Napovedovanje vremenskih pojavov z diskretno Morsovo teorijo

CVETKOVSKA, BISERKA (author), Mramor Kosta, Nežka (mentor)

Cilj naloge je raziskati možnost uporabe dinamike sprememb v slikah kot dodaten parameter pri avtomatičnem napovedovanju ekstremnih vremenskih pojavov. K problemu pristopimo s topološkimi metodami in uporabljamo diskretne Morsove teorije. V delu pokažemo, kako lahko z diskretno Morsovo teorijo zasledujemo spremembe v zaporedju vremenskih slik in z izgradnjo bifurkacijskih diagramov prikažemo sledi pomembnih značilnosti v slikah. Razvita metoda je preizkušena na realnih vremenskih radarskih slikah. Z namenom, da v čim večji meri eliminiramo vpliv šuma na slikah, smo razvili in implementirali tudi metodo za reduciranje šuma v podatkih, ki prav tako temelji na diskretni Morsovi teoriji. Na koncu predstavimo preprost model za klasifikacijo bifurkacijskih diagramov in prikažemo, kako lahko bifurkacijski diagrami skupaj z intenziteto padavin pomagajo pri napovedovanju ekstremnih vremenskih pojavov.

• Language: English
• Keywords: topologija, topološka analiza podatkov, diskretna morsova teorija, vreme, napovedovanje vremenskih pojavov, bifurkacijski diagrami
• Work type: Master's thesis/paper
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2015
• PID: 20.500.12556/RUL-72111
• Publication date in RUL: 27.08.2015

CVETKOVSKA, BISERKA, 2015, Napovedovanje vremenskih pojavov z diskretno Morsovo teorijo [online]. Master’s thesis. [Accessed 18 July 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=72111

Secondary language

• Language: Slovenian
• Title: Predicting weather phenomena using discrete Morse theory

Abstract

In this master thesis we concentrate on the dynamics of changes in the precipitation intensity through a time sequence of radar images and inspect how this can be used as a parameter in automatic severe weather prediction. We approach the problem from a topological standpoint and we demonstrate how discrete Morse theory can be used in tracking changes in a sequence of weather images and show how we can follow important features in the given sequence by building bifurcation diagrams. Our method is evaluated on real data represented as a sequence of weather images taken by a weather radar. In order to avoid noise and to obtain only those features from the images that are significant to our research, we also implement a method for reducing noise. At the end we present a simple model for classification of the bifurcation diagrams and show how the bifurcation diagrams and the amount of precipitation intensity could influence prediction of weather phenomena.

• Keywords: topology, topological data analysis, discrete morse theory, weather, weather prediction, bifurcation diagrams