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.     

Describing the recurrence interval of extreme floods using nonextensive thermodynamics and Tsallis statistics

This paper introduces Tsallis statistics and the q-exponential distribution as a means of analysing hydrological phenomena. The basic framework is introduced and then the method is used to derive a distribution for flood recurrence intervals using recently published data from the River Po, Italy. This fits the data much more effectively than the simple power-law applied in a previous study. Hence, a distribution derived from power-law considerations is more appropriate than the power-law itself. Nonextensive statistical mechanics has the potential for much broader utility in hydrology than is demonstrated here. Some potential avenues for future study are introduced.     

Impact of reach geometry on stream channel sensitivity to extreme floods

Predicting spatial and temporal variations in bank erosion due to extreme floods presents a long‐standing challenge in geomorphology. We develop two methodologies for rapid, regional‐scale assessments of stream reaches susceptible to channel widening. The first proposes that channel widening occurs when unit stream power exceeds a critical threshold (300 W/m²). The second is motivated by the observation that widening often occurs at channel bends. We introduce a new metric, the bend stress parameter, which is proportional to the centripetal force exerted on a concave bank. We propose that high centripetal forces generate locally high bank shear forces and enhance channel bank erosion. We test both metrics using the geomorphic signature of Tropical Storm Irene (2011) on the White and the Saxtons Rivers, Vermont. Specifically, we test if reaches where significant channel widening occurred during Irene required one or both metrics to exceed threshold values. We observe two distinct styles of channel widening. Where unit stream power and bend stress parameter are high, widening is usually due to bank retreat. Elsewhere widening is usually due to the stripping of the upstream end of mid‐channel islands. Excluding widening associated with the stripping of the heads of mid‐channel islands, almost all the widening (> 98%) occurred along reaches identified as susceptible to widening. The combined metrics identify up to one‐quarter of the reaches lacking susceptibility to channel widening. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

气候变暖下太湖极端洪水的归因探讨

全球增温引起的降水变化是否引起极端洪水的增加,发生在不同气候背景的极端洪水事件可提供不同参照系;而不同驱动因子下气候、水文数值模拟为认识洪水发生和归因提供了有效途径.本文结合机理数值模拟和随机统计模拟两种途径,针对1990s和1880s的太湖流域特大洪水,通过GCM气候模拟驱动的流域水文模拟和不确定性的阈值模拟,分析19世纪末和20世纪末极端洪水的发生强度和频率的变化,从而论证极端洪水发生的风险系数.结果表明,1990s的极端洪水流量(0.1%的极端洪水流量(Q0.1%)为2929~3601 m³/s,0.5%的极端洪水流量(Q0.5%)为1842~1893 m³/s)比工业革命前大气温室气体状况下(Q0.1%为2069~3119 m³/s,Q0.5%为1436~1561 m³/s)显著增大.与19世纪末相比,由于太湖流域人类活动改变的流域下垫面在1999年特大洪水中引起最大增量占35%,本文模拟和分析的20世纪末气候下的洪水最大增量占60%.去除人类活动影响的下垫面变化,估计特大洪水风险的最大增量为25%,因此认为20世纪末气候变化引起的太湖极端洪水风险在增加;这将为认识与全球增温相关联的洪水灾害预测预警提供科学依据.     

Non-Gaussian probability distributions of solar wind fluctuations

The probability distributions of field differences x()=x(t+)-x(t), where the variable x(t) may denote any solar wind scalar field or vector field component at time t, have been calculated from time series of Helios data obtained in 1976 at heliocentric distances near 0.3 AU. It is found that for comparatively long time lag , ranging from a few hours to 1 day, the differences are normally distributed according to a Gaussian. For shorter time lags, of less than ten minutes, significant changes in shape are observed. The distributions are often spikier and narrower than the equivalent Gaussian distribution with the same standard deviation, and they are enhanced for large, reduced for intermediate and enhanced for very small values of x. This result is in accordance with fluid observations and numerical simulations. Hence statistical properties are dominated at small scale by large fluctuation amplitudes that are sparsely distributed, which is direct evidence for spatial intermittency of the fluctuations. This is in agreement with results from earlier analyses of the structure functions of x. The non-Gaussian features are differently developed for the various types of fluctuations. The relevance of these observations to the interpretation and understanding of the nature of solar wind magnetohydrodynamic (MHD) turbulence is pointed out, and contact is made with existing theoretical concepts of intermittency in fluid turbulence.     

Detecting the impact of climate and reservoirs on extreme floods using nonstationary frequency models

Stochastic Environmental Research and Risk Assessment - The annual maximum flood records of the Danjiangkou reservoir displayed significant decreasing trends. The upper stream of the reservoir was...     

A comparison of two bivariate extreme value distributions

There are two distinct bivariate extreme value distributions constructed from Gumbel marginals, namely Gumbel mixed (GM) model and Gumbel logistic (GL) model. These two models have completely different structures and their dependence ranges are different. The product-moment correlation coefficient for the former is [0,2/3] and the latter is [0,1]. It is natural to ask which one is more appropriate for representing the joint probabilistic behavior of two correlated Gumbel-distributed variables. This study compares these two models by numerical experiments. The comparison is based on that: (i) if the two distribution models are identical, then the joint probability and the joint return period computed by the GM model should be the same as those by the GL model; and (ii) if a selected distribution is the true distribution from which sample data are drawn, then the probabilities computed by the theoretical model should provide a good fit to empirical ones. Comparison results indicate that in the range of correlation coefficient [0,2/3], both models provide identical joint probabilities and joint return periods, and both indicate a good fit to empirical probabilities; while for (2/3,1), only the Gumbel logistic model can be used.     

Simulation of probability distributions commonly used in hydrological frequency analysis

Random variable simulation has been applied to many applications in hydrological modelling, flood risk analysis, environmental impact assessment, etc. However, computer codes for simulation of distributions commonly used in hydrological frequency analysis are not available in most software libraries. This paper presents a frequency‐factor‐based method for random number generation of five distributions (normal, log–normal, extreme‐value type I, Pearson type III and log‐Pearson type III) commonly used in hydrological frequency analysis. The proposed method is shown to produce random numbers of desired distributions through three means of validation: (1) graphical comparison of cumulative distribution functions (CDFs) and empirical CDFs derived from generated data; (2) properties of estimated parameters; (3) type I error of goodness‐of‐fit test. An advantage of the method is that it does not require CDF inversion, and frequency factors of the five commonly used distributions involves only the standard normal deviate. Copyright © 2006 John Wiley & Sons, Ltd.     

Exceedance probability distributions of steady conduit flow in karst aquifers

Discharge exceedance probabilities are calculated for a simple model karst aquifer composed of a few multilevel conduits with recharge from a single sinking stream with an exponential flow exceedance distribution. It is assumed that outflow instantaneously matches inflow, so that the conduit volume is constant but discharge is governed by the head in a volumeless shaft at the top end of the system. It is shown that small single conduit aquifers will frequently overflow at the surface during floods and the exceedance probability of flow through the aquifer and over the surface can be defined as a function of the inflow distribution and the form of the aquifer. Systems with multiple conduits will overflow less frequently, but each conduit will exhibit a flow distribution characteristic of its form and position in the vertical hierarchy. Comparison of these findings with actual flow data from a conduit aquifer shows that the approach is valid, although imprecise. The model is unlikely to be applied directly, as it requires unusually detailed data. However, it provides for the first time an indication of typical flow durations for surface overflows and individual conduits in a karst aquifer. Contrasts in flow duration will have a profound influence on solutional and sedimentary processes in the karst system.     

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.     

Suspended sediment transport in the Gulf of Lions (NW Mediterranean): Impact of extreme storms and floods

In situ observations were combined with 3D modeling to gain understanding of and to quantify the suspended sediment transport in the Gulf of Lions (NW Mediterranean Sea). The outputs of a hydrodynamic–sediment transport coupled model were compared to near-bottom current and suspended sediment concentration measurements collected at the head of seven submarine canyons and at a shallow shelf site, over a 6-month period (November 2003–May 2004). The comparisons provide a reasonable validation of the model that reproduces the observed spatial and time variations. The study period was marked by an unusual occurrence of marine storms and high river inputs. The major water and sediment discharges were supplied by the Rhone, the largest Mediterranean river, during an exceptional flood accompanying a severe marine storm in early December 2003. A second major storm, with moderate flooding, occurred in February 2004. The estimate of river input during the studied period was 5.9 Mt. Our study reveals (i) that most of the particulate matter delivered by the Rhone was entrapped on the prodelta, and (ii) that marine storms played a crucial role on the sediment dispersal on the shelf and the off-shelf export. The marine storms occurring in early December 2003 and late February 2004 resuspended a very large amount of shelf sediment (>8 Mt). Erosion was controlled by waves on the inner shelf and by energetic currents on the outer shelf. Sediment deposition took place in the middle part of the shelf, between 50 and 100 m depth. Resuspended sediments and river-borne particles were transported to the southwestern end of the shelf by a cyclonic circulation induced by these onshore winds and exported towards the Catalan shelf and into the Cap de Creus Canyon which incises the slope close to the shore. Export taking place mostly during marine storms was estimated to reach 9.1 Mt during the study period.     

Estimation of the probability of strongest seismic disasters based on the extreme value theory

This paper presents the review of the experience in applying the approach based on the limiting distributions of the extreme value theory (the generalized Pareto distribution, GPS, and generalized extreme value distribution, GEV) for deriving the distributions of maximal magnitudes and related ground accelerations from the earthquakes on the future time intervals of a given duration. The results of analyzing the global and regional earthquake catalogs and the ground peak accelerations during the earthquakes are described. It is shown that the magnitude of the strongest possible earthquake M _max (and analogous characteristics for other types of data), which is often used in seismic risk assessment, is potentially unstable. We suggest a stable alternative for M _max in the form of quantiles Q _q (τ) of the maximal possible earthquake, which could occur during the future time interval of length τ. The quantity of the characteristic maximal event M _c, which has been introduced in our previous publications, is another helpful robust scalar parameter. All the cases of approximation of the tails of empirical distributions, which were studied in our works, turned out to be finite (bounded); however, the rightmost point of these distributions, M _max, is often poorly detectable and unstable. Therefore, the M _max parameter has a low practical value.     

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.     

Application of the theory of truncated probability distributions to studying minimal river runoff: Normal and gamma distributions

The possibility of applying unilaterally truncated probability distributions of minimal water flow is considered. Relationships between moment estimates of truncated and full distributions are considered for the case of normal and gamma distributions.     

A Multiple Criteria Decision Modelling approach to selection of estimation techniques for fitting extreme floods

The problem of fitting a probability distribution, here log-Pearson Type III distribution, to extreme floods is considered from the point of view of two numerical and three non-numerical criteria. The six techniques of fitting considered include classical techniques (maximum likelihood, moments of logarithms of flows) and new methods such as mixed moments and the generalized method of moments developed by two of the co-authors. The latter method consists of fitting the distribution using moments of different order, in particular the SAM method (Sundry Averages Method) uses the moments of order 0 (geometric mean), 1 (arithmetic mean), –1 (harmonic mean) and leads to a smaller variance of the parameters. The criteria used to select the method of parameter estimation are:

利用贝叶斯极值分布函数估算河套断陷带的发震概率

正Campbell(1982,1983)将贝叶斯概率理论和极值概率模型相结合,发展出一种估算地震发生概率的贝叶斯极值分布模型。在此模型中,地震活动的先验估计值是基于地震矩、滑动速率、地震复发率和震级等数据计算得到的,而后将估计值用于贝叶斯理论的后验估算,或者用于研究区的历史地震活动性的评估方面(李拴虎等,2016)。     

Mixed estimation methods for Halphen distributions with applications in extreme hydrologic events

The Halphen family of distributions is a flexible and complete system to fit sets of observations independent and identically distributed. Recently, it is shown that this family of distributions represents a potential alternative to the generalized extreme value distributions to model extreme hydrological events. The existence of jointly sufficient statistics for parameter estimation leads to optimality of the method of maximum likelihood (ML). Nevertheless, the ML method requires numerical approximations leading to less accurate values. However, estimators by the method of moments (MM) are explicit and their computation is fast. Even though MM method leads to good results, it is not optimal. In order to combine the advantages of the ML (optimality) and MM (efficiency and fast computations), two new mixed methods were proposed in this paper. One of the two methods is direct and the other is iterative, denoted respectively direct mixed method (MMD) and iterative mixed method (MMI). An overall comparison of the four estimation methods (MM, ML, MMD and MMI) was performed using Monte Carlo simulations regarding the three Halphen distributions. Generally, the MMI method can be considered for the three Halphen distributions since it is recommended for a majority of cases encountered in hydrology. The principal idea of the mixed methods MMD and MMI could be generalized for other distributions with complicated density functions.     

Chronology and sediment provenance of extreme floods of Siang River (Tsangpo-Brahmaputra River valley), northeast Himalaya

This study explores paleoflood deposits of the Siang River, known as the Tsangpo in Tibet. The river that often experiences large floods brings down huge amount of sediment and water that adversely affect the downstream regions with large human populations in the states of northeast Himalaya and its foreland. Along it's ~300 km mountainous stretch we collected samples for sedimentological, petrographic and Sr–Nd isotopic study to explore sediment provenance and dated the paleofloods (via optically stimulated luminescence, OSL). Geomorphic indices including precipitation and a geomorphic swath profile across the Brahmaputra catchment were studied to understand the interplay of mountain relief and rainfall that determine potential zones of high erosion and sediment supply. The OSL technique indicated the Siang River experienced at least eight large floods between 7 and 1 ka, possibly under the influence of warm and wet climatic conditions. The petrographic and isotopic data suggests that the eastern Himalayan syntaxis, which has the highest uplift and exhumation rate in the area, is not always the highest sediment producing zone. In some instances, the Tibetan plateau produces higher fluxes of sediments via glacial and landslide lake outburst floods (GLOFs and LLOFs). © 2020 John Wiley & Sons, Ltd.