Browsing by Author "Bárdossy, András (Prof. Dr. rer.nat. Dr.-Ing.)"

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Open Access
Addressing the input uncertainty for hydrological modeling by a new geostatistical method
(2013) Lebrenz, Hans-Henning; Bárdossy, András (Prof. Dr. rer.nat. Dr.-Ing.)
The variogram-based regionalization methods for precipitation and their application as input to the subsequent hydrological modeling are examined in this study. The variogram, as the central tool, is firstly reviewed and a new robust estimation method is proposed. The central core of the proposed method is the description of spatial dependence by the coefficient of Kendall’s tau; , instead of the commonly applied Pearson correlation coefficient. A Monte-Carlo simulation and a quantile-quantile transformation converts the coefficient of Kendall’s tau; into the corresponding covariance function. The proposed method suits the general case of empirical marginal distributions and is not limited to gaussianity. The cross-validation of the estimator revealed a superior estimation method for the empirical marginal distributions, which is robust against some artificially induced outliers. Next, the new interpolation method of Quantile Kriging is elaborated and compared to the traditional interpolation methods of Ordinary Kriging and External Drift Kriging. The proposed interpolation method fits a theoretical distribution to the observations of monthly precipitation at every raingauge and subsequently decomposes the actual variable into corresponding quantiles and the associated distribution parameters. Quantiles and parameters are separately interpolated to the unknown location, where they are ultimately reconverted to the actual variable of precipitation. The distribution parameters implicitly transfer information over time to the interpolation at a particular time step. The resulting cross-validation displays an overall improvement for the estimator by Quantile Kriging and exhibits a more appropriate description of the associated distribution of the estimation errors. Quantile Kriging further relates the magnitude of the estimator with the associated uncertainty, which is a major advancement compared to Ordinary Kriging and External Drift Kriging. Furthermore, the traditional methods are theoretically optimized with regard to the spatial bias, while Quantile Kriging improves the temporal bias. Therefore, Quantile Kriging offers an alternative interpolation methodology with regard to some practical applications. The principle of the decomposition into quantiles and parameters, prior to the regionalization, is further extended to Turning Bands Simulations. The proposed simulation of quantiles and parameters enables the simultaneous quantification of a random and a systematic error from the regionalization of precipitation. The random error bears a higher variability, but its accumulation over time does not diverge from zero. The systematic error is relatively small for one given time step, but exhibits a constant (systematic) trend over time. Therefore, the systematic error eventually surpasses the random error in magnitude. The separate simulation or the combined simulation of quantiles and parameters is, thus, serving as inputs to the hydrological modeling. The different precipitation simulations serve as input to the hydrological modeling of a selected catchment basin with mesoscale size. The ROPE algorithm calibrates the eight parameters of the conceptual HBV-IWS model and the propagation of the input uncertainties are hereby examined. The simultaneous quantification of two input uncertainties revealed that mainly one parameter of the HBV-IWS model closes the overall water balance during the calibration period, while another parameter is suspected to adapt the different variabilities to the observed discharge. The remaining six parameters of the HBV-IWS model show a relatively inert behavior on the different inputs and, therefore, indicate an overparameterization of the model.
Open Access
Analysis of real-world spatial dependence of subsurface hydraulic properties using copulas with a focus on solute transport behaviour
(2011) Haslauer, Claus; Bárdossy, András (Prof. Dr. rer.nat. Dr.-Ing.)
Copulas are a novel tool in geostatistics that allows modelling of pure spatial dependence independently of the marginal distribution and without an assumption of multivariate Gaussian dependence. By using a transformation via the marginal distribution, the effect of extreme values is substantially decreased compared to traditional Gaussian based geostatistical measures such as Kriging. Additionally, the dependence is not described as an average variance as in Kriging, but a different degree of dependence can be modelled for different quantiles of the marginal distribution. Two data-sets from field sites at Borden and North Bay, both in Ontario, Canada, were used to test the performance of copulas as stochastic models for spatial dependence. Furthermore, this thesis explores possible effects of modelling spatial dependence using non-Gaussian copulas on physical properties that are based on such heterogeneous fields. For comparison, the effects of Gaussian structures are evaluated. The Gaussian- and non-Gaussian structures can not be distinguished by their variograms. It was shown that neither of the two data-sets exhibits Gaussian dependence – despite the fact that the Borden aquifer is commonly thought of as a relatively homogeneous porous medium with a small variance of hydraulic conductivity. Two non-Gaussian copula models, v-copulas and maximum Gaussian copulas were fitted to the hydraulic conductivity data, to be compared with a Gaussian copula model. The theoretical copula models were subsequently used for spatial interpolation and simulation. In addition to evaluating the spatial dependence structure of the hydraulic conductivity data-sets, fitting theoretical copula models and using them for interpolation and simulation, the goal of this thesis is to explore if the structure of the hydraulic conductivity field influences a physical property, such as plume evolution as evaluated by second central moments of concentration fields. Despite the fact that Borden is a relatively homogeneous porous medium, and despite the fact that both types of spatial fields are not distinguishable by their variograms, the solute transport characteristics based on these two types of fields differ significantly in two- dimensional settings. The difference is less pronounced in three-dimensions. Non-Gaussian dependence can lead to a non-symmetric distribution of variance of concentration along the main direction of flow. Increasing the variance of a marginal distribution by a certain factor does not necessarily lead to a dispersivity increased by the same factor in the case of non-Gaussian fields. It is postulated that non-Gaussian spatial dependence of hydraulic conductivity and a more skewed marginal distribution of hydraulic conductivity will have significant implications in the other more heterogeneous aquifers.
Open Access
Copula based stochastic analysis of discharge time series
(2014) Sugimoto, Takayuki; Bárdossy, András (Prof. Dr. rer.nat. Dr.-Ing.)
Global climate change can have impact on characteristics of rainfall-runoff event and subsequently on the hydrological regime. Meanwhile, catchment itself changes due to the anthropogenic influences. In this context, it can be meaningful to investigate the existing long term discharge records for detecting catchment characteristics and its temporal change. For this aim, stochastic property of time series can be analysed. Widely used time series models are based on linear combinations of correlations. However, such statistical measure does not describe all the details of the dependence structure and, therefore, has risk of losing crucial information. Instead, copulas have the advantages to measure more detailed dependence structure in uniformed domain and possibly to reveal significant information of time series. In this paper, two measures are examined on copula domain. One is Asymmetry of discharge derived from intrinsic property of discharge, which can be related to the catchment characteristics. It is demonstrated how much this measure is related to hydrological characteristic of the catchments and how it temporally changes for 100 years daily discharge records. The other is copula distance which is a Cramér von Mises type distance applied to copula. This can be utilized for time series analysis similar to variance or correlation by comparing the local and global dependence structure of time series. The anthropogenic impacts were assessed by calculating the change of these statistics in moving time window. The main problem is that the change of stochastic property of discharge is caused not only by catchment change but also by temporal behavior of precipitation. A new approach is suggested for measuring interrelationship between discharge and precipitation time series based on copulas and hydrological model.
Open Access
Generation of spatially correlated synthetic rainfall time series in high temporal resolution : a data driven approach
(2013) Beck, Ferdinand; Bárdossy, András (Prof. Dr. rer.nat. Dr.-Ing.)
State of the art in sewage system design is the dimensioning of tubes and channels based on hydraulic simulations. For a correct estimation of flood and backwater risks not only single precipitation events but long rainfall time series of several decades are used in these simulations. Due to the fast response time in sewage systems, a temporal resolution of 1h or shorter is required. Temporally high resolution precipitation data show pronounced spatial variability. The area for which one 1h precipitation time series is representative is limited. Even a dense measurement network as it is available in Southwest Germany, with about one station in 120 square kilometres, cannot provide adequate measurements for every target location. Besides, the observed time series are rarely long enough for risk assessment. In this work a synthetic time series generator was developed to close the gap between the demand and the offer of high resolution precipitation data in Baden-Württemberg. It could be shown that the dependence structure between monthly rainfall sum, 1h rainfall probability, the average and standard deviation of hourly precipitation is approximately constant over the study region and that it can be described by a Gaussian copula. The copula is exploited to draw random values of the latter three parameters that are conditioned on the monthly precipitation sum. The generation is a two step process. Based on the monthly parameters, an initial time series if filled up with Weibull distributed hourly rainfall amounts. Then the temporal order of the time series is optimized by a simulated annealing scheme. It consecutively exchanges pairs of values in the time series and evaluates the modified time series by statistical target values, e. g. the autocorrelation at different aggregation levels. The optimization stops when the target values are attained as close as possible. The statistical target values are derived from all available rain gauges of Baden-Württemberg and regionalized on a regular grid of 1km times 1km. In a next step the simulation scheme is extended to the generation of several simultaneous, spatially dependent precipitation time series. Spatial information is incorporated at different levels. During the set up of the initial time series, the monthwise spatial dependence of the generation parameters at the different target locations is considered. During the optimization, the spatial correlations of 17 different atmospheric circulation patterns are used as target values in the optimization. The last chapter of this work deals with the detection of climate change signals in the precipitation regime of Baden-Württemberg. Several trend signals could be derived from observed precipitation time series and were extrapolated into the future by means of the global circulation model ECHAM5. It could be shown that there has been an increase in the frequency of extreme hourly precipitation sums during the last decades. It can be expected that this trend will continue in the future. It is discussed in this work how the discovered trend signals can be incorporated in the developed rainfall generation algorithms.
Open Access
The impact of spatial variability of precipitation on the predictive uncertainty of hydrological models
(2006) Das, Tapash; Bárdossy, András (Prof. Dr. rer.nat. Dr.-Ing.)
Hydrological models are simplified representations of a part of the hydrological cycle. The fact that natural processes are described with mathematical equations and the corresponding parameters are estimated using observations leads to uncertainties. The uncertainty stems from the parameters, the model structure and measurements of input and output data. Precipitation is one of the most important hydrological model inputs. Precipitation is often significantly variable in space and time within a catchment. The main aim of this dissertation was to investigate and quantify the impact of spatial variability of precipitation on the predictive uncertainty of hydrological model simulations. Given the importance of the role of the precipitation input in hydrological applications, the following research questions were addressed: (a) how does the spatial variability of precipitation influence the hydrological simulation results? (b) will a higher spatial resolution of model input data necessarily lead to a better model performance? (c) what is the impact on the simulated hydrographs of interpolated precipitation at different spatial resolutions through varying raingauge networks? (d) what is the benefit of using conditionally simulated precipitation in hydrological modeling? (e) how does uncertainty in precipitation affect parameter identification of a conceptual model? The modified rainfall-runoff model HBV was applied to investigate the majority of the objectives. Based on the HBV model concept, four different structures namely, fully-lumped, semi-lumped, semi-distributed and distributed were developed. The physically-based spatially-distributed modeling system SHETRAN was also used to investigate how uncertainty in precipitation affects parameter identification of a conceptual model? The upper Neckar catchment, located in south-west Germany, was selected as test catchment. A number of simulation experiments were carried out in line with the objectives and scope of this study. The study aimed to investigate the influence of spatial variability of precipitation in a rainfall-runoff model indicated no significant differences in the model performance when the model was run using averaged precipitation at different spatial scales. However, there was a clear deterioration in the model performance during the summer season. The results also highlight that there can be a significant deterioration in the model performance when the model calibrated using detailed precipitation is run using relatively less detailed input precipitation. The study on the comparison of modelling performance using different representations of spatial variability indicates that for the present study catchment semi-distributed and semi-lumped model structures out-perform the distributed and fully-lumped model structures for the given level of information. The results indicate that using interpolated precipitation on finer resolution does not improve the simulation accuracy in either the calibration or validation periods at the subcatchments’ outlets. The study suggests that there can be a trade-off among the model complexity and available observations. The study related to assess the impacts of raingauge density on the simulation results showed that the number and spatial distribution of raingauges affect the simulation results. It was found that the model performances worsen radically with an excessive reduction of raingauges. However, the performances were not significantly improved by increasing the number of raingauges more than a certain threshold number. The analysis also indicates that models using different raingauge networks might need their parameters recalibrated. Specifically, models calibrated with dense input precipitation information fail when run with sparse information. However, the models calibrated with sparse input precipitation information can perform well when run with dense information. Also the model calibrated with complete set of observed precipitation and being run with incomplete observed precipitation data associated with data estimated at the locations with missing measurements using multiple linear regression technique, performed well. Conditional spatial rainfall simulation indicates significantly more spatial variability in the simulated rainfall than interpolated rainfall. The model performs better for modeling the peak discharges using conditionally simulated rainfall than the model using interpolated rainfall. Thus conditional rainfall simulation is reasonable for flood modeling. The analysis also indicates that inadequate representation of spatial variability of precipitation in modeling is partly responsible for modeling errors and also this leads to the problems in parameter estimation of a conceptual hydrological model. Thus spatial variability must be captured and used as an input to the hydrological model in order to eliminate the errors due to input rainfall data.
Open Access
Processing and analysis of weather radar data for use in hydrology
(2013) Pfaff, Thomas; Bárdossy, András (Prof. Dr. rer.nat. Dr.-Ing.)
This thesis treats three major problems, which are of importance when using quantitative precipitation estimates based on weather radar data in hydrology. 1. Deterministic Correction of Errors in the Radar Measurement This chapter presents methods which are robust, efficient, and require only minimal amounts of input data to correct for - non-meteorological echos (also known as clutter), - signal attenuation by precipitation, and - artifacts due to the temporally discrete measurement of the continually moving precipitation field by the radar and quantifies their effectiveness. 2. Geostatistical Analysis and Correction using Rain Gauge Data The geostatistical analysis investigates first the influence of the radar measurement volume on the variogram that is derived from radar images. Second, a new method to adjust radar data to gauge measurements is developed. This method uses copulas as a tool to model the dependence between radar and gauge measurements, as well as the precipitation field's spatial structure, independent of the actual measurement values. Doing so leads to significantly improved estimates of the adjustment uncertainty. Two additional innovations, the assumption of precipitation following a censored continuous distribution, and directly taking the agreement between radar and gauge measurement into account, lead to reduced mathematical overhead as well as robust adjustment results. 3. Scale Analysis The concluding analysis of the differences between several interpolation and adjustment methods on various spatial scales shows that the high spatial resolution provided by the radar will have a major effect only up to a catchment size of approx. 1000 square kilometers. Beyond this scale, no significant improvement compared with precipitation estimates based on interpolations from a reasonably dense gauge network is to be expected.
Open Access
Upscaling of nanoparticle transport in porous media
(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodelierung der Universität Stuttgart, 2022) Glatz, Kumiko; Bárdossy, András (Prof. Dr. rer.nat. Dr.-Ing.)
Dissertation on the transport of nanoparticles in porous media on both 1D and 2D scales.