Roll error reduction on SWOT Roll on, thou deep and dark blue Ocean - Roll!, Lord Byron J.Lambin, R.Fjørtoft (CNES) G.Dibarboure, S.Labroue, M.Ablain (CLS) - 1 -
Introduction Two studies initiated by CNES Purpose of this work To demonstrate the feasibility of good roll estimates To develop a simulation framework for SWOT calibration and cross-calibration Hope for the best, get ready for the worst Conservative assumptions (error budget, magnitude of roll signal) Probably relevant only during the first years of SWOTʼs life End-to-end approach Multiple methods applied on all surfaces (land, ocean) Two step process: local roll estimates then global coverage with interpolation Step 1: Optimal inversion: a priori statistical knowledge of the problem Step 2: Optimal interpolation: 1D OI (exploiting error bars from step 1) - 2 -
Do we need a «roll» correction? Roll error comes from baseline distortion and/or platform pointing A single arcsec (0.00028 ) = 35cm Impossible to perfectly control the baseline angle BUT Roll error has a linear cross-track signature Know the roll angle remove the error SO HF Roll signal (3km pixels) Residual roll error comes for imperfect roll estimates (e.g. gyros = platform angle only) Improving roll estimates at all frequencies can help minimize the error spectrum - 3 -
Roll estimation in a nutshell H obs = H real + ε + Roll * d H real is what SWOT wants to observe ε is the error (roll excluded) d is the cross-track distance Crosstrack linear signature can be observed on topography data Empirical reduction is possible BUT: if there is a crosstrack trend on H real or ε we kill what looks like a roll signal For the empirical roll estimation, both ε and H real are to be minimized We can remove only accessible fractions of H real and ε Static component (e.g. DEM, MSS) «Slow» component > 10 days or repeat cycle A large scale fraction (observable from external data) less «error» for H obs - 4 -
Types of roll estimates Direct: remove a reference or first guess H ref (static, or large scale component of H real ) If the first guess is good, roll becomes visible Crossover: difference of two copies of H obs from different arcs (remove slow fraction of ε+h real ) If delta time is small, ε+h real partially cancels out and δroll is visible Colinear: difference from one cycle to the next (remove static component of ε+h real ) Accuracy and coverage are method-specific surface-specific (land, ocean) Orbit geometry and repeat cycle (3days/22days) control Distribution of calibration zones Delta time for crossover and colinear estimates Need to interpolate between calibration zones for a global solution - 5 -
End-to-end simulation scheme Estimating roll is a simple linear problem Either: H obs -H ref = Roll * D + Σ(AnnoyingStuff) Or: H obs1 -H obs2 = Roll1 * D1 - Roll2 * D2 + Σ(AnnoyingStuff) Optimal inverse method for local estimates (+ least squares for reference) Optimal interpolation (+ splines for reference) A priori knowledge is exploited (statistical assumptions on signal and errors) Better results Trustworthy error bars Computation is more intensive (problem solved locally blocks of roll estimates) - 6 -
Simulation inputs Roll angle signal Objective: long wavelength signal only (not HF vibrations or phase errors) Simple problem: 1 hour correlation with a magnitude of 0.3 arcsec (10 cm on H) Worst case: 120 sec ~800 km with a magnitude of 2 arcsec (70 cm on H) Presence of roll-free nadir measurements from SWOT Multi-mission cross-calibration: Jason and Sentinel-3 SWOT orbit (78, 970 km, 22 days) H real comes from eddy resolving models, DEM, Hydroweb for inland waters Error std along track corr cross track corr Orbit error 2 cm >5000 km constant Baseline length error 5 cm exter swath >5000 km quadratic Instrument (therm noise) (Pixel 20 m x 90 m) 50 cm on water 3 m on land random random random random Wet Tropo (optimistic) 5 cm 50 km 50 km DEM (long wavelength) 2 m >5000 km >5000 km DEM (short wavelength) 3 m 100 to 400 m 100 to 400 m - 7 -
Performance of local estimation Tested: crossovers (crude budget error approx on land), direct (generalization on ocean) Each estimation is performed on a block (crossover or along-track scene) RMS of simulated roll minus estimated roll (arcsec) Low frequency roll Ocean Crossover SW*SW Ocean Crossover SW*J3 Ocean Crossover SW*S3 Land Direct (150km blocks) Ocean Direct (assumed from MSS error) Land Crossover SW*SW (crude layover simulation) 0.09 0.11 0.12-0.2 0.02 Worst case scenario 0.17 0.14 0.15 0.15-0.4 Block Noise (or HF err) 0.1 0.1 0.1 0.15 0.2 0.6 Block Bias (or LF err) 0.02 0.03 0.03 0.1 0.1 0.07 Ocean is not a problem (<0.1 arcsec or 3cm) except in high oceanic variability areas Land is more tricky: resolution, DEM error, layover and wet tropo - 8 -
Performance of Interpolation ~7000 km Significantly better than «raw» local roll estimates thanks to Abundance of data Drastic editing of suspicious estimates (error bars) Optimal Interpolation exploiting trustworthy error bars and covariance of roll signal Simulated roll angle Estimated roll angle Ocean direct Ocean crossover Land direct Land crossover -0.2 Residual low frequency roll (>1h) non-existent Faster modes (120s or 800km) have small residuals ~2 arcsec Roll error residual after interpolation (multimission) 0.2 Ocean (multimission) : 0.05 arcsec rms (<2cm) Ocean (swot only) : 0.07 arcsec rms (3.5cm) Land : 0.08 arcsec rms (<3cm) Ocean 9- Land
Conclusions and Perspectives Low frequency Roll reduction is prototyped (2 method + interpolation) Open ocean: residual error of 0.05 arcsec (<2cm) down from the uncorrected 2 arcsec (70cm) Land: 0.08 arcsec (3cm) to 0.5 arcsec (<20cm) Error bars coherent with actual error (simulated estimated) What could be analyzed Accessibility of high-frequency roll & phase signal Colinear method 3-day orbit specificities (e.g. crossover delta T) Improve error budget inputs (e.g. wet tropo, rain, layover, future DEM & MSS) Transition on coastal zones These techniques provide a generic cross-calibration capability Baseline error, orbit error, geographically correlated errors Concurrent sensors add global coverage (50 to 240km segments) HF signals can be calibrated - 10 -
Crossover sampling SWOT x Jason SWOT Jason SWOT x Jason 2 crosscalibration sections 50km to 240km SWxJason (10d) Along-track cross-calibration window (Lʼʼ) obs = roll signal - 11 -
Backup material HF Roll LF Roll Reality (1km pixels) Roll signal added (3km pixels) Residual roll error - 12 -
Contribution of traditional altimetry SWOT+Nadir provide the observations for low frequency roll error reduction Exploiting Jason-3 and Sentinel-3 (or GFO-2) provides A first guess SSHA (corr scales > 150 to 300km) to minimize H real on all methods A nearly complete calibration coverage on ocean (more data for interpolation) Good observations (roll directly visible as Nadir altimetry is independent) < 0.1arcsec The ability to observe higher frequencies (if the error budget of high frequencies is critical) What about high frequency roll signal? High frequency roll or phase error (<10s or 70km) not simulated So far we assumed that the baseline would not oscillate that fast In all methods Roll estimates are provided at each time step HF is accessible (already observed on old WSOA simulations) Multi-mission is needed for a global coverage on ocean Colinear and direct methods should be able to complement on land Propagation between calibration friendly zones would require some spectral predictability Transition on coastal zones Incomplete estimation blocks (error content discrepancy) degradation of roll estimates Interpolation OI knows which data it can trust land contamination is limited - 13 -
Crosscalibration zone geometry - 14 -
Crossover sampling SWOT x SWOT SWOT x SWOT 4 crosscalibration diamonds obs = roll signal difference SWOT x Nadir 4 crosscalibration segments obs = roll signal SWOT x Nadir Along-track cross-calibration window (L ʼʼ) Nadir x Nadir 1 crosscalibration point obs = orbit error SWOT x SWOT Along-track cross-calibration window (L) - 15 -
Crossover sampling SWxSW (10d) Direct SWxJ3 (10d) SWxS3 (10d) 16 -
Prototype status - 17 -
Interpolation scheme Input data Direct method: land test cases are generalized + crude estimate on ocean Crossover: on ocean (SWOT, JA3, S3), on land (SWOT only, crude simulation) Roll estimates are simulated and injected in interpolation scheme Inversion : 1D OI Approximation of the roll correlation scales (basic knowledge of roll spectrum) cov(roll) Error bars from local estimates can be used as an input for the optimal interpolation cov(obs error) Global solution improved by a priori knowledge (e.g. error bars from crossover estimates) It is possible to minimize the impact of block biases from direct methods with cov(obs error) (e.g. long wavelength error from DEM and direct method) - 18 -
Nadir on SWOT and roll error Nadir-less simulations are very old (WSOA configuration) and limited to slow modes: 10% residual roll reduction (mono-mission) 15% better calibration coverage Not tested with SWOT orbit or error budget As far as roll error reduction is concerned Nadir data on SWOT are likely (not tested) Necessary for high frequency even if Jason-3 or Sentinel-3 are used A good addition for slow modes (120s or 800km) Not necessary if we need to correct for very slow modes (1h or more) Simulations for slow modes on Jason orbit (WSOA configuration) - 19 -
Difference between 22 days and 3 days SWOTxSWOT (roll residual arcsec) Worst case scenario Crossovers are limited to delta T < 10 days Lack of coverage is defined by orbit sampling SWOT results show a higher impact of oceanic variability than WSOA simulations Large crossover delta T in specific latitude range Results are not directly transposable to a 3 day phase or a different orbit Sparser crossovers (mono-mission) Shorter delta T (less HF variability absorbed) With a 3 day orbit, the colinear approach can complement the crossover coverage - 20 - SWOTxSWOT crossover delta time [0 to 10 days]