Fractal

Precipitation : time series

The studied data corresponds to a rainfall time series, obtained with the help of a tipping bucket rain gauge located in the county of Val-de-Marne (South-East of Paris). The resolution is 1 hour, and the 512 consecutive time steps (21.3 days) with the heaviest rainfall between 1993 and 2007 are taken into account. During the selected period 142 mm of rainfall depth were recorded. There is 86 % of zeros. The minimum non-zero value is 0.2mm/h, which corresponds to a tipping of the bucket. Figure 1 displays the time evolution of the studied rainfall series.

(a): Time evolution of the studied rainfall time series; (b) : Computation of the fractal dimension of the studied rainfall field

The figure (b) displays the fractal dimension of the rainfall time series. A break is visible at (which corresponds to a scale of roughly 5 days). For greater scales, it appears that , which basically means that it rains all the times. For small scales we find (the coefficient of determination of the linear regression is equal to 0.99).

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