Wadi flow in the Arabian Gulf states

Real data on wadi flood flows from Saudi Arabia, Yemen, Oman, Kuwait, UAE, Bahrain and Qatar were used to develop methodologies for the prediction of annual maximum flows and average monthly flows in the Arabian Gulf states. For the prediction of annual maximum floods, three methods have been investigated. In the first method, regional curves were developed and used together with the mean annual flood flow, estimated from the characteristics of the drainage basin, to estimate flood flows at a location in the basin. The second method fits data to various probability distribution functions, with a developed methodology introduced to account for floods generated by more than one system of climate, and the best fitted function was used for flood estimates. In the third method, only floods over a threshold, which depends on characteristics of the drainage basin, were considered and modelled. For the prediction of average monthly flows, stochastic simulation approaches of flood frequency analysis were used. Each of the prediction methods was verified by being applied in 40 different drainage basins. Based on the results obtained, recommendations were made on the best method to be applied (at present) by design engineers in the Arabian Gulf states. Copyright © 2006 John Wiley & Sons, Ltd.     

Bayes estimate of the probability of exceedance of annual floods

In this paper Lindley's Bayesian approximation procedure is used to obtain the Bayes estimate of the probability of exceedence of a flood discharge. The Bayes estimates of the probability of exceedence has been shown by S.K. Sinha to be equivalent to the estimate of the probability of exceedence from the predictive or Bayesian disribution, of a future flood discharge. The evaluation of complex ratios of multiple integrals common in a Bayesian analysis is not necessary using Lindley's procedure. The Bayes estimates are compared to those obtained by the method of maximum likelihood and the method of moments. The results show that Bayes estimates of the probability of exceedence are larger as expected, but have smaller posterior standard deviations.     

Towards estimation of extreme floods: examination of the roles of runoff process changes and floodplain flows

This paper presents the development and application of a distributed rainfall-runoff model for extreme flood estimation, and its use to investigate potential changes in runoff processes, including changes to the ‘rating curve’ due to effects of over-bank flows, during the transition from ‘normal’ floods to ‘extreme’ floods. The model has two components: a hillslope runoff generation model based on a configuration of soil moisture stores in parallel and series, and a distributed flood routing model based on non-linear storage-discharge relationships for individual river reaches that includes the effects of floodplain geometries and roughnesses. The hillslope water balance model contains a number of parameters, which are measured or derived a priori from climate, soil and vegetation data or streamflow recession analyses. For reliable estimation of extreme discharges that may extend beyond recorded data, the parameters of the flood routing model are estimated from hydraulic properties, topographic data and vegetation cover of compound channels (main channel and floodplains). This includes the effects of the interactions between the main channel and floodplain sections, which tend to cause a change to the rating curve. The model is applied to the Collie River Basin, 2545 km², in Western Australia and used to estimate the probable maximum flood (PMF) from probable maximum precipitation estimates for this region. When moving from normal floods to the PMFs, application of the model demonstrates that the runoff generation process changes with a substantial increase of saturation excess overland flow through the expansion of saturated areas, and the dominant runoff process in the stream channel changes from in-bank to over-bank flows. The effects of floodplain inundation and floodplain vegetation can significantly reduce the magnitude of the estimated PMFs. This study has highlighted the need for the estimation of a number of critical parameters (e.g. cross-sectional geometry, floodplain vegetation, soil depths) through concerted field measurements or surveys, and targeted laboratory experiments.     

Reconstructing extreme post‐wildfire floods: a comparison of convective and mesoscale events

In much of western United States destructive floods after wildfire are frequently caused by localized, short‐duration convective thunderstorms; however, little is known about post‐fire flooding from longer‐duration, low‐intensity mesoscale storms. In this study we estimate and compare peak flows from convective and mesoscale floods following the 2012 High Park Fire in the ungaged 15.5 km² Skin Gulch basin in the northcentral Colorado Front Range. The convective storm on 6 July 2012 came just days after the wildfire was contained. Radar data indicated that the total rainfall was 20–47 mm, and the maximum rainfall intensities (upwards of 50 mm h^?1) were concentrated over portions of the watershed that burned at high severity. The mesoscale storm on 9–15 September 2013 produced 220–240 mm of rain but had maximum 15‐min intensities of only 25–32 mm h^?1. Peak flows for each flood were estimated using three independent techniques. Our best estimate using a 2D hydraulic model was 28 m³ s^?1 km^?2 for the flood following the convective storm, placing it among the largest rainfall‐runoff floods per unit area in the United States. In contrast, the flood associated with the mesoscale flood was only 6 m³ s^?1 km^?2, but the long‐duration flood caused extensive channel incision and widening, indicating that this storm was much more geomorphically effective. The peak flow estimates for the 2013 flood had a higher relative uncertainty and this stemmed from whether we used pre‐ or post‐flood channel topography. The results document the extent to which a high and moderate severity forest fire can greatly increase peak flows and alter channel morphology, illustrate how indirect peak flow estimates have larger errors than is generally assumed, and indicate that the magnitude of post‐fire floods and geomorphic change can be affected by the timing, magnitude, duration, and sequence of rainstorms. Copyright © 2017 John Wiley & Sons, Ltd.     

Model averaging versus model selection: estimating design floods with uncertain river flow data

ABSTRACT

This study compares model averaging and model selection methods to estimate design floods, while accounting for the observation error that is typically associated with annual maximum flow data. Model selection refers to methods where a single distribution function is chosen based on prior knowledge or by means of selection criteria. Model averaging refers to methods where the results of multiple distribution functions are combined. Numerical experiments were carried out by generating synthetic data using the Wakeby distribution function as the parent distribution. For this study, comparisons were made in terms of relative error and root mean square error (RMSE) referring to the 1-in-100 year flood. The experiments show that model averaging and model selection methods lead to similar results, especially when short samples are drawn from a highly asymmetric parent. Also, taking an arithmetic average of all design flood estimates gives estimated variances similar to those obtained with more complex weighted model averaging.     

A comparison of three methods for regional flood frequency analysis in Saudi Arabia

The objective of the study was to compare the relative accuracy of three methodologies of regional flood frequency analysis in areas of limited flood records. Thirty two drainage basins of different characteristics, located mainly in the southwest region of Saudi Arabia, were selected for the study. In the first methodology, region curves were developed and used together with the mean annual flood, estimated from the characteristics of drainage basin, to estimate flood flows at a location in the basin. The second methodology was to fit probability distribution functions to annual maximum rainfall intensity in a drainage basin. The best fitted probability function was used together with common peak flow models to estimate the annual maximum flood flows in the basin. In the third methodology, duration reduction curves were developed and used together with the average flood flow in a basin to estimate the peak flood flows in the basin. The results obtained from each methodology were compared to the flood records of the selected stations using three statistical measures of goodness-of-fit. The first methodology was found best in a case of having short length of record at a drainage basin. The second methodology produced satisfactory results. Thus, it is recommended in areas where data are not sufficient and/or reliable to utilise the first methodology.     

A Bayesian Assessment of Seismic Semi-Periodicity Forecasts

Among the schemes for earthquake forecasting, the search for semi-periodicity during large earthquakes in a given seismogenic region plays an important role. When considering earthquake forecasts based on semi-periodic sequence identification, the Bayesian formalism is a useful tool for: (1) assessing how well a given earthquake satisfies a previously made forecast; (2) re-evaluating the semi-periodic sequence probability; and (3) testing other prior estimations of the sequence probability. A comparison of Bayesian estimates with updated estimates of semi-periodic sequences that incorporate new data not used in the original estimates shows extremely good agreement, indicating that: (1) the probability that a semi-periodic sequence is not due to chance is an appropriate estimate for the prior sequence probability estimate; and (2) the Bayesian formalism does a very good job of estimating corrected semi-periodicity probabilities, using slightly less data than that used for updated estimates. The Bayesian approach is exemplified explicitly by its application to the Parkfield semi-periodic forecast, and results are given for its application to other forecasts in Japan and Venezuela.     

Indirect estimation of ungauged peak discharges in a bedrock channel with reference to design discharge selection

Geomorphological evidence and recent trash lines were used as stage indicators in a step-backwater computer model of high discharges through an ungauged bedrock channel. The simulation indicated that the peak discharge from the 26.7 m² catchment was close to 150m³s^?1 during the passage of Hurricane Charlie in August 1986. This estimate can be compared with an estimate of 130–160 m³s^?1 obtained using the Flood Studies Report (FSR) unit hydrograph methodology. Other palaeostage marks indicate that higher stages have occurred at an earlier time associated with a discharge of 200 m³s^?1. However, consideration of both the geometry of a plunge pool and transport criteria for bedrock blocks in the channel indicates that floods since 1986 have not exceeded 150 m³s^?1. Given that the estimated probable maximum flood (PMF) calculated from revised FSR procedure is at least 240 m³s^?1, it is concluded that compelling evidence for floods equal to the PMF is lacking. Taking into consideration the uncertainty of the discharge estimation, the 1986 flood computed using field evidence has a minimum return period of 100 years using the FSR procedure. This may be compared with a return period for the same event in the neighbouring gauged River Greta of > 100 years and a rainfall return period of 190 years. In as much as discharges of similar order to FSR estimates are indicated, it is concluded (a) that regional geomorphological evidence and flood simulation within ungauged catchments may be useful as a verification for hydrological estimates of recent widespread flood magnitude and (b) that palaeohydraulic computation can be useful in determining the magnitude of the local maximum [historic] flood when determining design discharges for hydraulic structures within specific catchments.     

Compositional Bayesian indicator estimation

Indicator kriging is widely used for mapping spatial binary variables and for estimating the global and local spatial distributions of variables in geosciences. For continuous random variables, indicator kriging gives an estimate of the cumulative distribution function, for a given threshold, which is then the estimate of a probability. Like any other kriging procedure, indicator kriging provides an estimation variance that, although not often used in applications, should be taken into account as it assesses the uncertainty of the estimate. An alternative approach to indicator estimation is proposed in this paper. In this alternative approach the complete probability density function of the indicator estimate is evaluated. The procedure is described in a Bayesian framework, using a multivariate Gaussian likelihood and an a priori distribution which are both combined according to Bayes theorem in order to obtain a posterior distribution for the indicator estimate. From this posterior distribution, point estimates, interval estimates and uncertainty measures can be obtained. Among the point estimates, the median of the posterior distribution is the maximum entropy estimate because there is a fifty-fifty chance of the unknown value of the estimate being larger or smaller than the median; that is, there is maximum uncertainty in the choice between two alternatives. Thus in some sense, the latter is an indicator estimator, alternative to the kriging estimator, that includes its own uncertainty. On the other hand, the mode of the posterior distribution estimator, assuming a uniform prior, is coincidental with the simple kriging estimator. Additionally, because the indicator estimate can be considered as a two-part composition which domain of definition is the simplex, the method is extended to compositional Bayesian indicator estimation. Bayesian indicator estimation and compositional Bayesian indicator estimation are illustrated with an environmental case study in which the probability of the content of a geochemical element in soil being over a particular threshold is of interest. The computer codes and its user guides are public domain and freely available.     

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.     

Cautionary note on multicomponent flood distributions for annual maxima

Multicomponent probability distributions such as the two‐component Gumbel distribution are sometimes applied to annual flood maxima when individual floods are seen as belonging to different classes, depending on physical processes or time of year. However, hydrological inconsistencies may arise if only nonclassified annual maxima are available to estimate the component distribution parameters. In particular, an unconstrained best fit to annual flood maxima may yield some component distributions with a high probability of simulating floods with negative discharge. In such situations, multicomponent distributions cannot be justified as an improved approximation to a local physical reality of mixed flood types, even though a good data fit is achieved. This effect usefully illustrates that a good match to data is no guarantee against degeneracy of hydrological models. Copyright © 2016 John Wiley & Sons, Ltd.     

An improved nonstationary model for flood frequency analysis and its implication for the Three Gorges Dam,China

This study proposes an improved nonstationary model for flood frequency analysis by investigating the relationship between flood peak and flood volume, using the Three Gorges Dam (TGD), China, for verification. First, the generalized additive model for location, scale and shape (GAMLSS) is used as the prior distribution. Then, under Bayesian theory, the prior distribution is updated using the conditional distribution, which is derived from the copula function. The results show that the improvement of the proposed model is significant compared with the GAMLSS-based prior distribution. Meanwhile, selection of a suitable prior distribution has a significant effect on the results of the improvement. For applications to the TGD, the nonstationary model can obviously increase the engineering management benefits and reduce the perceived risks of large floods. This study provides guidance for the dynamic management of hydraulic engineering under nonstationary conditions.     

A cross entropy method for flood frequency analysis

The cross-entropy method with fractile constraints has been developed to estimate a random variable when the data are a set of independent observations of the variable. The method can claim several advantages over existing methods. It uses a reference distribution like the prior distribution in Bayesian analysis and likewise generates a posterior distribution.The method is of interest, in particular, because it satisfies two fundamental requirements for selfconsistency in the analysis of a probabilistic system based on data: a principle of invariance and a principle of data monotonicity.The method is applied to flood analysis. Robustness of the minimum cross-entropy method is compared with other methods: the methods of moments and the maximum likehood.     

Evaluation of risk concepts in partial duration series

Conventional design practice aims at obtaining optimal estimates of floods with specified exceedance probabilities. Such estimates are, however, known on the average to be exceeded more frequently than expected. Alternatively, methods focusing on the expected exceedance probability can be used. Two different methods are considered here; the first is based on the sample distribution of true exceedance probabilities. The second is a Bayesian analogue using the likelihood function and a noninformative prior to describe the variability of exceedance probabilities. Appropriate analytical solutions are presented in both cases using the partial duration series approach.     

Evaluation of risk concepts in partial duration series

Conventional design practice aims at obtaining optimal estimates of floods with specified exceedance probabilities. Such estimates are, however, known on the average to be exceeded more frequently than expected. Alternatively, methods focusing on the expected exceedance probability can be used. Two different methods are considered here; the first is based on the sample distribution of true exceedance probabilities. The second is a Bayesian analogue using the likelihood function and a noninformative prior to describe the variability of exceedance probabilities. Appropriate analytical solutions are presented in both cases using the partial duration series approach.     

Selection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in Australia

Selection of a flood frequency distribution and associated parameter estimation procedure is an important step in flood frequency analysis. This is however a difficult task due to problems in selecting the best fit distribution from a large number of candidate distributions and parameter estimation procedures available in the literature. This paper presents a case study with flood data from Tasmania in Australia, which examines four model selection criteria: Akaike Information Criterion (AIC), Akaike Information Criterion—second order variant (AIC_c), Bayesian Information Criterion (BIC) and a modified Anderson–Darling Criterion (ADC). It has been found from the Monte Carlo simulation that ADC is more successful in recognizing the parent distribution correctly than the AIC and BIC when the parent is a three-parameter distribution. On the other hand, AIC and BIC are better in recognizing the parent distribution correctly when the parent is a two-parameter distribution. From the seven different probability distributions examined for Tasmania, it has been found that two-parameter distributions are preferable to three-parameter ones for Tasmania, with Log Normal appears to be the best selection. The paper also evaluates three most widely used parameter estimation procedures for the Log Normal distribution: method of moments (MOM), method of maximum likelihood (MLE) and Bayesian Markov Chain Monte Carlo method (BAY). It has been found that the BAY procedure provides better parameter estimates for the Log Normal distribution, which results in flood quantile estimates with smaller bias and standard error as compared to the MOM and MLE. The findings from this study would be useful in flood frequency analyses in other Australian states and other countries in particular, when selecting an appropriate probability distribution from a number of alternatives.     

A Bayesian method for missing rainfall estimation using a conceptual rainfall–runoff model

The estimation of missing rainfall data is an important problem for data analysis and modelling studies in hydrology. This paper develops a Bayesian method to address missing rainfall estimation from runoff measurements based on a pre-calibrated conceptual rainfall–runoff model. The Bayesian method assigns posterior probability of rainfall estimates proportional to the likelihood function of measured runoff flows and prior rainfall information, which is presented by uniform distributions in the absence of rainfall data. The likelihood function of measured runoff can be determined via the test of different residual error models in the calibration phase. The application of this method to a French urban catchment indicates that the proposed Bayesian method is able to assess missing rainfall and its uncertainty based only on runoff measurements, which provides an alternative to the reverse model for missing rainfall estimates.     

Fifteen-stage operation of gated spillways for flood routing management through artificial reservoirs

Abstract

A procedure to identify sets of operational rules for gated spillways for optimal flood routing management of artificial reservoirs is proposed. The flood retention storage of a dam having a gated flood spillway is divided into 15 sub-storages whose surface elevations are identified as critical levels. The most suitable operation set for the downstream conditions and for the dam can be chosen from many derived operation sets. The spillway gates are operated in an optimum way for any floods from very small magnitudes to the probable maximum flood (PMF), without having to forecast the actual magnitude of the incoming flood hydrograph. Decision floods are formed by dividing the PMF into 15 sub-hydrographs by 5 and 10% increments in the ranges 5–50% and 50–100% of the PMF, respectively. Many potential spillway gate openings from closed to fully open are chosen initially. As a result of a series of routing simulations of 15 decision floods, a set of 15 gate openings is determined such that all floods from very small magnitudes to the PMF may be routed without overtopping the dam crest. Next, a few more 15-stage operation rules are determined such that the gate openings of the initial stages are decreased as their critical levels are increased stepwise, with the objective of attenuating smaller floods more effectively and releasing higher outflows for larger floods close to and including the PMF. The developed model is applied to the Catalan and Aslantas dams in Turkey, both of which serve for flood mitigation as well as hydropower generation.

Citation Haktanir, T., Citakoglu, H., and Acanal, N., 2013. Fifteen-stage operation of gated spillways for flood routing management through artificial reservoirs. Hydrological Sciences Journal, 58 (5), 1013–1031.

Editor Z.W. Kundzewicz; Associate editor A. Montanari     

Non-identical models for seasonal flood frequency analysis

Abstract

The aim is to build a seasonal flood frequency analysis model and estimate seasonal design floods. The importance of seasonal flood frequency analysis and the advantages of considering seasonal design floods in the derivation of reservoir planning and operating rules are discussed, recognising that seasonal flood frequency models have been in use for over 30 years. A set of non-identical models with non-constant parameters is proposed and developed to describe flows that reflect seasonal flood variation. The peak-over-threshold (POT) sampling method was used, as it is considered to provide significantly more information on flood seasonality than annual maximum (AM) sampling and has better performance in flood seasonality estimation. The number of exceedences is assumed to follow the Poisson distribution (Po), while the peak exceedences are described by the exponential (Ex) and generalized Pareto (GP) distributions and a combination of both, resulting in three models, viz. Po-Ex, Po-GP and Po-Ex/GP. Their performances are analysed and compared. The Geheyan and the Baiyunshan reservoirs were chosen for the case study. The application and statistical experiment results show that each model has its merits and that the Po-Ex/GP model performs best. Use of the Po-Ex/GP model is recommended in seasonal flood frequency analysis for the purpose of deriving reservoir operation rules.     

Bayesian flood frequency analysis in the light of model and parameter uncertainties

The specific objective of the paper is to propose a new flood frequency analysis method considering uncertainty of both probability distribution selection (model uncertainty) and uncertainty of parameter estimation (parameter uncertainty). Based on Bayesian theory sampling distribution of quantiles or design floods coupling these two kinds of uncertainties is derived, not only point estimator but also confidence interval of the quantiles can be provided. Markov Chain Monte Carlo is adopted in order to overcome difficulties to compute the integrals in estimating the sampling distribution. As an example, the proposed method is applied for flood frequency analysis at a gauge in Huai River, China. It has been shown that the approach considering only model uncertainty or parameter uncertainty could not fully account for uncertainties in quantile estimations, instead, method coupling these two uncertainties should be employed. Furthermore, the proposed Bayesian-based method provides not only various quantile estimators, but also quantitative assessment on uncertainties of flood frequency analysis.