Level 2 Scatterometer Processing Alex Fore Julian Chaubell Adam Freedman Simon Yueh

L2 Processing Flow L1B geolocated, calibrated TOI σ 0 Average over block; filter by L1B Qual. Flags L2 (lon, lat) L2 σ TOI + KPC L2 (lon, lat) L2 σ TOI + KPC Cross-Talk + Faraday Rotation Cross-Talk + Faraday Rotation L2 σ TOA + KPC Wind Retrieval L2 wind + σ wind ΔT B retrieval L2 ΔT B + σ ΔTB Ancillary Data: -ρ HHVV, f HHHV, f VVHV -Θ F (from rad or IONEX) Ancillary Data: -ρ HHVV, f HHHV, f VVHV -Θ F (from rad or IONEX) Ancillary Data: -NCEP wind dir. Ancillary Data: -NCEP wind dir. Ancillary Data: -PALS HIGHWINDS 2009 data Ancillary Data: -PALS HIGHWINDS 2009 data

Level 2 Scatterometer Cross-Talk and Faraday Rotation Mitigation Strategy Alex Fore Adam Freedman Simon Yueh

Forward Beam Integration We use Mueller matrix formalism M tot gives transformation from transmitted signal to received signal. Model S rx for transmit H (S rx H ) and transmit V (S rx V ). Received power for (H or V) is modeled as appropriate element of S rx H + that from S rx V times instrument gain + noise.

Simulated Total σ 0 Performance Total σ 0 performance is independent of any Faraday rotation corrections or cross-talk removal. -De-biased RMSE will be below 0.1 dB for high σ 0 for all beams. -Total L2 σ 0 as compared to a area-weighted 3 dB footprint model function σ 0 computed in forward simulation. -Total is σ 0 wind retrieval is our baseline algorithm. -In future we may use the area-gain weighted model function σ 0

L2 Faraday and Cross-Talk Mitigation Process Flow TOI: (σ HH, σ HV, σ VV ) TOI: (σ HH, σ HV, σ VV ) Ancillary Inputs: Faraday rotation angle -radiometer -IONEX Ancillary Inputs: Faraday rotation angle -radiometer -IONEX Cross-Talk Correction Faraday Rotation Correction Cross-Talk Corrected: (σ HH, σ HV, σ VV ) Cross-Talk Corrected: (σ HH, σ HV, σ VV ) TOA: (σ HH, σ HV, σ VV ) TOA: (σ HH, σ HV, σ VV ) Assumptions: (ρ HHVV, f HHHV, f VVHV ) per beam. Assumptions: (ρ HHVV, f HHHV, f VVHV ) per beam. Explicit fit trained on scale -model antenna patterns PALS HIGHWINDS data 2d non-linear minimization problem

Cross-Talk Correction 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 σ 0 at level 2). Computing the Fit: Perform a least-squares fit of the HV σ 0 in the absence of cross-talk to a simple distortion model. Perform a second least-squares fit to determine how to distribute the remaining σ 0 into the co-polarized channels. Yields an explicit 3 parameter (α, β, γ) fit for each beam Simplified Distortion Model:

Cross-Talk Correction - Beam 1 With cross-talk correction No cross-talk correction nesz≈-26.5

Cross-Talk Correction – Beam 2 No correction With correction nesz≈-25.5

Cross-Talk Correction - Beam 3 No correction With correction nesz≈-24

Faraday Rotation Correction Cost Function Measurement Model: Inputs: Faraday rotation angle. Observed HH, HV, VV σ 0. (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 σ 0 HH and σ 0 VV. (called sigma true below). Obtain σ 0 HV via conservation of total σ 0.

Faraday Rotation Correction – Beam 1 No correctionWith correction No correctionWith correction

Faraday Rotation Correction – Beam 2 No correction With correction No correction With correction

Faraday Rotation Correction – Beam 3 No correction With correction No correctionWith correction

Open Issues / Future Work 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

L2 Wind Retrieval Process Flow Wind Model Function -input: wind speed, relative azimuth angle, incidence angle (or beam #) -output: total sigma-0 Wind Model Function -input: wind speed, relative azimuth angle, incidence angle (or beam #) -output: total sigma-0 1d root-finding problem Inputs: -Total σ 0 -antenna azimuth -Kpc estimate Inputs: -Total σ 0 -antenna azimuth -Kpc estimate Ancillary Inputs: -NCEP wind direction Ancillary Inputs: -NCEP wind direction L2 Scat wind speed + error Solve for wind speed Newton’s Method Baseline algorithm: -total σ 0 approach. -Faraday rotation and cross-talk has no effect on total σ 0 approach. Newton’s Method:

L2 Wind Retrieval We also compute a wind speed error due to the uncertainty in the scatterometer σ 0,tot. – From the estimated kpc we have the variance of the observed σ 0,tot. – We numerically compute dw/dσ 0tot and propagate the error to a variance for wind.

Simulated Total σ 0 Wind Retrieval Performance Total σ 0 performance is independent of any Faraday rotation corrections or cross-talk removal. As compared to beam-center NCEP wind speed: B1 total std: m/s B2 total std: m/s B3 total std: m/s By construction, when we derive the model function from the data there will be no bias.

Wind Speed Retrievals

Open Issues / Future Work 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 σ wind 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

PALS HIGHWINDS 2009 Campaign 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 σ 0 and excess T B due to wind speed. – We also can derive the wind speed - radar σ 0 model function as well as the wind speed – ΔT B model function.

PALS HIGHWINDS Results We find very high correlation between wind speed and T B ( > 0.95 ). We also find a similarly high correlation between radar backscatter and T B. – Suggests radar σ 0 is a very good indicator of excess T B 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.

PALS HIGHWINDS Results (2)

PALS HIGHWINDS Results (3) From all of the data we derived a fit of the excess T B wind speed slope as a function of Θ inc.

L2 ΔT B L2 ΔT B will be the scatterometer wind speed times the PALS dT B /dw. (Note: not included in v1 delivery) – We estimate the ΔT B errors due to the wind RMSE numbers on previous slide. PALS Tb relation: Beam 1Beam 2Beam 3 dT v / dw dT h / dw σ ΔTv σ ΔTh

Comparison with Previous Measurements dT V /dWdTH/dW Incidence angle (deg) WISE * Hollinger ** PALSWISE * Hollinge r** SwiftPALS 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

L2 ΔT B

Open Issues / Future Work The wind speed - ΔT B coefficients will be updated with Aquarius data after launch.