1. Potential benefits from data assimilation of carbon observations for modellers and observers - prerequisites and current state J. Segschneider, Max-Planck-Institute for Meteorology, Hamburg WP 1: Prediction towards sustainable development with input from B. Pfeil (UiB), C.Heinze(UiB) directly linked WPs: 6, 11

2. why data assimilation? data assimilation is the general term for the combination of models and observations. it can be used to fill gaps in data sets identify errors in models and observations optimize initial conditions for future projections

3. can data assimilation fill gaps in observational data sets? in principle: yes examples: SST maps, sea level from altimeter maps two basic approaches: dynamic interpolation ( use a model to spread the information in space/time) statistical/optimal interpolation (requires definition of observation error to provide weights in a least squares fit and the definition of a radius of information in space and time)

4. Available Observations: Spatial coverage dataportal.carboocean.org : search for CO 2 dataportal.carboocean.org

5. tentative ‘radius of information’ some hope for overlap in NA little hope in SA/I Available Observations: CarboOcean VOS Tracks 2005

6. Quality control in the context of data assimilation do the observations represent scales that the models can resolve (‘null space’)? are neighbouring observations consistent? for which time window are the observations valid? observation error usually determined by standard deviation of data (as a whole), but different data sources could have different weights if instrumental errors are known whole work field in itself

8. Quality control in the context of data assimilation do the observations represent scales that the models can resolve (‘null space’)? are neighbouring observations consistent? for which time window are the observations valid? observation error usually determined by standard deviation of data (as a whole), but different data sources could have different weights if instrumental errors are known whole work field in itself

9. can we use data assimilation to optimize our initial conditions for climate projections?

10. The general problem of state estimation numerical models have errors B (background error) forcing fields have errors B observations have errors R (observation error)  the ‘true’ state is not known but: initial conditions impact on predictions The task is, to optimally combine models and observations

11. general formulation of state estimation y o = H (w t ) + e stochastic errors with covariance R, =0, = 0 for m=n observation vector true state (unknown) non linear operator OBS: State forecast: w F (t+dt) = M (w a (t)) non linear model operator, e.g. OGCM analysed state, w a =w F (t)+Kd,K=Kalman gain, = B F H T (H B F H T + R) -1 d =innovation vector, =y o - H w F (t) /

12. general formulation of state estimation B F = (D F ) 1/2 C (D F ) 1/2 background error covariance matrix correlations, constant in time background error variances OI: Kalman gain from OI K OI = B F H T (H B F H T + R) -1

13. Analysis cycle time. observed state at time t [t-  t obs /2, t+  t obs /2] simulated state (background, first guess) x state vector. x +. x +. x +. x +. x +. x + + analysis, x t = f (x t-1,  w t-1, ( , Q, P-E[t-1,t])) analysis increment  w

14. What do we want to optimize? TCO 2 (Total CO 2 ) initial state for future projections Alkalinity Nutrients (Phosphate, Nitrate, Silicate, Iron) biological production O 2 (Oxygen) N-cycle Ocean Colour (Chlorophyll a) primary production, but we are more interested in export production

15. www.ncof.gov.uk Phytoplankton background error before the first analysis. Phytoplankton analysis error after the first analysis, with data everywhere. Phytoplankton errors (mmolN/m 3 ) Results from 3-D Twin Experiments

16. www.ncof.gov.uk Daily mean RMS Errors in the North Atlantic Total Dissolved Inorganic Carbon (mmolC/m 3 ) Control - truth Assimilation - truth Results from 3-D Twin Experiments

17. Potential specifications of an operational carbon cycle analysis system A relatively simple assimilation scheme like multivariate OI should do. (but we could learn more from 4dVAR -- AWI: adjoint -- WP6) Seasonal or even annual averages will suffice for most purposes – no ‘near real time’ issues but test within PIRATA buoy array (Atlantic) How to define background and observation errors? Manual quality control or automatic? One or more carbon cycle models?

18. Potential Analysis Systems - Variables and WPs Sea Surface + in-situ Temperature, Salinity Total CO 2, alkalinity (WP8) Oxygen (WP 4) CO 2 flux atmosphere – ocean (WPs 5,6) Ocean colour (WP 6) Gas exchange coefficient (?) C ant (?) (WP 9)

19. Potential Analysis Systems - Requirements Automatic data acquisition and quality control Automized model/assimilation system runs Control of output quality Dissemination of analysis to potential users Conclusion: Not a trivial task!