Scale invariance of daily runoff time series in agricultural watersheds

Abstract. Fractal scaling behavior of long-term records of daily runoff time series in 31 sub-watersheds covering a wide range of size were examined using the shifted box-counting method and Hurst rescaled range (R/S) analysis. These sub-watersheds were associated with four agricultural watersheds of different climate and topography. The results showed that the records of daily runoff rate exhibited scale invariance over certain time scales. Two scaling ranges were identified from the shifted box-counting plots with a break point at about 9~12 months. Similar fractal dimensions were obtained for the sub-watersheds within each watershed, indicating that the runoff of these sub-watersheds have similar distribution of occurrence. The Hurst R/S analysis showed that the long-term memory was not present in runoff time series. The presence of scaling is not certain for runoff time series in agricultural watersheds.