Quantification of regional net CO~2~ flux errors in the Orbiting Carbon Observatory-2 (OCO-2) v10 model intercomparison project (MIP) ensemble using airborne measurements

Abstract. Inverse model intercomparison projects (MIPs) provide a chance to assess the uncertainties in inversion estimates arising from various sources. However, accurately quantifying ensemble CO2 flux errors remains challenging and often relies on the ensemble spread. This study proposes a method for quantifying the errors in regional net surface–atmosphere CO2 flux estimates from models taken from the Orbiting Carbon Observatory-2 (OCO-2) v10 MIP by using independent airborne CO2 measurements for the period 2015–2017. We first calculate the root mean square error (RMSE) between the ensemble mean of posterior CO2 concentrations and airborne observations and then isolate the CO2 concentration errors caused solely by the ensemble mean of posterior net fluxes by subtracting the observation, representation, and transport errors from seven regions. Our analysis reveals that the flux errors projected onto CO2 space account for 55 %–85 % of the regional average RMSE over the 3 years, ranging from 0.88 to 1.91 ppm. In five regions, the error estimates based on observations exceed those computed from the ensemble spread of posterior fluxes by a factor of 1.33–1.93, implying an underestimation of the actual flux errors, while their magnitudes are comparable in two regions. The adjoint sensitivity analysis identifies that the underestimation of flux errors is prominent where the magnitudes of fossil fuel emissions exceed those of terrestrial-biosphere fluxes by a factor of 3–31 over the 3 years. This suggests the presence of systematic biases in the inversion estimates associated with errors in the prescribed fossil fuel emissions common to all models. Our study emphasizes the value of airborne measurements for quantifying regional errors in ensemble net CO2 flux estimates.