ABSTRACT
Acknowledgments ......................................................................................................................491 References.....................................................................................................................................491
Data assimilation refers to the statistical techniques used to combine numerical and statistical models with observations to give an improved estimate of the state of a system or process. Typically a data assimilation problem has a sequential aspect where data as it becomes available over time is used to update the state or parameters of a dynamical system. Data assimilation is usually distinguished from more traditional statistical time series applications because the system can have complicated nonlinear dynamical behavior and the state vector and the number of observations may be large. One of its primary roles is in
estimating the state of a physical process when applied to geophysical models and physical measurements. Data assimilation has its roots in Bayesian inference and the restriction to linear dynamics and Gaussian distributions fits within the methods associated with the Kalman filter. Because data assimilation also involves estimating an unknown state based on possibly irregular, noisy, or indirect observations, it also has an interpretation as solving an inverse problem (e.g., Tarantola, 1987). One goal of this chapter is to tie these concepts back to a general Bayesian framework.
