Nonlinear Processes in Geophysics
Nonlinear Processes in Geophysics
NPG
Articles | Volume 24, issue 2
Articles | Volume 24, issue 2
https://doi.org/10.5194/npg-24-279-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/npg-24-279-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Articles | Volume 24, issue 2
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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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.
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