Model Error In Data Assimilation Research Articles

Using machine learning to correct model error in data assimilation and forecast applications

AbstractThe idea of using machine learning (ML) methods to reconstruct the dynamics of a system is the topic of recent studies in the geosciences, in which the key output is a surrogate model meant to emulate the dynamical model. In order to treat sparse and noisy observations in a rigorous way, ML can be combined with data assimilation (DA). This yields a class of iterative methods in which, at each iteration, a DA step assimilates the observations and alternates with a ML step to learn the underlying dynamics of the DA analysis. In this article, we propose to use this method to correct the error of an existing, knowledge‐based model. In practice, the resulting surrogate model is a hybrid model between the original (knowledge‐based) model and the ML model. We demonstrate the feasibility of the method numerically using a two‐layer, two‐dimensional, quasi‐geostrophic channel model. Model error is introduced by the means of perturbed parameters. The DA step is performed using the strong‐constraint 4D‐Var algorithm, while the ML step is performed using deep learning tools. The ML models are able to learn a substantial part of the model error and the resulting hybrid surrogate models produce better short‐ to mid‐range forecasts. Furthermore, using the hybrid surrogate models for DA yields a significantly better analysis than using the original model.

Correcting observation model error in data assimilation.

Standard methods of data assimilation assume prior knowledge of a model that describes the system dynamics and an observation function that maps the model state to a predicted output. An accurate mapping from model state to observation space is crucial in filtering schemes when adjusting the estimate of the system state during the filter's analysis step. However, in many applications, the true observation function may be unknown and the available observation model may have significant errors, resulting in a suboptimal state estimate. We propose a method for observation model error correction within the filtering framework. The procedure involves an alternating minimization algorithm used to iteratively update a given observation function to increase consistency with the model and prior observations using ideas from attractor reconstruction. The method is demonstrated on the Lorenz 1963 and Lorenz 1996 models and on a single-column radiative transfer model with multicloud parameterization.

Data Assimilation in a Multi-Scale Model

AbstractData assimilation for multi-scale models is an important contemporary research topic. Especially the role of unresolved scales and model error in data assimilation needs to be systematically addressed. Here we examine these issues using the Ensemble Kalman filter (EnKF) with the two-level Lorenz-96 model as a conceptual prototype model of the multi-scale climate system. We use stochastic parameterization schemes to mitigate the model errors from the unresolved scales. Our results indicate that a third-order autoregressive process performs better than a first-order autoregressive process in the stochastic parameterization schemes, especially for the system with a large time-scale separation.Model errors can also arise from imprecise model parameters. We find that the accuracy of the analysis (an optimal estimate of a model state) is linearly correlated to the forcing error in the Lorenz-96 model. Furthermore, we propose novel observation strategies to deal with the fact that the dimension of the observations is much smaller than the model states. We also propose a new analog method to increase the size of the ensemble when its size is too small.

Correcting Biased Observation Model Error in Data Assimilation

While the formulation of most data assimilation schemes assumes an unbiased observation model error, in real applications model error with nontrivial biases is unavoidable. A practical example is errors in the radiative transfer model (which is used to assimilate satellite measurements) in the presence of clouds. Together with the dynamical model error, the result is that many (in fact 99%) of the cloudy observed measurements are not being used although they may contain useful information. This paper presents a novel nonparametric Bayesian scheme that is able to learn the observation model error distribution and correct the bias in incoming observations. This scheme can be used in tandem with any data assimilation forecasting system. The proposed model error estimator uses nonparametric likelihood functions constructed with data-driven basis functions based on the theory of kernel embeddings of conditional distributions developed in the machine learning community. Numerically, positive results are shown with two examples. The first example is designed to produce a bimodality in the observation model error (typical of “cloudy” observations) by introducing obstructions to the observations that occur randomly in space and time. The second example, which is physically more realistic, is to assimilate cloudy satellite brightness temperature–like quantities, generated from a stochastic multicloud model for tropical convection and a simple radiative transfer model.