Abstract
Rainfall is a highly non-linear hydrological process that exhibits wide variability over a broad range of time and space scales. The strongly irregular fluctuations of rain are difficult to capture instrumentally and to handle mathematically. The purpose of this work is to contribute to a better understanding of the variability of rainfall by investigating the multifractal behaviour that is present in the temporal structure of rainfall. This type of rainfall analysis is based on the invariance of properties across scales, and it takes into account the persistence of the variability of the process over a range of scales.
The dissertation focuses on the analyses of point-rainfall data from 4 different locations in Europe. The data sets differ with respect to climatic origin, type of measuring device used, resolution of the data, and length of the records. The data are from recording and non-recording gauges. The highest resolution of the data is 1 minute, and the lowest is 1 month. The time span of the records varies from 4 years to 90 years.
The presence of scale-invariant and multifractal properties in the rainfall process are investigated with spectral analysis, and by studying the multiple scaling of probability distributions and statistical moments of the rainfall intensity. This study shows that the temporal structure of rainfall exhibits these properties across a wide range of scales. Within the range of scales studied, it analyzes the presence of different scaling regimes and seasonal variation in the statistics of rainfall. The empirical multifractal scaling exponent functions that describe the statistics of the rainfall process are derived. Special attention is given to discontinuities in the empirical scaling functions that are caused by the finite size of the samples, the divergence of moments, and the dynamic and temporal resolution of the rainfall measuring devices and data. The critical exponents associated with these multifractal phase transitions are studied empirically.
The applicability to rainfall of a theoretical multifractal model based on Lévy stochastic variables is studied. The adequacy of this model in describing the empirical scaling functions of rainfall is examined. Results indicate that it is possible to quantify the statistics of rainfall over a wide range of scales, and over a range of the process dynamics using only a few parameters. For an analysis of this type, it is essential to recognize the effects of such limitations as the sample size, and the type of acquisition of the experimental data and its resolution.
This dissertation shows that multifractals offer a good framework for the analysis of the temporal structure of rainfall. It provides a good description of both the average and the extreme events. The expectation is that this type of studies will help in solving problems related to the choice of suitable resolutions for data collection and in making a correct assessment of the 'quality' of data sets.
Original language | English |
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Qualification | Doctor of Philosophy |
Awarding Institution | |
Supervisors/Advisors |
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Award date | 23 Dec 1998 |
Place of Publication | Wageningen |
Publisher | |
Print ISBNs | 9789054859826 |
DOIs | |
Publication status | Published - 23 Dec 1998 |
Keywords
- rain
- hydrology
- statistics
- data processing
- europe