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The proxies used for earlier measurements are very flawed. Typically, they use ice cores from Greenland or Antarctica (hard to get ice cores from other places due to the lack of long term ice). However, the CO2 levels at such high latitudes are significantly lower (due to increased absorption by cold oceans (solubility of CO2 varies with water temperature, see Henry's Law)) and the CO2 trapped in ice also dissolves out over time, leading to a lower measurement than was actually present. The presented CO2 concentration graphs are an abomination, they are created by splicing ice core data, atmospheric flask data taken in Antarctica (atmospheric CO2 at the poles is about 50ppm lower) and instrumental measurement from Manua Loa in Hawaii (being close to the equator, it has a high CO2 level due to warm oceans). Splicing proxy data with observational data is a big red flag in any supposedly scientific measurement. These measurements are often not comparable, particularly when the observational measurement is effectively an instantaneous measurement and the proxy has a resolution that may be measured in centuries.

A much better proxy is plant stomata density (https://www.geocraft.com/WVFossils/stomata.html) which shows that the CO2 concentration, though varying considerably over the short term (hundreds of years) has remained fairly consistent around the 350ppm range for the last 15000 years or so.