02 Fakultät Bau- und Umweltingenieurwissenschaften

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    Simulation of remotely sensed rainfall fields using copulas
    (2010) AghaKouchak, Amir; Bárdossy, András (Prof. Dr. rer. nat. Dr.-Ing.)
    Rainfall is a major input in hydrological and meteorological models. Quantification of rainfall and its spatial and temporal variability is extremely important for reliable hydrologic and meteorological modeling. Hydrological and climate studies have long relied on rain gauge measurements. While rain gauge measurements do not provide reasonable areal representation of rainfall, remotely sensed precipitation estimates offer much higher spatial resolution. Recent technological advances in the field of remote sensing have led to an increase in available rainfall data on a regional and global scale. However, the advantages of remotely sensed data are limited by complications related to the indirect nature of remotely sensed estimates. Previous studies confirm that remotely sensed rainfall estimates are subject to various errors, and for future use in hydrologic and climate studies, efforts are required to determine the accuracy of data and their associated uncertainties. Despite extensive research, however, uncertainties associated with remotely sensed rainfall estimates are not yet well quantified. Radar rainfall estimates, for example, are associated with several different error types that arise from various factors such as beam over-shooting, partial beam filling, non-uniformity in vertical profiles of reflectivity (VPR), inappropriate $Z-R$ relationship, spatial sampling pattern, hardware calibration and random sampling error. It is expected that uncertainties in rainfall input data will propagate into predictions from hydrologic and meteorologic models; therefore, accurate characterization and quantification of such errors in radar data and the induced uncertainties in hydrologic applications is an extremely important, yet challenging issue. So far, a multitude of approaches and extensive research efforts have been undertaken to develop an uncertainty model for remotely sensed rainfall estimates. In order to assess rainfall uncertainties, one can simulate an ensemble of precipitation fields that consists of a large number of realizations, each of which represents a possible rainfall event that can occur. Subsequent runs of a hydrological or meteorological model using simulated ensembles of rainfall estimates would then allow an assessment of uncertainty propagation due to the precipitation input. One way to generate an ensemble of rainfall estimates is to stochastically simulate random error fields and impose them on radar estimates. This study intends to develop different stochastic techniques for simulation of radar-based rainfall fields through simulating random error fields and imposing them over remotely sensed rainfall estimates. Four different models are developed and discussed in this work. In the first and second models, two elliptical copulas, Gaussian and t-copula, are used to describe the dependence structure of radar rainfall error and to simulate multivariate rainfall error fields. In the third model, an asymmetrical v-transformed copula is employed for error simulations. In the fourth model, rainfall fields are generated by perturbing rainfall estimates with two normally distributed error terms: a purely random component and a component proportional to the magnitude of the rainfall rates. In the first three models, having described the dependencies using copulas, the empirical distribution function of observed rainfall error is numerically approximated and applied to the simulated error fields so that the simulated realizations are similar to those of the observed in terms of the distribution function. In the fourth model, however, the error is assumed to be normally distributed. In all the models, available observations of radar rainfall error (the differences between radar estimates and rain gauge measurements) are used to condition the simulated fields on observations. In order to examine reliability and performance of the developed models, several case studies are presented over a small watershed in Mississippi, USA, and a large watershed in Oklahoma, USA. Both radar reflectivity data (Level II) as well as Stage IV Next Generation Weather Radar (NEXRAD) multi-sensor precipitation estimates are used as input to the models. The simulated rainfall fields obtained from different models are compared with original radar estimates with respect to statistical properties, extreme values and spatio-temporal dependencies. Moreover, a physically based model is used to demonstrate the application of the presented rainfall field generators in streamflow analysis. In subsequent chapters, after introducing the models, their strong and weak points are highlighted and discussed in detail.