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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 24, issue 2
Nonlin. Processes Geophys., 24, 279–291, 2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Nonlin. Processes Geophys., 24, 279–291, 2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

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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Cited articles

Apte, A., Hairer, M., Stuart, A. M., and Voss, J.: Sampling the posterior: An approach to non-Gaussian data assimilation, Physica D, 230, 50–64,, 2007.
Atkinson, P. M. and Tate, N. J.: Spatial scale problems and geostatistical solutions: a review, Prof. Geogr., 52, 607–623,, 2000.
Bartle, R. G.: The Elements of Integration and Lebesgue Measure, Wiley, New York, 1995.
Billingsley, P.: Probability and Measure, 2nd Edn., John Wiley & Sons, New York, 1986.
Bocquet, M., Pires, C. A., and Wu, L.: Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation, Mon. Weather Rev., 138, 2997–3023,, 2010.
Publications Copernicus
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.
This is the first mathematical definitions of the spatial scale and its transformation based on...