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Introduction aux problèmes inverses Charles, Catherine in Notes de Statistique et d'Informatique (2014) cette note technique est une inititation aux problèmes inverses. Son objectif est d'expliquer au lecteur ses principes généraux, de montrer son large panel d'applications ainsi que de présenter ses ... [more ▼] cette note technique est une inititation aux problèmes inverses. Son objectif est d'expliquer au lecteur ses principes généraux, de montrer son large panel d'applications ainsi que de présenter ses méthodes de résolution les plus courantes. [less ▲] Detailed reference viewed: 108 (12 ULg)Different methods for spatial interpolation of rainfall data for operational hydrology and hydrological modeling at watershed scale: a review Ly, Sarann ; Charles, Catherine ; Degré, Aurore in Biotechnologie, Agronomie, Société et Environnement = Biotechnology, Agronomy, Society and Environment [=BASE] (2013), 17(2), 392-406 Watershed management and hydrological modeling require data related to the very important matter of precipitation, often measured using raingages or weather stations. Hydrological models often require a ... [more ▼] Watershed management and hydrological modeling require data related to the very important matter of precipitation, often measured using raingages or weather stations. Hydrological models often require a preliminary spatial interpolation as part of the modeling process. The success of spatial interpolation varies according to the type of model chosen, its mode of geographical management and the resolution used. The quality of a result is determined by the quality of the continuous spatial rainfall which ensues from the interpolation method used. The objective of this article is to review the existing methods for interpolation of rainfall data that are usually required in hydrological modeling. We review the basis for the application of certain common methods and geostatistical approaches used in interpolation of rainfall. Previous studies have highlighted the need for new research to investigate ways of improving the quality of rainfall data and ultimately, the quality of hydrological modeling. [less ▲] Detailed reference viewed: 244 (20 ULg)La représentation d'une matrice par biplot Palm, Rodolphe ; Charles, Catherine ; Claustriaux, Jean-Jacques in Notes de Statistique et d'Informatique (2012), (2), 1-22 Matrix factorization by means of singular value decomposition is examined and used to produce a graphical representation of a data matrix called biplot. The link between this biplot and the plots of the ... [more ▼] Matrix factorization by means of singular value decomposition is examined and used to produce a graphical representation of a data matrix called biplot. The link between this biplot and the plots of the variables and of the individuals usually given in principal component analysis is discussed and applied to an example. [less ▲] Detailed reference viewed: 36 (10 ULg)Effect of raingage density, position and interpolation on rainfall-discharge modelling Ly, Sarann ; Sohier, Catherine ; Charles, Catherine et al in Geophysical Research Abstracts (2012), 14(EGU2012), 2592 Precipitation traditionally observed using raingages or weather stations, is one of the main parameters that has direct impact on runoff production. This pPrecipitation data requires a preliminary spatial ... [more ▼] Precipitation traditionally observed using raingages or weather stations, is one of the main parameters that has direct impact on runoff production. This pPrecipitation data requires a preliminary spatial interpolation prior to hydrological modeling. The accuracy of modelling result is determined bydepends on the accuracy of the interpolated spatial rainfall which differs according to different interpolation methods. The accuracy of the interpolated spatial rainfall is usually determined by cross-validation method. The objective of this study is to assess the different interpolation methods of daily rainfall at the watershed scale through hydrological modelling and to explore the best methods that provides a good long term simulation. Four versions of geostatistics: Ordinary Kriging (ORK), Universal Kriging (UNK), Kriging with External Dridft (KED) and Ordinary Cokriging (OCK) and two types of deterministic methods: Thiessen polygon (THI) and Inverse Distance Weighting (IDW) are used to produce 30-year daily rainfall inputs for a distributed physically-based hydrological model (EPIC-GRID). This work is conducted in the Ourthe and Ambleve nested catchments, located in the Ardennes hilly landscape in the Walloon region, Belgium. The total catchment area is 2908 km², lies between 67 and 693 m in elevation. The multivariate geostatistics (KED and OCK) are also used by incorporating elevation as external data to improve the rainfall prediction. This work also aims at analysing the effect of different raingage densities and position used for interpolation, on the stream flow modelled to get insight in terms of the capability and limitation of the geostatistical methods. The number of raingage varies from 70, 60, 50, 40, 30, 20, 8 to 4 stations located in and surrounding the catchment area. In the latter case, we try to use different positions: around the catchment and only a part of the catchment. The result shows that the simple method like THI fails to capture the rainfall and to produce good flow simulation when using 4 raingages. The KED and UNK are comparable to other methods for a raingage case that in which stations are located around the catchment area, especially in the high elevation catchment but the worst methods for other raingage position cases where the rainfall stations are located only at a part and mostly outside of the catchment area. However, three methods (IDW, ORK and OCK) can overcome this problem since they are more robust and can provide good performance of simulation in all raingage densities. When using 70, 60, 50, 40, 30, 20, 8 raingages in the catchment area (2908 km²), no substantial differences in model performance are observed. [less ▲] Detailed reference viewed: 89 (14 ULg)Geostatistical interpolation of daily rainfall at catchment scale: the use of several variogram models in the Ourthe and Ambleve catchments, Belgium Ly, Sarann ; Charles, Catherine ; Degre, Aurore in Hydrology and Earth System Sciences (2011), 15(7), 2259-2274 Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (kriging) are widely applied in spatial interpolation from point measurement to ... [more ▼] Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (kriging) are widely applied in spatial interpolation from point measurement to continuous surfaces. The first step in kriging computation is the semi-variogram modelling which usually used only one variogram model for all-moment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km2 regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. This study leaned on 30-yr daily rainfall data of 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km2). This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical) were fitted to daily sample semi-variogram on a daily basis. These seven variogram models were also adopted to avoid negative interpolated rainfall. The elevation, extracted from a digital elevation model, was incorporated into multivariate geostatistics. Seven validation raingages and cross validation were used to compare the interpolation performance of these algorithms applied to different densities of raingages. We found that between the seven variogram models used, the Gaussian model was the most frequently best fit. Using seven variogram models can avoid negative daily rainfall in ordinary kriging. The negative estimates of kriging were observed for convective more than stratiform rain. The performance of the different methods varied slightly according to the density of raingages, particularly between 8 and 70 raingages but it was much different for interpolation using 4 raingages. Spatial interpolation with the geostatistical and Inverse Distance Weighting (IDW) algorithms outperformed considerably the interpolation with the Thiessen polygon, commonly used in various hydrological models. Integrating elevation into Kriging with an External Drift (KED) and Ordinary Cokriging (OCK) did not improve the interpolation accuracy for daily rainfall. Ordinary Kriging (ORK) and IDW were considered to be the best methods, as they provided smallest RMSE value for nearly all cases. Care should be taken in applying UNK and KED when interpolating daily rainfall with very few neighbourhood sample points. These recommendations complement the results reported in the literature. ORK, UNK and KED using only spherical model offered a slightly better result whereas OCK using seven variogram models achieved better result. [less ▲] Detailed reference viewed: 288 (23 ULg)Introduction aux applications des ondelettes Charles, Catherine in Notes de Statistique et d'Informatique (2011) Cette note fait suite à une note antérieure. Son objectif est de faire prendre conscience au lecteur de la large étendue d'applications des ondelettes. Elle se découpe en deux parties. La première ... [more ▼] Cette note fait suite à une note antérieure. Son objectif est de faire prendre conscience au lecteur de la large étendue d'applications des ondelettes. Elle se découpe en deux parties. La première illustre la théorie des ondelettes aux moyens d'applications tournées vers la statistique. La deuxième se tourne vers les applications en traitement du signal et de l'image. [less ▲] Detailed reference viewed: 41 (8 ULg)Introduction aux ondelettes Charles, Catherine in Notes de Statistique et d'Informatique (2011) Cette note technique à caractère mathématique est une introduction aux ondelettes, un des outils d'analyse du signal. Son objectif est d'initier le lecteur à la théorie des ondelettes. Elle se découpe en ... [more ▼] Cette note technique à caractère mathématique est une introduction aux ondelettes, un des outils d'analyse du signal. Son objectif est d'initier le lecteur à la théorie des ondelettes. Elle se découpe en deux parties. La première pose les bases théoriques des ondelettes. La deuxième partie traite des logiciels implémentés pour travailler avec les ondelettes. [less ▲] Detailed reference viewed: 80 (13 ULg)Effects of different spatial interpolators on the estimate of extreme precipitations Ly, Sarann ; Beckers, Eléonore ; Charles, Catherine et al in Geophysical Research Abstracts (2011), 13 The design values of the areal precipitation are needed for engineer to manage vital elements of our infrastructure. The areal precipitation can be generated by different interpolation methods. The ... [more ▼] The design values of the areal precipitation are needed for engineer to manage vital elements of our infrastructure. The areal precipitation can be generated by different interpolation methods. The problem involves choosing the interpolation method that we should use to estimate the extreme event. This work aimed at analyzing the effects of different interpolation methods on the estimate of extreme events of daily areal precipitations at catchment scale. The extreme rainfalls were estimated using areal daily rainfall interpolated by several interpolation methods (Thiessen polygon, Inverse Distance Weighting, Ordinary Kriging, Universal Kriging, Kriging with an External Drift and Ordinary Cokriging). We used thirty-years-long daily time series and different density of rain gages (from 4 to 70 rain gages). Our study is located in the Ourthe and Ambleve catchment area (2908 km²) in the southern part of Belgium). Spatial interpolation with the geostatistical and Inverse Distance Weighting algorithms outperformed considerably interpolation with the Thiessen polygon. Kriging with an External Drift and Ordinary Cokriging presented the highest Root Mean Square Error between the geostatistical and Inverse Distance Weighting methods. Ordinary Kriging and Inverse Distance Weighting were considered to be the best methods, as they provided smallest Root Mean Square Error for nearly all cases. However, it’s not really the case of extreme estimates for particular return period. The extreme daily rainfall, corresponding to return periods of 25, 50 and 100 years, were computed by fitting of a statistical model to the series of maximum annual precipitation. These estimates were conducted using HYFRAN which allows us to fit 16 different statistical models, in 2 or 3 parameters. The most known are the models of Gumbel, Gamma, Weibull, exponential, Pareto, lognormale, Pearson III and GEV. Our results showed that the behaviour of extreme daily areal rainfall in this area was best described via the Gumbel and lognormal distributions. Using 70 rain gages, little differences in extreme rainfall were observed between the interpolation methods. The estimates from these methods were in the area of 95% confidence intervals of the estimates using the Thiessen polygon. However, when the number of rain gages diminishes, the Universal Kriging and Kriging with External drift methods produced extreme estimates outside the area of 95% confidence intervals of the estimates using the Thiessen polygon with all available stations. The analysis described here provides a means to choose the interpolation method in view to calculate extreme events. It shows to engineers or hydrologists the need for a particular care when working in the regions of sparse data. [less ▲] Detailed reference viewed: 144 (36 ULg)Spatial interpolation of daily rainfall in Ourthe and Ambleve Basins, Belgium Ly, Sarann ; Sohier, Catherine ; Charles, Catherine et al in Geophysical Research Abstracts (2010, May) Spatial interpolation of precipitation data is of great importance for hydrological modelling. The methods of geostatistics (krigings) become more popular to make spatial interpolation from point ... [more ▼] Spatial interpolation of precipitation data is of great importance for hydrological modelling. The methods of geostatistics (krigings) become more popular to make spatial interpolation from point measurement to distributed hydrological models. However, most of existing geostatistic algorithms are available only for single-moment data. The first step of Kriging computation is the semi-variogramme modelling which usually uses only one variogramme model for all-day data. The objective of this paper is to review the implementation of an algorithm of spatial interpolation methods for daily rainfall and to compare the results of geostatistic and deterministic approaches. In this study, we will use daily rainfall data from 70 rain gauges in the hilly landscape of Ourthe and Ambleve Basins in Belgium (2751 km2). This area lies between 35 and 690 m in elevation and consists of river networks which are the tributaries of the Meuse River. The proposed algorithm will use the method of Cressie’s Approximate Weighted Least Squares to fit among sevens semi-variogramme models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical) to daily sample semi-variogrammes. These seven models are computed on a daily basis. Firstly, one model is chosen by considering the minimum of least squares coefficient. Secondly, if the chosen model gives negative interpolated values, other models will be chosen again until the result become positive. Cross validation will be used to compare the interpolation performance of geostatistic to deterministic methods usually known as Thiessen polygon and Inverse DistanceWeighting (IDW). [less ▲] Detailed reference viewed: 89 (30 ULg)Introduction à Latex. Charles, Catherine ; Lecharlier, Loïc ; in Notes de Statistique et d'Informatique (2008) Detailed reference viewed: 93 (22 ULg)Introduction à Octave Charles, Catherine in Notes de Statistique et d'Informatique (2008) Detailed reference viewed: 28 (11 ULg)HREELS Signal Processing Via Wavelets. Charles, Catherine ; ; in Surface and Interface Analysis [=SIA] (2004), 36 Detailed reference viewed: 16 (2 ULg)XPS data analysis via Wavelets and Fourier Transform. Charles, Catherine ; ; in Surface and Interface Analysis [=SIA] (2004), 36 Detailed reference viewed: 47 (6 ULg)Wavelet Applications in Surface Science: a comparison to Fourier transform. Charles, Catherine ; ; et al in Surface and Interface Analysis [=SIA] (2004), 36 Detailed reference viewed: 21 (4 ULg)Some wavelet applications to signal and image processing. Charles, Catherine Doctoral thesis (2003) Detailed reference viewed: 24 (4 ULg)Ondelettes et télédétection Charles, Catherine ; in Revue des Nouvelles Technologies de l'Information (2003), 1 Detailed reference viewed: 27 (0 ULg)Ondelettes et télédétection. Charles, Catherine in Actes des XXXVèmes Journées de Statistiques (2003) Detailed reference viewed: 15 (4 ULg)Wavelet denoising of Poisson-distributed data and applications. Charles, Catherine ; in Computational Statistics & Data Analysis (2003), 43 Detailed reference viewed: 22 (0 ULg)Wavelet denoising of Poisson-distributed data and applications. Charles, Catherine ; Report (2002) Detailed reference viewed: 16 (0 ULg)Estimation non-paramétrique de l'intensité d'un processus de Poisson. Charles, Catherine ; in GRETSI'01 (2001) Detailed reference viewed: 58 (0 ULg) |
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