Final answer:
Past atmospheric carbon dioxide concentrations are estimated primarily through the analysis of ice core samples, which preserve trapped gases from different periods. Alternate methods include examining plant stomatal indices, analyzing tree rings, and studying sediment cores.
Step-by-step explanation:
Scientists estimate past atmospheric carbon dioxide concentrations primarily through the analysis of ice core samples. These ice cores contain trapped gases from different periods, providing a historical record of atmospheric composition that can be used to infer climate conditions. Measurements of carbon dioxide in ice cores have revealed that concentrations in the atmosphere are at unprecedented levels in the past 800,000 years due to human activity, such as the burning of fossil fuels.
Other methods include studying the stomatal index of plants in herbarium samples which reflects atmospheric CO2 levels at the time they were growing, examining tree rings in the context of dendroclimatology, and analyzing sediment cores which might contain microscopic organisms or other data indicative of past CO2 levels.