Statistical models for drought indices

Ing. Filip Strnad

Doctoral thesis

Abstract:

Modelling of hydrological extremes and drought modelling in particular has received much attention over recent decades. The thesis gives an overview of the drought definitions and drought indices and approaches to extreme value analysis including the regional frequency analysis with focus on drought. The main aim of the thesis is the application and comparison of regional frequency analysis models for drought characteristics based on various parameter estimation methods, that involves modifying the methods in order to work with intermittent variables. The attention is be paid to the reduction of uncertainty in the estimated return levels, in the periods of drought events and in the parameters of the extremal model. The goodness-of-fit of the models is be evaluated through discordance analysis, as well as the Anderson–Darling tests, with the critical values estimated by a bootstrap procedures. Performance of presented methods is evaluated by designed experiments focusing on behaviour of parameter estimation algorithms with increasing sample size in various situations. Experiment is also assessing the index flood method performance with increasing p0 (probability of zero values, e.g. the fraction of years without drought). As part of the thesis a case study is presented that deals with development of an index flood model for deficit volumes for 133 catchments in the Czech Republic (1901--2015) that are simulated by hydrological model BILAN. The parameters of the regional distribution are estimated using L-moments. The goodness-of-fit of the statistical model is assessed by the Anderson Darling statistic test. For the estimation of critical values, sampling methods allowing for handling of years without drought were used.

Keywords

index-flood, L-moment, maximum likelihood, return levels, deficit volumes, drought

Language used: English

Date on which the thesis was submitted / produced: 7. 3. 2023

Thesis defence

• Date of defence: 21. 3. 2022
• Supervisor: prof. Ing. Martin Hanel, Ph.D.
• Reader: Vera Potopová, doc. Dr. Mgr., Ondřej Ledvinka, externi

Czech University of Life Sciences Prague

Faculty of Environmental Sciences

Doctoral programme / field:
Landscape Engineering / Environmental Modelling