Development of a diffusion kernel density estimator and application on marine carbon-13 isotope data

My work developed a kernel density estimator that well resolves typical structures of probability densities, which was demonstrated on a newly compiled marine data set of organic carbon-13 isotope ratios (δ13CPOC). All work was conducted within the emerging field of marine data science. I identified classical data science, a general understanding of ocean science, communication skills, and confidence as requirements for marine data scientists.

In the beginning of my work, the existing δ13CPOC data consisted of about 500 data points in the global ocean. I expanded the existing data set to 4732 data points in a first version, and additionally to 6952 in a second. Both are published at PANGAEA along with meta information such as measurement location, time, and method, and interpolations. I have published a description of the temporal and geographic distribution of the first version at Earth System Science Data.

I designed the development of the kernel density estimator algorithm on the existing concept of computing it as a solution of the diffusion equation. My algorithm uses finite differences in space and equidistant time steps with an implicit Euler method, and approximates the optimal smoothing parameter by two pilot steps. Compared to other well-known kernel density estimators, my algorithm produces reliable approximations of multimodal and boundary-close distributions on artificial and real marine data and is robust to noise. My implementation is published as a Python package on Zenodo, its description is submitted to Geoscientific Model Development.

I was able to show that my kernel density estimator reliably evalu- ates ocean data and thus lays a foundation for calibrating Earth system models. At the same time, I was able to contribute to the definition and establishment of the field of Marine Data Science.




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