Floods cause widespread damage to property and life in different parts of the world. Hence there is a paramount need to develop effective methods for design flood estimation to alleviate risk associated with these extreme hydrologic events. Methods that are conventionally considered for analysis of floods focus on estimation of continuous frequency relationship between peak flow observed at a location and its corresponding exceedance probability depicting the plausible conditions in the planning horizon. These methods are commonly known as at-site flood frequency analysis (FFA) procedures. The available FFA procedures can be classified as parametric and nonparametric. Parametric methods are based on the assumption that sample (at-site data) is drawn from a population with known probability density function (PDF). Those procedures have uncertainty associated with the choice of PDF and the method for estimation of its parameters. Moreover, parametric methods are ineffective in modeling flood data if multimodality is evident in their PDF. To overcome those artifacts, a few studies attempted using kernel based nonparametric (NP) methods as an alternative to parametric methods. The NP methods are data driven and they can characterize the uncertainty in data without prior assumptions as to the form of the PDF. Conventional kernel methods have shortcomings associated with boundary leakage problem and normal reference rule (considered for estimation of bandwidth), which have implications on flood quantile estimates. To alleviate this problem, focus of NP flood frequency analysis has been on development of new kernel density estimators (kdes). Another issue in FFA is that information on the whole hydrograph (e.g., time to the peak flow, volume of the flood flow and duration of the flood event) is needed, in addition to peak flow for certain applications. An option is to perform frequency analysis on each of the variables independently. However, these variables are not independent, and hence there is a need to perform multivariate analysis to construct multivariate PDFs and use the corresponding cumulative distribution functions (CDFs) to arrive at estimates of characteristics of design flood hydrograph. In this perspective, recent focus of flood frequency analysis studies has been on development of methods to derive joint distributions of flood hydrograph related variables in a nonparametric setting. Further, in real world scenario, it is often necessary to estimate design flood quantiles at target locations that have limited or no data. Regional Flood Frequency analysis (RFFA) procedures have been developed for use in such situations. These procedures involve use of a regionalization procedure for identification of a homogeneous group of watersheds that are similar to watershed of the target site in terms of flood response. Subsequently regional frequency analysis (RFA) is performed, wherein the information pooled from the group (region) forms basis for frequency analysis to construct a CDF (growth curve) that is subsequently used to arrive at quantile estimates at the target site. Though there are various procedures for RFFA, they are largely confined to only univariate framework considering a parametric approach as the basis to arrive at required quantile estimates. Motivated by these findings, this thesis concerns development of a linear diffusion process based adaptive kernel density estimator (D-kde) based methodologies for at-site as well as regional FFA in univariate as well as bivariate settings. The D-kde alleviates boundary leakage problem and also avoids normal reference rule while estimating optimal bandwidth by using Botev-Grotowski-Kroese estimator (BGKE). Potential of the proposed methodologies in both univariate and bivariate settings is demonstrated by application to synthetic data sets of various sizes drawn from known unimodal and bimodal parametric populations, and to real world data sets from India, USA, United Kingdom and Canada. In the context of at-site univariate FFA (considering peak flows), the performance of D- kde was found to be better when compared to four parametric distribution based methods (Generalized extreme value, Generalized logistic, Generalized Pareto, Generalized Normal), thirty-two ‘kde and bandwidth estimator’ combinations that resulted from application of four commonly used kernels in conjunction with eight bandwidth estimators, and a local polynomial–based estimator. In the context of at-site bivariate FFA considering ‘peakflow-flood volume’ and ‘flood duration-flood volume’ bivariate combinations, the proposed D-kde based methodology was shown to be effective when compared to commonly used seven copulas (Gumbel-Hougaard, Frank, Clayton, Joe, Normal, Plackett, and student’s-T copulas) and Gaussian kernel in conjunction with conventional as well as BGKE bandwidth estimators. Sensitivity analysis indicated that selection of optimum number of bins is critical in implementing D-kde in bivariate setting. In the context of univariate regional flood frequency analysis (RFFA) considering peak flows, a methodology based on D-kde and Index-flood methods is proposed and its performance is shown to be better when compared to that of widely used L-moment and Index-flood based method (‘regional L-moment algorithm’) through Monte-Carlo simulation experiments on homogeneous as well as heterogeneous synthetic regions, and through leave-one-out cross validation experiment performed on data sets pertaining to 54 watersheds in Godavari river basin, India. In this context, four homogeneous groups of watersheds are delineated in Godavari river basin using kernel principal component analysis (KPCA) in conjunction with Fuzzy c-means cluster analysis in L-moment framework, as an improvement over heterogeneous regions in the area (river basin) that are currently being considered by Central Water Commission, India. In the context of bivariate RFFA two methods are proposed. They involve forming site-specific pooling groups (regions) based on either L-moment based bivariate homogeneity test (R-BHT) or bivariate Kolmogorov-Smirnov test (R-BKS), and RFA based on D-kde. Their performance is assessed by application to data sets pertaining to stations in the conterminous United States. Results indicate that the R-BKS method is better than R-BHT in predicting quantiles of bivariate flood characteristics at ungauged sites, although the size of pooling groups formed using R-BKS is, in general, smaller than size of those formed using R-BHT. In general, the performance of the methods is found to improve with increase in size of pooling groups. Overall the results indicate that the D-kde always yields bona fide PDF (and CDF) in the context of univariate as well as bivariate flood frequency analysis, as probability density is nonnegative for all data points and integrates to unity for the valid range of the data. The performance of D-kde based at-site as well as regional FFA methodologies is found to be effective in univariate as well as bivariate settings, irrespective of the nature of population and sample size. A primary assumption underlying conventional FFA procedures has been that the time series of peak flow is stationarity (temporally homogeneous). However, recent studies carried out in various parts of the World question the assumption of flood stationarity. In this perspective, Time Varying Gaussian Copula (TVGC) based methodology is proposed in the thesis for flood frequency analysis in bivariate setting, which allows relaxing the assumption of stationarity in flood related variables. It is shown to be effective than seven commonly used stationary copulas through Monte-Carlo simulation experiments and by application to data sets pertaining to stations in the conterminous United States for which null hypothesis that peak flow data were non-stationary cannot be rejected.

The objective of this present thesis was to determine whether GEV (Generalized Extreme Value) itself can be a more conservative distribution than LP3 (Log Pearson III) associated with other methods, such as the B17B weighting procedure with Single Grubbs-Beck (SGB) for low outliers, when determining the projected floods in a flood frequency analysis (FFA) for Santa Ana and San Gabriel regions and other urbanized stream gages present in California. In this work, USGS PeakFQ was utilized. From the results obtained, it was possible to state that GEV fitting results were directly affected by the length of the data. When the length of the record is short, it is not accurate to use a projection of 100-year return period, for example, to represent future projection. Comparing the LP3 and GEV CDFs, for the majority of the stream gages analyzed in this project, GEV proves to be the most conservative method, with smaller return periods.

Key theoretical and empirical results from the past two decades have established that peak discharges exhibit power-law, or scaling, relation with drainage area across multiple scales of time and space. This relationship takes the form Q(A)= $#945;AΘ where Q is peak discharge, A is the drainage area, Θ is the flood scaling exponent, and α is the intercept. Motivated by seminal empirical studies that show that the flood scaling parameters α and Θ change from one rainfall-runoff event to another, this dissertation explores how certain rainfall and catchment physical properties control the flood scaling exponent and intercept at the rainfall-runoff event scale using a combination of extensive numerical simulation experiments and analysis of observational data from the Iowa River basin, Iowa. Results show that Θ generally decreases with increasing values of rainfall intensity, runoff coefficient, and hillslope overland flow velocity, whereas its value generally increases with increasing rainfall duration. Moreover, while the flood scaling intercept is primarily controlled by the excess rainfall intensity, it increases with increasing runoff coefficient and hillslope overland flow velocity. Results also show that the temporal intermittency structure of rainfall has a significant effect on the scaling structure of peak discharges. These results highlight the fact that the flood scaling parameters are able to be estimated from the aforementioned catchment rainfall and physical variables, which can be measured either directly or indirectly using in situ or remote sensing techniques. The dissertation also proposes and demonstrates a new flood forecasting framework that is based on the scaling theory of floods. The results of the study mark a step forward to provide a physically meaningful framework for regionalization of flood frequencies and hence to solve the long standing hydrologic problem of flood prediction in ungauged basins.

Flood frequency analysis over the western United States is complicated by annual peak flow records that frequently contain annual flows generated from distinctly different flood generating mechanisms. Bulletin17B (B17B) and its update Bulletin 17C (B17C) recognized the difficulties in determining flood frequency estimates with streamflow records that contain a mixed population of flood generated peaks, and recommend developing separate frequency curves when the hydrometeorologic mechanisms that generated the annual peak flows can be separated into distinct populations. Yet challenges arise when trying to consistently quantify the physical process that generated the observed flows. This thesis examines the role played by different flood producing mechanisms in generating annual maximum floods throughout the western United States using process-driven mixed populations. First I evaluate the impacts of hydrometeorological processes on flood frequency in the western United States, with emphasis on the spatial and fractional contributions of atmospheric rivers (ARs) and eastern North Pacific tropical cyclones and their remnants (TC events) on annual maximum flows throughout this area. Six main areas in which flooding are impacted by ARs at varying degrees are found throughout the western United States. The Pacific Northwest and the northern California coast have the highest fraction of AR-generated peaks (~80–100%), while eastern Montana, Wyoming, Utah, Colorado, and New Mexico have nearly no impacts from ARs. The individual regions of the central Columbia River Basin in the Pacific Northwest, the Sierra Nevada, the central and southern California coast, and central Arizona all show a mixture of 30–70% AR-generated flood peaks. Analyses related to the largest flood peaks on record highlight the strong impact of ARs on flood hydrology in this region. Conversely, TC events play a limited role in controlling the upper tail of the flood peak distributions across the western United States. Southern California, Arizona, southernmost Nevada and Utah, southern and western New Mexico, central Colorado, and Texas have the highest fractional contributions of TC-event-generated annual maximums flows (~5-14%). I then build on these insights to develop a statistical framework to perform a process-driven flood frequency analysis using the AR/non-AR-generated annual peak flows identified at 43 long-term U.S. Geological Survey (USGS) streamgages in the western United States. I use a simulation framework to perform flood frequency analyses in terms of mixed distributions and quantify the corresponding uncertainties by accounting for mixed populations. Sites with notably different quantile estimates in the upper tail of the distribution between the single (homogeneous) and the weighted (heterogeneous) population methodologies are found when (i) potentially influential low floods (PILFS) are identified and/or (ii) when the composite distribution contains markedly different at-site log-unit skews (shape parameter) among the AR/non-AR subpopulations compared to the single homogeneous population.

Hydraulic geometry relationships and regional curves are used in natural channel design to assist engineers, biologists, and fluvial geomorphologists in the efforts undertaken to ameliorate previous activities that have diminished, impaired or destroyed the structure and function of stream systems. Bankfull channel characteristics were assessed for 14 United States Geological Survey (USGS) gaged sites in the Inner Bluegrass and 15 USGS gaged sites in the Outer Bluegrass Regions of Kentucky. Hydraulic geometry relationships and regional curves were developed for the aforementioned regions. Analysis of the regression relationships showed that bankfull discharge is a good explanatory variable for bankfull parameters such as area, width and depth. The hydraulic geometry relationships developed produced high R2 values up to 0.95. The relationships were also compared to other studies and show strong relationships to both theoretical and empirical data. Regional curves, relating drainage area to bankfull parameters, were developed and show that drainage area is a good explanatory variable for bankfull parameters. R2 values for the regional curves were as high as 0.98.

L’estimation de l’aléa hydrologique en sites non jaugés présente un enjeu important pour la gestion des risques. La complexité du phénomène réside à la fois dans la nécessité d’avoir une approche multivariée (estimation de caractéristiques multiples des crues : durées, périodes de retour) qui propose une extrapolation raisonnable des événements. SHYREG est une méthode basée sur la simulation de scénarios de crues, qui présente ces avantages. Évaluée lors du projet ANR ExtraFlo, elle présente de bonnes performances en justesse et en stabilité lorsqu'elle est calée sur des données locales de débits. Cette méthode vise à estimer des débits de crue en tout point du territoire. Elle doit donc pouvoir être appliquée en site non jaugés.Le travail de thèse présenté ici se focalise sur le transfert de la méthode vers le non jaugé en s’intéressant aux valeurs des débits simulés mais aussi à leur cohérence. Tout d’abord, une révision du calage a permis de s’assurer de la cohérence des débits simulés le long d’un cours d’eau. Ensuite, l’application d’un large panel de méthodes de régionalisation a permis de déterminer que la régionalisation devait s’appuyer à la fois sur la structure spatiale et sur les caractéristiques physiographiques des bassins. Finalement, une méthode qui régionalise SHYREG simultanément à son calage a été retenue. Une comparaison avec d’autres approches régionalisées a mis en évidence la qualité du modèle développé. / Flood hazard estimation in ungauged sites presents a major challenge for risk management. The complexity of the phenomenon arises from both the need for a multivariate approach (estimation of different flood characteristics: peak flow, volume, duration ...), and for an approach which offers a reasonable extrapolation of extreme events. The SHYREG method is based on the simulation of flood scenarios and presents these benefits. It has been evaluated during the ANR ExtraFlo project. It showed good performance in both accuracy and stability when calibrated against local discharge data. However, weaknesses have been identified when implemented in ungauged sites.The objective of the present thesis is to develop the method in order to improve the SHYREG performances in ungauged sites. Two kinds of modifications were implemented. First, the calibration of the method in gauged sites was reviewed. The main idea was to integrate more data and to take more into account the coherence between simulated discharges in different sites. Then, diverse regionalisation schemes extracted from the scientific literature were considered. Their application demonstrated the necessity to exploit information from nearby sites and the physical properties of the catchments. Finally, a version which realises the regionalisation simultaneously to the calibration has been selected. Its comparison with other method showed the quality of this new version of SHYREG.

Doctor of Philosophy / Department of Biology / Keith B. Gido / Global climate change could lead to less frequent but more severe precipitation events in the Great Plains, altering the hydrologic regimes of streams. It is important to quantify species roles in these dynamic systems, because changes in stream communities are likely to accompany predicted changes in hydrology. The effects of species on ecosystem processes also are limited by the frequency of disturbance, because prairie streams are harsh, nonequilibrium systems characterized by a wide range of disturbances. In particular, frequent floods that reset the ecosystem to an early successional state can override the influence of consumer populations because the availability of resources is too unpredictable to maintain stable populations of those species or because species are absent following the flood. As flood frequency decreases, potential consumer effects may intensify. Using a combination of field and experimental stream mesocosm experiments, I (1) characterized the ecosystem effects of southern redbelly dace (Phoxinus erythrogaster), a grazing minnow, (2) tested the interactive effects of flood frequency and the presence of water column (red shiner; Cyprinella lutrensis) or grazing minnows (Phoxinus) on ecosystem processes, and (3) tested the effects of species loss from the grazer functional feeding group on stream ecosystem structure and function. I found that dace affected some aspects of ecosystem structure but not function, which suggested that grazer effects in prairie streams may not be consistent across taxa. In the context of flood frequency, both the water column omnivore and dace affected recovery of prairie stream primary producers following flooding disturbance by stimulating production, presumably through nutrient remineralization. However, some of these effects were transient or dependent on flood frequency, and my results indicate that consumer effects depend not only on environmental venue but also on the balance between consumptive losses and nutrient stimulation. In a comparison of the effects of removing different taxa from a grazer assemblage, the loss of crayfish, snails, or dace from a grazer assemblage did not differentially affect ecosystem processes, suggesting overlap in the ecosystem roles of these species in the context of this experiment.

Die Vorteile der Kernschätzung gegenüber dem Abzählen von Ereignissen in Zeitintervallen werden dargestellt. Für das beiden Methoden gemeinsame Glättungsproblem gestattet die Kreuzvalidierung eine Lösung. Für die Hochwasserereignisse der Oder im Zeitraum 1350 bis 1850 wird eine Abnahme der Häufigkeit nach ca. 1675 gefunden; weitergehende Aussagen bedingen eine Homogenisierung der Daten. Die dargestellte Methodik wird gegenwärtig in das Computerprogramm XTREND implementiert. / The advantages of kernel estimation over counting of events within time intervals are shown. Cross validation offers a solution for the smoothing problem which is common to both methods. As regards ooding events of the river Oder in 1350 to 1850, a decrease in the frequency after about 1675 is found. More detailed results demand homogenized data. The method is currently being implemented into the computer program XTREND.

Regional flood frequency techniques are commonly used to estimate flood quantiles when flood data are unavailable or the record length at an individual gauging station is insufficient for reliable analyses. These methods compensate for limited or unavailable data by pooling data from nearby gauged sites. This requires the delineation of hydrologically homogeneous regions in which the flood regime is sufficiently similar to allow the spatial transfer of information. Therefore, several Regional Flood Frequency Analysis (RFFA) methods are applied to the Ceyhan Basin. Dalyrmple (1960) Method is applied as a common RFFA method used in Turkey. Multivariate statistical techniques which are Stepwise and Nonlinear Regression Analysis are also applied to flood statistics and basin characteristics for gauging stations. Rainfall, Perimeter, Length of Main River, Circularity, Relative Relief, Basin Relief, Hmax, Hmin, Hmean and H&Delta / are the simple additional basin characteristics. Moreover, before the analysis started, stations are clustered according to their basin characteristics by using the combination of Ward&rsquo / s and k-means clustering techniques. At the end of the study, the results are compared considering the Root Mean Squared Errors, Nash-Sutcliffe Efficiency Index and % difference of results. Using additional basin characteristics and making an analysis with multivariate statistical techniques have positive effect for getting accurate results compared to Dalyrmple (1960) Method in Ceyhan Basin. Clustered region data give more accurate results than non-clustered region data. Comparison between clustered region and non-clustered region Q100/Q2.33 reduced variate values for whole region is 3.53, for cluster-2 it is 3.43 and for cluster-3 it is 3.65. This show that clustering has positive effect in the results. Nonlinear Regression Analysis with three clusters give less errors which are 29.54 RMSE and 0.735 Nash-Sutcliffe Index, when compared to other methods in Ceyhan Basin.

[Truncated abstract] Runoff generation behaviour and flooding in a lake dominated catchment are nonlinear, threshold-driven processes that result from the interactions between climate and various catchment characteristics. A complicating feature of the rainfall to runoff transformation, which may have implications for the flood frequency, is that the various surface and subsurface flow pathways are dynamic, heterogeneous and highly nonlinear, consisting of distinct thresholds. To understand the impact of threshold nonlinearities on the rainfall-runoff transformation in such catchments, a systematic examination was carried out to investigate runoff generation behaviour of the catchment itself, the overflow behaviour of a lake in combination with the catchment draining into it, as well as the lake organisation within a lake chain network. Three storage based thresholds were considered: the catchment field capacity storage governing catchment subsurface stormflow, total storage capacity governing catchment surface runoff, and lake storage capacity governing lake-overflow. ... Through these investigations, this thesis has provided valuable insights into the process controls of lake-overflow events and the associated flood frequency behaviour in lake dominated catchments. In particular, the relative roles of climate, soil depth, the soil?s drainage capacity, as well as the relative geometry of the lake vis a vis the contributing catchment, in the determination of the dynamic characteristics of lake-overflow events and associated flood frequency behaviour have been highlighted. In addition, the importance of lake organization, as expressed in terms of the average ratio of catchment area to lake area and the spatial variability of this ratio from upstream to downstream, and their impact upon connectivity and flood frequency have also been explored. The outcomes of this study highlight the importance of thresholds governing flood frequency, and provide insights into the complex interactions between rainfall variability and the various threshold nonlinearities in the rainfall-runoff process, which are shown to have a significant impact on the resulting flood frequency curves. The improved understanding of these process controls will be useful in assisting the 1 management of the catchment-lake system in the study region, and in regions elsewhere. In particular, the outcome of this study can provide guidance towards the adoption of various management strategies for lake chain systems by illustrating the effects of potential flow interruption and retardation as ways to assist in flood prevention and mitigation, whether it is aimed at decreasing the frequency of occurrence of lake overflows, or merely decreasing the flow magnitude for a given return period.