Assimilating ocean tracer data into the Bern3D model using an ensemble Kalman filter

Gerber, Markus (2009). Assimilating ocean tracer data into the Bern3D model using an ensemble Kalman filter (Unpublished). (Dissertation, Universität Bern, Philosophisch–naturwissenschaftliche Fakultät, Physikalisches Institut, Abteilung für Klima– und Umweltphysik)

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The overarching theme of this thesis is the assimilation of ocean tracer data into the Bern3D ocean model (Müller et al., 2006) with an Ensemble Kalman Filter (Evensen, 2003) to optimize unknown model states or processes in the marine carbon cycle.
The oceanic cycling of carbon is a very complex interplay between physical and biogeochemical processes, yet a very important element in the climate system through its great influence in regulating atmospheric carbon dioxide (CO2). With the background of an anthropogenic induced warming of the climate, the improvement of the knowledge about the marine carbon cycle and especially about the sources and sink fluxes is doubtless an important issue with great societal interest. However, due to the complexity and chaotic behavior of the involved processes it is difficult to properly model the marine carbon cycle, as the involved processes usually happen on different time and length-scales or are empirically derived. The modeling of such processes is often bonded with large uncertainties in model states or model parameters.
The Ensemble Kalman Filter (Evensen, 2003) is a sequential data assimilation method to optimize unknown model states or parameters. It has been successfully applied to many different nonlinear and chaotic problems in geosciences. The Bern3D model is an ocean general circulation model of intermediate complexity. Its adequate representation of the ocean circulation and ventilation times and its computational efficiency makes it very suitable for ensemble simulations. The implementation of the Ensemble Kalman Filter in the Bern3D model provides therefore a very promising tool to quantify processes of the marine carbon cycle.
The focus of this thesis is on the determination of regional air-sea fluxes of CO2. The contemporary flux can be separated into a natural and an anthropogenic component to explore physical and biogeochemical mechanism that drive the carbon sources and sink fluxes. The natural part reflects the gasexchange prior the beginning of the industrialization, the anthropogenic part is the human induced perturbation. As it is not possible to measure these two components separately, it is quite challenging to properly identify the underlying mechanism that drive the air-sea fluxes. Quantitative estimates of air-sea fluxes are therefore crucial to improve the knowledge about the driving mechanisms and processes.
The first chapter gives an introduction and motivation to model the oceanic carbon cycle. First, a general overview of the ocean and carbon cycle is provided. Then, the need for different modeling methods and especially the benefit from inverse modelling and data assimilation is shortly discussed. In the framework of inverse modeling, the Ensemble Kalman Filter and its applications are shortly introduced.
In chapter 2, the Ensemble Kalman Filter and its statistical background is presented. A short overview of the Bern3D ocean model is provided.
In chapter 3 we describe results of an assimilation of ocean interior data of anthropogenic carbon to estimate regional air-sea fluxes and transport rates in the ocean (Gerber et al., 2009a). In an iterative process, flux magnitudes and inferred transport rates are optimized to minimize deviations between modeled and data-based estimates of the oceanic distribution of anthropogenic carbon. Error analysis is crucial in any inverse simulation. To investigate the influence of systematic errors in the assimilated data, we have included estimates from six different published reconstruction methods (Gruber et al., 1996; Thomas and Ittekkot, 2001; Waugh et al., 2004; Lo Monaco et al., 2005; Touratier et al., 2007; Vázquez Rodríguez et al., 2008a). The findings of this study are in good agreement with earlier inverse studies (Gloor et al., 2003; Mikaloff Fletcher et al., 2006), but reveal a great sensitivity of the inversion towards the reconstruction method of anthropogenic carbon.
In chapter 4, the natural part of the contemporary air-sea flux is explored (Gerber and Joos, 2009b). From data of total dissolved inorganic carbon, it is possible to extract the part which is due to natural gas exchange with the atmosphere (Sarmiento and Gruber , 2006). The natural air-sea CO2 fluxes are then optimized by assimilating these data into the Bern3D model. We have analyzed the inferred results for their sensitivity to uncertainties in model transport and to uncertainties in the data-based estimates. The contemporary air-sea fluxes, which are basically the sum of the natural and anthropogenic components, are compared with data-based estimates (Takahashi et al , 2008) and other inverse studies (Gruber et al., 2009). We find reasonable agreement in aggregated contemporary air-sea fluxes among methods. However, on regional scale substantial differences in the natural component are found between the inverse study of Mikaloff Fletcher et al. (2007) and the Ensemble Kalman Filter inversion. Especially fluxes in the Southern Ocean show a strong sensitivity to differences in the assimilated data and the choice of the inverse method.
Chapter 5 includes the study of Mikaloff Fletcher et al. (2006), where air-sea fluxes of anthropogenic carbon are inferred with a Green’s function inverse method (Gloor et al., 2001; Gruber et al., 2001; Gloor et al., 2003). The inclusion of the Bern3D model in this multi ocean model study provides us a useful comparison between the Ensemble Kalman Filtering and Green’s function approach to quantify differences in the inverse modeling methods.
In chapter 6, potential future applications to questions that could be investigated within an Ensemble Kalman Filter inverse simulation are shortly introduced and discussed. Finally, the appendix provides useful technical details of the implementation and provides hints abouts the application of the Ensemble Kalman Filter to the Bern3D model. The Ensemble Kalman Filter has been tested in a so called twin run experiment, which is presented in there. In the second part of the appendix, ”Howto documents” are included to ease the application for potential users of the Filter.

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