Testing multivariate uniformity based on random geometric graphs

We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the null hypothesis as well as under fixed alternatives. The derived tests are consistent and their behaviour for some contiguous alternatives can be controlled. A simulation study suggests that the procedures can compete with or are better than established goodness-of-fit tests. We show with a real data example that the new tests can detect non-uniformity of a small sample data set, where most of the competitors fail.Comment: 36 pages, 2 figure

Characterizations of non-normalized discrete probability distributions and their application in statistics

From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop tools for the solution of statistical problems. Our characterizations, and hence the applications built on them, do not require any knowledge about normalization constants of the probability laws. To demonstrate that our statistical methods are sound, we provide comparative simulation studies for the testing of fit to the Poisson distribution and for parameter estimation of the negative binomial family when both parameters are unknown. We also consider the problem of parameter estimation for discrete exponential-polynomial models which generally are non-normalized.Comment: 24 pages, 3 figure

Session D1: Classification of Flow Patterns in a Nature-Oriented Fishway Based on 3D Hydraulic Simulation Results

Abstract: In order to fulfill the requirements of the EU Water Framework Directive concerning the restoration of fish passage in rivers, various types of (near-natural and technical) fishways have been built in recent years. For optimization of planned structures as well as for monitoring of the performance of existing fishways, their hydraulics has to be studied. 3D hydrodynamic numerical modelling is a useful tool to predict hydraulic quantities and analyse flow pattern. Many studies using hydraulic simulations deal with technical fishways. In contrast, nature-oriented fishways have rarely been numerically modelled so far. In the framework of R&D activities at Karlsruhe Institute of Technology, a high resolution 3D-hydraulic model of a section of a nature-oriented bypass channel (rock cascade pass) has been developed. The basis of a hydraulic model is a 3D-model of the fishway’s topography. Since fishways of a nature-oriented design type are characterized by highly irregular structures, the build-up of such a model is very challenging. In this study, the method of terrestrial laser scanning was used for detailed geodata acquisition. The hydraulic model was validated using, inter alia, acoustic Doppler velocity measurements. Simulations using the computational fluid dynamics software FLOW-3D were performed for two hydraulic scenarios. The simulated hydraulic quantities (velocities, water levels) and their distribution along the vertical and horizontal axes have been investigated and compared to critical values concerning fish passability specified in technical standards. A method of categorization of flow patterns is proposed, which enables a schematic visualization of complex flow conditions. In this way, potentially critical zones can be located and specific flow patterns can be identified. This method of analysis has a high potential in terms of addressing environmental issues concerning nature-oriented fishways and river restoration projects

Session D1: Experimental Study on Flow Patterns in Vertical Slot Fishways

Abstract: The vertical slot fishway is one of the most commonly used fish passage facilities in Germany. The flow conditions within fishway play an important role in the establishment of ecological connectivity, because they determine whether fish can pass, with regard of their given swimming performance. Earlier studies have shown that two different types of flow patterns, separated by a transition area, may develop in the pools depending on the width-to-length (B/L) ratio of the pools and the slope of the fishway. In order to gain insight in the formation of different flow patterns, an extensive study of different geometric parameters was performed, with a total of 60 different designs. Different pool geometries and slopes were installed in a physical model at Theodor-Rehbock-Laboratory of the Institute for Water and River Basin Management (IWG) in Karlsruhe. Flow patterns were recorded photo-optically by long time exposure, water depths were measured with an ultrasonic distance sensor and flow velocities by ADV. The measurements were analysed to obtain quantitative information about flow patterns, velocities, energy budget of the pools, relationship between discharge and flow depth and water level difference between adjacent pools. Unlike in previous studies, not only the B/L ratio but the entire pool geometry was varied in accordance to the German guidelines. Small slope ranges between 2.8 and 5 %, typical for Federal German waterways, were studied for the first time. Both flow patterns could be observed under identical B/L and slope. The results show that parameters apart from the B/L ratio and slope are essential for determining the formation of flow patterns. Especially the variation of the slot angle had a large influence on the flow patterns. The flow velocity measurements show differences between the two flow patterns in terms of position and magnitude of maximum velocities in the pools

A hydrologic contribution to risk assessment for the Caspian Sea

AbstractThe Caspian Sea (CS), the world's largest inland sea, may also be considered as large-scale limnic system. Due to strong fluctuations of its water level during the 20th century and the flooding of vast areas in a highly vulnerable coastal zone, economic and environmental risk potentials have to be considered. Since the major water input into the CS is attributed to the Volga river, the understanding of its long-term flow process is necessary for an appropriate risk assessment for the CS and its coastal area. Therefore, a top–down approach based on statistical analyses of long-term Volga flow series is pursued. For the series of annual mean flow (MQ) of the Volga river basin during the 20th century, a complex oscillation pattern was identified. Analyses for multiple gauges in the Volga river basin and Eurasian reference basins revealed that this oscillation pattern resulted from the superposition of oscillations with periods of ∼30 years (MQ) in the western part of the Volga river basin, and ∼14 years (flow volume of snowmelt events) and ∼20 years (flow volume of summer and autumn) in the eastern part of the Volga river basin (Kama river basin). Almost synchronous minima or maxima of these oscillations occurred just in the periods of substantial changes of the Caspian Sea level (CSL). It can thus be assumed that the described mechanism is fundamental for an understanding of the CSL development during the 20th century. Regarding the global climate change, it is still difficult to predict reliably the development of the CSL for the 21st century. Consequently, we suggest an ongoing, interdisciplinary research co-operation among climatology, hydrology, hydraulics, ecology and spatial data management