Multiscale Methods for Data Assimilation in Turbulent Systems

8 years 12 days ago

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Data assimilation of turbulent signals is an important challenging problem because of the extremely complicated large dimension of the signals and incomplete partial noisy observations which usually mix the large scale mean ﬂow and small scale ﬂuctuations. Due to the limited computing power in the foreseeable future, it is desirable to use multiscale forecast models which are cheap and fast to mitigate the curse of dimensionality in turbulent systems; thus model errors from imperfect forecast models are unavoidable in the development of a data assimilation method in turbulence. Here we propose a suite of multiscale data assimilation methods which use stochastic Superparameterization as the forecast model. Superparameterization is a seamless multiscale method for parameterizing the eﬀect of small scales by cheap local problems embedded in a coarse grid. The key ingredient of the multiscale data assimilation methods is the systematic use of conditional Gaussian mixtures which make ...

Yoonsang Lee, Andrew J. Majda

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