Flood Frequency Distribution Research Articles

Peak runoff contributing area as hydrological signature of the probability distribution of floods

For the analysis of hydrological extremes and particularly in flood prediction, deeper investigation is needed on the relative effects of different hydrological processes acting at the basin scale in different hydroclimatic areas of the world. In this framework, the theoretical derivation of flood distribution shows a great potential for development and knowledge advancement. In addition, another promising path of investigation is represented by the use of distributed hydrological models via simulation modelling (including Monte Carlo, discrete event and continuous simulation). In this paper results of a theoretically derived flood frequency distribution are analyzed and compared with the results of a simulation scheme that uses a distributed hydrological model (DREAM) in cascade with a rainfall generator (IRP). The numerical simulation allows the reproduction of a large number of extreme events and provides insight into the main control for flood generation mechanisms with particular emphasis to the peak runoff contributing areas, highlighting the relevance of soil texture and morphology in different climatic environments. The proposed methodology is applied here to the Agri and the Bradano basin, in Southern Italy.

Flood probability analysis for un-gauged watersheds by means of a simple distributed hydrologic model

A methodology is proposed for the inference, at the regional and local scales, of flood magnitude and associated probability. Once properly set-up, this methodology is able to provide flood frequencies distributions at gauged and un-gauged river sections pertaining to the same homogeneous region, using information extracted from rainfall observations. A proper flood frequency distribution can be therefore predicted even in un-gauged watersheds, for which no discharge time series is available. In regions where objective considerations allow the assumption of probability distribution homogeneity, regional approaches are increasingly adopted as they present a higher reliability. The so-called “third level” in regional frequency analysis, that is the derivation of the local dimensional probability distribution from its regional non-dimensional counterpart is often a critical issue because of the high spatial variability of the position parameter, usually called “index flood”. While in gauged sites the time series average is often a good estimator for the index flood, in un-gauged sites as much information as possible about the site concerned should be taken into account. To solve this issue, the present work builds from the experience developed for regional rainfall and flood frequency analyses, and a hydrologic model, driven by a specific hyetograph, is used to bridge the gap between rainfall and flood frequencies distributions, identifying flood discharge magnitudes associated with given frequencies. Results obtained from the application in the Liguria region, Northern Italy, are reported, and validation is proposed in gauged sites against local flood frequency distributions, obtained either from local records or from the regional frequency distribution of non-dimensional annual discharge maxima, made dimensional with the local discharge record.

Local Non-Stationary Flood-Duration-Frequency Modelling

Flood-duration-frequency modelling is an extension of standard flood frequency analysis that takes into account the multi-duration aspect of flood hydrographs. The key assumption of this approach is that the parameters describing the flood frequency distribution for any flood duration do not change over time. In reality, however, as a consequence of local and/or global anthropogenic activities, stationarity of hydrologic records cannot be assumed. New methods that take into account the non-stationarity of hydrologic records and that can properly deal with time-dependent parameters of flood frequency distributions need to be developed and used in practice. This study introduces formal aspects of non-stationary flood-duration-frequency modelling. The presented approach uses trend analysis to identify time-dependent components of the model and to predict their changes in the future. The significance of the time-dependent parameters is reflected in the structure of the model. The approach is illustrated on a study catchment in British Columbia, Canada.

Short-term changes in the magnitude, frequency and temporal distribution of floods in the Eastern Mediterranean region during the last 45 years — Nahal Oren, Mt. Carmel, Israel

Short-term changes in Eastern Mediterranean precipitation affecting flow regime were documented in Nahal Oren, a 35 km 2 ephemeral stream in Mt. Carmel, a 500 m high mountain ridge located at the NW coast of Israel. The rainy winter of the Mediterranean type climate (Csa) in Mt. Carmel is characterized by average annual rainfall of 550 mm at the coastal plain to 750 mm at the highest elevation while the summer is hot and dry. Stream flow generates after accumulated rainfall of 120–150 mm while “large floods”, defined as flows with peak discharge of > 5 m 3 s − 1 and/or > 150,000 m 3 in volume, are generated in response to rainfall of over 100 mm. Hence, large floods in Nahal Oren stream occur not earlier than December. Precipitation and flow data were divided into two sub-periods: 1957–1969 and 1991–2003 and compared to each other. The results indicate a clear increase in the frequency of large floods, their magnitudes and volumes during the second period with no parallel change in the annual precipitation. Similarly, an increase in storm rainfall–runoff ratio from < 5% to > 15% and a decrease in the threshold rainfall for channel flow by 16–25% were documented. These short-term variations in flooding behavior are explained by the clear decrease in the length of the rainy season and by the resulting significant shortening in the duration of the dry-spells. The increase in the number of large rainfall events and the large floods in each hydrological year together with the increasing number of years with no floods indicate strengthening of their uncertainty of behavior.

On the asymptotic behavior of flood peak distributions

Abstract. This paper presents some analytical results and numerical illustrations on the asymptotic properties of flood peak distributions obtained through derived flood frequency approaches. It confirms and extends the results of previous works: i.e. the shape of the flood peak distributions are asymptotically controlled by the rainfall statistical properties, given limited and reasonable assumptions concerning the rainfall-runoff process. This result is partial so far: the impact of the rainfall spatial heterogeneity has not been studied for instance. From a practical point of view, it provides a general framework for analysis of the outcomes of previous works based on derived flood frequency approaches and leads to some proposals for the estimation of very large return-period flood quantiles. This paper, focussed on asymptotic distribution properties, does not propose any new approach for the extrapolation of flood frequency distribution to estimate intermediate return period flood quantiles. Nevertheless, the large distance between frequent flood peak values and the asymptotic values as well as the simulations conducted in this paper help quantifying the ill condition of the problem of flood frequency distribution extrapolation: it illustrates how large the range of possibilities for the shapes of flood peak distributions is.

Regional flood-duration–frequency modeling in the changing environment

Flood-duration–frequency (QdF) analysis is becoming a popular tool for estimating the severity of flood events as an integrated function of return period and flood duration. QdF models are often applied in regional flood studies, leading to regional QdF relations derived for hydrologically homogeneous regions. Regional QdF models can be used to estimate flood quantiles for a given return period and flood duration at any ungaged site of a homogeneous region. By combining the information on sampling variability from hydrologically similar neighboring sites, the regional approach to QdF modeling also decreases the estimation uncertainty at gaged sites of the region. Regional QdF models have been developed for stable environmental conditions. Nevertheless, recent studies on stationarity of hydrologic records conducted in different parts of the world have identified significant changes in the statistical parameters of the analyzed records. Changing environmental conditions call for new flood estimation methods that can take into account the nonstationary character of hydrologic records and that can deal with time-dependent parameters of flood frequency distributions. This study defines the key concepts of a nonstationary approach to regional QdF modeling. The proposed approach uses regional trend analysis to identify time-dependent parameters of the model, and to estimate and predict flood quantiles for the present and near future time horizons. The model can be flexibly applied to various scenarios of nonstationarity at both local and regional scales. The approach is illustrated on a set of data from a hydrologically homogeneous region in Québec, Canada. A split-sample experiment is used to compare the performance of the proposed model with the traditional stationary regional QdF model. The case study results demonstrate that ignoring statistically significant nonstationarity of hydrologic records can seriously bias flood quantiles estimated for the near future.

Effects of Forest Fires on Flood Frequency Curves in a Mediterranean Catchment/Effets d'incendies de forêt sur les courbes de fréquence de crue dans un bassin versant Méditerranéen

The effect of land-use change on the flood frequency curve (FFC) in a natural catchment is analysed. To achieve this, a simple methodology for the derivation of FFCs in land-use change scenarios is proposed. The adopted methodology, using a stochastic model in Monte Carlo simulation of FFCs, was found to provide a useful framework for detecting changes in flood magnitudes in both pre- and post-fire conditions. In particular, the importance of the antecedent soil moisture condition in the determination of the flood frequency distribution was analysed. The analysis of FFCs for pre- and post-fire conditions shows an increase in the average value of Curve Number and a decrease in the catchment time lag. The derivation of FFCs shows a clear increase in flood quantiles. For the post-fire conditions, the FFC exhibits higher quantiles of the peak discharges showing a reduction in frequency of occurrence. This variation is more significant for low-return period quantiles than for high-return period quantiles. The results of the catchment studies reported here support the hypothesis that the hydrological response of the watershed changes as a result of fire, especially during the first years following a fire event.

Effects of Forest Fires on Flood Frequency Curves in a Mediterranean Catchment/Effets d'incendies de for�t sur les courbes de fr�quence de crue dans un bassin versant M�diterran�en

Abstract The effect of land-use change on the flood frequency curve (FFC) in a natural catchment is analysed. To achieve this, a simple methodology for the derivation of FFCs in land-use change scenarios is proposed. The adopted methodology, using a stochastic model in Monte Carlo simulation of FFCs, was found to provide a useful framework for detecting changes in flood magnitudes in both pre- and post-fire conditions. In particular, the importance of the antecedent soil moisture condition in the determination of the flood frequency distribution was analysed. The analysis of FFCs for pre- and post-fire conditions shows an increase in the average value of Curve Number and a decrease in the catchment time lag. The derivation of FFCs shows a clear increase in flood quantiles. For the post-fire conditions, the FFC exhibits higher quantiles of the peak discharges showing a reduction in frequency of occurrence. This variation is more significant for low-return period quantiles than for high-return period quantiles. The results of the catchment studies reported here support the hypothesis that the hydrological response of the watershed changes as a result of fire, especially during the first years following a fire event.

Flood frequency estimation by continuous simulation of subcatchment rainfalls and discharges with the aim of improving dam safety assessment in a large basin in the Czech Republic

This paper applies a continuous simulation approach to the estimation of flood frequency for a dam site in a large catchment (1186 km 2) in the Czech Republic. The models used allow for the simulation of both high intensity and low intensity rainfall events, and snowmelt events, over subcatchments in contributing to the flood frequency distribution. The methodology is implemented within a Generalised Likelihood Uncertainty Estimation framework that allows for uncertainty in the model parameters and for the realisation effect in reproducing the apparent statistics of potential flood events represented by the short series of observations. A fuzzy rules method is used to evaluate each model run, based on the available observations of peak discharges, flow duration curves and snow water equivalents. This yields a combined likelihood measure that is used to weight the flood predictions for each behavioural parameter set. The cumulative distribution for flood peaks for any chosen probability of exceedence over all behavioural models can then be estimated. This can be used to assess the risk of a potential flood peak (or duration or volume) within a risk based dam safety assessment.

Joint Seasonal /Annual Flood Frequency Analysis

Flood frequency analysis, as commonly practiced, focuses on the estimation of return periods associated with annual maximum flood peaks of various magnitudes. In some applications, it is desirable to perform joint (i.e., simultaneous) flood frequency analyses on seasonal as well as annual bases. However, a problem one encounters in seasonal flood frequency analysis is that the consistency or interrelationship that must exist between the annual maximum and individual seasonal flood frequency distributions may not be preserved. The most important cause of inconsistencies is that one cannot arbitrarily specify the parametric forms of the annual and all of the seasonal distributions. A correct theoretical analysis of the joint frequency problem would require the use of a rather unusual and complicated distributional model. Since this is not practical, this paper presents two approximate but useful methods for joint frequency analysis using the log Pearson Type 3 distribution. It is shown via examples that the two methods can be applied to reasonably model annual and five seasonal flood distributions in the Tennessee Valley.

Flood quantiles in a changing climate: Seasonal forecasts and causal relations

Recognizing that the frequency distribution of annual maximum floods at a given location may change over time in response to interannual and longer climate fluctuations, we compare two approaches for the estimation of flood quantiles conditional on selected “climate indices” that carry the signal of structured low‐frequency climate variation, and influence the atmospheric mechanisms that modify local precipitation and flood potential. A parametric quantile regression approach and a semiparametric local likelihood approach are compared using synthetic data sets and for data from a streamflow gauging station in the western United States. Their relative utility in different settings for seasonal flood risk forecasting as well as for the assessment of long‐term variation in flood potential is discussed.

Geomorphic and Hydrologic Assessment of Erosion Hazards at the Norman Municipal Landfill, Canadian River Floodplain, Central Oklahoma

The Norman, Oklahoma, municipal landfill closed in 1985 after 63 years of operation, because it was identified as a point source of hazardous leachate composed of organic and inorganic compounds. The landfill is located on the floodplain of the Canadian River, a sand-bed river characterized by erodible channel boundaries and by large variation in mean monthly discharges. In 1986, floodwaters eroded riprap protection at the southern end of the landfill and penetrated the landfill's clay cap, thereby exposing the landfill contents. The impact of this moderate-magnitude flood event (Q12) was the catalyst to investigate erosion hazards at the Norman landfill. This geomorphic investigation analyzed floodplain geomorphology and historical channel changes, flood-frequency distributions, an erosion threshold, the geomorphic effectiveness of discharge events, and other factors that influence erosion hazards at the landfill site. The erosion hazard at the Norman landfill is a function of the location of the landfill with respect to the channel thalweg, erosional resistance of the channel margins, magnitude and duration of discrete discharge events, channel form and hydraulic geometry, and cumulative effects related to a series of discharge events. Based on current climatic conditions and historical channel changes, a minimum erosion threshold is set at bankfull discharge (Q = 572 m3/s). The annual probability of exceeding this threshold is 0.53. In addition, this analysis indicates that peak stream power is less informative than total energy expenditures when estimating the erosion potential or geomorphic effectiveness of discrete discharge events. On the Canadian River, long-duration, moderate-magnitude floods can have larger total energy expenditures than shorter-duration, high-magnitude floods and therefore represent the most serious erosion hazard to floodplain structures.

Overcoming the joint probability problem associated with initial loss estimation in desgn flood estimation

Design flood estimation techniques currently used in Australia only partially account for the joint probability interactions between flood producing variables. The joint probability problem associated with initial loss estimation is particularly important. Failure to deal with it can introduce considerable bias into estimated flood frequency distributions for ungauged catchments. One solution to this problem is to use continuous simulation whereby a rainfall generation model is linked to a catchment water balance and flood routing model. This technique has been used to explore less complicated ways of overcoming the joint probability problem by allowing design rainfall obtained from Australian Rainfall and Runoff (ARR) to be directly converted into rainfall excess. This eliminates the need for assumptions regarding initial loss. A continuous simulation approach has been utilised here by means of a stochastic point rainfall model, coupled with a stochastic evaporation model and modified AWBM model. This enables the determination of the scaling required for the conversion of rainfall into rainfall excess. The technique is validated using a kinematic wave catchment runoff model and comparison with observed flood frequency curves. Through this method, the simplicity of the design flood estimation approach is retained by the use of rainfall excess frequency duration (REFD) curves instead of rainfall IFD curves. The REFD method has been calibrated and tested on a number of catchments in Australia. Presented here are the results from the Boggy Creek catchment in Victoria. The scaling of the ARR design rainfall required has been very similar across all average recurrence intervals and event durations. This should allow the approach to be extended to other catchments.

Stochastic modeling of flood peaks using the generalized extreme value distribution

The generalized extreme value (GEV) distribution is a standard tool for modeling flood peaks, both in annual maximum series (AMS) and in partial duration series (PDS). In this paper, combined maximum likelihood estimation (MLE) and L moment (LMOM) procedures are developed for estimating location, shape, and scale parameters of the GEV distribution. Particular attention is given to estimation of the shape parameter, which determines the “thickness” of the upper tail of the flood frequency distribution. Mixed MLE–LMOM methods avoid problems with both MLE (estimator variance) and LMOM (estimator bias) estimators of the shape parameter. The mixed MLE–LMOM procedure is extended to use the two largest flood peaks in a year. This extension is developed in a PDS framework. Estimation procedures are applied to flood peak observations from 104 central Appalachian basins. The estimated values of the shape parameter for the central Appalachian basins are more negative than has been considered physically reasonable, independent of the estimation procedure that is used. Twenty‐eight percent of mixed method estimators of the shape parameter have values less than −0.5, implying that the moments of order 2 and above are infinite. The estimated shape parameters for the central Appalachian basins do not depend on basin morphological parameters (such as drainage area) or land cover properties (such as percent urban, forest, or agricultural land use). Estimated values of the location and scale parameters for the central Appalachian watersheds correspond well with GEV‐based simple scaling theory. Estimated values of the shape parameter for central Appalachian watersheds are shown to differ markedly from those of southern Appalachian watersheds and the difference is shown to be linked to contrasting properties of extreme floods. To conclude the paper, analyses of mixture distribution models are presented to address the question of whether flood peaks really have extreme “heavy tail” behavior or whether the GEV distribution is not the appropriate model for flood peaks.

On the derived flood frequency distribution: analytical formulation and the influence of antecedent soil moisture condition

In this paper we present an analytical formulation of the derived distribution of peak flood and maximum annual peak flood, starting from a simplified description of rainfall and surface runoff processes, and we show how such a distribution is useful in practical applications. The assumptions on rainfall dynamics include the hypotheses that the maximum storm depth has a Generalized Pareto distribution, and that the temporal variability of rainfall depth in a storm can be described via power–law relationships. The SCS- CN model is used to describe the soil response, and a lumped model is adopted to transform the rainfall excess into peak flood; in particular, we analyse the influence of antecedent soil moisture condition on the flood frequency distribution. We then calculate the analytical expressions of the derived distributions of peak flood and maximum annual peak flood. Finally, practical case studies are presented and discussed.

Downscaling of global climate models for flood frequency analysis: where are we now?

AbstractThe issues of downscaling the results from global climate models (GCMs) to a scale relevant for hydrological impact studies are examined. GCM outputs, typically at a spatial resolution of around 3° latitude and 4° longitude, are currently not considered reliable at time scales shorter than 1 month. Continuous rainfall‐runoff modelling for flood regime assessment requires input at the daily or even hourly time‐step. A review of the different methodologies suggested in the literature to downscale GCM results at smaller spatial and temporal resolutions is presented. The methods, from simple interpolation to more sophisticated dynamical modelling, through multiple regression and weather generators, are, however, mostly based directly on GCM outputs, sometimes at daily time‐step. The approach adopted is a simple, empirical methodology based on modelled monthly changes from the HadCM2 greenhouse gases experiment for the time horizon 2050s. Three daily rainfall scenarios are derived from the same set of monthly changes, representing different possible changes in the rainfall regime. The first scenario represents an increase of the occurrence of frontal systems, corresponding to a decrease in the rainfall intensity; the second corresponds to an increase in convective storm‐type rainfall, characterized by extreme events with higher intensity; the third one assumes an increase in the monthly rainfall without any change in rainfall variability. A continuous daily rainfall‐runoff model, calibrated for the Severn catchment, was used to generate daily flow series for the 1961–90 baseline period and the 2050s, and a peaks‐over‐threshold analysis was undertaken to produce flood frequency distributions for the two time horizons. Though the three scenarios lead to an increase in the magnitude and the frequency of the extreme flood events, the impact is strongly influenced by the type of daily rainfall scenario applied. We conclude that if the next generation of GCMs produce more reliable rainfall variance estimates, then more appropriate ways of deriving rainfall scenarios could be developed using weather generators rather than empirical methods. Copyright © 2002 John Wiley &amp; Sons, Ltd.

Derivation of a curve number and kinematic-wave based flood frequency distribution

The physically-based flood frequency models use readily available rainfall data and catchment characteristics to derive the flood frequency distribution. In the present study, a new physically-based flood frequency distribution has been developed. This model uses bivariate exponential distribution for rainfall intensity and duration, and the Soil Conservation Service-Curve Number (SCS-CN) method for deriving the probability density function (pdf) of effective rainfall. The effective rainfall-runoff model is based on kinematic-wave theory. The results of application of this derived model to three Indian basins indicate that the model is a useful alternative for estimating flood flow quantiles at ungauged sites.

Evaluation of Mixed-Population Flood-Frequency Analysis

A mixed population of flood flows was shown to cause quality-of-fit problems if a single-popu- lation flood-frequency distribution was used to describe the flood data. The three populations in this mix were ''ordinary,'' tropical cyclone, and ice-jam-release floods. Parametric descriptions of the single and separated flood populations were evaluated using probability-plot correlation-coefficient tests. These tests quantified how well the flood-probability distributions agreed with plotting-position descriptions of the data and quantified the differences due to the mixed-population analysis. High outliers caused the high skewness found in the single- population analyses. The tropical cyclone component was underestimated by single-population analyses at gaug- ing stations in Massachusetts that had little data.

A derived flood frequency distribution for correlated rainfall intensity and duration

A derived flood frequency distribution (DFFD) combines a stochastic rainfall model with a deterministic rainfall–runoff model to obtain a physically based probability distribution of flood discharges. Previous DFFD studies have either assumed that rainfall intensity and duration are independent or negatively correlated. This study is more general than previous studies because it accommodates both positive and negative correlations between rainfall intensity and duration. Rainfall–runoff processes are modeled using a φ-index infiltration model and a geomorphoclimatic instantaneous unit hydrograph. Applications to four Indian watersheds and one US watershed demonstrates that (1) the correlation of rainfall intensity and duration has an important impact on the DFFD and (2) the DFFD provides a potentially useful alternative for estimating flood flow quantiles at ungaged sites.

Topographic Influences on Flood Frequency Analyses

A model that predicts the formation of variable source areas by using the catchment’s topographic index distribution is used to determine the impact of topography, and the variation in contributing area, on the flood frequency distribution of a small catchment in southern Ontario. Log Pearson Type III distributions were fit to data using four different topographic distributions and 1000 randomly-generated storms and antecedent moisture conditions. The four topographic distributions included one for the actual catchment, a second that produced smaller contributing areas, a third that produced larger contributing areas, and a fourth in which the entire catchment contributed to runoff, if runoff was generated during the storm. All data were fitted reasonably well, except for the fourth case which produced the poorest fit. For return periods of less than 10 years, all topographic distributions produced peak flow rates that were roughly similar in magnitude, with the fourth case having the lowest values. However, at return periods of more than 10 years, the third topographic distribution produced higher flow rates than the first and second topographic distributions, while the fourth distribution produced the highest flows of all.