Introduction to data assimilation
Data assimilation is about the combination of two sources of information - computational models and observations - to utilize both of their strengths and compensate for their weaknesses.
Computational models are available nowadays for a wide range of applications: weather prediction, environmental management, oil exploration, traffic management and so on. They use knowledge of different aspects of reality, e.g. laws of physics, empirical relations, human behavior, etc., to construct a sequence of computational steps, by which simulations of different aspects of reality can be made.
The strengths of computational models are the ability to describe/forecast future situations (also to explore what-if scenarios), in a large amount of spatial and temporal detail. For instance, weather forecasts are run at ECMWF using a horizontal resolution of about 50 km for the entire earth and a time step of 12 minutes. This is achieved with the tremendous computing power of modern-day computers, and with carefully-designed numerical algorithms.
However, computations are worthless if the system is not initialized properly: “Garbage in, garbage out”. Furthermore, the “state” of a computational model may deviate from reality more and more while running, because of inaccuracies in the model, aspects that are not considered or not modeled well, inappropriate parameter settings and so on. Observations or measurements are generally considered to be more accurate than model results. They always concern the true state of the physical system under consideration. On the other hand, the number of observations is often limited in both space and time.
The idea of data assimilation is to combine a model and observations, and optimally use the information contained in them.
Some theory that might be helpful to understand the basics of data assimilation includes the distinction between offline and online methods, the statistical framework used, the notions of deterministic and stochastic models, noise models, the combination of values (weights are needed), data assimilation on top of an existing model, and the general structure of filtering methods.
An open-source text book considering the fundamentals of data assimilation can be found here.