No, it goes well beyond "contention and assertion". It is based on analysis and synthesis of numerous data types. Some of the fluxes are better characterized than others, so there is uncertainty -- there always is in science -- but many aspects can be checked and double-checked independently, establishing their veracity.
From NOAA's Carbon Cycle Science Breakthroughs
"CO2 and CH4 concentrations have been increasing in the atmosphere since 1850 and are now higher than they have been for more than 400,000 years, primarily as a result of human use of fossil fuels and land clearing. Of the total emissions to the atmosphere, about half of the carbon emitted to the atmosphere (CO2 and CH4) is taken up by the oceans (and land). Specifically, the ocean (and land) is a sink for CO2, while CH4 is largely oxidized in the atmosphere (this explains why CO2 has a relatively longer atmospheric lifetime compared to CH4). Quantifying and reconciling these sinks with the remaining concentrations in the atmosphere has been and remains a major challenge, although recent advances have been made in understanding the continental U.S. land sink through NOAA-supported research."