99083 - DATA ASSIMILATION FOR DYNAMICAL SYSTEMS

Conoscenze e abilità da conseguire

The course aims at introducing the foundation of dynamical systems theory for ordinary differential equations, with a focus on chaotic dynamics. It will then treat data assimilation, the term used in geoscience to refer to state estimation theory.Data assimilation encompasses the entire sequence of operations that, starting from the observations of a system, and from additional statistical and/or dynamical information (such as an evolution model), provides an estimate of its state. It is common practice in numerical weather prediction, but its application is becoming widespread in many other areas of climate, atmosphere, ocean and environment modelling. The course will provide first the formulation of the problem from a Bayesian perspective and will then present the two popular families of Gaussian based approaches, the Kalman-filter/-smoother and the variational methods. Ensemble based methods will then be considered, starting from the well-known Ensemble Kalman filter, in its stochastic and deterministic formulations, and then the state-of-the-art ensemble-variational methods, as well as particle filters. The course will focus on the specific challenges that data assimilation has encountered to deal with high-dimensional chaotic systems, such as the atmosphere and ocean, and the countermeasures that have been taken and which have driven the recent dramatic development of the field. An overview of the nowadays and near future challenges for the discipline will conclude the course, with a focus on modern supervised machine learning methods and their use in numerical weather predictions and data assimilation.

Contenuti

Outlook on Probability theory and stochastic processes

● The inference problem under a Baysiean framework

○ Representation of the physical and of the observational systems

○ The three estimation problems: Prediction, Filter and Smoother

○ Statistical interpolation

● Linear estimation theory

○ Gauss-Markov Models

○ Observability and controllability

○ Minimum variance formulation - Kalman filter and smoother

○ Maximum a-posteriori formulation - Variational formalism

○ Joint state-parameter estimation

○ Filtering versus smoothing

○ Expectation maximization

● Nonlinear estimation theory: the ensemble Kalman filter and 4DVar

○ Minimum Variance approaches:

● The extended Kalman filter

● The ensemble Kalman filter and smoother

● Stochastic and Deterministic EnKF

● Filter stability and divergence

● Making the EnKF works: Inflation and localization

● Nonlinear least squares

○ Gauss-Newton

○ Adjoint-based minimization

○ 3D- and 4D-Var

○ Hybrid ensemble-variational techniques and other iterative methods

● Fully Bayesian estimation: Particle filters

● Data assimilation and Chaos

● Data assimilation and machine learning similarities and key differences

○ Estimating a model using ML

○ Estimating a model using DA

● Combining DA and ML

Testi/Bibliografia

Gli appunti delle lezioni di ciascun modulo (in inglese) saranno disponibili online.


Gli appunti delle lezioni contengono anche un'ampia bibliografia.


Letture consigliate:

https://wires.onlinelibrary.wiley.com/doi/abs/10.1002/wcc.535

https://epubs.siam.org/doi/book/10.1137/1.9781611974546

Metodi didattici

Le lezioni si svolgono di persona in aula, utilizzando sia diapositive che la lavagna.

Il corso comprende fino a 3 seminari tenuti da scienziati che lavorano sull'assimilazione dei dati o su argomenti correlati.

Modalità di verifica e valutazione dell'apprendimento

La valutazione finale avverrà sotto forma di esame orale (~45 minuti) in cui allo studente verranno poste alcune domande volte a verificare il suo grado di comprensione dei concetti, dei metodi e dei problemi spiegati nel corso.

Strumenti a supporto della didattica

Lavagna, diapositive proiettate e simulazioni al computer.

 

Studenti/sse con DSA o disabilità temporanee o permanenti: si raccomanda di contattare per tempo l’ufficio di Ateneo responsabile (https://site.unibo.it/studenti-con-disabilita-e-dsa/it): sarà sua cura proporre agli/lle studenti/sse interessati/e eventuali adattamenti, che dovranno comunque essere sottoposti, con un anticipo di 15 giorni, all’approvazione del/della docente, che ne valuterà l'opportunità anche in relazione agli obiettivi formativi dell'insegnamento.

Orario di ricevimento

Consulta il sito web di Natale Alberto Carrassi