Flood Frequency Distribution Research Articles

Comparison of nonstationary models in analyzing bivariate flood frequency at the Three Gorges Dam

Traditional flood frequency analysis is usually performed under the stationary assumption that flood elements, such as flood peak and flood volume, are independent and identically distributed (i.i.d). However, with global climate change and human activities across the landscape, stationary approaches cannot capture the nonstationary characteristics of flood events. This study aims to explore the key elements in establishing an effective bivariate nonstationary flood frequency model for flood peak and volume series at the Three Gorges Dam in China. A stationary reference model and six nonstationary models were established and rigorously compared to evaluate their benefits and limitations, including two time-informed models and four climate-informed models that consider time and climate indices as explanatory variables. The results suggest that nonstationary models are clearly superior to stationary models with respect to model performance based on the deviance information criterion (DIC). The time-informed nonstationary model provides a potential tool to project future trends in flood return periods with minimal data availability, yet the uncertainty in the estimation of design values of such models is limited. On the other hand, explicitly incorporating climate indices as explanatory variables of flood frequency distribution can significantly improve model performance and reduce uncertainty but at the cost of increased model complexity.

Regional Flood Frequency Analysis for a Poorly Gauged Basin Using the Simulated Flood Data and L-Moment Method

The design of hydraulic structures and the assessment of flood control measures require the estimation of flood quantiles. Since observed flood data are rarely available at the specific location, flood estimation in un-gauged or poorly gauged basins is a common problem in engineering hydrology. We investigated the flood estimation method in a poorly gauged basin. The flood estimation method applied the combination of rainfall-runoff model simulation and regional flood frequency analysis (RFFA). The L-moment based index flood method was performed using the annual maximum flood (AMF) data simulated by the rainfall-runoff model. The regional flood frequency distribution with 90% error bounds was derived in the Chungju dam basin of Korea, which has a drainage area of 6648 km2. The flood quantile estimates based on the simulated AMF data were consistent with the flood quantile estimates based on the observed AMF data. The widths of error bounds of regional flood frequency distribution increased sharply as the return period increased. The results suggest that the flood estimation approach applied in this study has the potential to estimate flood quantiles when the hourly rainfall measurements during major storms are widely available and the observed flood data are limited.

On the relationship between flood and contributing area

AbstractAlthough it is well known that the vast majority of the time only a portion of any watershed contributes run‐off to the outlet, this extent is rarely documented. Also, the power law form of the streamflow and contributing area (Q‐Ac) relationship has been known for a half century, but it is uncommon for it to be quantified, and time series of contributing area extensive enough to calculate its frequency distribution are almost non‐existent. Data from the Canadian Prairies, where there are extensive estimates of contributing area during the median annual flood, imply that the power law coefficient for any Q‐Ac curve is a function of flow magnitude and return period. These data also suggest that regional flood frequency curves are a construct of Q‐Ac curves from individual basins. This paper will discuss research that attempted to reproduce the Q‐Ac curves for the La Salle River Watershed with a semidistributed numerical hydrological model, MESH‐PDMROF. The model simulated streamflow reasonably well (Nash Sutcliffe values = 0.62) compared with published examples of comparable models applied in the region. Estimates of the coefficient and exponent of the Q‐Ac power law function ranged from 0.08–0.14 and 0.9–1.12, respectively. These exponent values were lower than those of regional flood frequency curves and support the theory that regional flood frequency curves are a construct of Q‐Ac curves. Simulations of the area contributing to the median annual flood were lower (0.3) than those derived from independent topographic analysis (0.9) described in earlier literature though there is uncertainty in both these estimates. This uncertainty was extended across the flood frequency distribution and may be too large to definitively verify the study hypothesis.

Implications of flood disturbance for conservation and management of giant panda habitat in human-modified landscapes

As certain extreme weather events are becoming frequent and intense, conservationists must identify areas across species' ranges recurrently affected, especially with regard to threatened species. Focusing on the giant panda (Ailuropoda melanoleuca) and historical flood frequency distribution, we determined overlaps between panda distribution affected by floods and nature reserves. We also examined the correspondence between areas subject to high flood exposure densities, areas with high panda habitat use, and areas that exhibit high human density. Of the 67 reserves established for giant panda conservation 7 included areas with the highest flood exposure densities while having a mean exposure ranging between 20 and 75%. In Sichuan province up to 32% of areas of high habitat use were subject to low flood density, and 10% overlapped with areas subject to high flood density. We also found that 40% of the total area with high human density was subject to a high flood density. Our findings indicate that high frequency of flooding is affecting areas of nature reserves where people are rather than areas which pandas are using more intensively. In areas occupied by pandas, strategies should remain focus on mitigating habitat degradation and fragmentation caused by human activities that can also reduce habitat resilience to floods. Management aimed at reducing vulnerability and enhancing resilience in flood-prone areas is warranted if we are to prevent negative indirect impacts on panda habitat driven by human responses to increasingly frequent and intense extreme weather events in the coming decades.

Incorporating reservoir impacts into flood frequency distribution functions

Assessing flood frequency is pivotal for hydrology, with implications for many fields ranging from river science to the insurance industry. Reservoir regulation may alter the characteristics of the flood frequency distribution function. This paper incorporates reservoir impacts as an inherent variable to derive an analytical solution of outflow peaks and proposes new flood frequency distributions. Steps are as follows: (1) the original flood without reservoir impacts is assumed to follow a Pearson type III distribution, (2) linear and nonlinear reservoir models, including numerical integration and triangular area calculation methods, are proposed to simulate the relationships between inflow and outflow peaks, and (3) the flood frequency distributions resulting from reservoir impacts are derived. Derived equations are applied to the Shuibuya and Wuqiangxi reservoirs in China. Results show that: (1) although the numerical integration method with the nonlinear model is comparable with the reservoir flood routing, the triangle area calculation method with the nonlinear model is recommended for its accuracy and simplicity, (2) the reservoir regulation changes the flood frequency distribution function entirely in the nonlinear reservoir model, while only change the parameter in the linear reservoir model, and (3) downstream flood’s CV can be increased or decreased, which depends on the reservoir regulating capacity. It is indicated that altering the parameters of the flood frequency distribution is not sufficient to characterize watershed under reservoir control. This paper proposes the analytical solution about inflow and outflow peaks, which can point out the possible changes in the watershed with reservoir construction in plan.

Frequency Analysis and Uncertainty Assessment of Annual Maximum Flood Series Using Bayesian MCMC Method

The calculation of flood quantiles and its uncertainty estimation are important subjects of hydraulic engineering planning and water resources management. In this study, the Bayesian theory is used to implement frequency analysis and uncertainty assessment of annual maximum flood series, the Generalized Extreme Value (GEV) distribution is considered as the flood frequency distribution line type, and the Markov chain Monte Carlo (MCMC) method based on Metropolis-Hastings algorithm is used to evaluate the GEV distribution parameters, then the posterior distributions of flood flow quantiles are used to calculate the point estimations and interval estimations of flood design values under different return periods. The results show that the fitting effect of the Bayesian MCMC method is the same as the maximum likelihood estimation (MLE), but the Bayesian MCMC more superior when the uncertainties were considered. Compared with the traditional methods of flood frequency analysis, the proposed Bayesian MCMC method provides not only the design flood estimated values, but also the confidence intervals of the estimated values. In addition, the lengths between upper confidence limits and estimated values are greater than the lower confidence limits and estimated values, this asymmetry is more realistic than the traditional methods such as the delta method, thus improve the reliability of flood frequency analysis.

How extreme was the October 2015 flood in the Carolinas? An assessment of flood frequency analysis and distribution tails

This paper examines the frequency, distribution tails, and peak-over-threshold (POT) of extreme floods through analysis that centers on the October 2015 flooding in North Carolina (NC) and South Carolina (SC), United States (US). The most striking features of the October 2015 flooding were a short time to peak (Tp) and a multi-hour continuous flood peak which caused intensive and widespread damages to human lives, properties, and infrastructure. The 2015 flooding was produced by a sequence of intense rainfall events which originated from category 4 hurricane Joaquin over a period of four days. Here, the probability distribution and distribution parameters (i.e., location, scale, and shape) of floods were investigated by comparing the upper part of empirical distributions of the annual maximum flood (AMF) and POT with light- to heavy- theoretical tails: Fréchet, Pareto, Gumbel, Weibull, Beta, and Exponential. Specifically, four sets of U.S. Geological Survey (USGS) gauging data from the central Carolinas with record lengths from approximately 65–125 years were used. Analysis suggests that heavier-tailed distributions are in better agreement with the POT and somewhat AMF data than more often used exponential (light) tailed probability distributions. Further, the threshold selection and record length affect the heaviness of the tail and fluctuations of the parent distributions. The shape parameter and its evolution in the period of record play a critical and poorly understood role in determining the scaling of flood response to intense rainfall.

Multi-temporal flood mapping and satellite altimetry used to evaluate the flood dynamics of the Bolivian Amazon wetlands

The Bolivian Amazon wetlands are extensive floodplains distributed over the Mamore, Beni, Madre de Dios and Guapore Rivers. Located within the upper Madeira River Basin, the wetlands play important roles in regulating the biogeochemical processes and hydrological cycle of the region. In addition, they have major ecological and hydrological relevance for the entire Amazon Basin. These wetlands are characterized by the occurrence of episodic floods that result from contrasting hydro-meteorological processes in the Andean Mountain region, the piedmont area and the Amazon lowlands. In this study, we characterized the flood dynamics of the region using multi-temporal flood mapping based on optical altimetry (MODIS – Moderate Resolution Imaging Spectroradiometer – M*D09A1) and satellite altimetry (ENVISAT RA-2 and SARAL AltiKa altimeters). This study provides new insights regarding the frequency, magnitude and spatial distribution of exogenous floods, which are created by flood waves from the Andes; and endogenous floods, which result from runoff originating in the lowlands. The maximum extent of flooding during 2001–2014 was 43144 km2 in the Mamore Basin and 34852 km2 in the Guapore Basin, and the total surface water storage in these floodplains reached 94 km3. The regionalization of flood regimes based on water stage time series signatures allowed those regions that are exposed to frequent floods, which are generally located along rivers without a direct connection with the Andes, to be distinguished from floodplains that are more dependent on flood waves originating in the Andes and its piedmonts. This information is of great importance for understanding the roles of these wetlands in the provision of ecosystem services.

Parent Flood Frequency Distribution of Turkish Rivers

Parent Flood Frequency Distribution of Turkish Rivers

Hydrological change: Towards a consistent approach to assess changes on both floods and droughts

Abstract Several studies have found that the frequency, magnitude and spatio-temporal distribution of droughts and floods have significantly increased in many regions of the world. Yet, most of the methods used in detecting trends in hydrological extremes 1) focus on either floods or droughts, and/or 2) base their assessment on characteristics that, even though useful for trend identification, cannot be directly used in decision making, e.g. integrated water resources management and disaster risk reduction. In this paper, we first discuss the need for a consistent approach to assess changes on both floods and droughts, and then propose a method based on the theory of runs and threshold levels. Flood and drought changes were assessed in terms of frequency, length and surplus/deficit volumes. This paper also presents an example application using streamflow data from two hydrometric stations along the Po River basin (Italy), Piacenza and Pontelagoscuro, and then discuss opportunities and challenges of the proposed method.

Evaluating the impact of climate change on fluvial flood risk in a mixed-use watershed

Predicting flood risk is important for climate change adaptation. We quantify fluvial flood risk due to changing climate in a mixed-use watershed in Michigan, USA. We apply two approaches to project future climate change: an ensemble of temperature and precipitation perturbations on the historical record and an ensemble of global and regional climate models. We incorporate climate projections into the Soil and Water Assessment Tool (SWAT) to estimate daily streamflow, then quantify flood risk using indices related to flood probability, duration, magnitude, and frequency. Results indicate rising temperatures may counteract small increases in precipitation, likely due to increased evapotranspiration. Climate model data without bias correction used in SWAT produced reasonable future streamflow changes—similar to the perturbation of historical climate—therefore retaining the predicted change in the flood frequency distribution. This work advances the application of climate models in SWAT for flood risk evaluation at watershed scales.

The complexities of urban flood response: Flood frequency analyses for the Charlotte metropolitan region

AbstractWe examine urban flood response through data‐driven analyses for a diverse sample of “small” watersheds (basin scale ranging from 7.0 to 111.1 km2) in the Charlotte Metropolitan region. These watersheds have experienced extensive urbanization and suburban development since the 1960s. The objective of this study is to develop a broad characterization of land surface and hydrometeorological controls of urban flood hydrology. Our analyses are based on peaks‐over‐threshold flood data developed from USGS streamflow observations and are motivated by problems of flood hazard characterization for urban regions. We examine flood‐producing rainfall using high‐resolution (1 km2 spatial resolution and 15 min time resolution), bias‐corrected radar rainfall fields that are developed through the Hydro‐NEXRAD system. The analyses focus on the 2001–2015 period. The results highlight the complexities of urban flood response. There are striking spatial heterogeneities in flood peak magnitudes, response times, and runoff ratios across the study region. These spatial heterogeneities are mainly linked to watershed scale, the distribution of impervious cover, and storm water management. Contrasting land surface properties also determine the mixture of flood‐generating mechanisms for a particular watershed. Warm‐season thunderstorm systems and tropical cyclones are main flood agents in Charlotte, with winter/spring storms playing a role in less‐urbanized watersheds. The mixture of flood agents exerts a strong impact on the upper tail of flood frequency distributions. Antecedent watershed wetness plays a minor role in urban flood response, compared with less‐urbanized watersheds. Implications for flood hazard characterization in urban watersheds and for advances in flood science are discussed.

Real-time updating of the flood frequency distribution through data assimilation

Abstract. We explore the memory properties of catchments for predicting the likelihood of floods based on observations of average flows in pre-flood seasons. Our approach assumes that flood formation is driven by the superimposition of short- and long-term perturbations. The former is given by the short-term meteorological forcing leading to infiltration and/or saturation excess, while the latter is originated by higher-than-usual storage in the catchment. To exploit the above sensitivity to long-term perturbations, a meta-Gaussian model and a data assimilation approach are implemented for updating the flood frequency distribution a season in advance. Accordingly, the peak flow in the flood season is predicted in probabilistic terms by exploiting its dependence on the average flow in the antecedent seasons. We focus on the Po River at Pontelagoscuro and the Danube River at Bratislava. We found that the shape of the flood frequency distribution is noticeably impacted by higher-than-usual flows occurring up to several months earlier. The proposed technique may allow one to reduce the uncertainty associated with the estimation of flood frequency.

On seasonal and semi-annual approach for flood frequency analysis

As a supplementary method to the conventional flood frequency analysis based on annual peak flows, we propose an approach in this paper to infer the flood frequency distribution on quarterly and semi-annual time scale, which are then converted to annual time scale to obtain the floods corresponding to return periods in unit of year. Two criteria for test of data independence, namely, minimum 7 and 15-day interval between two consecutive peak flows, are tested. The proposed approach was applied to Des Moines River at Fort Dodge, Iowa, USA using its 62 years of observation daily flows. The results show that the estimated floods for given return periods from quarter-annual data series are in general higher than the corresponding estimated floods from semi-annual data series, which is further larger than estimated floods from annual peak flows. The floods estimated from semi-annual data series agree well with the results of previous US Geological Survey study.

Comparative Study on the Selection Criteria for Fitting Flood Frequency Distribution Models with Emphasis on Upper-Tail Behavior

The upper tail of a flood frequency distribution is always specifically concerned with flood control. However, different model selection criteria often give different optimal distributions when the focus is on the upper tail of distribution. With emphasis on the upper-tail behavior, five distribution selection criteria including two hypothesis tests and three information-based criteria are evaluated in selecting the best fitted distribution from eight widely used distributions by using datasets from Thames River, Wabash River, Beijiang River and Huai River. The performance of the five selection criteria is verified by using a composite criterion with focus on upper tail events. This paper demonstrated an approach for optimally selecting suitable flood frequency distributions. Results illustrate that (1) there are different selections of frequency distributions in the four rivers by using hypothesis tests and information-based criteria approaches. Hypothesis tests are more likely to choose complex, parametric models, and information-based criteria prefer to choose simple, effective models. Different selection criteria have no particular tendency toward the tail of the distribution; (2) The information-based criteria perform better than hypothesis tests in most cases when the focus is on the goodness of predictions of the extreme upper tail events. The distributions selected by information-based criteria are more likely to be close to true values than the distributions selected by hypothesis test methods in the upper tail of the frequency curve; (3) The proposed composite criterion not only can select the optimal distribution, but also can evaluate the error of estimated value, which often plays an important role in the risk assessment and engineering design. In order to decide on a particular distribution to fit the high flow, it would be better to use the composite criterion.

Derived flood frequency distributions considering individual event hydrograph shapes

Derived in this paper is the frequency distribution of the peak discharge rate of a random runoff event from a small urban catchment. The derivation follows the derived probability distribution procedure and incorporates a catchment rainfall-runoff model with approximating shapes for individual runoff event hydrographs. In the past, only simple triangular runoff event hydrograph shapes were used, in this study approximating runoff event hydrograph shapes better representing all the possibilities are considered. The resulting closed-form mathematical equations are converted to the commonly required flood frequency distributions for use in urban stormwater management studies. The analytically determined peak discharge rates of different return periods for a wide range of hypothetical catchment conditions were compared to those determined from design storm modeling. The newly derived equations generated results that are closer to those from design storm modeling and provide a better alternative for use in urban stormwater management studies.

An assessment of using subsampling method in selection of a flood frequency distribution

In flood frequency analysis, a suitable probability distribution function is required in order to establish the flood magnitude-return period relationship. Goodness of fit (GOF) techniques are often employed to select a suitable distribution function in this context. But they have been often criticized for their inability to discriminate between statistical distributions for the same application. This paper investigates the potential utility of subsampling, a resampling technique with the aid of a GOF test to select the best distribution for frequency analysis. The performance of the methodology is assessed by applying the methodology to observed and simulated annual maximum (AM) discharge data series. Several AM series of different record lengths are used as case studies to determine the performance. Numerical analyses are carried out to assess the performance in terms of sample size, subsample size and statistical properties inherent in the AM data series. The proposed methodology is also compared with the standard Anderson–Darling (AD) test. It is found that the methodology is suitable for a longer data series. A better performance is obtained when the subsample size is taken around half of the underlying data sample. The methodology has also outperformed the standard AD test in terms of effectively discriminating between distributions. Overall, all results point that the subsampling technique can be a promising tool in discriminating between distributions.

Long term prediction of flood occurrence

Abstract. How long a river remembers its past is still an open question. Perturbations occurring in large catchments may impact the flow regime for several weeks and months, therefore providing a physical explanation for the occasional tendency of floods to occur in clusters. The research question explored in this paper may be stated as follows: can higher than usual river discharges in the low flow season be associated to a higher probability of floods in the subsequent high flow season? The physical explanation for such association may be related to the presence of higher soil moisture storage at the beginning of the high flow season, which may induce lower infiltration rates and therefore higher river runoff. Another possible explanation is persistence of climate, due to presence of long-term properties in atmospheric circulation. We focus on the Po River at Pontelagoscuro, whose catchment area amounts to 71 000 km2. We look at the stochastic connection between average river flows in the pre-flood season and the peak flows in the flood season by using a bivariate probability distribution. We found that the shape of the flood frequency distribution is significantly impacted by the river flow regime in the low flow season. The proposed technique, which can be classified as a data assimilation approach, may allow one to reduce the uncertainty associated to the estimation of the flood probability.

Incorporating seasonality into event-based joint probability methods for predicting flood frequency: A hybrid causative event approach

Summary Flood extremes are driven by highly variable and complex climatic and hydrological processes. Observational evidence has identified that seasonality of climate variables has a major impact on flood peaks. However, event-based joint probability approaches for predicting the flood frequency distribution (FFD), which are commonly used in practice, do not commonly incorporate climate seasonality. This study presents an advance in event-based joint probability approaches by incorporating seasonality using the hybrid causative events (HCE) approach. The HCE was chosen because it uses the true causative events of the floods of interest and is able to combine the accuracy of continuous simulation with the computational efficiency of event-based approaches. The incorporation of seasonality is evaluated using a virtual catchment approach at eight sites over a wide range of Australian climate zones, including tropical, temperature, Mediterranean and desert climates (virtual catchment data for the eight sites is freely available via digital repository). The seasonal HCE provided accurate predictions of the FFD at all sites. In contrast, the non-seasonal HCE significantly over-predicted the FFD at some sites. The need to include seasonality was influenced by the magnitude of the seasonal variation in soil moisture and its coherence with the seasonal variation in extreme rainfall. For sites with a low seasonal variation in soil moisture the non-seasonal HCE provided reliable estimates of the FFD. For the remaining sites, it was found difficult to predict a priori whether ignoring seasonality provided a reliable estimate of the FFD, hence it is recommended that the seasonal HCE always be used. The practical implications of this study are that the HCE approach with seasonality is an accurate and efficient event-based joint probability approach to derive the flood frequency distribution across a wide range of climatologies.

A recursive multi-scaling approach to regional flood frequency analysis

Summary Scaling approaches are widely used by hydrologists for Regional Frequency Analysis (RFA) of floods at ungauged/sparsely gauged site(s) in river basins. This paper proposes a Recursive Multi-scaling (RMS) approach to RFA that overcomes limitations of conventional simple- and multi-scaling approaches. The approach involves identification of a separate set of attributes corresponding to each of the sites (being considered in the study area/region) in a recursive manner according to their importance, and utilizing those attributes to construct effective regional regression relationships to estimate statistical raw moments (SMs) of peak flows. The SMs are then utilized to arrive at parameters of flood frequency distribution and quantile estimate(s) corresponding to target return period(s). Effectiveness of the RMS approach in arriving at flood quantile estimates for ungauged sites is demonstrated through leave-one-out cross-validation experiment on watersheds in Indiana State, USA. Results indicate that the approach outperforms index-flood based Region-of-Influence approach, simple- and multi-scaling approaches and a multiple linear regression method.