This chapter describes a novel approach for the treatment of model error in geophysical data assimilation. In this method, model error is treated as a deterministic process fully correlated in time. This allows for the derivation of the evolution equations for the relevant moments of the model error statistics required in data assimilation procedures, along with an approximation suitable for application to large numerical models typical of environmental science. In this contribution we first derive the equations for the model error dynamics in the general case, and then for the particular situation of parametric error. We show how this deterministic description of the model error can be incorporated in sequential and variational data assimilation procedures. A numerical comparison with standard methods is given using low-order dynamical systems, prototypes of atmospheric circulation, and a realistic soil model. The deterministic approach proves to be very competitive with only minor additional computational cost. Most importantly, it offers a new way to address the problem of accounting for model error in data assimilation that can easily be implemented in systems of increasing complexity and in the context of modern ensemble-based procedures.
A score-based particle flow filter for non-Gaussian data assimilation in high-dimensional chaotic systems
Hohai University（河海大学）；University of Northern British Columbia（北不列颠哥伦比亚大学）；Second Institute of Oceanography, Ministry of Natural Resources（自然资源部第二海洋研究所）
Data assimilation is an increasingly popular technique in Mars atmospheric science, but its effect on the mean states of the underlying atmosphere models has not been thoroughly examined. The robustness of results to the choice of model and assimilation algorithm also warrants further study. We investigate these issues using two Mars general circulation models (MGCMs), with particular emphasis on zonal wind and temperature fields. When temperature retrievals from the Mars Global Surveyor Thermal Emission Spectrometer (TES) are assimilated into the U.K.-Laboratoire de Météorologie Dynamique (UK…
Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the minimum variance linear unbiased estimator. Here, we formulate and implement a multi-model ensemble Kalman filter (MM-EnKF) based on this framework. The MM-EnKF can combine multiple model ensembles for both DA and forecasting in a flow-dependent manner; it uses adaptive model error estimation to provide matrix-valued weights for the separate models and the obse…
Recent years have seen a surge in interest in building deep learning-based fully data-driven models for weather prediction. Such deep learning models if trained on observations can mitigate certain biases in current state-of-the-art weather models, some of which stem from inaccurate representation of subgrid-scale processes. However, these data-driven models, being over-parameterized, require a lot of training data which may not be available from reanalysis (observational data) products. Moreover, an accurate, noise-free, initial condition to start forecasting with a data-driven weather model …
