Sequential Data Assimilation by Nudging

Data assimilation is the process of initializing a forecast (for example a weather forecast) from incomplete observation. We consider a system described by system of differential equations where not all degrees of free-dom are observable, either because this is not practical, as, for example, in the atmosphere where wind speed and temperature information above ground level is expensive to measure, or because these degrees of freedom are fundamentally inaccessible. We also assume that the system of dif-ferential equations is an accurate model of the real physics (leaving aside issues of model uncertainty), and that measured quantities are exact (leav-ing aside measurement errors). Thus, the task is to use the differential equation to determine the complete state at a fixed time from time series data on the accessible degrees of freedom. The simplest possible form of this so-called sequential data assimilation is called nudging or dynamical relaxation—we introduce additional force