Quantification of regional terrestrial biosphere CO₂ flux errors in v10 OCO-2 MIP models using airborne measurements

Abstract. Multi-inverse modeling inter-comparison projects (MIPs) provide a chance to assess the uncertainties in inversion estimates arising from various sources such as atmospheric CO₂ observations, transport models, and prior fluxes. However, accurately quantifying ensemble CO₂ flux errors remains challenging, often relying on the ensemble spread as a surrogate. This study proposes a method to quantify the errors of regional terrestrial biosphere CO₂ flux estimates from 10 inverse models within the Orbiting Carbon Observatory-2 (OCO-2) 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 concentration estimates and airborne observations and then isolate the CO₂ concentration error caused solely by the ensemble mean of posterior terrestrial biosphere CO₂ flux estimates by subtracting the errors of observation and transport in seven regions. Our analysis reveals significant regional variations in the average monthly RMSE over three years, ranging from 0.90 to 2.04 ppm. The ensemble flux error projected into CO₂ space is a major component that accounts for 58–84 % of the mean RMSE. We further show that in five regions, the observation-based error estimates exceed the atmospheric CO₂ errors computed from the ensemble spread of posterior CO₂ flux estimates by 1.37–1.89 times, implying an underestimation of the actual ensemble flux error, while their magnitudes are comparable in two regions. By identifying the most sensitive areas to airborne measurements through adjoint sensitivity analysis, we find that the underestimation of flux errors is prominent in eastern parts of Australia and East Asia, western parts of Europe and Southeast Asia, and midlatitude North America, suggesting the presence of systematic biases related to anthropogenic CO₂ emissions in inversion estimates. The regions with no underestimation were southeastern Alaska and northeastern South America. Our study emphasizes the value of independent airborne measurements not only for the overall evaluation of inversion performance but also for quantifying regional errors in ensemble terrestrial biosphere flux estimates.