Data assimilation: Mathematical and statistical perspectives

摘要: The bulk of this paper contains a concise mathematical overview the subject data assimilation, highlighting three primary ideas: (i) standard optimization approaches 3DVAR, 4DVAR and weak constraint are described their interrelations explained; (ii) statistical analogues these then introduced, leading to filtering (generalizing 3DVAR) form smoothing 4DVAR) methods shown be maximum posteriori estimators for probability distributions implied by approaches; (iii) taking general dynamical systems perspective on it is that incorporation Lagrangian can handled straightforward extension preceding concepts. We argue approach based 4DVAR, provides optimal solution assimilation space–time distributed into model. obtained distribution relevant class functions (initial conditions or time-dependent solutions). useful one in first instance because clarifies notion what solution, thereby providing benchmark against which existing evaluated. In longer term also potential new create ensembles solutions model, incorporating available an fashion. Two examples given illustrating both context data, other 4DVAR. former compared with ensemble Kalman filter, inaccurate variety scenarios.