Abstract
We are receiving lot of observations day to day from different platforms such as upper air, surface stations and remote sensing instruments. The difficulty is to use these data, which are sometimes conflicting, to find a best estimate of the state of the earth system which will be used for diverse applications. But we need to ensure that a time sequence of these estimated states is consistent with any known equations that govern the evolution of the system. The method to achieve this goal is known as data assimilation (Mathieu and O’Neill, 2008).
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Notes
- 1.
Since J in Eq. (11) is a quadratic function of the analysis increment (x - x b ), for a given generalized quadratic function F
$$ F(x)={\scriptscriptstyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{x}^T\kern0.5em Ax+{d}^T\kern0.5em x+c, $$(A)we have
$$ \nabla F(x)= Ax+d $$(B)and
$$ \nabla \left({d}^Tx\right)=\nabla \left({x}^Td\right)=d. $$(C)
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Routray, A., Osuri, K.K., Pattanayak, S., Mohanty, U.C. (2016). Introduction to Data Assimilation Techniques and Ensemble Kalman Filter. In: Mohanty, U.C., Gopalakrishnan, S.G. (eds) Advanced Numerical Modeling and Data Assimilation Techniques for Tropical Cyclone Prediction. Springer, Dordrecht. https://doi.org/10.5822/978-94-024-0896-6_11
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