1. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 1 - New diagnostics to assess the impact of satellite constellation for (sub)mesoscale applications Complementarity between SWOT and a large constellation of pulse-limited altimeters M.I.Pujol, G.Dibarboure, G. Larnicol (CLS) P.Y.Le Traon, P.Klein (IFREMER),

2. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 2 - Introduction SWOT will provide an unprecedented sampling capability by 2019 Iridium-NEXT telecommunication constellation renewed, starting from 2015 –Iridium satellites can take payloads of opportunity –It is technically possible to have AltiKa-like pulse-limited altimeters on Iridium-NEXT –The constellation itself would have intrinsic advantages (very cost efficient, temporal sampling, robustness vs failures, near real time…) –But a constellation of traditional sensors cannot replace SWOT images What could be the benefits of having a constellation of 6 Iridium-NEXT altimeters (+upcoming missions) in addition to SWOT for (sub)mesoscale retrieval ? Are Lagrangian diagnostics relevant for this study ?

3. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 3 - OSSE approach Protocol: –Reality: Earth Simulator outputs from Ifremer: mesoscale and submesoscale –Simulate observation by remote sensor (with error) –Reconstruct « observed ocean topography » from profile/swath observations using optimal interpolation mapping (DUACS center to generate the AVSIO products) The difference between the reality and the observed state is the sum of : –Remote sensing sampling weaknesses (blind spots) –Remote sensing measurement errors –Reconstruction imperfections (e.g. oversmoothing) Error is always measured in percentage of the reality signal variance

4. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 4 - Simulation details Configurations studied : –Classical nadir constellation: 3 x nadir altimeters (Jason-CS, Sentinel3-B, S3-C) –SWOT alone –SWOT + 3 altimeters –SWOT + 11 altimeters (6 Iridium, Jason-CS, S3-B, S3-C, HY-C, GFO2) Error levels: optimistic (both on SWOT and nadir altimetry) –only noise and residual roll for SWOT (after good cross-calibration) –1 cm noise for nadir (radiometer, dual frequency/Ka, and good POD) Reconstructing the topography at each time step and position: –Straightforward optimal interpolation (no model + assimilation) derived from DUACS tools –Mapping #1: standard DUACS mapping 100 km / 10 days (mesoscale) –Mapping #2: 2-step optimal down to 30 km and 5 days (small mesoscale / submesoscale) –Regional reconstruction (not just within the swath  temporal coherency analyzed)

5. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 5 - Ocean reality One year of Earth Simulator from Ifremer (Klein et al)  mesoscale and submesoscale Theoretical model: can be « projected » to any region or bathymetry configuration  North Pacific at two locations : [38°N,210°E] and [45°N,210°] RMS of the sea surface height anomaly: TOTAL> 100km < 100km

6. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 6 - Instantaneous observations (typical snapshot) 3 x Nadir1 x SWOT 11 x Nadir (Iridium 6 + Jason-CS +GFO2+ HYC+ S3A + S3B) 1 x SWOT + 11 x Nadir 2 x SWOT

7. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 7 - Objective Analysis (OA) method (Le Traon et al, 1998; Ducet et al, 2000) used for SLA reconstruction:  Large and medium mesoscale signal : direct OA with correlation scales 100km/10days  Short mesoscale signal : 2-step OA method with correlation scales 100km/10days and 30km/5days Along-track total SLA field Map of large/medium mesoscale SLA OA 100km/10days Map of residual short mesoscale SLA OA 30km/5days Map of large/medium+short mesoscale SLA + Along-track residual sub- mesoscale SLA field - Method  Errors on reconstructed fields are analyzed for SLA, surface geostrophic velocities (U,V), vorticity and vertical velocities (W) Map reconstructed with 1/8°x1/8° and 3 days resolution.

8. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 8 - Illustration of common diagnostics used for OSSEs SSH reconstruction error (diff = reference – reconstructed) Analysis made at 38°N (SWOT temporal sampling is optimal) Mesoscale SSHA reasonably resolved with 3 satellites (current applications of DUACS) SWOT alone performs like 4 altimeters Adding more sensors reduces the error but the gain is small SSHA Reconstruction error (% of reality signal variance)

9. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 9 - Mesoscale sampling (influence of latitude) Only one SWOT sensor  results change with latitude Blue is for 38° (optimal temporal sampling : 1 sample every 11 days) Grey is for 45° (poor sampling : 2 samples in 4 days, then 18 days with no data) Sampling discrepancies disappear when a large constellation is added Delta Time between ascending and descending arcs on SWOT x SWOT crossovers -10 days+10 days 38° 45°

10. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 10 - Mesoscale sampling (geostrophic velocities) Reconstruction error at 45°N on U (blue) and V (red) components Observing true gradients is much more difficult, even on « simple » mesoscale Second SWOT or constellation  error divided by a factor of 2 Direct benefit for traditional altimetry applications at regional scale Geostrophic velocities reconstruction error (% of reality signal variance)

11. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 11 - The lyapunov exponents Potential of using Lagrangian metrics to charactrise the impact of satellite constellation Test has been performed using a Lagrangian approach with the calculation of the Lyapunov exponents (FSLE for finite size Lyapunov exponents) of the velocity data set  direct measure of the local stiring  characterise the trajectories of initially close particules that are quickly separated along the streaching directions In practice: a set of tracers (initially separated with a specific distance) are followed in time during the advection by the velocity field. FSLE is the time it takes to the tracers to reach a given separation distance Ref papers: D’Ovidio et al. (GRL, 2004), D’Ovidio et al. (DSR, 2009) D’Ovidio et al.., (2004) software is rewriting and will be available soon.

12. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 12 - Reconstructing lyapunov exponents 3 x Nadir 1 x SWOT 1 x SWOT +11 x Nadir Reality (Earth Simulator)

13. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 13 - Do we need optimal 2-step mapping ? SWOT + 11 Nadir (standard) Reality (Earth Simulator)SWOT + 11Nadir (2-step)

14. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 14 - Integrated advection error Average error on tracer position 5 days Initial state : hundreds of particules to be advected  Position analyzed every 3 hours over 5 days The mean distance between reference and observed trajectories gives an estimate of the integrated error SWOT alone still has an average error (42km) superior to the mapping scales (30km)  observation lacking Adding a second SWOT or (better) a constellation of 11 nadir reduces the error by 50% (25km)

15. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 15 - Do we need optimal 2-step mapping ? If SWOT is alone, the 2-step mapper significantly reduces the error at regional scale (optimal interpolation uses statistical decay between sparse images) When a constellation is merged with SWOT, the dense 1D profiles can preserve the SWOT 2D information until a new swath refreshes the scene  improvements from 2- step mapping is marginal (standard maps are good enough if observation is not filtered) SWOT (standard) SWOT (2-step) SWOT+11 Nadir (standard) SWOT+11 Nadir (2-step)

16. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 16 - Conclusions : OSSE results A large altimetry constellation can complement SWOT images: To fill SWOT temporal gaps between 2D images (with dense 1D profiles) To fill SWOT observation weaknesses at certain latitudes (22-day orbit)  To better observe smaller scales (error divided by a factor of 2 for signals > 30km) Optimal 2-step mapping (vs. traditional DUACS mapping) : 2-step is not necessary for SWOT+constellation (dense measurements) 2-step is needed for SWOT alone to balance the sparser temporal observation (standard mapping would over-smooth between 2D images)

17. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 17 - Conclusions on Lagrangian metrics Lyapunov exponents useful but qualitative further work need to understand the fiability/sensitivity of this Lagrangian method ? (impact of the parameterisation, sensitivity to the sampling) Quantitative diagnostics with the Integrated advection error are satisfying. Are Lagrangian diagnostics relevant for a NRT monitoring (OSE)? DUACS Global product DUACS régional AMESD

18. GOV-CLIVAR workshop 13-17 june, Santa Cruz - 18 - Conclusions on Lagragian metrics Lyapunov exponents useful but qualitative further work need to understand the fiability/sensitivity of this Lagrangian method ? (impact of the parameterisation, sensitivity to the sampling) Quantitative diagnostics with the Integrated advection error are satisfying. Are Lagrangian diagnostics relevant for a NRT monitoring (OSE) Where is the truth ? How could we verify that the small scale introduced in the field are realistic ? Is there specific signatures on FSLE/FTLE results of some specific signals? (internal wave, sampling discontinuity,..), Consistency with tracers like ocean colour ? Interest to use Lyapunov exponent for model simulations intercomparison and validation ?