O

PD2 (observation)

Fig. 12.7 Proposed implementation of the BGC data assimilation involves simulations with both 3D and 0D BGC models and their interaction. In the figure, time increases from left to right, the top of the figure denotes the integration of the 3D model, the bottom denotes the integration of the 0D model, and the two black arrows denote the exchange of information between the two models. The observations are times when data is available to be assimilated, which in this example is only phytoplankton concentrations, the black text denotes information from the 3D model and the blue text denotes information from the 0D model. The numbers reflect the steps outlined in the text, which involve: (4) forward simulation of the 3D BGC model (cyan arrow) from an initial state BGC0 to the next observation (time 1), where BGCj is the 3D BGC state at time 1. (5) at every ocean grid point where the 0D BGC optimization will be applied compute (P*) the difference between the observed phytoplankton concentration (PD) and the value simulated by the 3D model (P). (6) Inversion step, which uses the 0D BGC model to obtained new BGC model parameters (red double arrow) from target value for P. The target value for P is determine by adding P* to the P value at time 1 obtained from the 0D simulation initialized with the 3D BGM values (BGC0) and the original model parameters from the 3D model. The approach attributes P* only to modification in the BGC model parameters. The inversion provides a revised estimate of the model parameters (m) along with anomaly correction to the BGC state at time 1 (BGC^). The anomaly correction is computed from 0D BGC simulations as the difference between the 0D BGC state at time 1 obtained with the original model parameters used in the 3D BGC simulation and 0D BGC state at time 1 obtained with the optimize model parameters (m). (7) update the BGC state variables (BGC1 + BGC'1) and the model parameters (m) of the 3D BGC model and integrate the 3D BGC model to the next observation time (time 2); repeat steps 5-7

a number of locations in the model domain to acquire a first guess at the range of acceptable BGC model parameter values. The estimated model parameters can be used as the initial values of the 3D BGC model. More important than the estimated model parameters, the data assimilation application will identify the subset of model parameters crucial to the evolution of the BGC fields. As shown by Kidston et al. (2010) this is expected to be a small subset of the model parameters. By identifying the crucial model parameters one would then only modify these parameters in the following application of sequential data assimilation 3. spin-up the unassimilating 3D BGC model using the initial BGC model parameter set determined from 2. The spin-up period will take several simulated years to get the mixed layer to a seasonally stable state. This BGC state will be used as the initial state for applying the BGC data assimilation. In running the unassimi-lating 3D BGC model the deeper nitrate values could be relaxed to the climato-logical observations to tailor the data assimilation application to BGC behavior in the photic zone and ensure a realistic sub-surface nitrate concentrations.

4. from an initial state run the 3D BGC model forward one day and at each ocean surface grid point compute the difference between the simulated phytoplankton concentration and the observed value.

5. at each ocean surface model grid point run an ensemble of 0D BGC simulations. The 0D BGC model will use the ocean physical information and the initial BGC values from step 4. From the ensemble of simulations the mean and uncertainty in the subset of model parameters identified in step 2 is determined that produce a correction to phytoplankton concentrations consistent with the difference estimated in step 4. The difference between the observed and simulated phytoplank-ton concentration from the 3D BGC model is assumed only to be due to BGC processes in the mixed layer. Note the 0D BGC model does retain the 3D ocean circulation effects since they are included in the difference between the 3D BGC simulated P and the observed value. Provided the modifications to the BGC state variables are small, the ocean circulation affects will be accurately represented in the 0D BGC model. The estimated BGC model parameters mean and uncertainty should be retained for later analysis.

6. from the spatially varying mean model parameter values determined in 5, run the 0D BGC model at all surface ocean grid points over the same day to estimate the mixed layer depth corrections to the BGC state variables.

7. add the corrected BGC state variables to the mixed layer values at the end of the one day run of the 3D BGC model and change the 3D BGC model parameters to the values determined in 5.

8. repeat steps 4-7 assimilating the next day of observed surface phytoplankton concentrations.

Within this system there will also be data assimilation of the physical system, which will alter the physical ocean state. The altered physical ocean state will be incorporated into the forward running of the 3D BGC model and into the 0D BGC simulations at the surface ocean grid points. It should be noted that the data assimilation updating of the physical state variables may produce an unbalanced physical state, which may cause problems in the BGC simulation. This should be investigated by running the model system but not applying BGC data assimilation to explore the impact of update the physical state on the BGC state variable evolution.

Although we suggest above to use the mean BGC model parameters determined from 0D BGC simulation a more sophisticated approach could be envisage where uncertainty in the observed phytoplankton concentration, temporal and spatial variability in the model parameters and their uncertainty could be incorporated into the revised estimate of the model parameters used in the next iteration of the 3D BGC model. For example, the study by Jones et al. (2010) show how to limit the temporal variability in the model parameters. Finally the temporal and spatial evolution of the optimized BGC model parameters determined in step 4 also provide independent information to assess the ecological realism of the BGC model and the ability of the data assimilation to extract additional from the observations beyond constraining the surface phytoplankton. The analysis of the optimized parameters should provide useful insight into the BGC model formulation. For example, we expect the model parameters to display spatial variability (Friedrichs et al. 2007; Follows et al. 2007) related to ecological regimes and the updated model parameters could be assessed against the expected ecological regimes in the ocean.

12.5 Conclusion

The field of BGC data assimilation is a relatively new but there are now many examples where the approach has been applied to both parameter estimation and state estimation problems. Data assimilation with BGC models provides a framework to extract information from BGC observations and refine prognostic models of carbon and nutrient cycling in the ocean. The existing GODAE data assimilation systems are an obvious avenue for expanding data assimilation to include BGC. Large BGC model uncertainties, strong non-linearity in the BGC model and high computational demands of the existing GODAE sequential data assimilation systems motivated us to propose a hybrid BGC data assimilation approach. The proposed approach utilizes the vertical information of the physical model and an ensemble of simulations of the 0D BGC representation of the 3D BGC model at each surface ocean grid point. From the 0D BGC ensemble of simulations one obtains an updated estimate of the BGC model parameters and revised BGC ocean state to use in the subsequent simulation of the 3D BGC model. As conceived the approach is computationally feasible, provides a way to estimate the BGC ocean state that is BGC balanced without resorting to BECs that are complex and difficult to determine. The application will generate spatially and temporally varying BGC model parameters, which will need to be ecologically evaluated. Future effort with the BLUELINK data assimilation system Oke et al. (2008) will be pursued using this approach to deliver 3D ocean state estimates of both the physical and BGC fields.

Our presentation has focused on modifying the GODAE system to include BGC but there may be value in constraining the physical data assimilation system with the remotely sensed ocean colour Chlorophyll a. As shown in Fig. 12.1, the field contains information about the eddy circulation in the surface ocean. Extracting such information may prove valuable and should be explored.

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Part V Data Assimilation

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