1. Skill Assessment for Coupled Physical-Biological Models of Marine Systems Daniel R. Lynch Dennis J. McGillicuddy, Jr. Francisco E. Werner Sponsors: NOAA - CSCOR NSF - CMG Prepared for: U.S. GLOBEC Pan-Regional Synthesis Workshop 27 November - 1 December 2006 NCAR, Boulder CO

2. Overview Goals Assess the state-of-the-art Provide recommendations in support of Agency programs Deliverables Special volume of peer-reviewed contributions Report to NOAA summarizing progress

3. Topical Organization Scientific Carbon Cycle Harmful Algal Blooms Ecosystem Dynamics and Fisheries Estuarine/Coastal Water Quality Cross -Cutting Themes Skill Vocabulary Metrics Data Assimilation

4. Participation Apex Contributions, Invited GLOBEC ECOHAB SAB JGOFS European Shelf Seas Contributions 18 -- 30 papers 42 et al -- 55 et al people

5. Timeline January '06 Invitations out July '06 Authors' Workshop 1 Vocabulary Rev. 1 Working Groups: DA, Metrics Dec ‘06 Working Group Reports to Editors Feb ‘07 Vocabulary Rev. 2 + Working Group Report Distribution March '07 Authors’ Workshop 2 April ‘07MS Submission; Peer Review Start April ‘08Final Copy to Printer Report goes to NOAA

6. Peer-Reviewed Publication Journal of Marine Systems Coordination 3 Community Pieces Vocabulary Metrics Data Assimilation http://www-nml.dartmouth. edu/ Publications/internal_reports/ NML-06-Skill/

7. Vocabulary

8. Vocabulary The first Bloom!

9. 55 GLOBEC Contributions Dartmouth WHOI UNH UNC Dalhousie Rutgers NMFS - WH NMFS - Narragansett NMFS - Sandy Hook DFO - Halifax DFO - St Andrew’s DFO - Victoria Reused in ECOHAB, SAB, EIRE, SWVI, NERRS, CICEET, RMRP, SeaGrant,

10. Skill: Conformance to Truth State of Model and Truth Processes - Internal Dynamics Modes of Expression - Properties, Features Equilibria Instabilities Spectra Covariance Population Structure The Realm of Error

11. Skill Assessment Judgement about Skill Future, Past The realm of Mistake

12. What is Truth?

13. DataModel dd mm Misfit 

14. What is Truth? DataModel Truth real but unknowable Errors unknowable Prediction a credible blend: Data + Model Blend: Invokes statistics of  d,  m Prediction Error: blend of  d,  m Misfit:  =  d -  m dd mm Misfit  Prediction pp

15. What is Truth? DataModel dd mm Misfit  Prediction pp Skill: Misfits Small, Noisy Deduced Inputs Small, Smooth Features Credible Truth real but unknowable Errors unknowable Prediction a credible blend: Data + Model Invokes statistics of  d,  m Prediction Error: blend of  d,  m Misfit:  =  d -  m

16. Features Ex: a Retentive Gyre Physical Features –Is there a gyre? –Size? –Location? –Timing? –Residence Time? –Entrance Paths? –Exit Paths? Relative to Organism –Cohort –Density –Scale –Age / Stage –Onset / Demise –Vital Rates Bloom!

17. Misfit Metrics Quadratic Form  =    W   W  = Cov -1 (  )   =   d +   m Importance of Data Error Model Error (Unmodeled part of Truth) “Dictatorship of Measurement”

18. Regularization Data Sparse --> Indeterminacy  =    W   p* W p p Importance of Prior  =    W    p* W  p  p Joint estimation of  and  p Regularization adds bias toward prior BPE - Best Prior Estimate BPE is PDG -->  small,  p small

19. Post-Optimality Judgement Beyond Misfit Model - Truth Criterion?

20. Causality Prior / Posterior Logical Previous / Subsequent Temporal Forward / Inverse Influence in Classic Initial/Boundary Value Problem

21. Statistics Distributions by Moments Value of Moments: mean, variance, … Ensemble within which Moments occur Ex: 3 different ensembles all previous realizations of a field “Field variability” all possible observations of this field “Instrument Error”, “Noise” all possible estimates of this field “Inverse Noise”

22. Data and State Estimation

23. Time of Occurrence (Ocean) Time of Availability (Information) Future (Now) Past Time

24. Time of Occurrence (Ocean) Time of Availability (Information) Forecast Nowcast Hindcast All Data

25. Time of Occurrence (Ocean) Time of Availability (Information) Forecast Nowcast Hindcast All Data

26. Time of Occurrence (Ocean) Time of Availability (Information) Forecast Nowcast Hindcast All Data Model ‘Data Product’

27. Time of Occurrence (Ocean) Time of Availability (Information) Forecast Nowcast Hindcast Data Used Bell

28. Time of Occurrence (Ocean) Time of Availability (Information) Forecast Nowcast Hindcast Data Used BellPublication