A theoretically based Wakeby distribution for annual flood series

Abstract

The exact distribution of the ratio of any magnitude to the sum of all magnitudes in an annual flood series satisfying the usual distribution-free assumptions of independence and identical distribution, and the additional parametric assumption of exponential tail behaviour with truncation, is shown to be a beta distribution of the first kind. A two-parameter linear transformation of the beta distribution completes the derivation and yields a Wakeby distribution which has the number of members in a series as a given parameter. The Wakeby distribution is developed to illustrate how, in principle, some perceived deficiencies in current flood frequency analysis may be met: more complex parametric assumptions should lead to distributions of wider application. In particular, the distribution has a secure theoretical basis and is hydrologically more realistic because it bounds the variate and requires the definition of a temporally finite annual series. Analytical expressions are obtained for estimating the two distribution parameters; the quantite standard error and a plotting rule. An example is given of the application of the distribution to the design flood problem and an annual flood series is modelled. It is further suggested that a suitable design value for the largest flood to be withstood by a protection work is a statistic of the largest flood occurring during its lifetime. For the derived Wakeby distribution this criterion specifies risk and probability of non-exceedance of the design flood once a lifetime is selected.     

Sedimentary environments and depositional characteristics of the Middle to Upper Eocene whale‐bearing succession in the Fayum Depression,Egypt

The discovery of whale fossils from Eocene strata in the Fayum Depression has provoked interest in the life and lifestyle of early whales. Excellent outcrop exposure also affords the dataset to develop sedimentological and stratigraphic models within the Eocene strata. Previous work generally asserts that the thick, sand‐rich deposits of the Fayum Depression represent shoreface and barrier island successions with fine‐grained lagoonal and fluvial associations capping progradational successions. However, a complete absence of wave‐generated sedimentary structures, a preponderance of thoroughly bioturbated strata and increasingly proximal sedimentary successions upwards are contrary to accepted models of the local sedimentological and stratigraphic development. This study considers data collected from two Middle to Upper Eocene successions exposed in outcrop in the Wadi El‐Hitan and Qasr El‐Sagha areas of the Fayum Depression to determine the depositional affinities of Fayum strata. Based on sedimentological and ichnological data, five facies associations (Facies Association 1 to Facies Association 5) are identified. The biological and sedimentological characteristics of the reported facies associations indicate that the whale‐bearing sandstones (Facies Association 1) record distal positions in a large, open, quiescent marine bay that is abruptly succeeded by a bay‐margin environment (Facies Association 2). Upwards, marginal‐marine lagoonal and shallow‐bay parasequences (Facies Association 3) are overlain by thick deltaic distributary channel deposits (Facies Association 4). The capping unit (Facies Association 5) represents a transgressive estuarine depositional environment. The general stratigraphic evolution resulted from a regional, tectonically controlled second‐order cycle, associated with northward regression of the Tethys. Subordinate cycles (i.e. third‐order and fourth‐order cycles) are evidenced by several Glossifungites‐ichnofacies demarcated discontinuities, which were emplaced at the base of flooding surfaces. The proposed depositional models recognize the importance of identifying and linking ichnological data with physical–sedimentological observations. As such – with the exception of wave‐generated ravinement surfaces – earlier assertions of wave‐dominated sedimentation can be discarded. Moreover, this study provides important data for the recognition of (rarely reported) completely bioturbated sand‐dominated offshore to nearshore sediments (Facies Association 1) and affords excellent characterization of bioturbated inclined heterolithic stratification of deltaic deposits. Another outcome of the study is the recognition that the whales of the Fayum Depression are restricted to the highstand systems tracts, and lived under conditions of low depositional energy, low to moderate sedimentation rates, and (not surprisingly) in fully marine waters characterized by a high biomass.     

Chemical versus Temporal Controls on the Evolution of Tholeiitic and Calc-alkaline Magmas at Two Volcanoes in the Alaska-Aleutian Arc

The Alaska–Aleutian island arc is well known for eruptingboth tholeiitic and calc-alkaline magmas. To investigate therelative roles of chemical and temporal controls in generatingthese contrasting liquid lines of descent we have undertakena detailed study of tholeiitic lavas from Akutan volcano inthe oceanic Aleutian arc and calc-alkaline products from Aniakchakvolcano on the continental Alaskan Peninsula. The differencesdo not appear to be linked to parental magma composition. TheAkutan lavas can be explained by closed-system magmatic evolution,whereas curvilinear trace element trends and a large range in⁸⁷Sr/⁸⁶Sr isotope ratios in the Aniakchak data appear to requirethe combined effects of fractional crystallization, assimilationand magma mixing. Both magmatic suites preserve a similar rangein ²²⁶Ra–²³⁰Th disequilibria, which suggests that thetime scale of crustal residence of magmas beneath both thesevolcanoes was similar, and of the order of several thousandyears. This is consistent with numerical estimates of the timescales for crystallization caused by cooling in convecting crustalmagma chambers. During that time interval the tholeiitic Akutanmagmas underwent restricted, closed-system, compositional evolution.In contrast, the calc-alkaline magmas beneath Aniakchak volcanounderwent significant open-system compositional evolution. Combiningthese results with data from other studies we suggest that differentiationis faster in calc-alkaline and potassic magma series than intholeiitic series, owing to a combination of greater extentsof assimilation, magma mixing and cooling. KEY WORDS: uranium-series; Aleutian arc; magma differentiation; time scales     

THE TAIKU DEPOSITS AND THE PROBLEM OF PLEISTOCENE CLIMATES

Introduction The Locality General Geological Structure Stratigraphy Physiography and Structure Age of the Taiku Fault Bearing of the Character of the Deposits on the Problem of Sanmenian Climate Correlation of Pleistocene Climatic Fluctuations     

印度南部麻粒岩地体Namakkal陆块新太古代钙硅酸盐岩的岩石学和锆石U-Pb年代学研究

本文对印度南部麻粒岩地体Namakkal陆块Tammampatti地区方柱石石榴子石钙硅酸盐岩进行了详细的岩石学、锆石U-Pb年代学和变质相平衡模拟研究,以研究其岩石成因和地质意义.岩相学观察识别出两阶段变质矿物组合:第一阶段为石榴子石+方柱石+斜长石+榍石+钛铁矿;第二阶段为石榴子石边部的绿帘石和方柱石边缘的方解石、...