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

Δ L = L 1 - L 2

(phases)

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

T E C = \frac{​ Δ L ​ ​}{​ 4 0 . 3 * 1 0 ​ 6 ​ ​ ​} \frac{​ f ​ 1 ​ 2 ​ ​ f ​ 2 ​ 2 ​ ​ ​ ​}{​ f ​ 1 ​ 2 ​ ​ - f ​ 2 ​ 2 ​ ​ ​}

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]

T E C (p) = T E C ​ 0 ​ ​ (p) + N ​ e ​ ​ (p ​ m a x ​ ​) \sqrt ​ \frac{​ π ​ ​}{​ 2 ​} H p ​ m a x ​ ​ ​ ​ ​ [1 - exp (\frac{​ p ​ m a x ​ ​ - p ​ ​}{​ H ​}) e r f c (\sqrt ​ \frac{​ p ​ m a x ​ ​ - p ​ ​}{​ H ​} ​ ​ ​)]

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)}

T E C (p) \approx 2 N ​ e ​ ​ (p ​ m a x ​ ​) \sqrt ​ 2 p ​ m a x ​ ​ (p ​ m a x ​ ​ - p) ​ ​ ​

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)

T E C (p)

TEC^2(p)

T E C ​ 2 ​ ​ (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})

N ​ e ​ ​ (p ​ m a x ​ ​)

N_e(p_i)

N ​ e ​ ​ (p ​ i ​ ​)

Reconstruction (mode 1 cont.)

Onion-Peeling method

given electron density at orbit height

N_e(p_{max})

N ​ e ​ ​ (p ​ m a x ​ ​)

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})

N ​ e ​ ​ (p ​ i ​ ​) = \frac{​ 3 ​ ​}{​ 4 ​} \frac{​ T E C ( p ​ i ​ ​ ) ​ ​}{​ \sqrt ​ 2 p ​ i ​ ​ ( p ​ i + 1 ​ ​ - p ​ i ​ ​ ) ​ ​ ​ ​} - \sum ​ k = 1 ​ n - i ​ ​ c ​ k, i ​ ​ N ​ e ​ ​ (p ​ i + k ​ ​)

c_{k,i}

c ​ k, i ​ ​

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

Reconstruction (mode 1 cont.)

c_{k,i}

c ​ k, 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)

N ​ e ​ ​ (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.