Assimilating Satellite Ocean Colour Observations into Oceanic Ecosystem Models

1. Assimilating Satellite Ocean Colour Observations into Oceanic Ecosystem Models John C. P. Hemmings, Meric A. Srokosz, Peter G. Challenor & Michael J. R. Fasham

3. 11 parameters phytoplankton mortality rate nutrient uptake half-saturation concentration initial slope of P-I curve light attenuation coefficient for phytoplankton chlorophyll phytoplankton chlorophyll:N ratio zooplankton assimilation efficiency zooplankton excretion rate zooplankton mortality parameter zooplankton maximum ingestion rate zooplankton ingestion half-saturation concentration export fraction of zooplankton faeces

4. Anderson, T. R. & Pondaven, P (2003). Non-Redfield carbon and nitrogen cycling in the Sargasso Sea: pelagic imbalances and export flux. Deep-Sea Research I. 45 parameters

6. Field estimation • Assume model gives unbiased estimate of background state • Improves hindcast/nowcast • Provides ICs for short term forecast Parameter estimation (inverse modelling/systems identification) • Appropriate for unproven empirical models of complex systems • Improves model for long term forecasts • Reduces bias in field estimation Data Assimilation in Ecosystem Modelling

7. Parameter Optimization

8. Project aims To develop a robust method of assimilating data into a range of models of the marine ecosystem To investigate the sufficiency or otherwise of currently available data from space for the constraint of such models

9. Outline • How many parameters can be constrained? • The split-domain calibration method • Testing the method: results for a simple model • Steps towards an improved model • Achievements & benefits to current research

10. Ecosystem model • 11 free parameters • 0-D mixed layer dynamics • Fixed cross-pycnocline mixing rate • Zero P, Z below Forcing data PAR: SeaWiFS 8 day mean sea surface PAR for 1998. Temperature: 8 day mean AVHRR sea surface temperature for 1998. MLD: Daily model output (MICOM) - climatological fluxes. Deep nutrient: log profiles fitted to WOA '98 annual mean nitrate at each station. How many parameters can be constrained? Experiments with a simple PZN model

11. Observations 1998 SeaWiFS chlorophyll 32.5°N 62.5°W 57.5°N 17.5°W 300 km mean log10(Chlorophyll) Error bars at 1 standard deviation

12. Nutrient Observations Estimated winter-time maximum of mixed layer nitrate concentration Method: profiles from WOA '98 analyzed data interpolated to Feb-Apr average MLD (c.f. Glover & Brewer, 1988)

13. Misfit: Misfit is averaged over all stations in group H and all observation times Cost function terms: • Mean misfits for log10(Chl) and nutrient maximum weighted equally • Misfit variance & parameter penalty terms included with low weighting Cost Function J(p,H)

14. Data sufficient to independently constrain 4 model parameters Parameter Reduction Experiment At each step the parameter whose removal causes the smallest increase in cost is permanently fixed

15. Posterior parameter distributions (best 90 of 100 ensemble members) Given a constrainable parameter set, results are not over-sensitive to sampling biases

16. Split-domain Calibration A method for evaluating a model for a large domain over which its ideal parameter set cannot be assumed to be invariant The number and geographic scope of parameter sets are sought which allow the best fit to independent validation data to be obtained

17. Sampling the Model Domain Latitude Calibration station Validation station Longitude

18. Calibration Algorithm • Seek the best single parameter set calibration (Whole-domain calibration) • Seek ways of dividing the domain in two which lead to improved calibrations (Split-domain calibration) • If found, accept the best domain division and apply the algorithm recursively to each sub-domain

19. The Station Aggregation Procedure Role: identify groups comprising different numbers of calibration stations such that each is the group of its size best satisfied by its optimal parameter vector For a group H: estimate of optimal parameter vector p=pBEST(H) obtained by minimizing J(p,H) Returns a sequence of ‘natural’ calibration groups of increasing size

20. Validation cost = J{pBEST(C),V} Validation cost Validation cost for whole-domain calibration 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Number of stations in calibration group C

21. 3 province indicator groups 5 stations, 12 stations & 13 stations

22. J{pBEST(CA),VA} Validation cost B 2 3 4 5 Number of stations in CA A J{pBEST(CB),VB} Validation cost 2 3 4 5 6 7 8 9 10 11 12 13 Number of stations in CB Validation cost for split-domain calibration: JSPLIT {pBEST(CA), VA, pBEST(CB), VB}

23. Station Aggregation Procedure How do we find ‘natural’ station groups? Seek the group of a particular size best satisfied by its optimal parameter vector Optimal parameter vector unknown! Search over a biased sample of parameter vectors

24. Calculate cost deviation J(p,S) = J(p,S) - J{pBEST(S),S} How do we find the station group of size n best satisfied by a given parameter vector p? • Select group Hn by choosing the n stations with the lowest cost deviations Minimizes the group maximum cost deviation JMAX(p,Hn) Want to minimize aggregation penalty JMAX{pBEST(Hn), Hn}

25. Cost Hn+1 1 Hn+1 2 Gn Group max. cost deviation p3 p1 p2 Parameter value Group

26. Cost deviation redefined as test statistic U(p,S) Allowing for Observation Error • Add noise to observations to get sample of possible truths • Calculate cost for each observation set in sample

27. Calibration Algorithm

28. Testing the Method: Results for PZN Model

29. m kchl chl KN P  g Kg   Z  Posterior Parameter Distributions Differences in parameter distributions between provinces can provide information for model development

30. Calibrated Model Output (1998 annual cycle) Chl P Southern-province validation station at 32.5°N 62.5°W (left) Northern-province validation station at 57.5°N 17.5°W (right) Z N

31. Steps Towards an Improved Model Forcing data Year-specific data from FOAM (mixed layer depth, vertical diffusion, vertical advection) now available through CASIX Ecosystem model Aim: find a model of minimum complexity which can adequately represent observed biological behaviour How do we model the microbial loop?

32. Anderson, T. R. & Pondaven, P (2003). Non-Redfield carbon and nitrogen cycling in the Sargasso Sea: pelagic imbalances and export flux. Deep-Sea Research I. 45 parameters

33. Non-identical Twin Experiments Synthetic truth: 11 compartment model output NPHD (7 free parameters) NPZD (5 free parameters) Fit to annual cycles of chorophyll & nutrient at 3 different latitudes

34. Annual production and export Lat. Model Primary Export Export (°N) production (gC m-2 y-1) ratio (gC m-2 y-1) (% production) 60 parent 1360 174 13% NPHD 674 ± 4 276 ± 21 41 ± 3% NPZD 740 ± 12 318 ± 20 43 ± 3% 50 parent 1280 183 14% NPHD 809 ± 2 343 ± 26 42 ± 3% NPZD 852 ± 9 387 ± 24 45 ± 3% 40 parent 230 48 21% NPHD 152 ± 1 85 ± 6 56 ± 4% NPZD 166 ± 2 109 ± 7 66 ± 4%

35. Summary of Achievements • Robust DA method exploiting the spatial coverage of satellite ocean colour data for comparing and evaluating different ecosystem models • Concluded (tentatively) that currently available data from space are insufficient for constraining the models • Demonstrated that absence of microbial loop could cause NPZD models to be prone to serious biases

36. Centre for Observation of Air-Sea Interaction and Fluxes • Primary goal: to accurately measure air-sea flux of CO2 on a global scale • Aims to exploit new earth observation data by assimilation into ocean carbon cycle models Links with Durham University Dept. of Mathematical Sciences Calibrating the plankton cycle: exploiting compartmental structure through derivatives in Bayesian emulation of computer simulators M. R. H. Killeya & M. Goldstein (submitted) Benefits to Current Research

37. Acknowledgements The authors would like to thank the SeaWiFS Project (Code 970.2) and the Distributed Active Archive Center (Code 902) at the Goddard Space Flight Center, Greenbelt, MD 20771, for the production and distribution of data respectively. These activities are sponsored by NASA's Mission to Planet Earth Program. Thanks are also due to the National Center for Atmospheric Research for data distribution. This research was supported under the NERC Data Assimilation Thematic Programme award number NER/T/S/1999/00104.

39. Publications Papers & Reports J.C.P. Hemmings, M.A. Srokosz, P. Challenor and M.J.R. Fasham, 2003. Assimilating satellite ocean colour observations into oceanic ecosystem models. Philosophical Transactions of the Royal Society of London. Series A, Mathematical, Physical and Engineering Sciences 361, 33-39. J.C.P. Hemmings, M.A. Srokosz, P. Challenor and M.J.R. Fasham, in press. Split-domain calibration of an ecosystem model using satellite ocean colour data. Journal of Marine Systems. J.C.P. Hemmings, M.A. Srokosz, P.G. Challenor and M.J.R. Fasham, 2004. Parameterizing the microbial loop: an experiment in reducing model complexity. Southampton Oceanography Centre Internal Document, No. 93, 36pp. Conference Proceedings J.C.P. Hemmings, M.A. Srokosz, P. Challenor and M.J.R. Fasham, 2001. Assimilating satellite ocean colour observations into oceanic ecosystem models. 33rd International Liège Colloquium on Ocean Hydrodynamics "The use of Data Assimilation in Coupled Hydrodynamic, Ecological and Biogeochemical Models of the Ocean", May 7-11 2001, Liège, Belgium. Abstracts, p22. J.C.P. Hemmings, M.A. Srokosz, P. Challenor and M.J.R. Fasham, 2002. Calibration and validation of an ecosystem model using satellite ocean colour data. International symposium "En route to GODAE", 13-15 June 2002, Biarritz, France. Proceedings, 277-278. J.C.P. Hemmings, M.A. Srokosz, P. Challenor and M.J.R. Fasham, 2003. Parameterizing the microbial loop: an alternative to a size-structured model. JGOFS Final Open Science Conference "A Sea of Change: JGOFS Accomplishments and the Future of Ocean Biogeochemistry", May 5-8 2003, Washington, D.C., USA. Program abstracts, p96.