Diminishing marginal effect in estimating the dissolved organic carbon export from a watershed

Dissolved organic carbon (DOC) can be initially moved from soils to inland waters with surface runoff, and then mineralized, buried, or eventually delivered to the coastal ocean. This land-to-ocean phase of the DOC flux must be accounted for to comprehensively understand the global carbon cycle. To estimate the terrestrial-aquatic DOC leaching, calculating the product of the riverine DOC concentration and the corresponding river discharge measured at the watershed outlet is a common method. However, it is challenging to frequently and exactly record riverine DOC concentrations, thus the relationship between DOC concentrations and discharges (C-Q relationship) are established and used to interpolate the time-series of DOC concentrations. We found that the widely used time-dependent and time-independent C-Q regression models are weak in representing their altered relationship when the discharge is extremely high, which was named as diminishing marginal effect. In this study, we evaluated the performance of two C-Q regression models and discussed possible reasons for the diminishing marginal effect. We suggest that repeated and long-term measurements of the DOC concentration are required to adequately analyze their relationships, especially during the early spring and seasons with heavy precipitations.