Asimilacija podataka s primjenama

master's thesis

• Title (english): Data assimilation with applications
• Author: Iskra Gašparić
• Mentor: Zlatko Drmač (mentor)
• Committee member: Zlatko Drmač (predsjednik povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Asimilacija podataka je skup matematičkih metoda usklađivanja modela s podacima. Metode obuhvaćene ovim radom mogu se podijeliti u dvije kategorije: varijacijske te sekvencijalne. Varijacijske metode minimiziraju funkciju cilja koja mjeri točnost predikcije u odnosu na model i opažanja, unutar određenog vremenskog intervala. Dva najpoznatija algoritma su 4D-Var algoritam te 3D-Var kao njegov poseban slučaj. Inkrementalni 4D-Var algoritam umjesto nelinearne funkcije cilja minimizira niz linearnih konveksnih funkcija. Sekvencijalne metode asimilacije podataka opažanja uvažavaju čim ona postanu dostupna. Jedan takav algoritam je Kalmanov filter, u kojem se pretpostavlja da su operatori korišteni u definiciji modela linearni, a greške normalno distribuirane. Ovo ograničenje rješava se u Extended Kalman filter algoritmu koji za neke korake koristi linearizaciju opratora. Osim toga, zbog numeričkih performansi, matrice korištene u metodi mogu se aproksimirati matricama manjeg ranga te tako dolazimo do sasvim novog skupa metoda. U ovom radu predstavljena je i na praktičnim primjerima ilustrirana samo nekolicina iz ogromnog skupa algoritama za asimilaciju podataka.

Abstract (english)

Data assimilation is a group of mathematical methods aimed at adjusting a model of interest with available data. The methods covered in this thesis can be divided into two categories: variational and sequential methods. Variational methods minimize the cost function that measures the accuracy of the prediction compared to the model and observations, in a specified time interval. Two most commonly used algorithms are 4D-Var algorithm and 3D-Var as its special case. Incremental 4D-Var algorithm minimizes a sequence of linear convex cost functions, instead of a nonlinear one as in 4D-Var. Sequential methods for data assimilation make use of observations as soon as they become available. One such sequential algorithm is the Kalman filter, in which the operators used in the model definition are assumed to be linear, and errors are assumed to be normally distributed. These limitations are dropped in Extended Kalman filter algorithm which uses linearizations of those operators for some steps. Furthermore, the matrices used in the method can be replaced by their low-rank approximations, for better numerical performance. That leads to a completely new set of methods. In this thesis only a small part of a rather large set of algorithms for data assimilation is introduced and illustrated on practical examples.

• Keywords: varijacijske metode asimilacije podataka; 4D-Var algoritam; 3D-Var algoritam; sekvencijalne metode asimilacije podataka; Kalmanov filter; Extended Kalman filter algoritam
• Keywords (english): variational methods for data assimilation; 4D-Var algorithm; 3D-Var algorithm; sequential methods for data assimilation; Kalman filter; Extended Kalman filter algorithm
• Language: croatian
• URN:NBN: urn:nbn:hr:217:135190
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-11-10 10:25:36