Flood Frequency Estimation Research Articles

Regional flood–rainfall duration-frequency modeling at small ungaged sites

Flood frequency data for different durations of floods are required in many practical hydrologic applications. The estimation of flood frequency as an integrated function of return period and flood duration can be accomplished by flood-duration-frequency modeling. This study introduces a new approach to regional flood-duration-frequency modeling that is based on statistical properties of combined flood–rainfall events. The approach integrates flood-duration-frequency (QDF) and rainfall depth-duration-frequency (DDF) models into one regional flood–rainfall duration-frequency model (QDDF). The proposed model has only one local parameter, which accounts for site-specific physiographic characteristics. Regional parameters of the model are determined from statistical properties of regional rainfall depth-duration-frequency curves. The main advantage of the proposed approach is that it relies on rainfall data, which are spatially and temporally more abundant than streamflow data, and usually also available in hydrologically ungaged areas. The regional QDDF model was applied to a set of small catchments from a hydro-climatologically homogeneous region in south-western Ontario, Canada. The performance of the model was compared to the performance of the conventional regional converging QDF model by means of a jack-knife procedure. The results showed that the proposed approach significantly outperformed the converging QDF model, leading to quantile estimates with three-times lower average BIAS and RMSE. The proposed QDDF model seems to be a promising alternative for the regional QDF modeling of floods in the study area.

Flash flooding in Spain: geomorphological approaches supporting flood frequency analysis, and the implications for the design of structures

AbstractConventional methods for the estimation of flood frequency are generally based on the statistical analysis of data series resulting from the measurement of water levels at specific locations, which are translated into discharges (m3/s) using standard stage/discharge relationships. Subsequently, these gauged flows are used to identify the largest flood event experienced by a river or catchment, and to produce growth curves used in the estimation of the return periods of specific flood events, as well as in the calculation of discharges for specific required design events (e.g. return period 1 in 100 year). In areas where gauging data records are scarce, and/or the data series are short or interrupted, geomorphological interpretation of the physical environment, dating of fluvial deposits and flooding episodes and hydraulic reconstruction of past flood events can be used as complementary tools aiding conventional hydrological and flood frequency analysis methods. This paper will discuss the undertaking of this approach in the Guadalope Catchment in northeast Spain. It will examine the findings in relation to the inadequate design of existing structures such as dams, spillways, canals and reservoirs, and will also look at the potential risks associated with flooding at present.

An investigation of site-similarity approaches to generalisation of a rainfall–runoff model

Abstract. This paper investigates a new approach to spatial generalisation of rainfall–runoff model parameters – site-similarity with pooling groups – for use in flood frequency estimation at ungauged sites using continuous simulation. The method is developed for the generalisation of a simple conceptual model, the Probability Distributed Model, with four parameters which require specific estimation. The study is based on a relatively large sample of catchments in Great Britain. Various options are investigated within the approach. In the final version, the pooling group comprises the 10 calibrated catchments closest, in catchment property space, to the target site, where the catchment properties used to define the space differ for each parameter of the model. An analysis that, explicitly, takes account of calibration uncertainty as a source of error enables the uncertainty associated with generalised parameter values to be reduced, justifiably. The approach uses calibration uncertainty estimated through jack-knifing and employs a weighting scheme within pooling groups that uses weights which vary both with distance in the catchment property space and with the calibration uncertainty. Models using generalised values from this approach perform relatively well compared with direct calibration. Although performance appears to be better in some areas of the country than others, there are no obvious relationships between catchment properties and performance.

Uncertainty analysis for estimating flood frequencies for ungauged catchments using rainfall-runoff models

Continuous simulation of flows for ungauged catchments is a methodology being developed for estimating flood frequencies where no flood records exist. This involves driving a rainfall-runoff model with either simulated or observed rainfalls, using values of the rainfall-runoff model parameters derived using a generalisation procedure based on analysing sets of parameter values for calibrated catchments. This paper examines the uncertainty associated with such generalised parameters, and carries this through to estimate the uncertainty of the generalised flood frequency curves for ungauged catchments. The approach used distinguishes two sources of uncertainty: the uncertainty in the parameters calibrated for individual catchments, and the uncertainty with which parameters for an ungauged catchment can be estimated based on calibrated parameters for other catchments and descriptors of those catchments. The uncertainty associated with estimates for ungauged catchments can then be reduced compared with a more direct approach, firstly by allowing one of the components of uncertainty to be omitted, and secondly by allowing the introduction of weighting schemes which reduce the effect of catchments where calibration uncertainty is high.

Climate Change and Floodplain Management in the United States

Federal agencies use flood frequency estimates to delineate flood risk, manage the National Flood Insurance Program, and ensure that Federal programs are economically efficient. The assumption behind traditional flood risk analysis is that climate is stationary, but anthropogenic climate change and better knowledge of interdecadal climate variability challenge the validity of the assumption. This paper reviews several alternative statistical models for flood risk estimation that do not assume climate stationarity. Some models require subjective judgement or presuppose an understanding of the causes of the underlying non-stationarity, which is problematic given our current knowledge of the interaction of climate and floods. Although currently out of favor, hydrometeorological models have been used for engineering design as alternatives to statistical models and could be adapted to different climate conditions. Floodplain managers should recognize the potentially greater uncertainty in flood risk estimation due to climate change and variability and try to incorporate the uncertainties into floodplain management decision-making and regulation.

Data-based comparison of seasonality-based regional flood frequency methods

During the last 10 years a growing number of regional flood frequency estimation studies have used flood seasonality descriptors for delineating hydrologically homogeneous regions. Seasonality of floods reflects a complex catchment’s hydrologic response to flood producing processes. Due to the high accuracy and robustness of flood date data, the use of flood seasonality indices became an attractive alternative to traditional regionalization approaches for the delineation of homogeneous regions, a key step in any regionalization study. This paper presents a data-based comparison of three flood seasonality regionalization methods. The methods are applied to a set of catchments in the province of Quebec (Canada). A jack-knife procedure is used to assess the performance of the methods in regional quantile estimation. The results are compared to those obtained from a traditional regionalization approach based on catchment physiographic similarities, and to the results from a scenario where information available in all catchments is used in the analysis. The seasonality method based on the peaks-over-threshold approach was concluded to lead to best results.

A comparison of three approaches to spatial generalization of rainfall–runoff models

The generalization of the parameters of rainfall-runoff models, to enable application at ungauged sites, is an important and ongoing area of research. This paper compares the performance of three alternative methods of generalization, for two parameter-sparse conceptual models (PDM and TATE), specifically for use in flood frequency estimation using continuous simulation. Two of the methods are based on fitting regression relationships between catchment properties and calibrated parameter values, using weighted or sequential regression (with weights based on estimates of calibration uncertainty), and the third is based on the use of pooling groups, defined through measures of site-similarity based on catchment properties. The study uses a relatively large sample of catchments in Britain. For the PDM, the site-similarity method performs best, but not greatly better than either regression method, so there may be cases where the use of regression would be preferable. For the TATE model, weighted regression performs best (with a very similar level of performance to that of the PDM with site-similarity), whereas site-similarity performs worst (due to poor performance for catchments with higher baseflow), indicating that the choice of model and generalization method should not be separated. The use of sequential regression, which was developed to try to allow for parameter interdependence, shows no clear advantage for either model. Other than the poor performance of the TATE model with site-similarity for catchments with a higher baseflow index, there are no clear relationships between performance of any model/method and catchment type.

RCM rainfall for UK flood frequency estimation. I. Method and validation

Regional Climate Models (RCMs) are a significant improvement over Global Climate Models (GCMs) in terms of their representation of rainfall at the spatial and temporal scale required for flood modelling. This paper presents the use of catchment rainfall and potential evaporation data derived directly from RCM data, as input to a spatially generalised continuous simulation rainfall-runoff model, for 15 catchments across Great Britain. The RCM (HadRM3H) is based on a ∼25 km grid across Europe and, rather than being nested within a GCM, is driven with boundary conditions determined by 15 years' of data from the ECMWF's global model for the period 1979–1993 (ERA-15). As the latter model continually assimilates observations of surface and atmospheric weather elements, output from the RCM can be expected to match observed conditions to a reasonable extent, enabling a direct comparison with simulations using observed input data. The rainfall-runoff model simulates continuous flow time-series, from which flood frequency curves are derived using a standard peaks-over-threshold method. The study covers return periods up to about 10 years (due to limited data availability) and relatively small catchments (<500 km 2). Overall, flood frequency curves derived using RCM inputs compare well with those using observed rainfall and evaporation inputs, although with a slight tendency to underestimate. Only two catchments show particularly bad underestimation however, which is due to their input RCM rainfall being significantly lower than that observed. Flood frequency estimation errors are in fact closely related to errors in annual average rainfall amounts for the RCM, which future improvements to the RCM will hopefully overcome.

RCM rainfall for UK flood frequency estimation. II. Climate change results

The first part of this two-part paper demonstrated the feasibility of the direct use of data from a high resolution (25 km) Regional Climate Model (RCM) to provide inputs for a rainfall-runoff model, in order to obtain estimates of flood frequency. This paper uses data from a climate change experiment with the same RCM (HadRM3H) to provide estimates of change in flood frequency between the 1970s and 2080s, for 15 catchments across Great Britain. This experiment is a rerun, at twice the horizontal resolution, of one of those used by the UK Climate Impacts Programme (UKCIP) in the construction of its UKCIP02 climate change scenarios for the UK. It thus allows an exploration of the implication of these scenarios using a resolution more suited to the detailed hydrological application addressed in this paper. Despite decreases in annual average rainfall in all but one catchment, eight show an increase in flood frequency at most return periods whereas two show substantial decreases. As part I of this paper showed a distinct positive correlation between errors in annual rainfall and errors in flood frequency, the fact that flood frequency can increase despite an overall decrease in rainfall implies a marked change in the distribution of rainfall, either in terms of the probability of rainfall events and/or its seasonal cycle. Decreases in flood peaks are shown for a number of the catchments in the south and east of England, despite an increase in winter mean and extreme rainfall. Increased summer and autumn soil moisture deficits are thought to be the reason for this. Other catchments, further north or west, show an increase in flood peaks, in some cases of over 50% at the 50-year return period. Care needs to be taken when interpreting these results, as they are based on a single RCM experiment (using driving data from one GCM under a single emissions scenario). Other RCM experiments may give quite different results, and ensemble runs would ideally be required to limit sample error.

The applicability of power-law frequency statistics to floods

Many natural hazards satisfy power-law (fractal) frequency-size statistics to a good approximation for medium and large events. Examples include earthquakes, volcanic eruptions, asteroid impacts, landslides, and forest fires. A major question is whether this is also true for floods. A number of authors have argued in favor of the applicability of power-law statistics to floods. We discuss these arguments and consider a number of examples, using both instrumental records and paleoflood studies. In our analyses we consider both annual and partial-duration flood series. We argue that use of annual floods for statistical considerations strongly biases the flood-frequency estimates, as in some years, the annual flood will be much smaller than a number of ‘statistically independent’ floods (partial-duration floods) in other years. We examine six USGS hydrologic stations with drainage areas from 41 to 95,300 km 2, representing very different climatic regions and hydrologic conditions, and with periods of records ranging from 74 to 110 water years. Excellent power-law fits to each partial-duration series are found taking Q∼ T α , with Q the discharge associated with the recurrence interval T, and the power-law exponent α ranging from 0.27 to 0.90. We also consider paleoflood estimates for Axehandle Alcove on the Colorado River and Bonza Alcove on the Paria River, and find that that power-law extrapolations based on instrumental partial-duration series for stations in each of these two areas is within a half order of magnitude when compared to their respective paleoflood estimates. Finally, we consider an alternative approach to extreme streamflows that has been proposed, examining the cumulative probability distribution of instrumental daily mean streamflows. We show that this distribution is in good agreement with the power-law correlation found using the partial-duration series.

Nonparametric Bayesian flood frequency estimation

A novel nonparametric Bayesian Monte-Carlo method is presented to estimate flood frequency. This method accommodates complex flood behaviors such as event clustering (repeated instances of similar magnitude floods) and can use varied data, such as gage and historical peak discharges, and paleohydrologic upper and lower bounds on peak discharge, while rigorously accounting for a wide variety of measurement uncertainties. In contrast to nonparametric kernel estimation approaches, the stochastic assumption is used to generate flood frequency models that span the data and provide about twice the number of degrees of freedom of the data. Each generated flood frequency model is scored using likelihoods that account for data measurement uncertainties. A parametric estimation approach ensures high precision because posterior sampling is known. However, parametric approaches can produce substantial biases because the classes of allowed flood frequency models are restricted. These biases are completely undetectable within a parametric paradigm. The nonparametric approach used here surrenders some precision in the pursuit of reduced bias and greater overall accuracy and assurance; it reveals the annual probabilities where discharge becomes unconstrained by the data, thereby eliminating unsubstantiated extrapolation. Parametric flood frequency estimation introduces strong extrapolation priors that make it difficult, if not impossible, to determine when flood frequency is not longer constrained by the data. Nonparametric and parametric flood frequency estimation using a demonstration data set shows that while parametric functions may sometimes provide reasonable fits to subsets of paleohydrologic data, parametric flood frequency estimates are likely to produce substantial biases over entire log cycles of annual exceedance probability, when using paleohydrologic data spanning thousands of years.

Reconstructing the ca. 100-year flood in Northern Thailand

The key utilities of palaeohydrological studies are the potential to extend the flood record of a catchment and improve estimates of flood frequency and magnitude. In this study, we use a hydraulic model to produce estimates of discharge based on PSI (Palaeo-Stage Indicator) evidence from large floods for a study reach of the Mae Chaem River, Thailand. Careful calibration of this model, especially Manning's n, was possible because of the availability of PSIs from several modern gauged flows. Organic PSI evidence, contained in a cave, permitted dating of the largest flood for which evidence was available, which is close to the 100-year flood. The magnitude of this flood is twice that predicted from an extrapolation of the 49-year gauging record employing the Gumbel EV1 flood frequency model, officially endorsed by water management agencies in Thailand. This magnitude of flood is, however, very similar to that predicted from a Power Law model and suggests that extreme flood magnitude and frequency in this catchment conform to Power Law behaviour. These results significantly increase the perception of flood risk for the area, and this palaeohydrological case study represents the first for the region.

A methodology for regional flood frequency estimation based on scaling properties

There is a persisting need for extreme value assessments of discharge for ungauged catchments for design purposes, flood protection and flood risk analysis. A methodology is put forward for estimating flood quantiles in ungauged catchments, taking into account the scaling behaviour of discharge in a homogeneous region. From an assumption that the spatial distribution of specific discharge generation is a shifted exponential distribution, theoretical expressions of the maximum specific discharge values relative to catchment size are developed and a regional scaling equation is presented. The homogeneity constraint refers to climatic conditions, whereas catchment heterogeneity due to physiographic features of catchments is incorporated in the models using multiple regression analysis. The methodology is tested for a region in Southern Norway with homogeneous climatic conditions but with varying physiographic catchment characteristics. It is investigated if the extreme discharge values estimated with traditional methods are adequately reproduced with the proposed methodology. For the tested region, the agreement between flood quantiles estimated with the proposed methodology and flood quantiles estimated from observed data is good. The effective lake percentage and the river gradient proved to be significant descriptors of the deviation from the scaling procedure. Copyright © 2004 John Wiley & Sons, Ltd.

Physiographical space‐based kriging for regional flood frequency estimation at ungauged sites

A physiographical space‐based kriging method is proposed for regional flood frequency estimation. The methodology relies on the construction of a continuous physiographical space using physiographical and meteorological characteristics of gauging stations and the use of multivariate analysis techniques. Two multivariate analysis methods were tested: canonical correlation analysis (CCA) and principal components analysis. Ordinary kriging, a geostatistical technique, was then used to interpolate flow quantiles through the physiographical space. Data from 151 gauging stations across the southern part of the province of Quebec, Canada, were used to illustrate this approach. In order to evaluate the performance of the proposed method, two validation techniques, cross validation and split‐sample validation, were applied to estimate flood quantiles corresponding to the 10, 50, and 100 year return periods. Results of the proposed method were compared to those produced by a traditional regional estimation method using the canonical correlation analysis. The proposed method yielded satisfactory results. It allowed, for instance, for estimating the 10 year return period specific flow with a coefficient of determination of up to 0.78. However, this performance decreases with the increase in the quantile return period. Results also showed that the proposed method works better when the physiographical space is defined using canonical correlation analysis. It is shown that kriging in the CCA physiographical space yields results as precise as the traditional estimation method, with a fraction of the effort and the computation time.

Confidence intervals for a spatially generalized, continuous simulation flood frequency model for Great Britain

There is growing interest in the application of “continuous simulation” conceptual rainfall‐runoff models for flood frequency estimation as an adjunct to event‐based or statistical design methodology. The approach has advantages that stem from the use of models with continuous water balance accounting. Conceptual rainfall‐runoff models usually require calibration, which in turn requires gauged rainfall and flow data. One of the key challenges is therefore to develop ways of generalizing models for use at ungauged sites. Recent work has produced a prototype scheme for achieving this aim in Great Britain for two catchment models by relating model parameters to spatial catchment properties, such as soils, topography, and geology. In this paper we present an analysis of the uncertainty associated with one of the generalized models (the “probability distributed model”) in terms of confidence intervals for simulations at test sites that are treated as if they were ungauged. This is done by fitting regression relationships between hydrological model parameters and catchment properties so as to estimate the parameters as distribution functions for the ungauged site case. Flood flow outputs are then simulated from the parameter distributions and used to construct approximate confidence intervals. Comparison with gauged data suggests that the generalized model may be tentatively accepted. Uncertainty in the modeled flood flows is often of a similar order to the uncertainty surrounding a more conventional statistical model, in this case a single‐site generalized Pareto distribution fitted to the gauged data.

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.

Likelihood-based approaches to flood frequency estimation

The aim of a flood frequency analysis is to make inferences about the frequency with which extreme river flows occur at a location of interest, hereafter referred to as the target site. It is a common practice to use information from several locations for this purpose, especially when flood data are limited or non-existent at the target site. A crucial issue is then how information from different locations is combined. Should data from the target site be predominant or should the estimated flood characteristics be some sort of average of those at the locations used? How should information on the variability in flood characteristics between different locations be used? How best can information on important hydrological variables be incorporated? This article examines these issues. Two likelihood-based approaches, a regression model and an empirical Bayes analysis, are described and related to the widely used region-of-influence approach. In the discussion a regression model incorporating random site effects is proposed.

Practical Extreme Value Modelling of Hydrological Floods and Droughts: A Case Study

Estimation of flood and drought frequencies is important for reservoir design and management, river pollution, ecology and drinking water supply. Through an example based on daily streamflow observations, we introduce a stepwise procedure for estimating quantiles of the hydrological extremes floods and droughts. We fit the generalised extreme value (GEV) distribution by the method of block maxima and the generalised Pareto (GP) distribution by applying the peak over threshold method. Maximum likelihood, penalized maximum likelihood and probability weighted moments are used for parameter estimation. We incorporate trends and seasonal variation in the models instead of splitting the data, and investigate how the observed number of extreme events, the chosen statistical model, and the parameter estimation method effect parameter estimates and quantiles. We find that a seasonal variation should be included in the GEV distribution fitting for floods using block sizes less than one year. When modelling droughts, block sizes of one year or less are not recommended as significant model bias becomes visible. We conclude that the different characteristics of floods and droughts influence the choices made in the extreme value modelling within a common inferential strategy.

Hydrological analysis of the river Aude, France, flash flood on 12 and 13 November 1999

On the 12th and the 13th November 1999, the Aude region received amounts of rainfall that locally exceeded 500 mm. This extreme rainfall event resulted in one of the century's most significant floods in the Aude river catchment area and produced remarkable flash floods in some of its tributaries. Peak flood discharges from many upstream watersheds (area smaller than 100 km 2) exceeded 10 m 3/s/km 2. An extensive post-flood investigation was carried out in 2000 to collect information concerning the floods in seven of these upstream tributaries and to analyse the hydrological behaviour of the watersheds during this extreme rainfall event. As well as analysing the available rainfall data and estimating peak discharges on the basis of high water marks, information related to the timing of the floods, as provided by eyewitnesses, was gathered. A simple hydrological model, based on the SCS method and the kinematic wave equation, was used to guide the hydrological interpretation. This study revealed some interesting aspects of the hydrological rainfall-runoff relation during flash flooding that could be important for estimating flood frequencies and flood forecasting: (1) around 200 mm of rainwater were retained in the catchments without contributing to the flood flow, (2) the response of the watersheds to the intense storm bursts was late and relatively sudden, (3) no significant effects resulting from different types of land use could be identified. These conclusions, based on inaccurate data, were validated for the entire Aude river catchment. They also concur with some other reported flash flood data.

Discussion of “Uncertainty Assessment of Regionalized Flood Frequency Estimates” by C. De Michele and R. Rosso

Discussion of “Uncertainty Assessment of Regionalized Flood Frequency Estimates” by C. De Michele and R. Rosso