Modelling CO2 degassing from small acidic rivers using water pCO2, DIC and δ13C-DIC data

Degassing of terrestrially-respired CO2 from streams and small rivers appears to be a significant component in watershed carbon budgets. Here we propose an original approach to quantify CO2 degassing in small headwater bodies using pCO2, DIC (or total alkalinity, TA) and δ13C-DIC data in stream waters that avoids the difficulty of measuring or choosing a gas transfer velocity. Our inversed model applies to acidic, non-buffered (humic-type) waters and relies on two main assumptions, i.e., the stable isotopic composition of DIC in groundwater seeping to surface water (CO2 from respired soil organic carbon and HCO3- from weathering) and on kinetic fractionation at the water-air interface (12CO2 degases to the atmosphere more rapidly than 13CO2). We first consider both the soil organic matter isotopic composition and the isotopic fractionation of CO2 in the soil, to derive the δ13C-CO2 in that soil and groundwater. From the HCO3- concentrations in streams, we estimate the relative contribution of silicate and carbonate weathering (the latter being minor in these waters) to the HCO3- and its associated isotopic composition. Model calculations start from the δ13C-DIC value computed by the aforementioned method and consist of two interlocked iterative procedures. The first procedure simulates the decrease in pCO2 and the increase in δ13C-DIC that occur along the stream watercourse during degassing, starting from an assumed initial soil pCO2 and ending at the in situ pCO2 or δ13C-DIC. The second iteration procedure consists of adjusting the initial soil pCO2 until pCO2 and δ13C-DIC simultaneously reach the in situ measured values. After convergence is obtained, the model computes a theoretical concentration of DIC, [DIC]ex., that has been lost as CO2 to the atmosphere from the headwater to the sampling point in the river. [DIC]ex. can be multiplied by the river discharge to derive the quantity of carbon degassed from the river surface. The model was tested on seasonal field datasets from three small rivers draining sandy podsols in southern France and gave annual areal degassing rates comparable to those reported in other studies, though somewhat larger (upper half range in two rivers, ∼10 times the average in one stream). Part of this discrepancy might have been caused by an intense degassing in the vicinity of groundwater seeps, which was accounted for our integrative method but not by classical methods based on stream water pCO2 and gas transfer velocity. The sensitivity of the model results on the assumption of the importance of carbonate weathering might also explain part of this high degassing rate. The model reproduced consistent values and seasonal trends of soil pCO2 (maximal in summer) and gas transfer velocity (maximal at high water flow). We discuss the sensitivity of the model to the different parameters and assumptions and propose some improvements including groundwater sampling, for better constraining the computed degassing rates.