Hybrid DA Method with Stochastic Parameterized Models and Machine Learning
REFERENCE: Mou, C., Smith, L. M., & Chen, N. (2023). Combining Stochastic Parameterized Reduced-Order Models with Machine Learning for Data Assimilation and Uncertainty Quantification with Partial Observations. Journal of Advances in Modeling Earth Systems, 15(10), e2022MS003597.
Figure. A schematic illustration of the hybrid data assimilation method.
The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning model that builds a nonlinear map between the coefficients of observed and unobserved state variables for each spectral mode. In particular, a cheap low-order nonlinear stochastic surrogate model, i.e., stochastic parameterized extended Kalman filter (SPEKF) model, is employed as the forecast model in the ensemble Kalman filter to deal with each mode associated with the observed variables. The resulting ensemble members are then fed into the machine learning model to create an ensemble of the corresponding unobserved variables. In addition to the ensemble spread, the training residual in the machine learning-induced nonlinear map is further incorporated into the state estimation, advancing the the posterior uncertainty quantification by Gaussian mixtures.
We test this method using the precipitation Quasi-geostrophic equations(PQG) which includes the effects of water vapor, clouds, and rainfall beyond the classical two-level QG model. In a figure below, numerical results show upper-level zonally averaged wind over time for both truth and filter (hybrid method). The reconstructed velocity field accurately captures zonal jet locations and northward jet propagation.
Figure. Truth (top) and filter (bottom), recovered time evolution of the zonally averaged zonal wind at the top level of atmosphere