Observations provided by satellites and field campaigns, numerical models, and climatologies by amassed statistical data: there is a wide variety of methods to improve our understanding of an atmospheric system, each of which highlighting special aspects. In view of all their specific advantages and weaknesses, is it possible to combine all this information in a way which exhibits us a most likely system state and its temporal evolution? Or, alternatively, are we able to identify, to what extent our system knowledge is incomplete or impertinent?
To this end, advanced data assimilation and inverse modelling algorithms are designed to exploit three different sources of information:
Combining these components information about the system in a mathematically rigorous way, an enhanced scientific value can be extracted from the output of expensively developed satellites and work intense measurement campaigns.
There are presently two methods, which are theoretically able to provide a requested ``Best Linear Unbiased Estimate'' (BLUE) of a system state, while making use of all available information: the 4-dimensional variational data assimilation (4D-var) method, and Kalman-filtering (-smoothing). While the latter is computationally only feasible with a massively reduced complexity, all approaches at RIU/EURAD are following the 4D-var method. However, this approach requires the development and coding of the adjoint code of the numerical model. In recompense, a smoothed model trajectory is given, which, after introduction of proper error covariances, fulfills the requirements of providing a BLUE. Thanks to this property, 4D-var also allows for an a posteriori evaluation of the analysis quality.
Despite the high demands in both, development and computational efforts, advanced space-time data assimilation algorithms provide a unique level of detail in analysing partly observed atmospheric systems.