Estimating marine biogeochemical rates of the carbonate pH system—A Kalman filter tested

Oxygen (O₂), nitrate (NO₃), dissolved inorganic carbon (DIC) or pCO₂, and pH or total alkalinity (TA), are useful indices of marine chemical, physical and biological processes operating on varying time-scales. Although these properties are increasingly being monitored at high frequency, they have not been extensively used for studying ecosystem dynamics. We test whether we can estimate time-evolving biogeochemical rates (e.g. primary production, respiration, calcification and carbonate dissolution, and nitrification) from synthetic high frequency time-series of O₂, NO₃, DIC, pCO₂, TA or pH. More specifically, a Kalman filter has been implemented in a very simplified biogeochemical model describing the dynamics of O₂, NO₃, DIC and TA and linking the concentration data to biogeochemical fluxes. Different sets of concentration data are assimilated and biogeochemical rates are estimated. The frequency of assimilation required to get acceptable results is investigated and is compared with the frequency of sampling in the field or in controlled experimental settings.Smoothing of the data to remove data noise before assimilation improves the estimation of the biogeochemical rates. The best estimated rates are obtained when assimilating O₂, NO₃ and TA although the assimilation of DIC instead of TA also gives satisfactory results. In case pH or pCO₂ is assimilated rather than DIC or TA, the linearization of the (now nonlinear) observation equation introduces perturbations and the Kalman filter behaves suboptimal. We conclude that, given the resolution of data required, the tool has potential to estimate biogeochemical rates of the carbonate system under controlled settings.