Multiscale statistical analysis of thermal and non-thermal components of seawater <i>p</i> CO ₂ in the Western English Channel: scaling, time-reversibility, and dependence

Abstract. High-frequency variability of the partial pressure of CO2 (pCO2) in coastal environments reflects the complex interplay of physical, chemical and biological drivers. Multiscale statistical approaches provide a robust framework for understanding dynamics across timescales and for reliably assessing coastal carbon processes. In this study, pCO2 has been measured on the Astan cardinal buoy (Brittany, west coast of France) with at 30 min 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 1.73–1.85 for timescales spanning from 12 h to at least 80–100 d. 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 d. 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 50–70 d. 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.