Using topology to test the underlying dynamics of global scale ocean biogeochemical models

The need to understand the global carbon cycle has led to increasingly complex models of ocean ecology and biogeochemistry are being developed [1] and embedded in high-resolution ocean circulation models, with global simulations being run over several decades. Usually to verify such simulations on the global scale, phytoplankton abundance (the most commonly measured ecosystem component) is compared to satellite ocean colour observations of chlorophyll, a proxy for phytoplankton. This is done because ocean colour chlorophyll data are the only global biogeochemical observations available over decadal time scales. Such comparisons only verify the spatio-temporal phytoplankton patterns and do not address the question of whether the underlying dynamics are qualitatively the same in the models and the observations, and therefore the extent to which models capture essential features of the biogeochemical dynamics. Here novel mathematical methods [2] will be used to extract important features of the dynamics [3] from the topology of the model output and the ocean colour data to determine whether the underlying dynamics of the ecosystem / biogeochemistry are qualitatively the same in the model as the real world. This is a big data problem with the aim of determining how well models represent the real world.
Methodology:
The primary model output to be used is from the biogeochemical MEDUSA model embedded in the 1/12˚ (~9km) NEMO ocean circulation model run at NOC. The simulation covers the period 1990-2015, with output available globally every 5 days. Ocean colour data will be obtained from the ESA CCI [www.oceancolour.org], and are available globally at 4 km resolution, every 5 days, for 1998-2016 (currently).

The model output and data will be analysed to determine the topology of the underlying dynamics. This will be done by combining well-established methods in attractor reconstruction from dynamical systems theory [4] with more recent advances in computational topology [2]. The results will show whether the model and the observations display the same qualitative features everywhere, or only in some regions, or not at all. Circumstances in which the model and the data differ qualitatively are significant, indicating deficiencies in the model, and therefore areas for potential improvement.

Once developed and tested these methods could be applied to study the dynamics of other biogeochemical models, such as those used in IPCC assessments. Additionally, the ¼˚ and 1˚ versions of MEDUSA / NEMO could be analysed to see whether changes in model resolution lead to substantially different dynamics.

The SPITFIRE DTP programme provides comprehensive personal and professional development training alongside extensive opportunities for students to expand their multi-disciplinary outlook through interactions with a wide network of academic, research and industrial/policy partners. The student will be registered at the University of Southampton and hosted at National Oceanography Centre Southampton. Specific training will include:

The use and analysis of MEDUSA / NEMO 1/12˚ ocean model output
The use and analysis of remotely sensed ocean colour data
Mathematical methods to determine dynamics from the topology of data
If possible, an opportunity to go to sea on a research cruise to learn about making shipboard measurements