Title Primjena analize empirijskih ortogonalnih funkcija na određivanje nestacionarnosti vremenskih nizova Title (english) Implementation of the empirical orthogonal functions analysis to determine nonstationarity of time series Author Valentino Neduhal Mentor Željko Večenaj (mentor)Committee member Željko Večenaj (predsjednik povjerenstva)Committee member Branko Grisogono (član povjerenstva)Committee member Ivica Sović (član povjerenstva)Committee member Maja Telišman Prtenjak (član povjerenstva)Committee member Josip Stipčević (član povjerenstva)Granter University of Zagreb Defense date and country 2020-07-17, Croatia Scientific / art field, NATURAL SCIENCES Abstract Statistička stacionarnost je vrlo važan koncept u statističkoj teoriji turbulencije. Parametrizacije površinskog sloja, koje povezuju turbulentne tokove s gradijentima srednje vrijednosti preko Monin-Obukovljeve teorije sličnosti, pretpostavljaju stacionarnost turbulentnog procesa. U literaturi ne postoji konsenzus o jedinstvenom kriteriju na temelju kojeg bi odredili da li je vremenski niz (realizacija procesa) stacionaran ili nestacionaran, no postoji mnogo metoda razvijenih na temelju različitih pretpostavki. To ostavlja prostora za dodatna istraživanja na tom području dajući upravo i motivaciju ovog rada. Metoda empirijskih ortogonalnih funkcija (EOF) omogućuje dekompoziciju vremenskog niza na svojstvene ortogonalne modove. Rezultat primjene EOF analize na vremenski niz je matrica čiji je svaki stupac jedna ortogonalna funkcija (matricu tih funkcija također nazivamo EOF) i matrica čiji je svaki stupac jedna glavna komponenta (matricu glavnih komponenti nazivamo PC). Množenjem n-tog stupca matrice EOF i n-tog stupca matrice PC dobiva se n-ti mod EOF dekompozicije vremenskog niza. Također, moguće je odrediti udio svakog moda u varijabilnosti početnog niza. Kako bi prepoznali na koji način EOF analiza reagira na nestacionarnost unutar nizova, primijenjena je u tri koraka na četiri različita tipa vremenskih nizova. U trećem koraku, EOF analiza je primijenjena na realnim vremenskim nizovima. Oni su dobiveni mjerenjima brzina vjetra i sonične temperature na tornju blizu Masleničkog mosta, sjeverno od Zadra u razdoblju od 9. listopada 2015. do 9. listopada 2016. za vrijeme epizoda bure. Na temelju rezultata tih primjena doneseno je nekoliko važnih zaključaka. Najvažniji od njih je da EOF analiza doista može prepoznati nestacionarnost statističkih momenata prvog i drugog reda vremenskih nizova. Štoviše, uočene su razlike u matricama EOF, PC i raspodjelama udjela modova dobivenih primjenom EOF analize na nizove nestacionarnog prvog momenta, te na nizove nestacionarnog drugog momenta. Na temelju donesenih zaključaka može se naslutiti da postoji mogućnost (uz adekvatno denirane kriterije i metodologiju) razvitka EOF metode, koja bi uz prepoznavanje nestacionarnosti niza, mogla raspoznati i porijeklo te nestacionarnosti (je li to nestacionarnost momenta prvog ili drugog reda). To ostavlja pregršt prostora za daljnja istraživanja.
Abstract (english) Statistical stationarity is a very important concept in the statistical theory of turbulence. Surface layer parameterizations, that relate the turbulent fluxes to mean gradients through Monin-Obukhov similarity theory, assume the stationarity of the turbulent processes. There is no consensus in the literature on a single criterion to determine whether a time series (process realization) is stationary or non-stationary, but there are many methods developed based on different assumptions. This leaves room for additional research in the area, giving the motivation for this work. The empirical orthogonal function (EOF) analysis allows the decomposition of a time series into different orthogonal modes. The result of applying EOF analysis to a time series is a matrix whose each column is an orthogonal function (the matrix of these functions is also called EOF) and a matrix whose each column is one principal component (the matrix of principal components is called PC). It is also possible to determine the share of each mode in the variability of the initial time series. To identify how EOF analysis responds to non-stationarity within time series, it was applied in 3 steps to 4 different types of time series. In the third step, EOF analysis is applied on time series of wind speed and sonic temperature measured near Maslenica bridge, north of the city of Zadar in the period from October 9, 2015, to October 9, 2016, during events of bora. Based on the results of these applications, several important conclusions have been drawn. The most important of these is that EOF analysis can indeed recognize the non-stationarity of the first and second-order statistical moments. Moreover, differences between EOF, PC matrices and the distributions of shares of modes obtained by applying EOF analysis to the series with non-stationary first-moment and the series with non-stationary second-moment, were observed. Based on the conclusions reached, it can be suggested that there is a possibility (with adequately defined criteria and methodology) of developing an EOF method, which, by recognizing the non-stationarity of a series, could also recognize the origin of that non-stationarity (whether it is the non-stationarity of the first or second-order moment). This leaves plenty of room for further research.
Keywords
EOF analiza
nestacionarnost
određivanje nestacionarnosti
analiza empirijskih ortogonalnih funkcija
Keywords (english)
EOF analysis
non-stationarity
determination of non-stationarity
empirical orthogonal function analysis
Language croatian URN:NBN urn:nbn:hr:217:661716 Study programme Title: Graduate university study pf Physics - Geophysics; specializations in: Seismology and Physics of the Earth's Interior, Meteorology and Physical Oceanography Type of resource Text File origin Born digital Access conditions Open access Terms of use Created on 2020-07-28 12:11:36
