To what extent is your data assimilation scheme designed to find the posterior mean, the posterior mode or something else?
Recently there has been a surge in interest in coupling ensemble-based data assimilation methods with variational methods (commonly referred to as 4DVar). Here we discuss a number of important differences between ensemble-based and variational methods that ought to be considered when attempting to f...
Main Authors: | , , |
---|---|
Other Authors: | |
Language: | en |
Published: |
CO-ACTION PUBLISHING
2016
|
Subjects: | |
Online Access: | http://hdl.handle.net/10150/621807 http://arizona.openrepository.com/arizona/handle/10150/621807 |
id |
ndltd-arizona.edu-oai-arizona.openrepository.com-10150-621807 |
---|---|
record_format |
oai_dc |
spelling |
ndltd-arizona.edu-oai-arizona.openrepository.com-10150-6218072016-12-23T03:00:31Z To what extent is your data assimilation scheme designed to find the posterior mean, the posterior mode or something else? Hodyss, Daniel Bishop, Craig H. Morzfeld, Matthias Univ Arizona, Dept Math data assimilation ensemble methods variational methods Recently there has been a surge in interest in coupling ensemble-based data assimilation methods with variational methods (commonly referred to as 4DVar). Here we discuss a number of important differences between ensemble-based and variational methods that ought to be considered when attempting to fuse these methods. We note that the Best Linear Unbiased Estimate (BLUE) of the posterior mean over a data assimilation window can only be delivered by data assimilation schemes that utilise the 4-dimensional (4D) forecast covariance of a prior distribution of non-linear forecasts across the data assimilation window. An ensemble Kalman smoother (EnKS) may be viewed as a BLUE approximating data assimilation scheme. In contrast, we use the dual form of 4DVar to show that the most likely non-linear trajectory corresponding to the posterior mode across a data assimilation window can only be delivered by data assimilation schemes that create counterparts of the 4D prior forecast covariance using a tangent linear model. Since 4DVar schemes have the required structural framework to identify posterior modes, in contrast to the EnKS, they may be viewed as mode approximating data assimilation schemes. Hence, when aspects of the EnKS and 4DVar data assimilation schemes are blended together in a hybrid, one would like to be able to understand how such changes would affect the mode-or mean-finding abilities of the data assimilation schemes. This article helps build such understanding using a series of simple examples. We argue that this understanding has important implications to both the interpretation of the hybrid state estimates and to their design. 2016-09-30 Article To what extent is your data assimilation scheme designed to find the posterior mean, the posterior mode or something else? 2016, 68 (0) Tellus A 1600-0870 0280-6495 10.3402/tellusa.v68.30625 http://hdl.handle.net/10150/621807 http://arizona.openrepository.com/arizona/handle/10150/621807 TELLUS A- DYNAMIC METEOROLOGY AND OCEANOGRAPHY en http://www.tellusa.net/index.php/tellusa/article/view/30625 © 2016 D. Hodyss et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License. CO-ACTION PUBLISHING |
collection |
NDLTD |
language |
en |
sources |
NDLTD |
topic |
data assimilation ensemble methods variational methods |
spellingShingle |
data assimilation ensemble methods variational methods Hodyss, Daniel Bishop, Craig H. Morzfeld, Matthias To what extent is your data assimilation scheme designed to find the posterior mean, the posterior mode or something else? |
description |
Recently there has been a surge in interest in coupling ensemble-based data assimilation methods with variational methods (commonly referred to as 4DVar). Here we discuss a number of important differences between ensemble-based and variational methods that ought to be considered when attempting to fuse these methods. We note that the Best Linear Unbiased Estimate (BLUE) of the posterior mean over a data assimilation window can only be delivered by data assimilation schemes that utilise the 4-dimensional (4D) forecast covariance of a prior distribution of non-linear forecasts across the data assimilation window. An ensemble Kalman smoother (EnKS) may be viewed as a BLUE approximating data assimilation scheme. In contrast, we use the dual form of 4DVar to show that the most likely non-linear trajectory corresponding to the posterior mode across a data assimilation window can only be delivered by data assimilation schemes that create counterparts of the 4D prior forecast covariance using a tangent linear model. Since 4DVar schemes have the required structural framework to identify posterior modes, in contrast to the EnKS, they may be viewed as mode approximating data assimilation schemes. Hence, when aspects of the EnKS and 4DVar data assimilation schemes are blended together in a hybrid, one would like to be able to understand how such changes would affect the mode-or mean-finding abilities of the data assimilation schemes. This article helps build such understanding using a series of simple examples. We argue that this understanding has important implications to both the interpretation of the hybrid state estimates and to their design. |
author2 |
Univ Arizona, Dept Math |
author_facet |
Univ Arizona, Dept Math Hodyss, Daniel Bishop, Craig H. Morzfeld, Matthias |
author |
Hodyss, Daniel Bishop, Craig H. Morzfeld, Matthias |
author_sort |
Hodyss, Daniel |
title |
To what extent is your data assimilation scheme designed to find the posterior mean, the posterior mode or something else? |
title_short |
To what extent is your data assimilation scheme designed to find the posterior mean, the posterior mode or something else? |
title_full |
To what extent is your data assimilation scheme designed to find the posterior mean, the posterior mode or something else? |
title_fullStr |
To what extent is your data assimilation scheme designed to find the posterior mean, the posterior mode or something else? |
title_full_unstemmed |
To what extent is your data assimilation scheme designed to find the posterior mean, the posterior mode or something else? |
title_sort |
to what extent is your data assimilation scheme designed to find the posterior mean, the posterior mode or something else? |
publisher |
CO-ACTION PUBLISHING |
publishDate |
2016 |
url |
http://hdl.handle.net/10150/621807 http://arizona.openrepository.com/arizona/handle/10150/621807 |
work_keys_str_mv |
AT hodyssdaniel towhatextentisyourdataassimilationschemedesignedtofindtheposteriormeantheposteriormodeorsomethingelse AT bishopcraigh towhatextentisyourdataassimilationschemedesignedtofindtheposteriormeantheposteriormodeorsomethingelse AT morzfeldmatthias towhatextentisyourdataassimilationschemedesignedtofindtheposteriormeantheposteriormodeorsomethingelse |
_version_ |
1718405575170064384 |