Hydrological behaviour through experimental and modelling approaches

The present work is related to the recent research topics in hydrology devoted to the integration of field knowledge into the hydrological modelling. The study catchment is the Haute-Mentue experimental basin (12.5 km2) located in western Switzerland, in the Plateau region. In order to complete the existing knowledge about the hydrological behaviour of the study catchment, a field experimental approach has been conducted at two scales: catchment (environmental tracing) and local scale (TDR soil moisture measurements). The environmental tracing application has led to the same conclusion as previous researches: hydrological behaviour is strongly influenced by the catchment antecedent conditions and by the rainfall duration and intensity. The geology characteristics (moraine or molasse) explain the main differences in the hydrological behaviour that have been observed so far. As the environmental tracing does not allow easy identification of the mechanisms responsible for the runoff generation, TDR equipments have been installed on two hillslopes with different geological characteristics, which allowed monitoring of the soil moisture at different depths along the hillslope during two intensive campaigns in 2002 and 2003. Association of the environmental tracing and TDR technique has finally allowed precising the conceptual model of two head sub-catchments of the Haute-Mentue catchment. The second part of the research is devoted to the hydrological modelling. A simple conceptual model (TOPMODEL) has been considered as an appropriate representation of the hydrological processes on the Haute-Mentue catchment. In order to estimate TOPMODEL parameters and to take into account uncertainty associated with estimated parameters and model output, a Bayesian approach has been proposed and two Bayesian techniques have been compared: GLUE (Generalized Likelihood Uncertainty Estimation) and MCMC (Monte Carlo Markov Chains). The role of the statistical corrections on the resulting parameters and model output uncertainty has been assessed. In the last part of the present research, the Bayesian methodology has been extended to the case of multi-response calibration. Previous field acquired knowledge (i.e. soil storage saturation deficit, stream water silica and calcium concentrations) has been used to constrain parametrization of the classical and of a modified version of TOPMODEL. In both cases, multi-calibration led to trade-off behaviour of the efficiencies of the simulated responses. The total modelling uncertainty of the new introduced responses was considerably reduced at the expense of an increase in the total modelling uncertainty of the simulated discharges.

Bayesian risk analysis of financial time series

Christophe Osinski

This thesis is a contribution to financial statistics. One of the principal concerns of investors is the evaluation of portfolio risk. The notion of risk is vague, but in finance it is always linked to possible losses. In this thesis, we present some measures allowing the valuation of risk with the help of Bayesian methods. An exploratory analysis of data is presented to describe the sampling properties of financial time series. This analysis allows us to understand the origins of the daily returns studied in this thesis. Moreover, a discussion of different models is presented. These models make strong assumptions on investor behaviour, which are not always satisfied. This exploratory analysis shows some differences between the behaviour anticipated under equilibrium models, and that of real data. The Bayesian approach has been chosen because it allows one to incorporate all the variability, in particular that associated with model choice. The models studied in this thesis allow one to take heteroskedasticity into account, as well as particular shapes of the tails of returns. ARCH type models and models based on extreme value theory are studied. One original aspect of this thesis is its use of Bayesian analysis to detect change points in financial time series. We suppose that a market has two phases, and that it switches from a state to the other at random. Another new contribution is a model integrating heteroskedasticity and time dependence of extreme values, by superposition of the model proposed by Bortot and Coles (2003) and a GARCH process. This thesis uses simulation intensively for the estimation of risk measures. The drawback of simulation is the amount of time needed to obtain accurate estimates. However, simulation allows one to produce results when direct calculation is not feasible. For example, simulation allows one to compute risk estimates for time horizons greater than one day. The methods presented in this thesis are illustrated on simulated data, and on real data from European and American markets. This thesis involved the construction of a library containing C and S code to perform risk analysis using GARCH and extreme value theory models. The results show that model uncertainty can be incorporated, and that risk measures for time horizons greater than one can be obtained by simulation. The methods presented in this thesis have a natural representation involving conditioning. Thus, they permit the computation of both conditional and unconditional risk estimates. Three methods are described: the GARCH method; the two-state GARCH method; and the HBC method. Unconditional risk estimation using the GARCH method is satisfactory on data which seem stationary, but not reliable on data which are non-stationary, such as data with change points. The two-state GARCH model does a little better, but gives very satisfactory results when the risk is estimated conditionally on time. The HBC method does not give satisfactory results.

EPFL2006

Rate allocation and optimized decoding in inter-session network coding

Eirina Bourtsoulatze

Recent advances in data processing and communication systems have led to a continuous increase in the amount of data communicated over today’s networks. These large volumes of data pose new challenges on the current networking infrastructure that only offers a best effort mechanism for data delivery. The emergence of new distributed network architectures, such as peer-to-peer networks and wireless mesh networks, and the need for efficient data delivery mechanisms have motivated researchers to reconsider the way that information is communicated and processed in the networks. This has given rise to a new research field called network coding. The network coding paradigm departs from the traditional routing principle where information is simply relayed by the network nodes towards the destination, and introduces some intelligence in the network through coding at the intermediate nodes. This in-network data processing has been proved to substantially improve the performance of data delivery systems in terms of throughput and error resilience in networks with high path diversity. Motivated by the promising results in the network coding research, we focus in this thesis on the design of network coding algorithms for simultaneous transmission of multiple data sources in overlay networks. We investigate several problems that arise in the context of inter-session network coding, namely (i) decoding delay minimization in inter-session network coding, (ii) distributed rate allocation for inter-session network coding and (iii) correlation-aware decoding of incomplete network coded data. We start by proposing a novel framework for data delivery from multiple sources to multiple clients in an overlay wireline network, where intermediate nodes employ randomized inter-session network coding. We consider networks with high resource diversity, which creates network coding opportunities with possibly large gains in terms of throughput, delay and error robustness. However, the coding operations in the intermediate nodes must be carefully designed in order to enable efficient data delivery. We look at the problem from the decoding delay perspective and design solutions that lead to a small decoding delay at clients through proper coding and rate allocation. We cast the optimization problem as a rate allocation problem, which seeks for the coding operations that minimize the average decoding delay in the client population. We demonstrate the validity of our algorithm through simulations in representative network topologies. The results show that an effective combination of intra- and inter-session network coding based on randomized linear coding permits to reach small decoding delays and to better exploit the available network resources even in challenging network settings. Next, we design a distributed rate allocation algorithm where the users decide locally how many intra- and inter-session network coded packets should be requested from the parent nodes in order to get minimal decoding delay. The capability to take coding decisions locally with only a partial knowledge of the network statistics is of crucial importance for applications where users are organized in dynamic overlay networks. We propose a receiver-driven communication protocol that operates in two rounds. First, the users request and obtain information regarding the network conditions and packet availability in their local neighborhood. Then, every user independently optimizes the rate allocation among different possible intra- and inter-session packet combinations to be requested from its parents. We also introduce the novel concept of equivalent flows, which permits to efficiently estimate the expected number of packets that are necessary for decoding and hence to simplify the rate allocation process. Experimental results indicate that our algorithm is capable of eliminating the bottlenecks and reducing the decoding delay of users with limited resources. We further investigate the application of the proposed distributed rate allocation algorithm to the transmission of video sequences and validate the performance of our system using the NS-3 simulator. The simulation results show that the proposed rate allocation algorithm is successful in improving the quality of the delivered video compared to intra-session network coding based solutions. Finally, we investigate the problem of decoding the source information from an incomplete set of network coded data with the help of source priors in a finite algebraic field. The inability to form a complete decoding system can be often caused by transmission losses or timing constraints imposed by the application. In this case, exact reconstruction of the source data by conventional algorithms such as Gaussian elimination is not feasible; however, partial recovery of the source data may still be possible, which can be useful in applications where approximate reconstruction is informative. We use the statistical characteristics of the source data in order to perform approximate decoding. We first analyze the performance of a hypothetical maximum a posteriori decoder, which recovers the source data from an incomplete set of network coded data given the joint statistics of the sources. We derive an upper bound on the probability of erroneous source sequence decoding as a function of the system parameters. We then propose a constructive solution to the approximate decoding problem and design an iterative decoding algorithm based on message passing, which jointly considers the network coding and the correlation constraints. We illustrate the performance of our decoding algorithm through extensive simulations on synthetic and real data sets. The results demonstrate that, even by using a simple correlation model expressed as a correlation noise between pairs of sources, the original source data can be partially decoded in practice from an incomplete set of network coded symbols. Overall, this thesis addresses several important issues related to the design of efficient data delivery methods with inter-session network coding. Our novel framework for decoding delay minimization can impact the development of practical inter-session network coding algorithms that are appropriate for applications with low delay requirements. Our rate allocation algorithms are able to exploit the high resource diversity of modern networking systems and represent an effective alternative in the development of distributed communication systems. Finally, our algorithm for data recovery from incomplete network coded data using correlation priors can contribute significantly to the improvement of the delivered data quality and provide new insights towards the design of joint source and network coding algorithms.

EPFL2013

Typology of recent groundwaters from different aquifer environments based on geogenic tracer elements

A key problem in environmental science and in engineering geology is the often incomplete understanding of the origin of dissolved components in groundwater. The dissolved contents of trace elements in groundwater are of special importance for groundwater quality control. The AQUITYP project aims to establish a detailed typology of recent groundwaters based on their geogenic trace element compositions, and to derive a so-called "geo-reference" for groundwaters from five principal aquifer lithologies in the Alpine belt. This geo-reference provides a database for investigations related to groundwater contamination, groundwater resources management and engineering geology. Groundwaters from crystalline, carbonate, and evaporite rocks, as well as molasse and flysch sediments in Switzerland and in neighbouring countries were sampled and documented by previous researchers (Dubois, 1993; Dematteis, 1995; Mandia, 1993; Hesske, 1995; Basabe, 1993). Based on a statistical analysis of the data and examination of the relationship between aquifer lithology and chemical groundwater composition these researchers identified a number of characteristic tracer elements (geogenic tracers). The present study includes (1) a synthesis of the hydrogeology and the hydrochemistry of recent groundwaters in these five aquifer types based on groundwater data acquired within the AQUITYP project, and (2) a hydro-geochemical investigation of the origin and chemical behaviour of the geogenic tracer chromium, based on a comprehensive field and laboratory study. To enable a comparison of the chemical groundwater data gathered and analysed over a time span of 20 years, a rigorous quality control of the entire database was made. An assessment was made of the sampling techniques, the sample treatment and the analytical methods applied in the AQUITYP project since 1981. Different tests were carried out to evaluate the quality and comparability of the data, including geochemical model calculations, comparison of different analytical techniques, and tests to estimate the influence of the filtration procedure. In order to make this large number of quality controlled data accessible also for future investigations, a groundwater data storage system was developed (AQUITYP-DataBase). 1.) Typology of recent groundwaters In the synthesis of groundwater hydrochemistry, the emphasis was laid on the hydro-geochemical evolution leading to the characteristic groundwater composition in each of the five aquifer types. Chemical characteristics and differences between the groundwaters from the different aquifer types were identified and natural concentration ranges for each aquifer type derived. The proposed geogenic tracers were evaluated and the potential sources of these tracers identified. The dominant processes leading to the typical mineralisation of recent groundwaters were investigated using geochemical modelling strategies. Finally, the concentrations of chemical elements in the groundwaters from the different aquifer types were compared to the Swiss drinking water standards in order to assess the quality of the investigated groundwaters. It has been found that each rock type contributes in a characteristic way to the major and trace element composition of the corresponding groundwater: The groundwaters derived from the crystalline Mont-Blanc and Aiguilles-Rouges massifs are characterised by a low total mineralisation (TDS 22 to 158 mg/L) dominated by Ca2+, Na+, Mg2+, alkalinity, SO42-, and F- (Ca-Na-HCO3,-SO4, waters). Elevated amounts of Mo, U, W, and As occur. These groundwaters derive their mineralisation mainly from the interaction with hydrothermal minerals present along fractures. Fractures act as major groundwater flow paths. Minerals relevant for groundwater mineralisation include carbonates (Ca2+, Mg2+, HCO3-), clay minerals (Ca-Na ion exchange), fluorite (F-, Ca2+), Fe-, As-, and Mo-sulphides (SO42-, As, Mo), and U- and W-minerals (U, W). In these crystalline groundwaters the natural concentrations of F- (23% of the investigated springs) and As (7%) exceed the Swiss limits for drinking water. In addition, the WHO guideline values for U are exceeded in 65% of the cases and for Mo in 15% of the cases. The carbonate karst groundwaters obtain their low to intermediate mineralisation (TDS 161 to 547 mg/L) from the dissolution of calcite (Ca-HCO3, waters), as well as in certain regions dolomite (Ca-Mg-HCO3, waters) and gypsum (Ca-Mg-HCO3,-SO4, waters). Together with their very short residence times, the carbonate karst groundwaters generally contain very low trace element contents. Nevertheless, geogenic trace elements occur in specific regions in relation with fossil organic matter (I, V) and accessory minerals such as barite in deep sea limestones (Ba), evaporite minerals (gypsum, celestite: Sr, Li), clay- and Fe-minerals (V), and Mo-sulphides and U-minerals in dolomitic limestones (Mo, U). In 18% of the carbonate karst springs atmospheric derived Pb exceeds the Swiss drinking water quality target value. The groundwaters from Triassic evaporites in the Swiss Rhone basin are characterised by a high total mineralisation (TDS 760 to 2788 mg/L) expressed by elevated amounts of Ca2+, Mg2+, Sr2+, SO42-, and alkalinity (Ca-Mg-SO4-HCO3 waters). Elevated amounts of the trace elements Mn, Ni, Cu, Li, Rb, Y, and Cd occur. The hydrochemical evolution of these groundwaters is governed by incipient dedolomitisation, involving dissolution of gypsum, celestite and dolomite and simultaneous precipitation of calcite. The Na+ and K+ contents probably controlled by ion-exchange reactions on clay minerals. Characteristic trace elements originate mainly from the dissolution of dolomite (Mn, Ni) and small amounts of apatite (Y, Cd), and from the oxidation of sulphide minerals (Cu, Ni, Cd). The elevated concentrations of the highly soluble Li and Rb may be related to brine inclusions in evaporite minerals and eventually to clay minerals. These evaporite groundwaters contain SO42- concentrations exceeding the Swiss quality target for drinking water in all springs, and the concentrations of U and Ni exceed the WHO guideline values in respectively 58% and 2% of the cases. In addition, Mn, Cd, and As concentrations exceed the Swiss quality targets in respectively 11%, 10%, and 7% of the investigated springs. Recent groundwaters circulating in the porous and fissured molasse sandstones and conglomerates acquire their intermediate mineralisation (TDS 48 to 714 mg/L) primarily by dissolution of calcite and minor dolomite (Ca-Mg-HCO3 waters). The particular mineralogy of certain Molasse formations is reflected in specific trace element compositions of corresponding groundwaters: ophiolite detritus in OMM sandstones in western Switzerland (Cr), barite fracture mineralisations in subalpine and folded Molasse units (Ba), granitic detritus containing sulphides (Mo), U-minerals (U) and abundant mica (Li) in the "Glimmersand" (OSM, Ca-Mg-HCO3-SO4 waters), and evaporite minerals (Li, Sr), sulphides (Mo), and U-minerals (U) in the "Gypsum-bearing Molasse" (USM, highly mineralised Ca-Mg-SO4-HCO3 waters, TDS 984 to 1346 mg/L) . In these molasse groundwaters the Swiss quality target values for drinking water of Cr and Pb are exceeded in 36% and 6% of the springs, respectively. The U concentrations of 14% of the molasse groundwaters ("Gypsum-bearing Molasse" and "Glimmersand"), exceed the WHO guideline value. The groundwaters from the "Gypsum-bearing Molasse" display similar quality problems as the evaporite groundwaters. Groundwaters derived from the shallow flysch aquifers in the Niesen and Gurnigel nappes are poorly evolved Ca-(Mg)-HCO3 waters. Their low to intermediate total mineralisation (TDS 160 to 459 mg/L) is acquired primarily by dissolution of calcite and to a lesser degree dolomite. The low trace element content is dominated by Ba originating from barite fracture mineralisations. The poor chemical evolution of recent flysch groundwaters results from (1) their short residence time in the fractured flysch rocks, and (2) the absence of readily dissolving minerals except carbonates and barite. In 32% of the flysch springs Pb derived from atmospheric sources exceeds the Swiss quality target value. 2.) Case study on the chemical weathering of molasse sandstone: Sources and chemical behaviour of Cr For the characterisation of the potentially toxic tracer element Cr a comprehensive field study was carried out on a selected catchment (Lutry spring catchment near Lausanne) situated in a molasse sandstone (OMM, Burdigalian). The investigation of the processes controlling the dissolved Cr content in these groundwaters was based on the groundwater chemical data, as well as on mineralogical, geochemical, and hydrological data. Relic Cr-bearing spinel and pyroxene in the sandstone were identified to be the primary sources of Cr. An electron microscope study showed that in the Burdigalian sandstone and overlying soil these minerals are strongly weathered. The slow weathering of these minerals is the major Cr releasing process. Under the oxidising conditions reigning in the investigated groundwaters, Cr prevails in solution in its highly soluble and toxic hexavalent state (CrO42-). In this case, retention by secondary Cr-hydroxide phases does not occur, as can be shown by geochemical model calculations. Laboratory leaching experiments were carried out with Burdigalian molasse sandstone from the field site, in order to support the field study findings and to quantify the processes responsible for the Cr mineralisation observed in the Lutry groundwater. Two experiments with mountain-wet oxidised and reduced sandstone were carried out over a time span of 2 months each, to obtain information about the influence of the oxidation state of the substratum on the mobilisation of Cr. The experiments clearly showed that the Cr-releasing processes are fast enough to explain the Cr contents found in the groundwater, and that the release of Cr into the groundwater depends on the weathering state of the sandstone. In the oxidised, Fe-hydroxide-coated sandstone, Cr is faster released into solution than in the less altered reduced sandstone. This indicates that the Cr contained in the reduced sandstone is in a more stable state, i.e. mainly incorporated in detrital minerals, while in the oxidised sandstone, the Cr is partly in an unstable state, i.e. adsorbed on the surface of secondary Fe-hydroxides, from where it is more easily leached.

EPFL2001