ASCAT RADIOMETRIC PERFORMANCE
J. J. W. Wilson
May 2009
Slide 1
BASIC ERROR CONTRIBUTIONS
Static Calibration Bias Error
Gain Error ε = ± 0.017 dB
Corresponding Cross-Section Error e ( ε ) = ± 0.034 dB
Quasi-static Bias Error Around Orbit
Gain Error δ = + 0.0525 dB Worst Case LA
δ = + 0.0029 dB Best Case RM
Corresponding Cross-Section Error e ( δ ) = + 0.1044 dB WC
e ( δ ) = + 0.0058 dB BC
Calibration Noise-like Error (1 sigma )
Gain Error ∆ = ± 0.054 dB
Corresponding Cross-Section Error σ ( ∆ ) = ± 0.10734 dB
May 2009
Slide 2
TOTAL ERROR (WORST CASE) ON SINGLE
MEASUREMENT OF IDEAL POINT TARGET
Total Cross-Section Error Estimate ( 95.4 % confidence )
e ( ε ) + e ( δ ) + 2 σ ( ∆ ) = ± 0.35 dB
Part of this error comes from the transponder stability.
The budget transponder radiometric stability error ( 1 sigma )
σ ( TS ) = ± 0.07 dB
ASCAT only Radiometric Accuracy Error ( 95.4 % confidence )
e ( ε ) + e ( δ ) + 2 Sqrt ( σ2( ∆ ) - σ2( TS ) ) = ± 0.30 dB
ASCAT only Radiometric Accuracy Error ( 99.7 % confidence )
e ( ε ) + e ( δ ) + 3 Sqrt ( σ2( ∆ ) - σ2( TS ) ) = ± 0.381 dB
May 2009
Slide 3
TOTAL ERROR (BEST CASE) ON SINGLE
MEASUREMENT OF IDEAL POINT TARGET
Total Cross-Section Error Estimate ( 95.4 % confidence )
e ( ε ) + e ( δ ) + 2 σ ( ∆ ) = ± 0.252 dB
Part of this error comes from the transponder stability.
The budget transponder radiometric stability error ( 1 sigma )
σ ( TS ) = ± 0.07 dB
ASCAT only Radiometric Accuracy Error ( 95.4 % confidence )
e ( ε ) + e ( δ ) + 2 Sqrt ( σ2( ∆ ) - σ2( TS ) ) = ± 0.202 dB
ASCAT only Radiometric Accuracy Error ( 99.7 % confidence )
e ( ε ) + e ( δ ) + 3 Sqrt ( σ2( ∆ ) - σ2( TS ) ) = ± 0.283 dB
May 2009
Slide 4
TOTAL ERROR (WORST CASE) AFTER MANY
MEASUREMENTS OF IDEAL POINT TARGET
Error on Mean of Sample for Sample Size N=90: Error on Final Estimated Gain
Pattern due to Calibration Noise-like Error (1 sigma)
Gain Error ∆M = ± 0.054 dB / Sqrt( N )
Corresponding Cross-Section Error σ ( ∆M ) = ± 0.10734 dB / Sqrt ( 90 )
σ ( ∆M ) = ± 0.0115 dB
Total Cross-Section Error Estimate ( 95.4 % confidence )
e ( a ) + e ( ε ) + e ( δ ) + 2 σ ( ∆M ) = ± 0.162 dB
Total Cross-Section Error Estimate ( 99.7 % confidence )
e ( a ) + e ( ε ) + e ( δ ) + 3 σ ( ∆M ) = ± 0.173 dB
Part of this error comes from the transponder stability.
The budget transponder radiometric stability error ( 1 sigma )
σ ( TSM ) = ± 0.07 dB / Sqrt( 90 )
σ ( TSM ) = ± 0.0073 dB
ASCAT only Radiometric Accuracy Error ( 95.4 % confidence )
e ( a ) + e ( ε ) + e ( δ ) + 2 Sqrt ( σ2( ∆M ) - σ2( TSM ) ) = ± 0.147 dB
ASCAT only Radiometric Accuracy Error ( 99.7 % confidence )
e ( a ) + e ( ε ) + e ( δ ) + 3 Sqrt ( σ2( ∆M ) - σ2( TSM ) ) = ± 0.151 dB
May 2009
Slide 5
TOTAL ERROR (BEST CASE) AFTER MANY
MEASUREMENTS OF IDEAL POINT TARGET
Error on Mean of Sample for Sample Size N=90:
Error on Final Estimated Gain Pattern due to Calibration Noise-like Error (1 sigma )
Gain Error ∆M = ± 0.054 dB / Sqrt( N )
Corresponding Cross-Section Error σ ( ∆M ) = ± 0.10734 dB / Sqrt ( 90 )
σ ( ∆M ) = ± 0.0115 dB
Total Cross-Section Error Estimate ( 95.4 % confidence )
e ( a ) + e ( ε ) + e ( δ ) + 2 σ ( ∆M ) = ± 0.0628 dB
Total Cross-Section Error Estimate ( 99.7 % confidence )
e ( a ) + e ( ε ) + e ( δ ) + 3 σ ( ∆M ) = ± 0.0743 dB
Part of this error comes from the transponder stability.
The budget transponder radiometric stability error ( 1 sigma )
σ ( TSM ) = ± 0.07 dB / Sqrt( 90 )
σ ( TSM ) = ± 0.0073 dB
ASCAT only Radiometric Accuracy Error ( 95.4 % confidence )
e ( a ) + e ( ε ) + e ( δ ) + 2 Sqrt ( σ2( ∆M ) - σ2( TSM ) ) = ± 0.0576 dB
ASCAT only Radiometric Accuracy Error ( 99.7 % confidence )
e ( a ) + e ( ε ) + e ( δ ) + 3 Sqrt ( σ2( ∆M ) - σ2( TSM ) ) = ± 0.0664 dB
May 2009
Slide 6
ALGORITHM ERROR e(a) & SATELLITE
REFLECTION – LM BEAM
May 2009
Slide 7
ERROR (WORST CASE) ON A SINGLE MEASUREMENT
OF A PREFECT DISTRIBUTED TARGET
ASCAT only Calibration Noise-like Error on Cross-Section (1 sigma )
σ ( MEAS ) = Sqrt ( σ2( ∆ ) - σ2( TS ) ) = ± 0.0819 dB = ± 0.0191
Distributed Target Noise-like Statistical Measurement Error (1 sigma)
σ ( Kp ) = ± Kp . SZO
Total Cross-Section Error on Single Measurement of Distributed Target
E(DT, p) = e ( ε ) + e ( δ ) + p Sqrt ( σ2( MEAS ) + ( Kp . SZO )2 )
Typically Kp is between 2% and 3.5%. For Kp = 3%:
95.4% Confidence:
For SZO = 0 dB, E(DT, 2) = ± 0.438 dB
For SZO = - 10 dB, E(DT, 2) = ± 0.304 dB
For SZO = - 20 dB, E(DT, 2) = ± 0.302 dB
99.7% Confidence:
For SZO = 0 dB, E(DT, 3) = ± 0.579 dB
For SZO = - 10 dB, E(DT, 3) = ± 0.384 dB
For SZO = - 20 dB, E(DT, 3) = ± 0.381 dB
May 2009
Slide 8
ERROR (BEST CASE) ON A SINGLE MEASUREMENT OF
A PREFECT DISTRIBUTED TARGET
ASCAT only Calibration Noise-like Error on Cross-Section (1 sigma )
σ ( MEAS ) = Sqrt ( σ2( ∆ ) - σ2( TS ) ) = ± 0.0819 dB = ± 0.0191
Distributed Target Noise-like Statistical Measurement Error (1 sigma)
σ ( Kp ) = ± Kp . SZO
Total Cross-Section Error on Single Measurement of Distributed Target
E(DT, p) = e ( ε ) + e ( δ ) + p Sqrt ( σ2( MEAS ) + ( Kp . SZO )2 )
Typically Kp is between 2% and 3.5%. For Kp = 3%:
95.4% Confidence:
For SZO = 0 dB, E(DT, 2) = ± 0.395 dB
For SZO = - 10 dB, E(DT, 2) = ± 0.206 dB
For SZO = - 20 dB, E(DT, 2) = ± 0.204 dB
99.7% Confidence:
For SZO = 0 dB, E(DT, 3) = ± 0.481 dB
For SZO = - 10 dB, E(DT, 3) = ± 0.286 dB
For SZO = - 20 dB, E(DT, 3) = ± 0.283 dB
May 2009
Slide 9
RE-CALIBRATION ERROR ASSUMING STABILITY
Re-Calibration Error Assuming Stability (ASCAT +
TRANSPONDERS)
95.4% Confidence:
e ( a ) + e ( ε ) + 2 σ ( ∆M ) = ± 0.058 dB
99.7% Confidence:
e ( a ) + e ( ε ) + 3 σ ( ∆M ) = ± 0.069 dB
Re-Calibration Error Assuming Stability (ASCAT ONLY)
95.4% Confidence:
e ( a ) + e ( ε ) + 2 Sqrt ( σ2( ∆M ) - σ2( TSM ) ) = ± 0.043 dB
99.7% Confidence:
e ( a ) + e ( ε ) + 3 Sqrt ( σ2( ∆M ) - σ2( TSM ) ) = ± 0.047 dB
May 2009
Slide 10
SUMMARY OF RADIOMETRIC PERFORMANCE
Point Target Cross-Section Single Measurement
Best Case
Worst Case
± 0.20 dB (2 sigma)
± 0.30 dB (2 sigma)
± 0.28 dB (3 sigma)
± 0.38 dB (3 sigma)
Distributed Target Normalised Cross-Section Single Measurement for Kp = 3%
Best Case
Worst Case
± 0.20 dB (2 sigma)
± 0.30 dB (2 sigma)
± 00.28
28 dB (3 sigma)
± 00.38
38 dB (3 sigma)
Residual Bias Contribution
Best Case
Worst Case
± 0.06 dB (2 sigma)
± 0.15 dB (2 sigma)
± 0.07 dB (3 sigma)
± 0.15 dB (3 sigma)
Re-Calibration Error Assuming Stability
± 0.06 dB (2 sigma)
± 0.07 dB (3 sigma)
May 2009
Slide 11
RAIN FOREST GAMMA ZERO 2007: ASC & DES
May 2009
Slide 12
RAIN FOREST GAMMA ZERO ASC+DES: YEAR ON YEAR
May 2009
Slide 13
Kp (Approx.) versus Sigma Zero
One week / Left Mid
May 2009
Slide 14
SUMMARY & RECOMMENDATIONS
• ASCAT is a very accurate and stable radar
• Make use of these characteristics to improve models / develop new
applications
• Future Instrument Engineering Work:
– Future Work on Kp: alg & stats.
– Future Work on Rain Forest, Stable Ice & Ocean Calibration
– Periodic Calibration Campaigns to monitor / correct antenna gain pattern
aging if any
• Implications for Future Radar Wind Scatterometers
May 2009
Slide 15