Mathematics of Data Assimilation

Data assimilation is a sophisticated mathematical technique used to combine observations with model data. The technique can be used to give a best estimate of the state or parameters of a system (and the uncertainty in that estimate). Assimilations may be used to initialize forecasts, or in studies of climate and general circulation, such as in flux calculations. Data assimilation also produces statistics on the fit of observations to model output, which can be used for model validation and assessment of the quality of observing systems. Data assimilation is a well established tool for providing initial conditions for weather forecasting. However, its use in the context of the terrestrial carbon cycle is not as well developed. There are many fundamental theoretical questions that need to be addressed, as well as a skills shortage in this area of earth observation science. One of the goals of this working group has been to develop and make available simple, yet non-trivial, models that can be used to study the salient mathematical features of the data assimilation problems in ways that are readily accessible to graduate students and non-experts.