Multiscale statistical analysis of thermal and non-thermal components of seawater pCO₂ in the Western English Channel: scaling, time-reversibility, and dependence

Abstract. The partial pressure of carbon dioxide (pCO₂) has been measured on the ASTAN cardinal buoy (Brittany, west coast of France) with at 30-minute intervals by Gac et al. (2020), yielding a dataset of 32,582 data points collected over a period of nearly five years. These measurements were then coupled with others of sea surface temperature and salinity, chlorophyll a, oxygen saturation and atmospheric pressure. The aim of this study was to consider the statistical properties of the thermal and non-thermal component of pCO₂, based on its relation with temperature established by Takahashi et al. (2009). Using Fourier spectral analysis, it was demonstrated that all marine scalars exhibited scaling properties with power-law slopes ranging from 1.73 to 1.85 for timescales spanning from 12 hours to at least 80-100 days. The results obtained from this analysis indicate a turbulent and intermittent dynamics for all the considered scalars, including sea surface temperature and salinity, chlorophyll a, oxygen saturation, pCO₂, and pCO₂ thermal and non-thermal components. A time-reversibility analysis evidenced the irreversibility of the pCO₂ components above 30 days. The irreversibility exhibited by the thermal component was found to be higher than that of the non-thermal component, with an average value of the associated irreversibility index that was approximately 3.5 times higher than that of the non-thermal component over the period of 50 to 70 days. Furthermore, a methodology known as the Probability Density Function quotient was employed, a method that has not been widely utilized. This approach enabled the identification of values for which there were statistical relationships between variables. This facilitated the quantification of the influence of primary production on the non-thermal pCO₂, or the influence of periods of depression on supersaturation due to atmospheric or terrigenous inputs. This provided new insights into the stochastic coupling between biological and physical processes, when considering high-frequency pCO₂ variability.