András Bárdossy

Spatial distribution of soil moisture in a small catchment. Part 1: geostatistical analysis

Soil moisture measurements were performed weekly at about 60 locations in a small catchment (6.3 km2) in southwest Germany over a period of 6 years. The measurements were carried out by using time domain reflectometry at four different depths. The data was analyzed and a time independent semivariogram was derived. For interpolation, five different methods, ordinary kriging, external drift kriging, indicator kriging, external drift indicator kriging and Bayes-Markov updating were used. Additional information such as topographical parameters derived from a digital elevation model, were used to improve the estimation in the external drift methods. In the Bayesian case, even qualitative information such as land use could be used. Depending on the assumptions, the interpolated maps differed significantly. The performance of the different methods was compared using a cross-validation approach. The results indicate improvement in the interpolation quality by using the topographic index or land use as additional information.

Development of a fuzzy logic-based rainfall-runoff model

Abstract Rainfall-runoff models are used to describe the hydrological behaviour of a river catchment. Many different models exist to simulate the physical processes of the relationship between precipitation and runoff. Some of them are based on simple and easy-to-handle concepts, others on highly sophisticated physical and mathematical approaches that require extreme effort in data input and handling. Recently, mathematical methods using linguistic variables, rather than conventional numerical variables applied extensively in other disciplines, are encroaching in hydrological studies. Among these is the application of a fuzzy rule-based modelling. In this paper an attempt was made to develop fuzzy rule-based routines to simulate the different processes involved in the generation of runoff from precipitation. These routines were implemented within a conceptual, modular, and semi-distributed model-the HBV model. The investigation involved determining which modules of this model could be replaced by the new approach and the necessary input data were identified. A fuzzy rule-based routine was then developed for each of the modules selected, and application and validation of the model was done on a rainfall-runoff analysis of the Neckar River catchment, in southwest Germany.

Multivariate stochastic downscaling model for generating daily precipitation series based on atmospheric circulation

The goal of the paper is to present a model for generating daily precipitation time series and its applications to two climatologically different areas. The rainfall is modeled as stochastic process coupled to atmospheric circulation. Rainfall is linked to the circulation patterns using conditional model parameters. Any kind of circulation pattern classification can be used for this purpose. In this study a new fuzzy rule based method of circulation patterns classification was used. The advantage of this classification technique is the fact that in contrast to common circulation patterns classifications its objective is to explain the variability of local precipitation. It means that the circulation patterns explain the relation between large-scale atmospheric circulation and surface climate (precipitation). Therefore the circulation patterns obtained by this classification method are suitable as input for the subsequent precipitation downscaling. The model was successfully applied in two regions with different climate conditions: Central Europe (Germany) and Eastern Mediterranean (Greece). Several tests like comparison of mean seasonal cycles, comparison of mean values and deviations of yearly totals and other standard diagnostics showed that simulated values agree fairly well with historical data.

Fuzzy rule-based classification of remotely sensed imagery

The purpose of this paper is to investigate the applicability of fuzzy rule-based modeling to classify a LANDSAT TM scene from 1984 of an area located in the south of Germany. Both a land cover map with four different categories and an image depicting the degree of ambiguity of the classification for each pixel is the expected output. The fuzzy classification algorithm will use a rule system derived from a training set using simulated annealing as an optimization algorithm. The results are then validated and compared with a common classification method in order to judge the effectiveness of the proposed technique. It will also be shown that the proposed method with only nine rules for four different land cover classes performs slightly better than the maximum likelihood classifier (MLC). For error assessment, the traditional error matrix and fuzzy operators have been used.

Combination of fuzzy numbers representing expert opinions

Abstract Expert opinions or imprecise estimates of a physical variable are expressed as fuzzy numbers and five techniques for combining these numbers into a single fuzzy number estimate are developed. Seven characteristics of the combination technique are defined; namely, agreement preservation, order independence, transformation variance, possibility conservation, possibility interval conservation, relationship between uncertainty of individual estimates and overall uncertainty, and desirability of resultant estimate. The five techniques, listed in increasing order of preference, are (1) crisp weighting, (2) fuzzy weighting, (3) minimal fuzzy extension, (4) convex fuzzy extension and (5) mixed linear extension. An example of estimating nitrate concentration in ground water illustrates the approach. The cases of equally versus unequally reliable estimates are distinguished and guidelines for choice of combination technique are provided.

Modeling daily rainfall using a semi-Markov representation of circulation pattern occurrence

Abstract The daily rainfall occurrence process is modeled as a process coupled to atmospheric circulation. Atmospheric circulations are classified into a finite number of circulation patterns. Time series of circulation patterns are modeled with the help of a semi-Markov field. Rainfall is linked to the circulation patterns using conditional probabilities. The model is applied using the classification scheme of the German Weather Service for the time period 1881–1988. Precipitation data measured at different locations for a period of 34 years are linked to the circulation patterns. Using the model several series of circulation patterns and corresponding rainfall occurrences are simulated. Statistics of the simulated and the observed sequences are similar. The model is also applicable for the simulation of nonstationary atmospheric conditions like climate change.

Application of a space-time stochastic model for daily precipitation using atmospheric circulation patterns

Space-time series of daily precipitation amount conditioned on daily circulation pattern (CP) types are calculated. A stochastic hydroclimatological model is used to define daily precipitation under the climate of eastern Nebraska. Principal component analysis and k means method result in nine CP types in west central United States on the basis of 40 years of data. Both the probability and the amount of daily precipitation are strongly related to CP types. The approach can be used to predict the regional or local hydrological effect of climate change.

Supervised Classification of Remotely Sensed Imagery Using a Modified

Nearest neighbor (NN) techniques are commonly used in remote sensing, pattern recognition, and statistics to classify objects into a predefined number of categories based on a given set of predictors. These techniques are particularly useful in those cases exhibiting a highly nonlinear relationship between variables. In most studies, the distance measure is adopted a priori. In contrast, we propose a general procedure to find Euclidean metrics in a low-dimensional space (i.e., one in which the number of dimensions is less than the number of predictor variables) whose main characteristic is to minimize the variance of a given class label of all those pairs of points whose distance is less than a predefined value. k-NN is used in each embedded space to determine the possibility that a query belongs to a given class label. The class estimation is carried out by an ensemble of predictions. To illustrate the application of this technique, a typical land cover classification using a Landsat-5 Thematic Mapper scene is presented. Experimental results indicate substantial improvement with regard to the classification accuracy as compared with approaches such as maximum likelihood, linear discriminant analysis, standard k-NN, and adaptive quasi-conformal kernel k-NN.

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Precipitation is a major input in hydrological models. Radar rainfall data compared with rain gauge measurements provide higher spatial and temporal resolutions. However, radar data obtained form reflectivity patterns are subject to various errors such as errors in reflectivity-rainfall Z-R relationships, variation in vertical profile of reflectivity, and spatial and temporal sampling among others. Characterization of such uncertainties in radar data and their effects on hydrologic simulations is a challenging issue. The superposition of random error of different sources is one of the main factors in uncertainty of radar estimates. One way to express these uncertainties is to stochastically generate random error fields and impose them on radar measurements in order to obtain an ensemble of radar rainfall estimates. In the present study, radar uncertainty is included in the Z-R relationship whereby radar estimates are perturbed with two error components: purely random error and an error component that is proportional to the magnitude of rainfall rates. Parameters of the model are estimated using the maximum likelihood method in order to account for heteroscedasticity in radar rainfall error estimates. An example implementation of this approached is presented to demonstrate the model performance. The results confirm that the model performs reasonably well in generating an ensemble of radar rainfall fields with similar stochastic characteristics and correlation structure to that of unperturbed radar estimates.

-NN Technique

Abstract In this article, we suggest that giving greater prominence to the analysis of failures and errors would more fruitfully advance the hydrological sciences. As widely recognised by philosophers of science, we can all learn from our mistakes, and errors can lead to discovery if they are properly diagnosed. However, failure stories are very seldom communicated and published, even though they represent the bulk of the results obtained by researchers and modellers. This article is the result of passionate discussions held in a workshop called the Court of Miracles of Hydrology held in Paris in June 2008. The participants had been invited to present their unpublished experience with what could be called monsters, anomalies, outliers and failures in their everyday practice of hydrology. The review of these studies clearly shows that in-depth analysis of these observations and results that deviate from the expected norm blazes a trail that can only lead to progress. Citation Andréassian, V., Perrin, C., Parent, E. & Bárdossy, A. (2010) Editorial – The Court of Miracles of Hydrology: can failure stories contribute to hydrological science? Hydrol. Sci. J. 55(6), 849–856.