Fractal analysis of high‐resolution rainfall time series

Abstract

Two‐year series of 1‐min rainfall intensities observed by rain gages at six different points are analyzed to obtain information about the fractal behavior of the rainfall distribution in time. First, the rainfall time series are investigated using a monodimensional fractal approach (simple scaling) by calculating the box and correlation dimensions, respectively. The results indicate scaling but with different dimensions for different time aggregation periods. The time periods where changes in dimension occur can be related to average rainfall event durations and average dry period lengths. Also, the dimension is shown to be a decreasing function of the rainfall intensity level. This suggests a multidimensional fractal behavior (multiscaling), and to test this hypothesis, the probability distribution/multiple scaling method was applied to the time series. The results confirm that the investigated rainfall time series display a multidimensional fractal behavior, at least within a significant part of the studied timescales, which indicates that the rainfall process can be described by a multiplicative cascade process.

Cascade-based disaggregation of continuous rainfall time series: the influence of climate

“…Lovejoy and Schertzer, 1990) on rainfall time series (e.g. Hubert et al, 1993;Olsson et al, 1993;Tessier et al, 1993Tessier et al, , 1996de Lima and Grasman, 1999), but other random cascade models have also been employed (e.g. Menabde et al, 1997Menabde et al, , 1999Deidda et al, 1999).…”

Multifractal analysis of the rainfall time distribution on the metropolitan area of Barcelona (Spain)

“…As known, regional and local climatological and meteorological features introduce characteristic scales imposing limits on the theoretically overall scale-independent multifractal approach (Fraedrich and Larnder 1993;Olsson et al 1993). The scale invariant range or scaling regime has to be evaluated before applying the multifractal analysis.…”

“…In most studies on scale properties of the precipitation process, multifractal behavior has been investigated without distinction between observations related to different mechanisms of rainfall generation. However, it is known that rain processes are related to certain scales (Fraedrich and Larnder 1993;Olsson et al 1993). It can be assumed that there is a scale independence within limits related to properties of rainfall ranging from climatological characteristics to regional and local meteorological properties.…”

Fractal rain distributions and chaotic advection

“…The function r(τ ) is then defined as the number of rainy subintervals at scale τ . Olsson et al found that this distribution follows a power law, r ∼ τ −γ , with γ 0.8, over a certain range of durations [2]. Note that for τ ≈ T , r → N (all subintervals are rainy), while for τ much shorter than the characteristic time between raindrops, r saturates at a value M equal to the total number of raindrops incident on the station during the interval T .…”

“…For T /τ C in the range 0.1 -2, power-law rain-intensity and drought duration distributions are found, as in Eqs. (1) and (2). The rain-intensity distribution follows a power law over 4 -5 1/2 decades, with an exponent τ I in the range 0.93 -1.02.…”