Data assimilation and its applications - big data challenge

The objective in data assimilation is generally to find the state of some system. To find the state one can use a model, but the modeled estimate is subject to uncertainties from simplifications and weak assumptions. The model input uncertainties e.g. imperfect forcing data and uncertain model parameters are also an important source of uncertainties. One could also just observe the state using either ground-based observations or remote-sensing. Remote-sensing offers many advantages. Data assimilation is a way to combine models and observations in an optimal way to obtain an estimate of the state that is better than that from models or observations alone. The optimal estimate should be closer to the truth than either the observations or the model. The huge dimension of the numerical models of the climate system, the vast amount of Earth observational data at our disposal, and the pressure to deliver timely accurate forecasts, have motivated an extraordinary research activity that has led to enormous advances which have subsequently spread out to other domains of science. At the same time, geophysical DA is an exemplar of a Big Data problem: models have O(109) and the observational datasets O(108). Computationally efficient state estimation and uncertainty quantification must be carried out using massive datasets and huge dynamical models.