The dissolved organic carbon flux from the UK - A new Bayesian approach to flux calculation

The study of regional and national-scale fluxes of biogeochemically relevant elements (e.g. carbon) has been hampered by inconsistency of long-term sampling. In this study we solve the issue of sporadic, low-density and low-frequency sampling for nutrients by using Bayesian hierarchical generalised linear modelling. The Bayesian approach means that it is possible to estimate a distribution of the expected value of the nutrient of interest for each location within a survey, no matter whether it was surveyed in a particular year, as long as that site was sampled sometime during the entire study period and that somewhere within the wider survey was sampled in the particular year, i.e. there is no minimum number of samples for a site to be included save that the site was sampled during the entire study period. The method developed was applied to problem of understanding the long-term flux of dissolved organic carbon (DOC) for the UK. The method was applied to 251 monitoring sites across the UK from 1974 to 2019 and the approach was similarly applied to river discharges so as to infill gaps in flow records. The results showed that: I. The annual expected value of the DOC concentration at the UK tidal limit sites has significantly declined over the period from 1974 to 2019. II. Statistically significant changes in DOC concentration were observed over the period from 1974 to 2018 with DOC concentrations rising at the majority sites until the late 1990 s, before declining to a minimum in 2007 with modest increases to 2018. III. The DOC flux from the UK peaked in the year 2000 at 1103 +/- 141 ktonnes C/yr (4.5 tonnes C/km(2)/yr) and reached a minimum of 503 +/- 63 ktonnes C/yr (2.1 tonnes C/km(2)/yr) in 2018. IV. The spatial pattern of DOC export shows large declines in the south and east of the UK where urban centres dominate while catchments in the north of the country show continuing high exports (up to 21 tonnes C/km(2)/yr) but exports as low as 0.16 tonnes C/km(2)/yr in eastern England. The flux method developed here makes maximal use of the available data allowing for calculation of long time series, even with sporadic sampling, and gives results with a coherent and consistent measure of their uncertainty.