Organizers:

Head: Illia Horenko (Università della Svizzera italiana, Switzerland) and Sebastian Reich (University of Potsdam, Germany)

Co-ordination: Thomas von Larcher (Freie Universitaet Berlin, Germany, larcher@math.fu-berlin.de)

Administration: Ulrike Eickers and Sarah Jaeger (Freie Universitaet Berlin, Germany, +49-(0)30-838-75415, eickers@math.fu-berlin.de, sjaeg@zedat.fu-berlin.de)
Scope
Due to a rapid development of measurement instruments and techniques, as well as due to the growing complexity of simulation model outputs, adequate and efficient assessment of information hidden in experimental and simulation data plays increasingly important role in all areas of fluid mechanics, meteorology and climate research.

The main focus of the summer school will be on providing a necessary theoretical and practical background for understanding and proper usage of the modern methods of time series analysis and data assimilation.

Further emphasize will be placed on explaining essential mathematical and statistical concepts, accompanied by computer exercises demonstrating their application to meteorological, climatological and fluid-mechanical problems. Participants should have a basic knowledge of linear algebra, analysis and elementary concepts from probability theory (e.g., properties of probability, probability distribution, expectation value and variance). Computer exercises will be based on MATLAB, participants will need to use their own LapTops and to have an installed version of MATLAB on them.

Program:For the daily program, see below.

Venue:Harnack-Haus, Ihnestrasse 16, 14195 Berlin, Germany, http://www.harnackhaus-berlin.mpg.de/

Accomodation: Accomodation is self-organized by participants.

Registration: To register, please send an E-Mail including your name and affiliation to the administration (Ulrike Eickers and Sarah Jaeger). The Deadline for registration is 2 May.

Fees: The workshop is free of charge. This also includes Coffee Breaks and Lunch Buffets. Accomodation costs are to be borne by the participants.

In case questions arise, please do not hesitate to contact the organizers.

Program

• Monday, 04. June 2012
– Morning session (I. Horenko): standard methods of statistical data analysis (Gaussian
statistics, PCA/EOFs and spectral methods, statistical regression), stationary
VARX-processes, Log-Likelihood-concept and approaches of parameter estimation,
concept of ill-posedness, regularization strategies (Tykhonov regularization and regularized
spline interpolation), some examples (from meteorology and climate).
– Afternoon session: hands-on software training.
• Tuesday, 05. June 2012
– Morning session (I. Horenko): mathematical derivation of the statistical entropy,
Occam’s principle and derivation of the Akaike Information Criterium for statistical
model discrimination, Bayes theorem and its implications, Bayesian Information
Criterium (with derivation and implications).
– Afternoon session: hands-on software training.

• Wednesday, 06. June 2012
– Morning session (I. Horenko): foundations of discrete processes (Bernoulli-, Markovprocesses
and their properties). Concepts of master equation and Fokker-Planck
equation, spectral theory of discrete processes on the basis of the master equation,
parameter estimation for discrete processes, standard methods (generalised linear
models, logit regression, artificial neural networks). Application to cloud physics as
an example.
– Afternoon session: hands-on software training.

• Thursday, 07. June 2012
– Morning session (I. Horenko): non-stationary and non-homogenous statistical methods,
Finite-Element-Methods of data analysis with Bounded Variation of the model
parameters (FEM-BV), examples from meteorology and climate research.
– Afternoon session (S. Reich): introduction to the basic concepts of data assimilation,
recursive Bayes-formula, 3D-VAR, 4D-VAR and their connection to the Tykhonovregularization.
– Afternoon session: hands-on software training.

• Friday, 08. June 2012
– Morning session (S. Reich): Ensemble Kalman-filtering, Markov Chain Monte Carlo
and beyond.