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- PublicationAccès libreModeling Fine-Scale Geological Heterogeneity?Examples of Sand Lenses in Tills(2013-1-10)
;Kessler, Timo Christian ;Comunian, Alessandro ; ; ;Nilsson, Bertel ;Klint, Knud ErikBjerg, Poul Løgstrup
- PublicationAccès libreStochastic simulation of rainfall and climate variables using the direct sampling techniqueAn accurate statistical representation of hydrological processes is of paramount importance to evaluate the uncertainty of the present scenario and make reliable predictions in a changing climate. A wealth of historic data has been made available in the last decades, including a consistent amount of remote sensing imagery describing the spatio-temporal nature of climatic and hydrological processes. The statistics based on such data are quite robust and reliable. However, to explore their variability, most stochastic simulation methods are based on low-order statistics that can only represent the heterogeneity up to a certain degree of complexity.
In the recent years, the stochastic hydrogeology group of the University of Neuchâtel has developed a multiple-point simulation method called Direct Sampling (DS). DS is a resampling technique that allows the preservation of the complex data structure by simply generating data patterns similar to the ones found in the historical data set. Contrarily to the other multiple-point methods, DS can simulate either categorical or continuous variables, or a combination of both in a multivariate framework.
In this thesis, the DS algorithm is adapted to the simulation of rainfall and climate variables in both time and space. The developed stochastic weather or climate generators include the simulation of the target variable with a series of auxiliary variables describing some aspects of the complex statistical structure characterizing the simulated process. These methods are tested on real application cases including the simulation of rainfall time-series from different climates, the variability exploration of future climate change scenarios, the missing data simulation within flow rate time-series and the simulation of spatial rainfall fields at different scales. If a representative training data set is used, the proposed methodologies can generate realistic simulations, preserving fairly well the statistical properties of the heterogeneity. Moreover, these techniques result to be practical simulation tools, since they are adaptive to different data sets with minimal effort from the user perspective. Although leaving large room for improvement, the proposed simulation approaches show a good potential to explore the variability of complex hydrological processes without the need of a complex statistical model.
- PublicationAccès libre
- PublicationAccès libreSimulation of rainfall time series from different climatic regions using the direct sampling techniqueThe direct sampling technique, belonging to the family of multiple-point statistics, is proposed as a nonparametric alternative to the classical autoregressive and Markovchain-based models for daily rainfall time-series simulation. The algorithm makes use of the patterns contained inside the training image (the past rainfall record) to reproduce the complexity of the signal without inferring its prior statistical model: the time series is simulated by sampling the training data set where a sufficiently similar neighborhood exists. The advantage of this approach is the capability of simulating complex statistical relations by respecting the similarity of the patterns at different scales. The technique is applied to daily rainfall records from different climate settings, using a standard setup and without performing any optimization of the parameters. The results show that the overall statistics as well as the dry/wet spells patterns are simulated accurately. Also the extremes at the higher temporal scale are reproduced adequately, reducing the well known problem of overdispersion.
- PublicationAccès libreModeling Fine-Scale Geological Heterogeneity: Examples of Sand Lenses in Tills
;Kessler, Timo Christian ;Comunian, Alessandro ; ; ;Nilsson, Bertel ;Klint, Knud ErikBjerg, Poul LøgstrupSand lenses at various spatial scales are recognized to add heterogeneity to glacial sediments. They have high hydraulic conductivities relative to the surrounding till matrix and may affect the advective transport of water and contaminants in clayey till settings. Sand lenses were investigated on till outcrops producing binary images of geological cross-sections capturing the size, shape and distribution of individual features. Sand lenses occur as elongated, anisotropic geobodies that vary in size and extent. Besides, sand lenses show strong non-stationary patterns on section images that hamper subsequent simulation. Transition probability (TP) and multiple-point statistics (MPS) were employed to simulate sand lens heterogeneity. We used one cross-section to parameterize the spatial correlation and a second, parallel section as a reference: it allowed testing the quality of the simulations as a function of the amount of conditioning data under realistic conditions. The performance of the simulations was evaluated on the faithful reproduction of the specific geological structure caused by sand lenses. Multiple-point statistics offer a better reproduction of sand lens geometry. However, two-dimensional training images acquired by outcrop mapping are of limited use to generate three-dimensional realizations with MPS. One can use a technique that consists in splitting the 3D domain into a set of slices in various directions that are sequentially simulated and reassembled into a 3D block. The identification of flow paths through a network of elongated sand lenses and the impact on the equivalent permeability in tills are essential to perform solute transport modeling in the low-permeability sediments.
- PublicationAccès libreSimulation of rainfall time series from different climatic regions using the direct sampling techniqueThe direct sampling technique, belonging to the family of multiple-point statistics, is proposed as a nonparametric alternative to the classical autoregressive and Markov-chain-based models for daily rainfall time-series simulation. The algorithm makes use of the patterns contained inside the training image (the past rainfall record) to reproduce the complexity of the signal without inferring its prior statistical model: the time series is simulated by sampling the training data set where a sufficiently similar neighborhood exists. The advantage of this approach is the capability of simulating complex statistical relations by respecting the similarity of the patterns at different scales. The technique is applied to daily rainfall records from different climate settings, using a standard setup and without performing any optimization of the parameters. The results show that the overall statistics as well as the dry/wet spells patterns are simulated accurately. Also the extremes at the higher temporal scale are reproduced adequately, reducing the well known problem of overdispersion.
- PublicationAccès libreSimulating rainfall time-series: how to account for statistical variability at multiple scales?(2018)
; ;Mehrotra, R ;Mariéthoz, Grégoire ; ;Sharma, ADaily rainfall is a complex signal exhibiting alternation of dry and wet states, seasonal fluctuations and an irregular behavior at multiple scales that cannot be preserved by stationary stochastic simulation models. In this paper, we try to investigate some of the strategies devoted to preserve these features by comparing two recent algorithms for stochastic rainfall simulation: the first one is the modified Markov model, belonging to the family of Markov-chain based techniques, which introduces non-stationarity in the chain parameters to preserve the long-term behavior of rainfall. The second technique is direct sampling, based on multiple-point statistics, which aims at simulating a complex statistical structure by reproducing the same data patterns found in a training data set. The two techniques are compared by first simulating a synthetic daily rainfall time-series showing a highly irregular alternation of two regimes and then a real rainfall data set. This comparison allows analyzing the efficiency of different elements characterizing the two techniques, such as the application of a variable time dependence, the adaptive kernel smoothing or the use of low-frequency rainfall covariates. The results suggest, under different data availability scenarios, which of these elements are more appropriate to represent the rainfall amount probability distribution at different scales, the annual seasonality, the dry-wet temporal pattern, and the persistence of the rainfall events.
- PublicationAccès libreMissing data simulation inside flow rate time-series using multiple-point statistics(2016-10)
; ; ; ;The direct sampling (DS) multiple-point statistical technique is proposed as a non-parametric missing data simulator for hydrological flow rate time-series. The algorithm makes use of the patterns contained inside a training data set to reproduce the complexity of the missing data. The proposed setup is tested in the reconstruction of a flow rate time-series while considering several missing data scenarios, as well as a comparative test against a time-series model of type ARMAX. The results show that DS generates more realistic simulations than ARMAX, better recovering the statistical content of the missing data. The predictive power of both techniques is much increased when a correlated flow rate time-series is used, but DS can also use incomplete auxiliary time-series, with a comparable prediction power. This makes the technique a handy simulation tool for practitioners dealing with incomplete data sets.
- PublicationAccès libreBinary upscaling on complex heterogeneities: The role of geometry and connectivityThe equivalent conductivity (Keq) of a binary medium is known to vary with the proportion of the two phases, but it also depends on the geometry and topology of the inclusions. In this paper, we analyze the role of connectivity and shape of the connected components through a correlation study between Keq and two topological and geometrical indicators: the Euler number and the Solidity indicator. We show that a local measure such as the Euler number is weakly correlated to Keq and therefore it is not suitable to quantify the influence of connectivity on the global flux; on the contrary the Solidity indicator, related to the convex hull of the connected components, presents a direct correlation with Keq. This result suggests that, in order to estimate Keq properly, one may consider the convex hull of each connected component as the area of influence of its spatial distribution on flow and make a correction of the proportion of the hydrofacies according to that. As a direct application of these principles, we propose a new method for the estimation of Keq using simple image analysis operations. In particular, we introduce a direct measure of the connected fraction and a non-parametric correction of the hydrofacies proportion to compensate for the influence of the connected components shape on flow. This model, tested on a large ensemble of isotropic media, provides a good Keq approximation even on complex heterogeneities without the need for calibration.