0:gps 50934 2.8707346020729292E+04 0.564
0:gps 51138 2.7751283896612065E+04 0.543 N 0:gps 82761 9.1646957113037395E+04 1.107
0:gps 83635 5.1683558671757288E+04 0.618
0:gps 83705 5.1001526772670179E+04 0.609 BA

24. Experiments setup Case: 2010/02/01 12Z CTRL: no compressibility factor, old coefficient for N EXP0: Compressibility Factor + old coefficient for N EXP1: Compressibility Factor + Rueger’s Coefficient for N EXP2: (Compressibility Factor + Rueger’s Coefficient for N) for GPS only Yu-Chun Chen EXP0 V.S.CTRL EXP1 V.S.CTRLNorthern Hemisphere

25. CTRLanl V.S. EXP1anl CTRLanl V.S. EXP2anl

26. EXP1anl V.S. EXP2anl Small differences 0.3%~0.7%

27. Summary • NCEP’s operational assimilation algorithm for GPS RO makes use of a three-term forward operator for refractivity • Current work focuses on the use of a (local) bending angle operator • Compressibility factors will be further evaluated and tested in a future parallel run • Future work should address the horizontal gradients of refractivity (non-local operators)