Hydrological studies are useful in designing, planning, and managing water resources, infrastructure, and ecosystems. Probability distribution models are applied in extreme flood analysis, drought investigations, reservoir volumes studies, and time-series modelling, among other various hydrological studies. However, the selection of the most suitable probability distribution and associated parameter estimation procedure, as a fundamental step in flood frequency analysis, has remained the most difficult task for many researchers and water practitioners. This paper explains the current approaches that are used to identify the probability distribution functions that are best suited for the estimation of maximum, minimum, and mean streamflows. Then, it compares the performance of six probability distributions, and illustrates four fitting tests, evaluation procedures, and selection procedures through using a river basin as a case study. An assemblage of the latest computer statistical packages in an integrated development environment for the R programming language was applied. Maximum likelihood estimation (MLE), goodness-of-fit (GoF) tests-based analysis, and information criteria-based selection procedures were used to identify the most suitable distribution models. The results showed that the gamma (Pearson type 3) and lognormal distribution models were the best-fit functions for maximum streamflows, since they had the lowest Akaike Information Criterion values of 1083 and 1081, and Bayesian Information Criterion (BIC) values corresponding to 1087 and 1086, respectively. The Weibull, GEV, and Gumbel functions were the best-fit functions for the annual minimum flows of the Tana River, while the lognormal and GEV distribution functions the best-fit functions for the annual mean flows of the Tana River. The choices of the selected distribution functions may be used for forecasting hydrologic events and detecting the inherent stochastic characteristics of the hydrologic variables for predictions in the Tana River Basin. This paper also provides a significant contribution to the current understanding of predicting extreme hydrological events for various purposes. It indicates a direction for hydro-meteorological scientists within the current debate surrounding whether to use historical data and trend estimation techniques for predicting future events with issues of non-stationarity and underlying stochastic processes.

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Identification of the Most Suitable Probability Distribution Models for Maximum, Minimum, and Mean Streamflow

................................................................................................................... 17 ΕΚΤΕΝΗΣ ΠΕΡΙΛΗΨΗ ................................................................................................... 18 1.INTRODUCTION ......................................................................................................... 32 1.1 Motivation .........................................................................................................32 1.2 Framing the research question .......................................................................33 1.3 Structure of thesis ............................................................................................35 1.4 Innovation points .............................................................................................36 2.STOCHASTIC DEPENDENCE DYNAMICS FROM THE PARENT PROCESS TO THE EXTREMES: A REVIEW ................................................................................................................ 37 2.1 Definitions in a stochastic framework ..........................................................37 Random variables, stochastic processes and timeseries ..............37 Distribution function and moments ...............................................38 Stationarity, cyclostationarity and ergodicity ..............................39 Dependence in time...........................................................................40 2.2 Second-order properties, scaling laws and HK dynamics .........................40 Climacogram and climacogram-based modelling ........................41 Scaling in time by the entropic view: from predictability to uncertainty .....................................................................................42 2.3 Dependence in extremes: theory and diagnostics .......................................43 The development of classic extreme value theory ........................43 Extreme value theory under dependence ......................................44 Other measures of extremal dependence .......................................47 Cases of stronger dependence .........................................................47 2.4 Treatment of dependence and extremes in common modelling approaches ............................................................................................................................48

Stochastic investigation of hydrological extremes: influence of temporal variability and dependence

Extreme weather outcomes are a multi-dimensional function of interacting physical processes. Actual compound events correspond to particular specific historical realisations of these coupled processes. But due to their intrinsic stochastic nature, they might have led to different outcomes. Historical meteorological studies tend to focus on explaining what actually happened, rather than on considering the phase space of other possibilities. In contrast with extreme event catalogues, information about near misses and proximity to tipping points is not systematically collated. Consequently, stakeholder awareness of such high risk system states is limited. The exploration of alternative realisations provides a counterfactual perspective on compound weather risk, which broadens understanding of extreme weather events, especially in respect of severe impact consequences. This perspective would be an insightful supplement to statistical studies of extreme compound events.

A counterfactual perspective on compound weather risk

In this study, we conducted flood mapping of a hypothetical dam break by coupling the Hydrologic Engineering Center’s Hydrologic Modeling System (HEC-HMS) and River Analysis System (HEC-RAS) models under different return periods of flood inflow. This study is presented as a case study on the Kesem embankment dam in Ethiopia. Hourly hydrological and meteorological data and high-resolution land surface datasets were used to simulate the design floods for piping dam failure with empirical dam breach methods. Based on the extreme inflows and the dam physical characteristics, the dam failure was simulated by a two-dimensional, unsteady flow hydrodynamic model. As a result, the dam will remain safe for up to 50-year return-period inflows, but it breaks for 100- and 200-year return periods and floods the downstream area. For the 100-year peak inflow, a 208 km2 area will be inundated by a maximum depth of 20 m and for a maximum duration of 46 h. The 200-year inflow will inundate a 240 km2 area with a maximum depth of 31 m for a maximum duration of 93 h. The 2D flood map provides satisfactory spatial and temporal resolution of the inundated area for evaluation of the affected facilities.

https://www.mdpi.com/2306-5338/8/2/89/pdf

Flood Mapping from Dam Break Due to Peak Inflow: A Coupled Rainfall–Runoff and Hydraulic Models Approach

67th Executive meeting of the International Commission on Large Dams (ICOLD)

In February 2017, a failure occurring in Oroville Dam’s main spillway risked causing severe damages downstream. A unique aspect of this incident was the fact that it happened during a flood scenario well within its design and operational procedures, prompting research into its causes and determining methods to prevent similar events from reoccurring. In this study, a hydroclimatic analysis of Oroville Dam’s catchment is conducted, along with a review of related design and operational manuals. The data available allows for the comparison of older flood-frequency analyses to new alternative methods proposed in this paper and relevant literature. Based on summary characteristics of the 2017 floods, possible causes of the incident are outlined, in order to understand which factors contributed more significantly. It turns out that the event was most likely the result of a structural problem in the dam’s main spillway and detrimental geological conditions, but analysis of surface level data also reveals operational issues that were not present during previous larger floods, promoting a discussion about flood control design methods, specifications, and dam inspection procedures, and how these can be improved to prevent a similar event from occurring in the future.

https://www.mdpi.com/2076-3263/9/1/37/pdf

Tracey Williamson

Papers

Insights into the Oroville Dam 2017 Spillway Incident