Identification

Title

Exact nonlinear state estimation

Abstract

The majority of data assimilation (DA) methods in the geosciences are based on Gaussian assumptions. While such approximations facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Nonparametric, particle-based DA algorithms have superior accuracy, but their application to high-dimensional models still poses operational challenges. Drawing inspiration from recent advances in the fields of measure transport and generative artificial intelligence, this paper develops a new estimation-theoretic framework which can incorporate general invertible transformations in a principled way. Specifically, a conjugate transform filter (CTF) is derived and shown to extend the celebrated Kalman filter to a much broader class of non-Gaussian distributions. The new filter has several desirable properties, such as its ability to preserve statistical relationships in the prior state and converge to highly accurate observations. An ensemble approximation of the new filtering framework is also presented and validated through idealized examples. The numerical demonstrations feature bounded quantities with non-Gaussian distributions, which is a typical challenge in Earth system models. Results suggest that the greatest benefits from the new filtering framework occur when the observation errors are small relative to the forecast uncertainty and when state variables exhibit strong nonlinear dependencies.

Resource type

document

Resource locator

Unique resource identifier

code

https://n2t.net/ark:/85065/d7bz6bgk

codeSpace

Dataset language

eng

Spatial reference system

code identifying the spatial reference system

Classification of spatial data and services

Topic category

geoscientificInformation

Keywords

Keyword set

keyword value

Text

originating controlled vocabulary

title

Resource Type

reference date

date type

publication

effective date

2016-01-01T00:00:00Z

Geographic location

West bounding longitude

East bounding longitude

North bounding latitude

South bounding latitude

Temporal reference

Temporal extent

Begin position

End position

Dataset reference date

date type

publication

effective date

2025-04-01T00:00:00Z

Frequency of update

Quality and validity

Lineage

Conformity

Data format

name of format

version of format

Constraints related to access and use

Constraint set

Use constraints

Limitations on public access

None

Responsible organisations

Responsible party

contact position

OpenSky Support

organisation name

UCAR/NCAR - Library

full postal address

PO Box 3000

Boulder

80307-3000

email address

opensky@ucar.edu

web address

http://opensky.ucar.edu/

name: homepage

responsible party role

pointOfContact

Metadata on metadata

Metadata point of contact