Errors in Ocean Syntheses: Estimation and Impact Armin Köhl University Hamburg 9/8/10
Outline 1. Ocean synthesis directory hosted at KlimaCampus for the EASYint project. Eample results from GSOP ocean synthesis intercomparison efforts 3. Error estimation for an ocean synthesis Armin Köhl IfM Hamburg 9/8/10
Clisap GSOP (Global Synthesis and Observations Panel: http://www.clivar.org/organization/gsop/gsop.php) 1. Develop strategies for a synthesis of global ocean atmosphere and coupled climate information. Promote activities to develop surface flu data sets 3. Identify the requirements for the development of an observing system for CLIVAR. 4. Provide an overview of and directions to CLIVAR data management 5. Be responsible for the definition and fulfilment of CLIVAR's global needs for sustained observations and fostering the use of resulting data sets in global synthesis efforts. 3 Armin Köhl IfM Hamburg 9/8/10
EasyINIT Ocean Synthesis Directory Data access via: OPeNDAP FTP and LAS 4 Armin Köhl IfM Hamburg 9/8/10
Use this link Download OPeNDAP provides remote access to subsets of data without downloading the entire data set 5 Armin Köhl IfM Hamburg 9/8/10
6 Armin Köhl IfM Hamburg 9/8/10 LAS Server
GSOP Workshops: Intercomparison of Ocean Syntheses Ensemble of Ocean Syntheses 1.evaluate ocean syntheses.identify quantities that can be estimated reliably Ocean Obs 09 community white paper OCEAN INFORMATION PROVIDED THROUGH ENSEMBLE OCEAN SYNTHESES D. Stammer(1) A. Köhl(1) T. Awaji() M. Balmaseda(3) D. Behringer(4) J. Carton(5) N. Ferry(6) A. Fischer(7) I. Fukumori(8) B. Giese(9) K. Haines(10) E. Harrison(11) P. Heimbach(1) M. Kamachi(13) C. Keppenne(14) T. Lee(8) S. Masina(15) D. Menemenlis(8) R. Ponte(16) E. Remy(6) M. Rienecker(14) A. Rosati(17) J. Schröter(18) D. Smith(19) A. Weaver(0) C. Wunsch(1) and Y. Xue(4) 7 Armin Köhl IfM Hamburg 9/8/10
No Model z-level Model ERA40 NCEP HOPE OPA/NEMO POP MOM MIT Rela. Rela. Bias corr. E-P. CORE QSCA TGPC P Rela. Rela. EN3 DePreSys ECMWF INGV Mercator URDG SODA GFDL GODAS K-7 GECCO.5 o.5 o 3D-Var/OI 4D-Var 1 o 1 o o o 8 Armin Köhl IfM Hamburg 9/8/10 DATA
URDG Trend in Thermosteric Sea Level 199-001 (cm/yr) INGV ECMWF GECCO Mercator/ CERFACS SODA GODAS 9 Armin Köhl IfM Hamburg 9/8/10
Heat Transport Anomaly (PW) / mean plus +/- 95% Interval (PW) Atlantic 5N Atlantic 5N Equatorial Pacific Equatorial Pacific 10 Armin Köhl IfM Hamburg 9/8/10
GSOP Workshops: Intercomparison of Ocean Syntheses Clustered Models How to estimate the error of a synthesis (none of the syntheses provide a formal error estimate 1. Does agreement imply confidence?. Can the error be estimated from the ensemble spread? Syntheses need to provide formal error estimates Larger errors than spread -> clustered models Errors similar to spread -> independent models Smaller errors than spread -> flawed errors Independent Models Models Syntheses Truth In the following: error estimate for MOC variability 11 Armin Köhl IfM Hamburg 9/8/10
Analysis Error Estimation in the Adjoint Framework Cost Function for the model y=h J ( ) = ( y obs! H) 1. Analysis Error 1! 1 ó = J"" and approimations of the inverse Hessian J""! 1 ( ) ( ) from : 1. Lanczos. Randomization T R! 1 ( y obs! H) + (! b ) T! 1 (! Covar. of the model-data diff Background error covar. B b ) 3. BFGS is for free since part of the optimization Fisher and Courtier (1995) However ó y! Sampling is needed : ó y = Hó H the variance of ó and projection with T H Necessary is a correct model : 1 Armin Köhl IfM Hamburg 9/8/10 y = H t t
Error Estimation continued.rms Difference (STD) Observational error is small: ε ArgoT <0.00 o C ε ArgoS < 0.005psu ε SSH =-3cm Limited data! # y ( y! y )( y! y ) T stationarity of the error assumed Cautious remark: Powell and Moore (009) found the RMS difference to the assimilated data smaller than the differences between observational products (gridded SST SSH) for a high resolution 14 day synthesis " obs mod obs mod 13 Armin Köhl IfM Hamburg 9/8/10
From GECCO to GECCO New in GECCO Sea Ice model Bulk flu formulae forcing Atm. state estimation Truly global 1 0 30km 50 levels GECCO: 1948 009 started from WOA005 GECCO_0-07: 00-007 started from NCEP forced spinup 1948-001 no initial condition change anomaly data assimilation. Long-Lat grid telescopic equatorial MOC 6N Arctic cap 14 Armin Köhl IfM Hamburg 9/8/10-0-07
GECCO_0-07 vs RAPID MOC Estimation Uniformly linear convergence of in all components Indication for a reasonable approimation of the Hessian MOC 6N RAPID Reference GECCO 15 Armin Köhl IfM Hamburg 9/8/10 Reference: r=0.61 STD=3.0 Sv GECCO: r=0.71 STD=.8 Sv RAPID: STD=4.7 Sv
Posterior Error Estimates Temperature in 400m depth Analysis error shows lower values in regions with strong eddy variability The represention error is not seen by the anlysis error RMS Diff. projected analysis error 16 Armin Köhl IfM Hamburg 9/8/10
Posterior Error Estimates Temperature in 400m depth Is this a useful etra piece of information for the initialization community? For comparison/selection of synthesis products Nudging time scales according to the error: undisturbed model dynamics where the synthesis does not have much skill e.g. Eddies will not be damped in an eddy permiting model RMS Diff. analysis error 17 Armin Köhl IfM Hamburg 9/8/10
18 Armin Köhl IfM Hamburg 9/8/10 Gaussian Error Propagation for MOC Meridional Velocity = Geostrophy + Ekman Velocity Error Assumption: all errors are uncorrelated! 0 ( ) ( ) e z w y z t V y z t ddz! = " " ) ( 1 )) ( ) ( ( 1 ) ( ) ( 0 0 t y f t z y S t z y T f t y f g t z y v! " " " # $ % + % = 0 0 0 1 1 1 ) ( " #! $ # $ $ # $ $ # " " # f S f T f f g z y S T v % & & ' ( ) ) * + + & & ' ( ) ) * + + & ' ( ) * + =
Temperature Error Contribution (m /s) Very small values in the interor & $ $ % 0 ( ) 1000m & 1 $ % + 0 f ' T ' T #! * " T dz #!! " 1/ Error determined by the eddy rich regions and regions near the bounday therefore: Observations at the boundary are most important Improve model at the boundary RMS Diff. analysis error 19 Armin Köhl IfM Hamburg 9/8/10
Salinity Error Contribution Smaller contribution than for Temperature Larger errors in the projects analysis error in the eastern half of the basin Only diagonal of the Hessian: Temporal correlation of the error is not accounted for. RMS Diff. analysis error 0 Armin Köhl IfM Hamburg 9/8/10
Sea Level Error Contribution Similar to temperature for RMS diff. Large amplitudes in the Indian Ocean RMS Diff. analysis error 1 Armin Köhl IfM Hamburg 9/8/10
Ekman Error contributions Equatorial focus Boundary current regions (Storm tracks) RMS Diff. analysis error Armin Köhl IfM Hamburg 9/8/10
Total vertically integrated velocity error contributions (m /s) RMS Diff: strong contrast between the high energy/boundar regions and the interior Analysis error: more uniform RMS Diff. analysis error 3 Armin Köhl IfM Hamburg 9/8/10
Error Estimates for Monthly Mean Atlantic MOC Errors are dominated by the error in the eddy-rich regions Assumption of uncorrelated errors is pobably not valid MOC is a small residual of large transports (absolut transports sum up to 10 Sv: <10% error) RMS Diff. Analysis Error Annual mean MOC 4 Armin Köhl IfM Hamburg 9/8/10
Reconstructed MOC time series from Coupled Ocean Data Assimilation based on GFDL CM.0 Identical Twin Eperiment Skill (Zhang et al. 010) Argo: RMS=0.74S Atm: RMS=1.04 Sv Argo+Atm: RMS=0.7Sv (GECCO Argo+NCEP: STD=.7Sv) Biased model skill for the Argo observing system without atmos. data (Zhang and Rosati 010) RMS=.6-.9Sv 5 Armin Köhl IfM Hamburg 9/8/10
Summary EASYinit: submit/download data Transport estimates of ocean syntheses show larger ensemble spread in the North Atlantic while in the equatorial Pacific very good agreement eists: many more eamples therefore no clear statement possible Comparison to RAPID: Small gain in realism of the transport variability due to assimilating data however simulations are already quite reasonable: Value of the Argo/SSH data in comparison to atmospheric data? Formal error estimates reveal large errors for the MOC mainly emerging from the unresolved eddy variability. The errors are probably overly pessimistic due to neglected correlations: Does the large formal error eplain the small gain in realism for monthly MOC variability For the estimation of transports error distributions suggest to focus more on boundaries: Better physics in upwelling overflow and western boundary current regions Boundary observations not only Argo 6 Armin Köhl IfM Hamburg 9/8/10