Professor: Pierre Gauthier

**Email:** pierre.gauthier@uqam.ca

**Description**

- Data assimilation and its relationship to the initial value problem of numerical weather prediction.
- Inverse problem: how to
reconstruct
the instantaneous
state of the atmosphere when the number of observations is less than
the
number of degrees of freedom. Regularization based on an
*a priori*estimate, the background state.

- Random variable, probability distribution. Variance, covariance and correlation. Univariate and multivariate linear regression.

- Minimum variance estimate.
- Statistical interpolation algorithm: univariate case.
- Forecast error variance and covariance.
- Impact of the forecast error statistics on the analysis.
- The variational form of statistical interpolation: the 3D-Var.

- Bayes' theorem and generalization of statistical estimation to non-Gaussian error statistics
- Application to the quality control of observations: variational form
- Use of innovations for observation monitoring and estimation of error statistics
- Diagnosing the optimality of an assimilation system: the Chi-square test.

- Embedding of dynamical constraints within the background-error statistics.
- Forward models of observation operators. Observation quality control.

- Sequential estimation algorithm for 4D data assimilation: the Kalman filter.
- Derivation of the basic equations of the Kalman filter.
- Extension to the nonlinear case: the extended Kalman filter, the reduced rank Kalman filter and the ensemble Kalman filter.

- Continuous variational assimilation of observations distributed in time.
- The tangent-linear and adjoint models.
- Implicit dynamical structures of background-error covariances of 4D-Var.
- Singular vectors and their relationship to precursors to dynamical instability.

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John
Hopkins University Press, 476 pages.

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*Numerical
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Cambridge
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University
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theory
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Physics, vol.2, 238 pages.

Tarantola, A., 1987: *Inverse problem theory: methods for data
fitting
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Wunsch, C., 1996: *The ocean circulation inverse problem.*
Cambridge
University Press, 442 pages.

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pages.

Fisher, M., 2001: Assimilation techniques: 3D-VarFisher, M., 2001: Assimilation techniques: 4D-Var

Fisher, M., 2001: Assimilation techniques: Approximate Kalman Filters and Singular Vectors

Bouttier, F. and P. Courtier, 2000: Data assimilation concepts and methods

Järvinen, H., 1998: Observations and diagnostic tools for data assimilation: