Ensemble optimal interpolation for adjoint-free biogeochemical data assimilation.

Advanced marine ecosystem models can contain more than 100 biogeochemical variables, making data assimilation for these models a challenging prospect. Traditional variational data assimilation techniques like 4dVar rely on tangent linear and adjoint code, which can be difficult to create for complex ecosystem models with more than a few dozen variables. More recent hybrid ensemble-variational data assimilation techniques use ensembles of model forecasts to produce model statistics and can thus avoid the need for tangent linear or adjoint code. We present a new implementation of a four-dimensional ensemble optimal interpolation (4dEnOI) technique for use with coupled physical-ecosystem models. Our 4dEnOI implementation uses a small ensemble, and spatial and variable covariance localization to create reliable flow-dependent statistics. The technique is easy to implement, requires no tangent linear or adjoint code, and is computationally suitable for advanced ecosystem models. We test the 4dEnOI implementation in comparison to a 4dVar technique for a simple marine ecosystem model with 4 biogeochemical variables, coupled to a physical circulation model for the California Current System. In these tests, our 4dEnOI reference implementation performs similarly well to the 4dVar benchmark in lowering the model observation misfit. We show that the 4dEnOI results depend heavily on covariance localization generally, and benefit from variable localization in particular, when it is applied to reduce the coupling strength between the physical and biogeochemical model and the biogeochemical variables. The 4dEnOI results can be further improved by small modifications to the algorithm, such as multiple 4dEnOI iterations, albeit at additional computational cost.

A Bayesian approach to modeling phytoplankton population dynamics from size distribution time series.

The rates of cell growth, division, and carbon loss of microbial populations are key parameters for understanding how organisms interact with their environment and how they contribute to the carbon cycle. However, the invasive nature of current analytical methods has hindered efforts to reliably quantify these parameters. In recent years, size-structured matrix population models (MPMs) have gained popularity for estimating division rates of microbial populations by mechanistically describing changes in microbial cell size distributions over time. Motivated by the mechanistic structure of these models, we employ a Bayesian approach to extend size-structured MPMs to capture additional biological processes describing the dynamics of a marine phytoplankton population over the day-night cycle. Our Bayesian framework is able to take prior scientific knowledge into account and generate biologically interpretable results. Using data from an exponentially growing laboratory culture of the cyanobacterium Prochlorococcus, we isolate respiratory and exudative carbon losses as critical parameters for the modeling of their population dynamics. The results suggest that this modeling framework can provide deeper insights into microbial population dynamics provided by size distribution time-series data.

Dual number-based variational data assimilation: Constructing exact tangent linear and adjoint code from nonlinear model evaluations.

Dual numbers allow for automatic, exact evaluation of the numerical derivative of high-dimensional functions at an arbitrary point with minimal coding effort. We use dual numbers to construct tangent linear and adjoint model code for a biogeochemical ocean model and apply it to a variational (4D-Var) data assimilation system when coupled to a realistic physical ocean circulation model with existing data assimilation capabilities. The resulting data assimilation system takes modestly longer to run than its hand-coded equivalent but is considerably easier to implement and updates automatically when modifications are made to the biogeochemical model, thus making its maintenance with code changes trivial.