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Abstract State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface observations. Directly implementing an ensemble Kalman filter based on the full forecast model is usually expensive. One widely used method in practice projects the information of the observed layer to other layers via linear regression. However, large errors appear when nonlinearity in the highly turbulent flow field becomes dominant. In this paper, we develop a multi-step nonlinear data assimilation method that involves the sequential application of nonlinear assimilation steps across layers. Unlike traditional linear regression approaches, a conditional Gaussian nonlinear system is adopted as the approximate forecast model to characterize the nonlinear dependence between adjacent layers. At each step, samples drawn from the posterior of the current layer are treated as pseudo-observations for the next layer. Each sample is assimilated using analytic formulae for the posterior mean and covariance. The resulting Gaussian posteriors are then aggregated into a Gaussian mixture. Therefore, the method can capture strongly turbulent features, particularly intermittency and extreme events, and more accurately quantify the inherent uncertainty. Applications to the two-layer quasi-geostrophic system with Lagrangian data assimilation demonstrate that the multi-step method outperforms the one-step method, particularly as the tracer number and ensemble size increase. Results also show that the multi-step CGDA is particularly effective for assimilating frequent, high-accuracy observations, which are scenarios where traditional EnKF methods may suffer from catastrophic filter divergence.
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Data Assimilation of High‐Latitude Electric Fields: Extension of a Multi‐Resolution Gaussian Process Model (Lattice Kriging) to Vector Fields
Abstract We develop a new methodology for the multi‐resolution assimilation of electric fields by extending a Gaussian process model (Lattice Kriging) used for scalar field originally to vector field. This method takes the background empirical model as “a priori” knowledge and fuses real observations under the Gaussian process framework. The comparison of assimilated results under two different background models and three different resolutions suggests that (a) the new method significantly reduces fitting errors compared with the global spherical harmonic fitting (SHF) because it uses range‐limited basis functions ideal for the local fitting and (b) the fitting resolution, determined by the number of basis functions, is adjustable and higher resolution leads to smaller errors, indicating that more structures in the data are captured. We also test the sensitivity of the fitting results to the total amount of input data: (a) as the data amount increases, the fitting results deviate from the background model and become more determined by data and (b) the impacts of data can reach remote regions with no data available. The assimilation also better captures short‐period variations in local PFISR measurements than the SHF and maintains a coherent pattern with the surrounding. The multi‐resolution Lattice Kriging is examined via attributing basis functions into multiple levels with different resolutions (fine level is located in the region with observations). Such multi‐resolution fitting has the smallest error and shortest computation time, making the regional high‐resolution modeling efficient. Our method can be modified to achieve the multi‐resolution assimilation for other vector fields from unevenly distributed observations.
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- PAR ID:
- 10375494
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Space Weather
- Volume:
- 20
- Issue:
- 1
- ISSN:
- 1542-7390
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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