The first challenge addresses the complexity of the data as high dimensionality in space and time quickly leads to bottlenecks in computational resources. This was solved with approximation approaches that analyzed the trade-off between predictive performance and computational demands.
The second task deals with providing a model framework for the CO2 concentrations, that allows for a space-time prediction of the sparse dataset and uses this correlation structure within the data. Spatial modelling captured the space-time dynamics.
The major challenge was to identify the CO2 sources and sinks as well as to find out how much CO2 has been emitted and how much variation in the surface CO2 concentrations relates to terrestrial vegetation or is caused by the population. The complete carbon cycle was integrated in the model framework including seasonally varying vegetation.
In the end, it was possible to quantify CO2 emissions caused by mankind.