Articles | Volume 24, issue 2
https://doi.org/10.5194/npg-24-279-2017
https://doi.org/10.5194/npg-24-279-2017
Research article
 | 
15 Jun 2017
Research article |  | 15 Jun 2017

Formulation of scale transformation in a stochastic data assimilation framework

Feng Liu and Xin Li

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Interactive discussion

Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
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Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision
AR by Feng LIU on behalf of the Authors (30 Oct 2016)  Manuscript 
ED: Referee Nomination & Report Request started (01 Nov 2016) by Olivier Talagrand
RR by Peter Jan van Leeuwen (20 Nov 2016)
RR by Anonymous Referee #1 (24 Nov 2016)
ED: Reconsider after major revisions (further review by Editor and Referees) (28 Nov 2016) by Olivier Talagrand
AR by Feng LIU on behalf of the Authors (27 Jan 2017)  Author's response 
ED: Referee Nomination & Report Request started (01 Feb 2017) by Olivier Talagrand
RR by Anonymous Referee #1 (14 Feb 2017)
RR by Peter Jan van Leeuwen (19 Feb 2017)
ED: Publish subject to minor revisions (further review by Editor) (22 Feb 2017) by Olivier Talagrand
AR by Feng LIU on behalf of the Authors (14 Mar 2017)  Author's response   Manuscript 
ED: Publish subject to minor revisions (further review by Editor) (10 Apr 2017) by Olivier Talagrand
AR by Feng LIU on behalf of the Authors (20 Apr 2017)  Author's response   Manuscript 
ED: Publish subject to technical corrections (03 May 2017) by Olivier Talagrand
AR by Feng LIU on behalf of the Authors (11 May 2017)  Author's response   Manuscript 
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Short summary
This is the first mathematical definitions of the spatial scale and its transformation based on Lebesgue measure. An Ito process-formed geophysical variable with respect to scale was also provided. The stochastic calculus for data assimilation discovered the new expressions of error caused by spatial scale transformation. The results improve the ability to understand the spatial scale transformation and related uncertainties in Earth observation, modelling and data assimilation.