Available online at www.sciencedirect.com Physica A 330 (2003) 283–290 www.elsevier.com/locate/physa A stochastic model of river discharge uctuations V. Livina a ; ∗ , Y. Ashkenazy b; c , Z. Kizner d , V. Strygin e , A. Bunde f , S. Havlin d a Minerva Center, Bar-Ilan University, Ramat-Gan 52900, Israel b Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA c Department of Environmental Sciences, Weizmann Institute, Rehovot, Israel d Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel e Department of Applied Mathematics and Mechanics, Voronezh State University, Universitetskaya pl. 1, Voronezh 394693, Russia f Institute f ur Theoretische Physik III, Justus-Liebig-Universit at Giessen, Heinrish-Bu-Ring 16, 35392 Giessen, Germany Abstract We study the daily river ow uctuations of 30 international rivers. Using the detrended uctu- ation analysis, we study the correlations in the magnitudes of river ow increments (volatilities), and nd power-law correlations in volatilities for time scales less than 1 year; these correlations almost disappear for time scales larger than 1 year. Using surrogate data test for nonlinearity, we show that correlations in the magnitudes of river ow uctuations are a measure for nonlinear- ity. We propose a simple nonlinear stochastic model for river ow uctuations that reproduces the main scaling properties of the river ow series as well as the correlations and periodicities in the magnitudes of river ow increments. According to our model, the source of nonlinear- ity observed in the data is an interaction between a long-term correlated process and the river discharge itself. c  2003 Elsevier B.V. All rights reserved. PACS: 92.40.Cy; 05.40.-a; 02.70.Hm Keywords: Scaling analysis; DFA; Periodic volatility; Long-term volatility; Nonlinearity; Stochastic modeling 1. Introduction The climate system often exhibits irregular and complex behavior. Although the climate system is driven by the well-dened seasonal periodicity, it is also a subject to * Corresponding author. E-mail address: livina@ory.ph.biu.ac.il (V. Livina). 0378-4371/$-see front matter c  2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2003.08.012