Current fossil fuel emissions are leading to changes in the natural balance of carbon dioxide in the atmosphere, ocean and on land. Atmospheric carbon dioxide levels are rising at an unprecedented rate and the ocean is becoming more acidic due to carbon uptake. Projected climate change is due to alter the ability of terrestrial ecosystems to store carbon. Due to the complex interactions between atmospheric carbon dioxide levels, climate, terrestrial ecosystems and ocean circulation, predictions about how today's fossil fuel emissions will alter the future world are very uncertain. Yet the consequences of today's fossil fuel emissions could be great for humankind in the coming decades and centuries. The present day is not the only known time period in which atmospheric carbon dioxide and climate have changed. Carbon dioxide concentrations have been measured within air bubbles that became trapped in polar ice cores dating back up to 800 000 years. These air bubbles reveal that atmospheric carbon dioxide levels have fluctuated many times as the Earth's climate has changed between ice ages and warm periods. Carbon dioxide levels are found to have been about 40% higher during warm periods than during ice ages. These carbon dioxide increases are thought to both contribute to the warmer climates (through the greenhouse effect) and have been caused by the warmer climates. When atmospheric carbon dioxide levels were low, the ocean stored more carbon, and when atmospheric levels were high the ocean stored less carbon. However, the precise mechanisms by which changes in climate alter atmospheric carbon dioxide levels remain unknown. Identifying these mechanisms will not only help us to understand the past, but will also help to us understand the likely future consequences of today's fossil fuel emissions. This proposal aims to constrain the possible causes of the past glacial-interglacial changes in atmospheric carbon dioxide. Two specific research questions will be posed. Firstly, precisely what new data needs to be gathered to accurately constrain the causes of carbon dioxide changes? The existing carbon-cycle data cannot distinguish between competing explanations of carbon dioxide change: many alternative explanations all appear to agree with the data. In order to know what explanation truly explains the glacial-interglacial CO2 change, we need to identify data that will agree with only one of the possible explanations. This research proposal will implement a novel matrix based method to determine what new data is required to test the alternative explanations. Secondly, this proposal will answer 'why do different types of computer models of the ocean appear to store carbon in different ways?' Recent theoretical advances will be utilised, which allow carbon storage in computer models to be analysed in a new quantitative way. Until we understand the differences between ocean models, we cannot understand how the real ocean stores carbon, and how this carbon storage changed over glacial-interglacial cycles. The coupled changes in climate and the carbon cycle at the transition from the last ice-age to the modern warm period are an important analogue for the present system. Just how sensitive should we expect climate to be to our human carbon emissions? And, in return, how sensitive to the fossil fuel induced climate change will the future carbon cycle be? A better understanding of natural carbon cycle behaviour, during the transition between past ice-ages and warm periods, will help to improve predictions about the future of climate and the carbon cycle. This will, in turn, help to inform us of the likely outcomes of the choices we make regarding fossil fuel emissions.