We introduce a conditional Gaussian framework for data assimilation and prediction of nonlinear turbulent dynamical systems.The talk will include 1)a physics-constrained nonlinear stochastic model in predicting the Madden-Julian oscillation indices with strongly intermittent features,2)data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers,and 3)solving high-dimensional Fokker-Planck equation with highly non-Gaussian features.