COSMIC Procssing of Ionosphere Observables

Brian Breitsch

Radio Occultation (RO)

COSMIC

Constellation: Observing System for Meteorology, Ionosphere, and Climate

  • GPS RO receivers
    • 4 antennas
      • 2 limb-facing, 2 outward
    • L1CA, L1/L2P tracking
  • TIP (Tiny Ionosphere Photometer)
    • measures radiative recombination emission (1356Å)

CDAAC

COSMIC Data Analysis and Archival Center

  • processes COSMIC data
  • stores data for COSMIC, CHAMP, MET/OP, SAC-C, TerraSAR-X, GPS/MET missions
  • UCAR subsidiary

http://cdaac-www.cosmic.ucar.edu/

Raw Observables

  • time (GPS seconds)
  • precise ECI coordinates of LEO/GPS satellites
  • ECI velocities of LEO/GPS satellites

 

  • L1/L2 excess phase

Derived Observables

  • geodetic location of perigee/tangency point
  • azimuth angle of occultation plane

 

  • calibrated TEC (TECU) below LEO orbit

 

  • electron density profile (#/cm³)

 

  • vertical TEC below (tec0) and above (tec1) LEO
  • critical frequency at point of maximum electron density

Phase & TEC Calibration (mode 1)

(extensive outline of processing in `atec` documentation)

 

phase calibration--remove excess phase term due to ionosphere delay between LEO orbit altitude and GPS orbit altitude

\Delta L = L1 - L2
ΔL=L1L2

(phases)

TEC = \frac{\Delta L}{40.3 * 10^6}\frac{f_1^2f_2^2}{f_1^2 - f_2^2}
TEC=40.3106ΔLf12f22f12f22

Phase & TEC Calibration (mode 0)

Skips a-priori phase calibration and goes straight into reconstruction. Performs quasi-calibration during reconstruction.

TODO: I don't understand this yet...

TEC(p) = TEC_0(p) + N_e(p_{max})\sqrt{\frac{\pi}{2}Hp_{max}} \left[1 - \exp(\frac{p_{max} - p}{H}) \text{erfc}(\sqrt{\frac{p_{max} - p}{H}}) \right]
TEC(p)=TEC0(p)+Ne(pmax)2πHpmax[1exp(Hpmaxp)erfc(Hpmaxp)]

Reconstruction (mode 1)

  • electron density at orbit altitude is found by linear regression of the square of the calibrated TEC for the uppermost few kilometers of tangent point heights
TEC(p) \approx 2N_e(p_{max})\sqrt{2p_{max}(p_{max} - p)}
TEC(p)2Ne(pmax)2pmax(pmaxp)
  • for the rest of the TEC profile, use TEC derived from calibrated L1/L2 phase difference

Reconstruction (mode 1 cont.)

We have a TEC profile for various tangent heights:

  • perform spline interpolation (using square of TEC values) onto regular grid
    • 300 heights between 50-800km
TEC(p)
TEC(p)
TEC^2(p)
TEC2(p)

Reconstruction (mode 1 cont.)

Onion-Peeling method

  • given electron density at orbit height

 

  • compute electron density at grid heights

 

 

  • assume spherical symmetry
    • essentially a discretized version of 2D Abel transform
N_e(p_{max})
Ne(pmax)
N_e(p_i)
Ne(pi)

Reconstruction (mode 1 cont.)

Onion-Peeling method

  • given electron density at orbit height
N_e(p_{max})
Ne(pmax)
N_e(p_i) = \frac{3}{4} \frac{TEC(p_i)}{\sqrt{2p_i(p_{i+1} - p_i)}} - \sum_{k=1}^{n-i} c_{k,i} N_e(p_{i+k})
Ne(pi)=432pi(pi+1pi)TEC(pi)k=1nick,iNe(pi+k)
c_{k,i}
ck,i

are weighting constants derived in (Syndergaard et al., 2004)

Reconstruction (mode 1 cont.)

c_{k,i}
ck,i

weighting coefficients "spread" the contribution of TEC

Reconstruction (mode 1 cont.)

We now have an electron density profile for each grid height

N_e(p)
Ne(p)
p
p
  • vertical TEC observable computed by integrating retrieved profile while ignoring negative values

Abel transform + spherical symmetry assumption

reconstructed electron density values at lower heights can be negative!

Examples

References

  • Syndergaard S., W. S. Schreiner, C. Rocken, D. C. Hunt, and K. F. Dymond. "Preparing for COSMIC: Inversion and Analysis of Ionospheric Data Products." Inversion and Analysis of COSMIC Ionospheric Data Products (2005)
  • Syndergaard, Stig, Robert E. Kursinki, and Benjamin M. Herman. "A Refractive Index Mapping Operator for Assimilation of Occultation Data." Monthly Weather Review 133
  • Algorithms for Inverting Radio Occultation Signals in the Ionosphere. 2006. CDAAC, UCAR, Boulder.