Waveform Processing of Nadir-Looking Altimetry Data

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1 Waveform Processing of Nadir-Looking Altimetry Data Mònica Roca and Richard Francis ESA/ESTEC Noordwijk The Netherlands

2 Contents 1. the concept 2. introduction 3. the on-board waveform [how the return signal is windowed and averaged by the instrument] 4. instrument corrections [e.g. IF filter correction]; 5. modelling of the echo waveform over ocean: the ocean echo: general convolutional model assumptions [antenna pattern, distribution function of height of scatterers, dependence of sigma-0 on incidence angle, small doppler bandwidth] retrieval of "traditional" geophysical parameters; retrieval of "new" parameters; discussion of different models; 6. the nature of the echo over non-ocean surfaces 7. propagation corrections: ionosphere wet troposphere (water vapour) dry troposphere 8. discussion of performance, resolution and accuracy.

3 1. Radar Altimeter Concept Instrument Corrections hd = H - h - hg Geoid Satellite Orbit (H) Sea Surface Range (h) Atmospheric Refraction Correction Air-Sea Interface Corrections hd Ellipsoid hg

4 Altimeter characteristics: 2. Introduction pulsed radar; nadir looking; LEO (~800 km altitude); carrier frequency ~13.6 GHz (Ku-band); bandwidth ~300 MHz; Applications: born to measure ocean surface height; later proved very useful also for ice and land applications

5 3. Pulse Repetition Frequency (PRF) Coherent radiation illuminating a surface which is rough at the wavelength scale produces speckle (multiplicative noise). Effect of speckle can be reduced by averaging decorrelated echoes (limit on PRF). Higher PRF provides more echoes in a given time. 2 limitations: PRI = 1/PRF decorrelation time; and orbit altitude. TX RX t T 1 t

6 3. Pulse Width (1) High (vertical) range resolution; driven by the bandwidth (B): cτ c r = = 2 2B High SNR; driven by transmitted energy (P t τ) and noise bandwidth (B) SNR P tτ B Solution: decouple the two problems by using a signal where B is not a function of τ: Chirp (linear frequency modulated) ω 2 Acos t+ t t At () = ω0 0 τu 2 τu 0 otherwise Def.: compressed pulse width (τ c ) B= f τ = 1 c f = 1 B 1 τ u

7 3. Full Deramp Technique Required altimeter performance: range resolution ~ 50 cm implies τ c ~ 3 ns and f ~ 300 MHz Solution: map relative time delay into frequency offsets. f Deramp Mixer f f t t B f f t t τ u t Chirp Generator B 2 h f = f2 f1 = t = B τ τ c u u

8 3. Frequency Sampling - Range Window FFT equivalent to bank of contiguous filters B N = 1 / τu N B N samples Height resolution is given by the compressed pulsewidth (and total window size - total possible height observed, H): c cτ h = = c H = N h 2 f 2 By changing the Chirp bandwidth we obtain different resolutions (and total range window size):

9 3. Effect of Resolution Changes Ocean Mode (0.5 m resolution, 32 m range window) Ice Mode (2 m resolution, 128 m range window) Percentage of Time in Acquisition Mode

10 Maintain the echo in the range window; controls tracking point and resolution; 3 resolutions adapted to different scenarios (ocean, ice, ice sheets, sea ice and land). 3. The On-Board Tracker Power Threshold Height Error Tracking Point resolution bandwidth range window 0.5 m 320 MHz 64 m 2 m 80 MHz 256 m 8 m 20 MHz 1024 m Centre of Gravity 0 63

11 4. PTR Shape Measured on Hardware Power (dbm) Frequency (khz)

12 4. Effect of IF Filter Shape Normalised Echo Power Theoretical Waveform Measured Waveform IF Filter Response (ERS-2) Normalised IF Response Relative Time Delay

13 4. Instrument Corrections: USO

14 4. Height errors induced by datation errors Orbit height rate ±ḣ m/s; Datation error δt seconds; Resulting height error δh=± h δt m. EnviSat example: height rate ± 25 m/s; datation < 10 µsec Resulting error δh = ±0.25 mm

15 5. Background: Radar Equations P λσ G λ cσ = P G 3 4 = P ( 4π) hl 4( 4π) L h τ r t t 2 3 c σ = σ A SNR Pr G λ cσ = = Pt 2 3 τ P 44 ( π) L h ktb F N 2 2 n c h cτ c 2 P = t 2 3 SNR 44 ( π) L h ktbn F 2 2 G λ cσ τ c r A=πτ c c h

16 5. Ocean Echo: Convolutional Model I(t) Radar Impulse Response P r (t) = I(t) * S(ct) * P fs (t) S(ct) P fs (t) Flat Surface Response Height distribution of surface scatterers

17 5. Ocean Return Echo: Assumptions Scattering surface has a sufficiently large number of random independent scatterers. Surface height statistics constant over the total area illuminated by the radar when building the echo. Scattering is scalar with no polarisation effects nor frequency dependent within the pulse bandwidth. Dependence of scattering on incidence angle is only given by σ and the antenna pattern. Doppler effect due to radial velocity is small compared to the pulse bandwidth. Impulse response (I(t)), antenna pattern and pdf of surface scatterers (S(ct)) are all assumed gaussian

18 5. Ocean Return Echo: Brown Model P( τ ) r = 1 ηpp t fs( 0) 2πσ p 1+ erf 2 1 ηpp t fs( τ) 2πσ p 1+ erf 2 τ 2σ τ 2σ c c τ < τ 0 0 where P fs ( τ ) 2 2 G λ c 4 2 4c c σ ( ) exp sin ξ cos I sin ( π ) Lh p γ γh τ ξ τ = ξ Ψ γ h

19 5. Return Echo: Brown Model Parameters P r τ = average return echo power = two-way ranging time η = pulse compression ratio P t = transmit power P fs = flat surface impulse response σ p = point-target response width σ c = surface scatterer scale size G = antenna gain λ = radar wavelength c = velocity of light σ (Ψ 0 ) = surface backscatter coefficient at incidence Ψ 0 L p = propagation loss h = satellite height γ = parameter related to antenna beamwidth ξ = antenna mispointing

20 5. Surface backscatter coefficient at incidence Ψ 0 Assumption: Gaussian dependence on incidence angle (reduces the illuminated area): [ ] 0 2 ( Ψ ) σ ( Ψ ) σ ( 0) exp αtan 0 in the case of undulating surface dominant factor in the return power. New exponential term in echo equation 4 exp sin 2 4c ξ cos2 tan 2 ( 0) γ γ τ ξ α Ψ h difficult to distinguish whether: α 0 or ξ 0; α > 0 or ξ > 0

21 5. Return Echo: Typical Ocean Echoes Mispointing induced by satellite roll-tilt mode

22 5. Previous Altimeters ERS Range Window 64 samples; tracking point in 0 frequency; 50 pulses averaged (PRF = 1020); mispointing budget ~0.20 (in-flight estimate < 0.05 ); m 10 m Relative time delay (ns)

23 5. Previous Altimeters TOPEX waveform not corrected for (significant) instrument effects. quality of ERS and TOPEX waveforms not enough for fine estimations. Therefore: assumptions for the retracking σ ( Ψ 0 ) = σ ( 0) Ψ 0 No consideration of higher order terms

24 5. Return Echo: Parameters estimated m 10 m Relative time delay (ns) Echo delay time from half power point. Significant Waveheight from leading edge slope. Surface σ from integrated echo power.

25 5. Comparison of ERS and EnviSat Waveforms The EnviSat RA-2 Range Window 128 samples + 2 intermediate samples; tracking moved to sample -18; 100 pulses averaged (RA-2 PRF = 1795); better mispointing budget (budget value < 0.04 ); ERS EnviSat Normalised echo power Relative time delay [ns] ns

26 5. New Possibilities Assumptions can be different Õ new parameters can be estimated, e.g.: σ ( Ψ ) = f( Ψ ) P(h) 0 0 λ : skewness µ : kurtosis δ : cross-skewness. wave period Skewed Gaussian Gaussian Mean Sea Level Mean Scattering Surface 3σ 0 3σ h Median Scattering Surface

27 Brown (1977): 5. Other models simple : all functions assumed to be gaussian (antenna pattern, point target response, height distribution of specular points). Hayne (1980): Computationally driven; Introduced skewness and kurtosis to all gaussian functions. Rodriguez, Srokosz, Challenor, Chapron, Elfouhaily: Phenomenologically driven; Skewness, cross-skewness and kurtosis applied to height distribution of specular points. Recent ideas will introduce measurements of Point Target Response.

28 6. Non-Ocean Surfaces Antarctic Ice Sheet Sea Ice

29 7. Propagation Corrections Refractive Index of atmosphere (troposphere, stratosphere, ionosphere) is greater than unity. Introduces group delay to electromagnetic waves. Magnitude of the effect is proportional to density and frequency dependent. At Ku-Band the major contributors are: oxygen and nitrogen ( dry component): 240 cm, relatively stable ; water vapour ( wet component) 0 30 cm, variable; free electrons (ionospheric component) 0 20 cm, variable.

30 7. Neutral Atmosphere - Dry Oxygen and nitrogen are major atmospheric components and have constant scale height; Measurement of surface pressure is sufficient to characterise total content, (limited range, < 10%); Delay is proportional to surface atmospheric pressure: 1 mb is equivalent to 2.3 mm in range. Correction is based on predicted or analysed pressure fields (typically from ECMWF). Typical accuracy using ECMWF predictions: cm

31 7. Neutral Atmosphere - Wet Water vapour mainly exists in troposphere (< 10 km); Great variation in space and vertical distribution; Surface measurement is insufficient to characterise vertical integrated content; Need to use sounding technique; Possible measurement sources and performances: on-board MWR: 1 2 cm rms, 0.3 cm bias (>60 km from the coast); ground-based upward looking microwave radiometers: random error cm (in clear skies); ground-based GPS receivers: agreement cm wrt WVR; other space-borne instruments (eg SSM/I); radiosondes. atmospheric models.

32 7. Ionospheric Compensation Time delay due to refraction in ionosphere 1 f 2 Use of two frequencies, e.g. Ku and S-band, to compensate this delay R i Ku = f S 2 f Ku 2 f S 2 ( R cku R cs ) TEC = Total Electron Content, in the vertical path. Residual error 0.3 cm. R i Ku f Ku 2 TEC = [e m 2 ] 40.25

33 8. ERS RA Range Performance Summary Contributor Non- Corrected Effect [cm] Residual Error after Correction [cm] Comments Instrument E rror 4 Generally accepted height noise Orbit ~5 E stimation of best available orbits Ionosphere No consideration of frequencies of orbit manoeuvres Large scale Short scale Sea-State Bias 0 20 ~2 E stimated global RM S accuracy Dr y tropospher e ~230 < 1 a-postiori analysed fields Wet troposphere Using MWR data NB: these are off-line precision-processed (OPR) values

34 8. EnviSat RA-2 Range Performance Summary Contributor Non- Corrected Effect [cm] Residual Error after Correction [cm] Comments Instrument Error 2.67 SWH = 4 m (from F M testing) Orbit ~3 Based on DORIS tracking of SPOT 2 which has a similar orbit to E nvisat No consideration of frequencies of orbit manoeuvres Ionosphere Real Time use of 2 nd RA-2 frequency (S-band) Sea-State Bias 0 20 ~2 E stimated global RM S accuracy (effect at RA-2 frequencies under study) Dry troposphere ~ Real time use o f E CMWF predictions Wet troposphere Real time use o f MWR data

35 8. Conclusions The high levels of performance achieved today in nadirlooking altimetry has required development of these points over a long period. Drivers of the error budget changed over the years Originally: orbit and instrument noise; Today: subtle geophysical effects, e.g. Sea State Bias, and small internal instrument effects become important. Existing studies of these effects have to be reconsidered for the bistatic case.

A short course on Altimetry

1 A short course on Altimetry Paolo Cipollini 1, Helen Snaith 2 1 National Oceanography Centre, Southampton, U.K. 2 British Oceanographic Data Centre, Southampton, U.K. with contributions by Peter Challenor,