Tracer Transport

Modeling biogeochemical variables introduces different requirements for tracer transport schemes. For example, to prevent numerical instabilities when representing nutrient limited biological processes it is necessary to use positive definite advection schemes in the advection of nutrient species. Some of the schemes used in our models are described here.

Carbonate Chemistry System

In order to determine the air-sea fluxes of CO2 in numerical models it is necessary to solve for the local equilibrium partitioning of the carbonate system. Typically this involves solution of a high order polynomial at each surface grid point using a method such as Newton-Raphson iteration. We have developed an efficient scheme for solving this system which requires no iteration. Hence it is a compact and efficient code and is easily differentiated for adjoint model applications.

Biogeochemical Parameterizations

One important aspect of the ocean biogeochemistry model is the development of parameterizations of key ocean processes. Modeling the iron cycle is an important example. It is now clear that the supply of iron to the euphotic zone of the oceans plays a key role in modulating biological productivity of the the oceans, yet until recently the important processes and mechanisms which control the distribution and transport of iron within the oceans have not been understood. With former graduate student Payal Parekh and Prof. Ed Boyle at MIT we have developed and implemented a parameterization of the oceanic iron cycle which represents many of the key processes. However, the current paucity of observations of iron in the ocean and uncertainties about the key processes are still limiting.

Adjoint Modeling

We are developing the adjoint of the biogeochemical model which will provide a mechanism for systematically and efficiently exploring the sensitivities of the model to boundary conditions and parameter choices. In addition we may use the model and its adjoint to optimize the biogeochemical model, bringing the model solution into consistency with observed data through systematic adjustment of model parameters and boundary conditions.

Using this framework it will be possible, for example, to infer the regional variations in the export of organic nutrients and carbon from the surface euphotic zone to depth by bringing into consistency the modeled and observed dissolved inorganic carbon and nutrient fields, to the extent that the model circulation represents the observed ocean.

In a preliminary study we have used the model and its adjoint to infer the mean residence time of a carbon-like tracer with respect to interior sources in the ocean model. In the figure below we illustrate the residence times for "carbon" emitted from sources at three depth levels in the model.

Due to the efficiency of the adjoint method the residence times for all possible sources in the model were evaluated simultaneously at a small fraction of the computational cost than if each source were treated independently in a perturbation experiment.