By Seon Ki Park, Liang Xu
This booklet includes the latest growth in information assimilation in meteorology, oceanography and hydrology together with land floor. It spans either theoretical and applicative features with a number of methodologies reminiscent of variational, Kalman filter out, ensemble, Monte Carlo and synthetic intelligence equipment. along with info assimilation, different vital subject matters also are coated together with focusing on remark, sensitivity research, and parameter estimation. The e-book can be precious to person researchers in addition to graduate scholars for a reference within the box of knowledge assimilation.
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Extra resources for Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. III)
34) The control of both errors of model and of data can be carried out simultaneously if a model of observation error were added. 4 Example: Saint-Venant’s Equations Saint-Venant’s equations, also known as shallow water equations, are used for an incompressible ﬂuid for which the depth is small with respect to the horizontal dimensions. General equations of geophysical ﬂuid dynamics are vertically integrated using the hydrostatic hypothesis, therefore vertical acceleration is neglected. 37) In this system X = (u, v, ????)T is the state variable, u and v are the components of the horizontal velocity; ???? is the geopotential (proportional to the height of the free surface) and f the Coriolis’ parameter.
Introducing sparsity of data in time using variational tools has led to 4-D data assimilation for numerical weather prediction models. To perform a forecast a meteorological model requires an initial condition. This initial condition must be as close as possible to the observations while remaining compatible with the model. The problem of initialization may be stated as a variational problem and solved in this way. A general formalism of variational problems has to deal with observations but these observations may not necessarily be physical ones.
The last section will be devoted to future developments and potential applications of variational methods in meteorology. 1 Definition of a Variational Method In the most condensed way a variational method may be deﬁned as a search, amongst all the possible solutions of a model, of the solution closest to a given observation. -X. Le Dimet et al. ∙ An atmospheric variable X, describing the state of the atmosphere. 1) where A is a linear or non-linear operator. 1) some additional information has to be provided.
Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. III) by Seon Ki Park, Liang Xu