Bernard De Baets - Academia.edu (original) (raw)
Papers by Bernard De Baets
Hydrology and Earth System Sciences, Mar 19, 2012
The calibration of stochastic point process rainfall models, such as of the Bartlett-Lewis type, ... more The calibration of stochastic point process rainfall models, such as of the Bartlett-Lewis type, suffers from the presence of multiple local minima which local search algorithms usually fail to avoid. To meet this shortcoming, four relatively new global optimization methods are presented and tested for their ability to calibrate the Modified Bartlett-Lewis Model. The list of tested methods consists of: the Downhill Simplex Method, Simplex-Simulated Annealing, Particle Swarm Optimization and Shuffled Complex Evolution. The parameters of these algorithms are first optimized to ensure optimal performance, after which they are used for calibration of the Modified Bartlett-Lewis model. Furthermore, this paper addresses the choice of weights in the objective function. Three alternative weighing methods are compared to determine whether or not simulation results (obtained after calibration with the best optimization method) are influenced by the choice of weights. Since the formulation of the original BL model by Rodriguez-Iturbe et al. (1987a), this model has been subjected to a number of modifications and extensions. Introducing a jitter, for example, results in more realistically irregular cell intensities (Onof and Wheater, 1994a; Gyasi-Agyei and Willgoose, 1999). Allowing for different cell types to exist, introduces certain variations between storms, which is in accordance with the existence of different types of rainfall
European Society for Fuzzy Logic and Technology Conference, 2003
Abstract In this paper, the use of fuzzy models re- lating rainfall to catchment,discharge is in-... more Abstract In this paper, the use of fuzzy models re- lating rainfall to catchment,discharge is in- vestigated for the Zwalm catchment in Bel- gium. The models are built along the lines of Gaweda’s method,[4]. Since acceptable models were not obtained for this data set, the method,was further adapted. The newly obtained models are of comparable,perfor- mance,as Takagi‐Sugeno models,based on the
EGU General Assembly Conference Abstracts, May 1, 2010
EGU General Assembly Conference Abstracts, May 1, 2010
Proper precipitation forcing is paramount to hydrological modelling. However, the available obser... more Proper precipitation forcing is paramount to hydrological modelling. However, the available observations often do not meet the scale requirements of the model. To mitigate this, many authors have attempted to use downscaling techniques. These techniques often assume that the field at a scale smaller than the observed pixels follows a scaled distribution of the coarse scale field. If this assumption is incorrect, the estimated reliability of the model output is likely to be wrong as well. In this presentation we show that although this assumption is correct if the entire field is considered, it is not valid for the distribution of the rainfall field within a single pixel. It is found that the scaling behaviour is a function of the intensity of the rainfall field. In order to model the subpixel variability, a copula-based methodology was developed which outperforms the classical approaches.
Vegetation patterns arise from the interplay between intraspecific and interspecific biotic inter... more Vegetation patterns arise from the interplay between intraspecific and interspecific biotic interactions and from different abiotic constraints and interacting driving forces and distributions. In this study, we constructed an ensemble learning model that, based on spatially distributed environmental variables, could model vegetation patterns at the local scale. The study site was an alluvial floodplain with marked hydrologic gradients on which different vegetation types developed. The model was evaluated on accuracy, and could be concluded to perform well. However, model accuracy was remarkably lower for boundary areas between two distinct vegetation types. Subsequent application of the model on a spatially independent data set showed a poor performance that could be linked with the niche concept to conclude that an empirical distribution model, which has been constructed on local observations, is incapable to be applied beyond these boundaries.
A first order Takagi-Sugeno model is used as a basis for a groundwater model describing the water... more A first order Takagi-Sugeno model is used as a basis for a groundwater model describing the water movement in the unsaturated zone. Fuzzy rules are used for estimating the water flux. Combining this fuzzy rule base with the continuity equation allows the modeling of water movement in the unsaturated zone
Lecture Notes in Computer Science, 2003
ABSTRACT Three different methods for building Takagi-Sugeno models relating rainfall to catchment... more ABSTRACT Three different methods for building Takagi-Sugeno models relating rainfall to catchment discharge are tested on the Zwalm catchment. They correspond to the following identification methods: Grid Partitioning (GP), Subtractive Clustering (SC), and Gustafson-Kessel clustering (GK). The models are parametrized on a one-year identification data set and tested against the complete five-year data set. Although these models show a similar behaviour, resulting in comparable values of the Nash and Suttcliffe criterion and the root mean square error, the best values are obtained for the models generated using the GK method.
Hydrological Sciences Journal
Evapotranspiration is an important process in the water cycle that represents a considerable amou... more Evapotranspiration is an important process in the water cycle that represents a considerable amount of moisture lost through evaporation from the soil surface and transpiration from plants in a watershed. Therefore, an accurate estimate of evapotranspiration rates is necessary, along with precipitation data, for running hydrological models. Often, daily reference evapotranspiration is modelled based on the Penman, Priestley-Taylor or Hargraeves equation. However, each of these models requires extensive input data, such as daily mean temperature, wind speed, relative humidity and solar radiation. Yet, in design studies, such data is unavailable in case stochastically generated time series of precipitation are used to force a hydrologic model. In the latter case, an alternative model approach is needed that allows for generating evapotranspiration data that are consistent with the accompanying precipitation data. This contribution presents such an approach in which the statistical dep...
Hydrology and Earth System Sciences, 2015
Copulas have already proven their flexibility in rainfall modelling. Yet, their use is generally ... more Copulas have already proven their flexibility in rainfall modelling. Yet, their use is generally restricted to the description of bivariate dependence. Recently, vine copulas have been introduced, allowing multi-dimensional dependence structures to be described on the basis of a stage by stage mixing of 2-dimensional copulas. This paper explores the use of such vine copulas in order to incorporate all relevant dependences between the storm variables of interest. On the basis of such fitted vine copulas, an external storm structure is modelled. An internal storm structure is superimposed based on Huff curves, such that a continuous time series of rainfall is generated. The performance of the rainfall model is evaluated through a statistical comparison between an ensemble of synthetical rainfall series and the observed rainfall series and through the comparison of the annual maxima.
Hydrology and Earth System Sciences Discussions, 2013
Of all natural disasters, the economic and environmental consequences of droughts are among the h... more Of all natural disasters, the economic and environmental consequences of droughts are among the highest because of their longevity and widespread spatial extent. Because of their extreme behaviour, studying droughts generally requires long time series of historical climate data. Rainfall is a very important variable for calculating drought statistics, for quantifying historical droughts or for assessing the impact on other hydrological (e.g. water stage in rivers) or agricultural (e.g. irrigation requirements) variables. Unfortunately, time series of historical observations are often too short for such assessments. To circumvent this, one may rely on the synthetic rainfall time series from stochastic point process rainfall models, such as Bartlett-Lewis models. The present study investigates whether drought statistics are preserved when simulating rainfall with Bartlett-Lewis models. Therefore, a 105 yr 10 min rainfall time series obtained at Uccle, Belgium is used as test case. First, drought events were identified on the basis of the Effective Drought Index (EDI), and each event was characterized by two variables, i.e. drought duration (D) and drought severity (S). As both parameters are interdependent, a multivariate distribution function, which makes use of a copula, was fitted. Based on the copula, four types of drought return periods are calculated for observed as well as simulated droughts and are used to evaluate the ability of the rainfall models to simulate drought events with the appropriate characteristics. Overall, all Bartlett-Lewis type of models studied fail in preserving extreme drought statistics, which is attributed to the model structure and to the model stationarity caused by maintaining the same parameter set during the whole simulation period.
International Journal of Applied Earth Observation and Geoinformation, 2015
Operational flood mitigation and flood modeling activities benefit from a rapid and automated flo... more Operational flood mitigation and flood modeling activities benefit from a rapid and automated flood mapping procedure. A valuable information source for such a flood mapping procedure can be remote sensing synthetic aperture radar (SAR) data. In order to be reliable, an objective characterization of the uncertainty associated with the flood maps is required. This work focuses on speckle uncertainty associated with the SAR data and introduces the use of a non-parametric bootstrap method to take into account this uncertainty on the resulting flood maps. From several synthetic images, constructed through bootstrapping the original image, flood maps are delineated. The accuracy of these flood maps is also evaluated w.r.t. an independent validation data set, obtaining, in the two test cases analyzed in this paper, F-values (i.e. values of the Jaccard coefficient) comprised between 0.50 and 0.65. This method is further compared to an image segmentation method for speckle analysis, with which similar results are obtained. The uncertainty analysis of the ensemble of bootstrapped synthetic images was found to be representative of image speckle, with the advantage that no segmentation and speckle estimations are required. Furthermore, this work assesses to what extent the bootstrap ensemble size can be reduced while remaining representative of the original ensemble, as operational applications would clearly benefit from such reduced ensemble sizes.
ABSTRACT For several hydrological applications, long time series of rainfall are necessary. If in... more ABSTRACT For several hydrological applications, long time series of rainfall are necessary. If insufficient data are available, one may resort to using stochastically generated time series, such as rectangular pulses models. One commonly used type of these models is the Bartlett-Lewis model. Such model is characterized by several parameters, which define probability distribution functions of different properties of the rectangular pulses, including the height, the width, the timing of occurrence, etc. Generally, these models are being calibrated based on minimizing a cost function that is based on the comparison between a number of analytically calculated moments and those corresponding from observations. Several problems have been reported with these models, especially with respect to the generation of extreme events. Different improvements have been made or suggested for these models. One option would be to include a dependence structure between parameters or between properties of the pulses. However, it remains unclear whether and, if so, which parameters show mutual dependence. This study attempts to demonstrate the different dependences between the parameters of the Modified Bartlett-Lewis (MBL) model and the Modified Bartlett-Lewis Gamma (MBLG) model, based on a Monte Carlo experiment. The results of this analysis could be used for including copulas into the Bartlett-Lewis model which embed these dependencies into the model structure.
Water Resources Research, 2010
The use of copulas as flexible tools for constructing marginal-free distribution functions for mu... more The use of copulas as flexible tools for constructing marginal-free distribution functions for multivariate phenomena, such as rainfall, recently enjoys substantial attention by researchers in hydrology. In this study, commonly used bivariate copulas and techniques for fitting such bivariate copulas are applied to different couples of storm variables based on an extensive data set of 105 years of 10 min rainfall, observed at Uccle, Belgium. In the analysis, various problems that can occur are highlighted, and opportunities for further research are outlined. After selecting storms and introducing a meaningful solution to circumvent the presence of abundant ties in the data, a detailed seasonal dependence analysis is provided, together with a study on tail dependence. Further, different existing parameter estimation techniques and goodness-of-fit methods for selecting the most appropriate bivariate copulas are applied and compared. Finally, attention is given to the presence of asymmetric dependence and nonexchangeability.
International Journal of Applied Earth Observation and Geoinformation, 2012
The Integral Equation Model (IEM) is frequently used to retrieve moisture content of bare soils f... more The Integral Equation Model (IEM) is frequently used to retrieve moisture content of bare soils from synthetic aperture radar (SAR) images. This physically-based backscatter model requires surface roughness parameters, generally obtained by in situ measurements, which unfortunately often result in inaccurately retrieved soil moisture contents. Furthermore, when the retrieved soil moisture contents need to be used in data assimilation applications, it is important to also assess the retrieval uncertainty. Therefore, in this paper a regression-based method is developed that allows for the parameterization of roughness and that provides an estimation of its uncertainty by means of a probability distribution. By further propagating this distribution through the inversion of the IEM, a probability distribution of soil moisture content is obtained. It was found that 70% of the thus obtained distributions are skewed and non-normal. Furthermore, it is shown that their interquartile range varies depending on soil moisture conditions. Comparison of soil moisture measurements with the retrieved median values of the soil moisture histograms results in a root mean square error (RMSE) of approximately 3.5 vol%.
Water Resources Research, 2007
Radar remote sensing of bare soil surfaces has been shown to be very useful for retrieving soil m... more Radar remote sensing of bare soil surfaces has been shown to be very useful for retrieving soil moisture. However, the error on the retrieved value depends on the accuracy of the roughness parameters (RMS height and correlation length). Several studies have demonstrated that these parameters show a high variability within a field, and therefore a lot of soil roughness profiles need to be measured to obtain accurate estimates. However, in an operational mode, soil roughness measurements are not available and therefore, for different types of tillage, roughness parameters are ill known. Possibility theory offers a way of handling this type of uncertainty, by modeling roughness parameters by means of possibility distributions. Inverting the integral equation model then leads to a possibility distribution for soil moisture. After transforming these possibilities into probabilities, mean soil moisture values and the uncertainty thereupon (given by the standard deviation) are obtained. It...
Water Resources Research, 2011
Because of a lack of historical rainfall time series of considerable length, one often has to rel... more Because of a lack of historical rainfall time series of considerable length, one often has to rely on simulated rainfall time series, e.g., in the design of hydraulic structures. One way to simulate such time series is by means of stochastic point process rainfall models, such as the Bartlett‐Lewis type of model. For the evaluation of model performance, with a focus on the reproduction of extreme rainfall events, often a univariate extreme value analysis is performed. Recently developed concepts in statistical hydrology now offer other means of evaluating the overall performance of such models. In this study, a copula‐based frequency analysis of storms is proposed as a tool to evaluate differences between the return periods of several types of observed and modeled storms. First, this study performs an analysis of several storm variables, which indicates a problem with the modeling of the temporal structure of rainfall by the models. Thereafter, the bivariate frequency analysis of st...
Hydrology and Earth System Sciences, Mar 19, 2012
The calibration of stochastic point process rainfall models, such as of the Bartlett-Lewis type, ... more The calibration of stochastic point process rainfall models, such as of the Bartlett-Lewis type, suffers from the presence of multiple local minima which local search algorithms usually fail to avoid. To meet this shortcoming, four relatively new global optimization methods are presented and tested for their ability to calibrate the Modified Bartlett-Lewis Model. The list of tested methods consists of: the Downhill Simplex Method, Simplex-Simulated Annealing, Particle Swarm Optimization and Shuffled Complex Evolution. The parameters of these algorithms are first optimized to ensure optimal performance, after which they are used for calibration of the Modified Bartlett-Lewis model. Furthermore, this paper addresses the choice of weights in the objective function. Three alternative weighing methods are compared to determine whether or not simulation results (obtained after calibration with the best optimization method) are influenced by the choice of weights. Since the formulation of the original BL model by Rodriguez-Iturbe et al. (1987a), this model has been subjected to a number of modifications and extensions. Introducing a jitter, for example, results in more realistically irregular cell intensities (Onof and Wheater, 1994a; Gyasi-Agyei and Willgoose, 1999). Allowing for different cell types to exist, introduces certain variations between storms, which is in accordance with the existence of different types of rainfall
European Society for Fuzzy Logic and Technology Conference, 2003
Abstract In this paper, the use of fuzzy models re- lating rainfall to catchment,discharge is in-... more Abstract In this paper, the use of fuzzy models re- lating rainfall to catchment,discharge is in- vestigated for the Zwalm catchment in Bel- gium. The models are built along the lines of Gaweda’s method,[4]. Since acceptable models were not obtained for this data set, the method,was further adapted. The newly obtained models are of comparable,perfor- mance,as Takagi‐Sugeno models,based on the
EGU General Assembly Conference Abstracts, May 1, 2010
EGU General Assembly Conference Abstracts, May 1, 2010
Proper precipitation forcing is paramount to hydrological modelling. However, the available obser... more Proper precipitation forcing is paramount to hydrological modelling. However, the available observations often do not meet the scale requirements of the model. To mitigate this, many authors have attempted to use downscaling techniques. These techniques often assume that the field at a scale smaller than the observed pixels follows a scaled distribution of the coarse scale field. If this assumption is incorrect, the estimated reliability of the model output is likely to be wrong as well. In this presentation we show that although this assumption is correct if the entire field is considered, it is not valid for the distribution of the rainfall field within a single pixel. It is found that the scaling behaviour is a function of the intensity of the rainfall field. In order to model the subpixel variability, a copula-based methodology was developed which outperforms the classical approaches.
Vegetation patterns arise from the interplay between intraspecific and interspecific biotic inter... more Vegetation patterns arise from the interplay between intraspecific and interspecific biotic interactions and from different abiotic constraints and interacting driving forces and distributions. In this study, we constructed an ensemble learning model that, based on spatially distributed environmental variables, could model vegetation patterns at the local scale. The study site was an alluvial floodplain with marked hydrologic gradients on which different vegetation types developed. The model was evaluated on accuracy, and could be concluded to perform well. However, model accuracy was remarkably lower for boundary areas between two distinct vegetation types. Subsequent application of the model on a spatially independent data set showed a poor performance that could be linked with the niche concept to conclude that an empirical distribution model, which has been constructed on local observations, is incapable to be applied beyond these boundaries.
A first order Takagi-Sugeno model is used as a basis for a groundwater model describing the water... more A first order Takagi-Sugeno model is used as a basis for a groundwater model describing the water movement in the unsaturated zone. Fuzzy rules are used for estimating the water flux. Combining this fuzzy rule base with the continuity equation allows the modeling of water movement in the unsaturated zone
Lecture Notes in Computer Science, 2003
ABSTRACT Three different methods for building Takagi-Sugeno models relating rainfall to catchment... more ABSTRACT Three different methods for building Takagi-Sugeno models relating rainfall to catchment discharge are tested on the Zwalm catchment. They correspond to the following identification methods: Grid Partitioning (GP), Subtractive Clustering (SC), and Gustafson-Kessel clustering (GK). The models are parametrized on a one-year identification data set and tested against the complete five-year data set. Although these models show a similar behaviour, resulting in comparable values of the Nash and Suttcliffe criterion and the root mean square error, the best values are obtained for the models generated using the GK method.
Hydrological Sciences Journal
Evapotranspiration is an important process in the water cycle that represents a considerable amou... more Evapotranspiration is an important process in the water cycle that represents a considerable amount of moisture lost through evaporation from the soil surface and transpiration from plants in a watershed. Therefore, an accurate estimate of evapotranspiration rates is necessary, along with precipitation data, for running hydrological models. Often, daily reference evapotranspiration is modelled based on the Penman, Priestley-Taylor or Hargraeves equation. However, each of these models requires extensive input data, such as daily mean temperature, wind speed, relative humidity and solar radiation. Yet, in design studies, such data is unavailable in case stochastically generated time series of precipitation are used to force a hydrologic model. In the latter case, an alternative model approach is needed that allows for generating evapotranspiration data that are consistent with the accompanying precipitation data. This contribution presents such an approach in which the statistical dep...
Hydrology and Earth System Sciences, 2015
Copulas have already proven their flexibility in rainfall modelling. Yet, their use is generally ... more Copulas have already proven their flexibility in rainfall modelling. Yet, their use is generally restricted to the description of bivariate dependence. Recently, vine copulas have been introduced, allowing multi-dimensional dependence structures to be described on the basis of a stage by stage mixing of 2-dimensional copulas. This paper explores the use of such vine copulas in order to incorporate all relevant dependences between the storm variables of interest. On the basis of such fitted vine copulas, an external storm structure is modelled. An internal storm structure is superimposed based on Huff curves, such that a continuous time series of rainfall is generated. The performance of the rainfall model is evaluated through a statistical comparison between an ensemble of synthetical rainfall series and the observed rainfall series and through the comparison of the annual maxima.
Hydrology and Earth System Sciences Discussions, 2013
Of all natural disasters, the economic and environmental consequences of droughts are among the h... more Of all natural disasters, the economic and environmental consequences of droughts are among the highest because of their longevity and widespread spatial extent. Because of their extreme behaviour, studying droughts generally requires long time series of historical climate data. Rainfall is a very important variable for calculating drought statistics, for quantifying historical droughts or for assessing the impact on other hydrological (e.g. water stage in rivers) or agricultural (e.g. irrigation requirements) variables. Unfortunately, time series of historical observations are often too short for such assessments. To circumvent this, one may rely on the synthetic rainfall time series from stochastic point process rainfall models, such as Bartlett-Lewis models. The present study investigates whether drought statistics are preserved when simulating rainfall with Bartlett-Lewis models. Therefore, a 105 yr 10 min rainfall time series obtained at Uccle, Belgium is used as test case. First, drought events were identified on the basis of the Effective Drought Index (EDI), and each event was characterized by two variables, i.e. drought duration (D) and drought severity (S). As both parameters are interdependent, a multivariate distribution function, which makes use of a copula, was fitted. Based on the copula, four types of drought return periods are calculated for observed as well as simulated droughts and are used to evaluate the ability of the rainfall models to simulate drought events with the appropriate characteristics. Overall, all Bartlett-Lewis type of models studied fail in preserving extreme drought statistics, which is attributed to the model structure and to the model stationarity caused by maintaining the same parameter set during the whole simulation period.
International Journal of Applied Earth Observation and Geoinformation, 2015
Operational flood mitigation and flood modeling activities benefit from a rapid and automated flo... more Operational flood mitigation and flood modeling activities benefit from a rapid and automated flood mapping procedure. A valuable information source for such a flood mapping procedure can be remote sensing synthetic aperture radar (SAR) data. In order to be reliable, an objective characterization of the uncertainty associated with the flood maps is required. This work focuses on speckle uncertainty associated with the SAR data and introduces the use of a non-parametric bootstrap method to take into account this uncertainty on the resulting flood maps. From several synthetic images, constructed through bootstrapping the original image, flood maps are delineated. The accuracy of these flood maps is also evaluated w.r.t. an independent validation data set, obtaining, in the two test cases analyzed in this paper, F-values (i.e. values of the Jaccard coefficient) comprised between 0.50 and 0.65. This method is further compared to an image segmentation method for speckle analysis, with which similar results are obtained. The uncertainty analysis of the ensemble of bootstrapped synthetic images was found to be representative of image speckle, with the advantage that no segmentation and speckle estimations are required. Furthermore, this work assesses to what extent the bootstrap ensemble size can be reduced while remaining representative of the original ensemble, as operational applications would clearly benefit from such reduced ensemble sizes.
ABSTRACT For several hydrological applications, long time series of rainfall are necessary. If in... more ABSTRACT For several hydrological applications, long time series of rainfall are necessary. If insufficient data are available, one may resort to using stochastically generated time series, such as rectangular pulses models. One commonly used type of these models is the Bartlett-Lewis model. Such model is characterized by several parameters, which define probability distribution functions of different properties of the rectangular pulses, including the height, the width, the timing of occurrence, etc. Generally, these models are being calibrated based on minimizing a cost function that is based on the comparison between a number of analytically calculated moments and those corresponding from observations. Several problems have been reported with these models, especially with respect to the generation of extreme events. Different improvements have been made or suggested for these models. One option would be to include a dependence structure between parameters or between properties of the pulses. However, it remains unclear whether and, if so, which parameters show mutual dependence. This study attempts to demonstrate the different dependences between the parameters of the Modified Bartlett-Lewis (MBL) model and the Modified Bartlett-Lewis Gamma (MBLG) model, based on a Monte Carlo experiment. The results of this analysis could be used for including copulas into the Bartlett-Lewis model which embed these dependencies into the model structure.
Water Resources Research, 2010
The use of copulas as flexible tools for constructing marginal-free distribution functions for mu... more The use of copulas as flexible tools for constructing marginal-free distribution functions for multivariate phenomena, such as rainfall, recently enjoys substantial attention by researchers in hydrology. In this study, commonly used bivariate copulas and techniques for fitting such bivariate copulas are applied to different couples of storm variables based on an extensive data set of 105 years of 10 min rainfall, observed at Uccle, Belgium. In the analysis, various problems that can occur are highlighted, and opportunities for further research are outlined. After selecting storms and introducing a meaningful solution to circumvent the presence of abundant ties in the data, a detailed seasonal dependence analysis is provided, together with a study on tail dependence. Further, different existing parameter estimation techniques and goodness-of-fit methods for selecting the most appropriate bivariate copulas are applied and compared. Finally, attention is given to the presence of asymmetric dependence and nonexchangeability.
International Journal of Applied Earth Observation and Geoinformation, 2012
The Integral Equation Model (IEM) is frequently used to retrieve moisture content of bare soils f... more The Integral Equation Model (IEM) is frequently used to retrieve moisture content of bare soils from synthetic aperture radar (SAR) images. This physically-based backscatter model requires surface roughness parameters, generally obtained by in situ measurements, which unfortunately often result in inaccurately retrieved soil moisture contents. Furthermore, when the retrieved soil moisture contents need to be used in data assimilation applications, it is important to also assess the retrieval uncertainty. Therefore, in this paper a regression-based method is developed that allows for the parameterization of roughness and that provides an estimation of its uncertainty by means of a probability distribution. By further propagating this distribution through the inversion of the IEM, a probability distribution of soil moisture content is obtained. It was found that 70% of the thus obtained distributions are skewed and non-normal. Furthermore, it is shown that their interquartile range varies depending on soil moisture conditions. Comparison of soil moisture measurements with the retrieved median values of the soil moisture histograms results in a root mean square error (RMSE) of approximately 3.5 vol%.
Water Resources Research, 2007
Radar remote sensing of bare soil surfaces has been shown to be very useful for retrieving soil m... more Radar remote sensing of bare soil surfaces has been shown to be very useful for retrieving soil moisture. However, the error on the retrieved value depends on the accuracy of the roughness parameters (RMS height and correlation length). Several studies have demonstrated that these parameters show a high variability within a field, and therefore a lot of soil roughness profiles need to be measured to obtain accurate estimates. However, in an operational mode, soil roughness measurements are not available and therefore, for different types of tillage, roughness parameters are ill known. Possibility theory offers a way of handling this type of uncertainty, by modeling roughness parameters by means of possibility distributions. Inverting the integral equation model then leads to a possibility distribution for soil moisture. After transforming these possibilities into probabilities, mean soil moisture values and the uncertainty thereupon (given by the standard deviation) are obtained. It...
Water Resources Research, 2011
Because of a lack of historical rainfall time series of considerable length, one often has to rel... more Because of a lack of historical rainfall time series of considerable length, one often has to rely on simulated rainfall time series, e.g., in the design of hydraulic structures. One way to simulate such time series is by means of stochastic point process rainfall models, such as the Bartlett‐Lewis type of model. For the evaluation of model performance, with a focus on the reproduction of extreme rainfall events, often a univariate extreme value analysis is performed. Recently developed concepts in statistical hydrology now offer other means of evaluating the overall performance of such models. In this study, a copula‐based frequency analysis of storms is proposed as a tool to evaluate differences between the return periods of several types of observed and modeled storms. First, this study performs an analysis of several storm variables, which indicates a problem with the modeling of the temporal structure of rainfall by the models. Thereafter, the bivariate frequency analysis of st...
This paper is devoted to classify all idempotent uninorms defined on the finite scale L n = {0, 1... more This paper is devoted to classify all idempotent uninorms defined on the finite scale L n = {0, 1, . . . , n}, called discrete idempotent uninorms. It is proved that any discrete idempotent uninorm with neutral element e ∈ L n is uniquely determined by a decreasing function g : [0, e] → [e, n] and vice versa. Based on this correspondence, the number of all possible discrete idempotent uninorms on a finite scale of n + 1 elements is given depending on n.