OOPC-GODAE workshop on OSE/OSSEs Paris, IOCUNESCO, November 5-7, 2007

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1 OOPC-GODAE workshop on OSE/OSSEs Paris, IOCUNESCO, November 5-7, 2007 Design of ocean observing systems: strengths and weaknesses of approaches based on assimilative systems Pierre Brasseur CNRS / LEGI - Grenoble, France OUTLI NE: Assimilative models: tools for observing system design Altimetry missions: AltiKa orbit determination Advanced diagnostics of information content Conclusions and future plans

2 Data assimilative models: ideal tools for OSE/OSSEs? Expected functionalities of assimilation systems 4D dynamical interpolation, featuring the actual space-time sampling of (space, in situ) ocean observing systems Multivariate estimation, yielding measurable impact from different data types on model fields Error estimation on analysis and forecast, supporting optimisation and selection between different scenarios Correction of model errors (weak constraints). Practical/operational settings of GODAE systems «sophisticated» 3D+1D OI-type schemes (FGAT, IAU) Uneven assimilation skills for SLA, T/S profiles, SST, Poor skill in estimating realistic errors (fixed background error cov) Few systems properly account for model errors.

3 Preparing futur observing systems: SMOS (2008) AQUARIUS SMOS OSSEs to characterize the strengths and weaknesses of different observation configurations (Tranchant et al., 2007) 1-day sampling Mean error (time) in MERCATOR system The study showed the best impact from the assimilation of L2 products: is it a robust result?

4 AltiKa/SARAL : a Ka-band altimetry system in tandem with JASON-2 ALTIMETRIC MEASUREMENTS: SSH, SWH, WIND SPEED AT NADIR POSSIBLE SCENARIO FOR OPERATIONAL CONVERGENCE BETWEEN THE USA & EUROPE deg inclination JASON-2 TOPEX-POSEIDON EUR-US M1 JASON-1 US-European Convergence onjoint operational system (2orbits) High inclination ERS -2 ENVISAT AltiKa GMES-1/S3 G F O GODAE In orbit Approved AltiKa designed to Planned/pending approval Proposed Scenario Fill the post-envisat «gap» in complement to Jason-2 Reach the mission objectives derived from postgodae/igos requirements * An ocean circulation observing system requires two altimeter missions simultaneously in orbit for proper sampling/coverage. * US contribution to joint operational system part of NPOESS ( altimetry is part of NPOESS baseline)

5 AltiKa: scientific objectives Sea state Geodesy Ice sheet monitoring Low-rains Mesoscale Variability Operational Oceanography Sea level Continental waters Coastal ocean

6 AltiKa: mission design Space-time sampling issue: what is the optimal orbit period for a constellation with Jason-2? Preliminary exploration of open ocean control capabilities with Observing System Simulation Experiments (OSSEs)

7 AltiKa: tested scenarios One satellite: Jason2 GFO Altika35 3 days of Jason Two satellites Jason2+AltiKa35 Jason2+AltiKa17 Jason2+AltiKa10 3 days of Jason+AltiKa35 Three satellites e.g., AltiKa35 + Jason + GFO

8 OSSEs using SEEK as an assimilation tool SEEK: Singular Evolutive Extended Kalman filter (Brasseur and Verron, 2006) Basic ingredients (Pham et al., 1998) : «Singular» : Rank-deficient error covariance matrices «Evolutive» : Dynamical evolution of error-subspace «Extended» : Non-linear models and obs. operator (as EKF) (linearized or interpolated variants) Implemented in different model types (Brankart et al., 2003; Berline et al., 2006; Tranchant et al., 2007): Circulation models: QG, reduced-gravity, PE Coupled physical-biogeochemical models (1D, 3D) Operational systems: SAM-2 (Global 1/4 MERCATOR ) Similarities with Ensemble-based methods (Brusdal et al., 2003; Nerger et al., 2005) : Intercomparisons with the EnKF, SEIK, RRSQRT filters, EnKS

9 OPA EKE (cm2.s-2) Altimetric data assimilation in eddy-resolving models of the North Atlantic 1/4 1/4 1/12 HYCOM STD_SSH (cm) 1/12 Model simulation Data Assimilation

10 OSSEs: performance in equatorial regions Control of TI Ws phasing Real Perturbed Velocity Jason Any single satellite can correct for TIWs phasing

11 OSSEs: performances at mid-latitudes Control of assimilated data (SSH) Jason+AltiKa35 Jason+AltiKa17 Jason+AltiKa10 1 satellite 1 satellite 2 satellites SSH Rms Error (cm) 2 satellites AltiKa35 GFO Jason Free model satellite 2 66% error reduction thanks to DA GFO>Jason>AltiKa35 2 satellites Further reduction of 11 % Any satellite in addition to Jason2 would be similar

12 OSSEs:performances at mid-latitudes 1 satellite 2 satellites Control of temperature at depth Jason+AltiKa35 Jason+AltiKa17 Jason+AltiKa10 1 satellite 2 satellites Temperature Rms Error ( C) Larger errors at thermocline depth 1 satellite AltiKa35 GFO Jason About 63% error reduction thanks to DA GFO>Jason>AltiKa35 2 satellites Free model 0 0,05 0,1 0,15 Further reduction of 12 % Any satellite in addition to Jason2 would give similar results (AltiKa35 slightly better) 0,2 0,25

13 How to compare the performance of several observing systems? Standard deviations Reference simulation (r): Test simulation (f) Correlation Coefficient R: Centered RMS error: Bias: Statistical relationship: Taylor, K.E., Summarizing multiple aspects of model performance in a single diagram, J. Geophys. Res., 106, D7, , 2001

14 Basic tool for comparison between several observing systems: Taylor diagram (Orr 2007)

15 EKE for 1-satellite and 3-satellite constellations G = GFO T=Topex J=Jason A = AltiKa35 Recommendation for AltiKA: 35 days period

16 How do OSSE results depend on assimilation methods and prescribed error statistics? How to assess the robustness of results and improve our OSSE methodologies? How to derive comparable measures of information content from different assimilation systems?

17 Assimilation cycle: basic operations x ia ( ) x if+1 = M x ia Forecast Pi +f 1 = MP ia M T + Q Analysis Pia K i + 1 = P i +f 1 H T (HP i +f 1 H T + R) 1 ( ( )) x ia+1 = x i f+1 + K i +1 y i +1 H x i f+1 Pia+1 = ( I K i +1 H ) Pi +f 1 yi+1 i i+1

18 Assimilation cycle: basic operations Sequential assimilation = repeated forecast/analysis cycles i i+1 i+2 i+3 The best estimate at a given time is influenced by all previous observations (Kalman «filter»), and the analysis error covariance reflects the competition between this accumulation of past information and the error growth due to model imperfections.

19 Error reduction at analysis step Pi +f 1 Pia+1 = Pi +f 1 ( I K i +1 H ) Pi +f 1 j = K i +1 HP i +f 1 = K i +1 Π Tj Π j HP i +f 1 OBS j where Π j is selecting the observation subset j. The total error variance reduction is: r = Tr ( K i +1 HP The error variance reduction associated to subset j is: r j = Tr ( K i +1 Π Tj Π j HP i +f 1 ) The impact of any data subset can be computed quite easily with sequential or variational schemes (Desroziers et al., 2005) f i +1 )

20 Partition of information content : NWP example Cardinali et al. (2004) The relative impact of different data types can be measured using ri, consistently with the assimilation statistics Can be extended to measure the data impact on FORECAST error reduction (Desroziers et al., 2005) Maximization of r (w.r.t. H, R) provides guidelines for the design of OS Quite standard in NWP, not yet a current practice in GODAE world.

21 Degrees of freedom for signal (DFS) ( ) x ia+1 = x i f+1 + K i +1 y i +1 H x i f+1 = ( I K i +1 H ) x i f+1 + K i +1 y i +1 H x ia+1 = ( I HK f ) H x i +1 i HK i + 1 y i + 1 H x a T = ( HK ) = sensitivity of analysis to assimilated data y DFS = Tr ( HK ) : «how the assimilation uses the observations to pull the signal from the background (Rabier 2005)» number of useful independent quantities in obs system (Wahba 1985)

22 Degrees of freedom for signal (DFS) Practical computation of DFS (in the linear limit) : ( DFS = x x a i +1 ) f T i +1 f 1 i +1 P (x a i +1 ) x i f+1 = J b ( x ia+1 ) (Rodgers 2000) ( y i*+1 y i +1 ) T R 1 H ( x ia+*1 x ia+1 ) where y i*+1 is a perturbati on of y i +1 (Chapnik et al., 2004) For optimal assimilation systems: J b ( x ) = DFS a i +1 J o ( x ia+1 ) = DFN ( noise ) and DFS + DFN = total number of observatio ns

23 Evaluation of DFS : NWP example Importance of different observing systems in Météo-France 4DVAR analyses

24 2007 EUMETSAT/AMS Satellite Conference Conclusions 1. Assimilative models are ideal tools to conduct design studies: efforts invested to build operational systems in GODAE should be profitable to the optimal design of future observing systems (which in turn will feed the global/regional assimilation centers) 2. This will require consolidated operational implementations for : (i) 4D space-time assimilation, (ii) systematic production of error estimates, (iii) improved assimilation from multiple data sources (altimetry + all others ) 3. Advanced diagnostics provide relevant measures of information content for impact studies and optimal design: the NWP expertise is unique in this field and should be extended to meet oceanographic requirements. 4. Statistically consistent assimilation systems will be required, which will synergistically benefit to more robust OSSEs and more skillful analysis/forecasts.

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