ALBERT

Description: Biogeochemical models, capturing the major feedbacks of the pelagic ecosystem of the world ocean, are today often embedded into Earth system models which are increasingly used for decision making regarding climate policies. These models contain poorly constrained parameters (e.g., maximum phytoplankton growth rate), which are typically adjusted until the model shows reasonable behavior. Systematic approaches determine these parameters by minimizing the misfit between the model and observational data. In most common model approaches, however, the underlying functions mimicking the biogeochemical processes are nonlinear and non-convex. Thus, systematic optimization algorithms are likely to get trapped in local minima and might lead to non-optimal results. To judge the quality of an obtained parameter estimate, we propose determining a preferably large lower bound for the global optimum that is relatively easy to obtain and that will help to assess the quality of an optimum, generated by an optimization algorithm. Due to the unavoidable noise component in all observations, such a lower bound is typically larger than zero. We suggest deriving such lower bounds based on typical properties of biogeochemical models (e.g., a limited number of extremes and a bounded time derivative). We illustrate the applicability of the method with two real-world examples. The first example uses real-world observations of the Baltic Sea in a box model setup. The second example considers a three-dimensional coupled ocean circulation model in combination with satellite chlorophyll a.

Description: Global biogeochemical ocean models contain a variety of different biogeochemical components and often much simplified representations of complex dynamical interactions, which are described by many (≈10–≈100) parameters. The values of many of these parameters are empirically difficult to constrain, due to the fact that in the models they represent processes for a range of different groups of organisms at the same time, while even for single species parameter values are often difficult to determine in situ. Therefore, these models are subject to a high level of parametric uncertainty. This may be of consequence for their skill with respect to accurately describing the relevant features of the present ocean, as well as their sensitivity to possible environmental changes. We here present a framework for the calibration of global biogeochemical ocean models on short and long time scales. The framework combines an offline approach for transport of biogeochemical tracers with an Estimation of Distribution Algorithm (Covariance Matrix Adaption Evolution Strategy, CMAES). We explore the performance and capability of this framework by five different optimizations of six biogeochemical parameters of a global biogeochemical model. First, a twin experiment explores the feasibility of this approach. Four optimizations against a climatology of observations of annual mean dissolved nutrients and oxygen determine the extent, to which different setups of the optimization influence model's fit and parameter estimates. Because the misfit function applied focuses on the large-scale distribution of inorganic biogeochemical tracers, parameters that act on large spatial and temporal scales are determined earliest, and with the least spread. Parameters more closely tied to surface biology, which act on shorter time scales, are more difficult to determine. In particular the search for optimum zooplankton parameters can benefit from a sound knowledge of maximum and minimum parameter values, leading to a more efficient optimization. It is encouraging that, although the misfit function does not contain any direct information about biogeochemical turnover, the optimized models nevertheless provide a better fit to observed global biogeochemical fluxes.

Description: Global biogeochemical ocean models are often tuned to match the observed distributions and fluxes of inorganic and organic quantities. This tuning is typically carried out “by hand”. However, this rather subjective approach might not yield the best fit to observations, is closely linked to the circulation employed and is thus influenced by its specific features and even its faults. We here investigate the effect of model tuning, via objective optimisation, of one biogeochemical model of intermediate complexity when simulated in five different offline circulations. For each circulation, three of six model parameters have been adjusted to characteristic features of the respective circulation. The values of these three parameters – namely, the oxygen utilisation of remineralisation, the particle flux parameter and potential nitrogen fixation rate – correlate significantly with deep mixing and ideal age of North Atlantic Deep Water (NADW) and the outcrop area of Antarctic Intermediate Waters (AAIW) and Subantarctic Mode Water (SAMW) in the Southern Ocean. The clear relationship between these parameters and circulation characteristics, which can be easily diagnosed from global models, can provide guidance when tuning global biogeochemistry within any new circulation model. The results from 20 global cross-validation experiments show that parameter sets optimised for a specific circulation can be transferred between similar circulations without losing too much of the model's fit to observed quantities. When compared to model intercomparisons of subjectively tuned, global coupled biogeochemistry–circulation models, each with different circulation and/or biogeochemistry, our results show a much lower range of oxygen inventory, oxygen minimum zone (OMZ) volume and global biogeochemical fluxes. Export production depends to a large extent on the circulation applied, while deep particle flux is mostly determined by the particle flux parameter. Oxygen inventory, OMZ volume, primary production and fixed-nitrogen turnover depend more or less equally on both factors, with OMZ volume showing the highest sensitivity, and residual variability. These results show a beneficial effect of optimisation, even when a biogeochemical model is first optimised in a relatively coarse circulation and then transferred to a different finer-resolution circulation model.

Description: Global biogeochemical ocean models help to investigate the present and potential future state of the ocean, its productivity and cascading effects on higher trophic levels such as fish. They are often subjectively tuned against data sets of inorganic tracers and surface chlorophyll and only very rarely against organic components such as particulate organic carbon or zooplankton. The resulting uncertainty in biogeochemical model parameters (and parameterisations) associated with these components can explain some of the large spread of global model solutions with regard to the cycling of organic matter and its impacts on biogeochemical tracer distributions, such as oxygen minimum zones (OMZs). A second source of uncertainty arises from differences in the model spin-up length as, so far, there seems to be no agreement on the required simulation time that should elapse before a global model is assessed against observations. We investigated these two sources of uncertainty by optimising a global biogeochemical ocean model against the root-mean-squared error (RMSE) of six different combinations of data sets and different spin-up times. Besides nutrients and oxygen, the observational data sets also included phyto- and zooplankton, as well as dissolved and particulate organic phosphorus (DOP and POP, respectively). We further analysed the optimised model performance with regard to global biogeochemical fluxes, oxygen inventory and OMZ volume. Following the optimisation procedure, we evaluated the RMSE for all tracers located in the upper 100 m (except for POP, for which we considered the entire vertical domain), regardless of their consideration during optimisation. For the different optimal model solutions, we find a narrow range of the RMSE, between 14 % of the average RMSE after 10 years and 24 % after 3000 years of simulation. Global biogeochemical fluxes, global oxygen bias and OMZ volume showed a much stronger divergence among the models and over time than RMSE, indicating that even models that are similar with regard to local surface tracer concentrations can perform very differently when assessed against the global diagnostics for oxygen. Considering organic tracers in the optimisation had a strong impact on the particle flux exponent (Martin b) and may reduce much of the uncertainty in this parameter and the resulting deep particle flux. Independent of the optimisation setup, the OMZ volume showed a particularly sensitive response with strong trends over time, even after 3000 years of simulation time (despite the constant physical forcing); a high sensitivity to simulation time; and the highest sensitivity to model parameters arising from the tuning strategy setup (variation of almost 80 % of the ensemble mean). In conclusion, calibration against observations of organic tracers can help to improve global biogeochemical models even after short spin-up times; here especially, observations of deep particle flux could provide a powerful constraint. However, a large uncertainty remains with regard to global OMZ volume and its evolution over time, which can show very dynamic behaviour during the model spin-up, which renders temporal extrapolation to a final equilibrium state difficult if not impossible. Given that the real ocean shows variations on many timescales, the assumption of observations representing a steady-state ocean may require some reconsideration.