Browsing by Author "Lebrenz, Hans-Henning"

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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.