Investigating the complex relationship between in situ Southern Ocean $pCO_{2}$ and its ocean physics and biogeochemical drivers using a nonparametric regression approach

Abstract

The objective in this paper is to investigate the use of a non-parametric approach to model the relationship between oceanic carbon dioxide $(pCO_2)$ and a range of ocean physics and biogeochemical in situ variables in the Southern Ocean, which influence its in situ variability. The need for this stems from the need to obtain reliable estimates of carbon dioxide concentrations in the Southern Ocean which plays an important role in the global carbon flux cycle. The main challenge involved in this objective is the spatial limitation and seasonal bias of the in situ data. Moreover, studies have also reported that the relationship between $pCO_2$ and its drivers is complex. As such, in this paper, we use the non-parametric kernel regression approach since it is able to accurately capture the complex relationships between the response and predictor variables. In this analysis we use the in situ data obtained from the SANAE49 return leg journey between Antarctic to Cape Town. To the best of our knowledge, this is the first time this data set has been subjected to such analysis. The model variants were developed on a training data subset, and the ‘goodness’ of the models were assessed on an “unseen” test data subset. Results indicate that the nonparametric approach consistently captures the relationship more accurately in terms of mean square error, root mean square error and mean absolute error, over a standard parametric approach (multiple linear regression). These results provide a platform for using the developed nonparametric regression model based on in situ measurements to predict $pCO_2$ for a larger spatial region in the Southern Ocean based on satellite biogeochemical measurements of predictor variables, given that satellites do not measure $pCO_2$.