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Level 2 Scatterometer Processing

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Level 2 Scatterometer Processing

Alex Fore

Julian Chaubell

Adam Freedman

Simon Yueh

L1B geolocated, calibrated TOI σ0

Average over block; filter by L1B Qual. Flags

L2 (lon, lat)

L2 σTOI + KPC

- Ancillary Data:
- ρHHVV, fHHHV, fVVHV
- ΘF (from rad or IONEX)

L2 σTOA + KPC

Cross-Talk +

Faraday Rotation

Wind Retrieval

L2 wind + σwind

- Ancillary Data:
- -PALS HIGHWINDS 2009 data

- Ancillary Data:
- NCEP wind dir.

ΔTB retrieval

L2 ΔTB+ σΔTB

Level 2 Scatterometer Cross-Talk and Faraday Rotation Mitigation Strategy

Alex Fore

Adam Freedman

Simon Yueh

- We use Mueller matrix formalism
- Mtot gives transformation from transmitted signal to received signal.
- Model Srx for transmit H (SrxH) and transmit V (SrxV).
- Received power for (H or V) is modeled as appropriate element of SrxH + that fromSrxV times instrument gain + noise.

- Total σ0 performance is independent of any Faraday rotation corrections or cross-talk removal.
- De-biased RMSE will be below 0.1 dB for high σ0 for all beams.
- Total L2 σ0 as compared to a area-weighted 3 dB footprint model function σ0 computed in forward simulation.
- Total is σ0 wind retrieval is our baseline algorithm.
- In future we may use the area-gain weighted model function σ0

TOI:

(σHH, σHV, σVV)

Explicit fit trained on scale -model antenna patterns

Cross-Talk Correction

Cross-Talk Corrected:

(σHH, σHV, σVV)

2d non-linear minimization problem

Ancillary Inputs:

Faraday rotation angle

-radiometer

-IONEX

TOA:

(σHH, σHV, σVV)

Faraday Rotation Correction

Assumptions:

(ρHHVV, fHHHV, fVVHV ) per beam.

PALS HIGHWINDS

data

- Training data:
- Forward simulated data with nominal antenna model.
- Forward simulated data where cross-talk explicitly set to zero in beam integration. (This was done in a way to conserve total σ0 at level 2).

- Computing the Fit:
- Perform a least-squares fit of the HV σ0 in the absence of cross-talk to a simple distortion model.
- Perform a second least-squares fit to determine how to distribute the remaining σ0 into the co-polarized channels.
- Yields an explicit 3 parameter (α, β, γ) fit for each beam

Simplified Distortion Model:

No cross-talk correction

With cross-talk correction

nesz≈-26.5

With correction

No correction

nesz≈-25.5

No correction

With correction

nesz≈-24

- Inputs:
- Faraday rotation angle.
- Observed HH, HV, VV σ0. (symmetrized cross-pol)
- HH-VV correlation; ratio of HV to both HH and VV channels. This factor may need to be tuned depending on if cross-talk removal is or is not performed before Faraday rotation correction.

- Method:
- Non-linear measurement model.
- Minimize cost function to solve for Faraday rotation corrected σ0 HH and σ0 VV. (called sigma true below).
- Obtain σ0 HV via conservation of total σ0.

Measurement Model:

Cost Function

No correction

With correction

No correction

With correction

With correction

No correction

With correction

No correction

No correction

With correction

No correction

With correction

- Antenna patterns:
- The cross-talk from the theory and scale-model antenna patterns seems to be significantly different.
- Will the cross-talk in the as-flown configuration differ from both the theory and scale-model patterns?

- The error estimate for Faraday rotation correction needs to be analyzed for nominal ionospheric TEC, not worst case.
- We need to develop a strategy to determine antenna patterns post-launch.

Level 2 Scatterometer Wind Retrieval

Alex Fore

Julian Chaubell

Adam Freedman

Simon Yueh

Baseline algorithm:

-total σ0 approach.

-Faraday rotation and cross-talk has no effect on total σ0 approach.

Ancillary Inputs:

-NCEP wind direction

Inputs:

-Total σ0

-antenna azimuth

-Kpc estimate

L2 Scat wind speed + error

Solve for wind speed

Newton’s Method:

1d root-finding problem

Newton’s Method

Wind Model Function

-input: wind speed, relative azimuth angle, incidence angle (or beam #)

-output: total sigma-0

- We also compute a wind speed error due to the uncertainty in the scatterometer σ0,tot.
- From the estimated kpc we have the variance of the observed σ0,tot.
- We numerically compute dw/dσ0tot and propagate the error to a variance for wind.

- Total σ0 performance is independent of any Faraday rotation corrections or cross-talk removal.
- As compared to beam-center NCEP wind speed:
- B1 total std: 0.205 m/s
- B2 total std: 0.186 m/s
- B3 total std: 0.226 m/s

- By construction, when we derive the model function from the data there will be no bias.

- Derivation of model function from the data.
- Re-perform the analysis using averaged wind over 3-dB footprint as the truth for training
- Comparison of predicted σwind to observed RMSE of retrieved wind as compared to beam center wind.
- Use individual polarizations to retrieve winds after calibration of individual channels.

Level 2 Scatterometer Delta TB Estimation

Alex Fore

Adam Freedman

Simon Yueh

- NASA/JPL conducted HIGHWINDS 2009 campaign with following instruments:
- POLSCAT, a Ku band scatterometer.
- PALS, a L-band scatterometer and radiometer.

- From POLSCAT we determine the wind speed, and then we consider the relationship to the observed L-band active and passive observations
- From this data we can show the high correlation between radar σ0 and excess TB due to wind speed.
- We also can derive the wind speed - radar σ0 model function as well as the wind speed – ΔTB model function.

- We find very high correlation between wind speed and TB( > 0.95 ).
- We also find a similarly high correlation between radar backscatter and TB.
- Suggests radar σ0 is a very good indicator of excess TB due to wind speed.
- Caveat: we need ancillary wind direction information for Aquarius: PALS results show a significant dependence on relative angle between the wind and antenna azimuth.

- From all of the data we derived a fit of the excess TB wind speed slope as a function of Θinc.

- L2 ΔTB will be the scatterometer wind speed times the PALS dTB/dw. (Note: not included in v1 delivery)
- We estimate the ΔTB errors due to the wind RMSE numbers on previous slide.

PALS Tb relation:

- Horizontal polarization has very good agreement with the measurements from WISE ground-based campaign.
- Large discrepancy for vertical polarization
- Cause is uncertain
- Wave effects?

- WISE – Camps et al., TGRS 2004
- Hollinger – TGE, 1971
- Swift – Swift, Radio Science, 1974

- The wind speed - ΔTB coefficients will be updated with Aquarius data after launch.