An official website of the United States government
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.
more »
« less
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.
more »
« less
- 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
More Like this
-
-
Abstract Mountain winds are the driving force behind snow accumulation patterns in mountainous catchments, making accurate wind fields a prerequisite to accurate simulations of snow depth for ecological or water resource applications. In this study, we examine the effect that wind fields derived from different coarse data sets and downscaling schemes has on simulations of modeled snow depth at resolutions suitable for basin‐scale modeling (>50 m). Simulations are run over the Tuolumne River Basin, CA for the accumulation season of Water Year 2017 using the distributed snow model, SnowModel. We derived wind fields using observations from either sensor networks, the North American Land Data Assimilation System (12.5 km resolution), or High‐Resolution Rapid Refresh (HRRR, 3 km resolution) data, and downscaled using terrain‐based multipliers (MicroMet), a mass‐conserving flow model (WindNinja), or bilinear interpolation. Two wind fields derived from 3 km HRRR data and downscaled with respect to terrain produced snow depth maps that best matched observations of snow depth from airborne LiDAR. We find that modeling these wind fields at 100 and 50 m resolutions do not produce improvements in simulated snow depth when compared to wind fields modeled at a 150 m resolution due to their inability to represent wind dynamics at these scales. For input to distributed snow models at the basin‐scale, we recommend deriving wind fields from high resolution numerical weather prediction model output and downscaling with respect to terrain. Future studies should compare suspension schemes used in blowing snow models and investigate wind downscaling schemes of complexity between statistical and fluid dynamic models.more » « less
-
We present a non‐Gaussian ensemble data assimilation method based on the maximum‐likelihood ensemble filter, which allows for any combination of Gaussian, lognormal, and reverse lognormal errors in both the background and the observations. The technique is fully nonlinear, does not require a tangent linear model, and uses a Hessian preconditioner to minimise the cost function efficiently in ensemble space. When the Gaussian assumption is relaxed, the results show significant improvements in the analysis skill within two atmospheric toy models, and the performance of data assimilation systems for (semi)bounded variables is expected to improve.more » « less
-
null (Ed.)Abstract. In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Euclidean distance used in classic data assimilation methodologies, the Wasserstein metric can capture the translation and difference between the shapes of square-integrable probability distributions of the background state and observations. This enables us to formally penalize geophysical biases in state space with non-Gaussian distributions. The new approach is applied to dissipative and chaotic evolutionary dynamics, and its potential advantages and limitations are highlighted compared to the classic ensemble data assimilation approaches under systematic errors.more » « less
-
Abstract. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through the inclusion of cross-domain terms in the background error covariance matrix.When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work, we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari–Cohn localization function; the within-component localization functions are standard Gaspari–Cohn with different localization radii, while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices which are suitable for use in both Kalman filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz 96 system. In our experiments, the multivariate Gaspari–Cohn function leads to better performance than any of the other multivariate localization functions.more » « less
