The Multiscaling Behavior of the Time Generalized q-Entropy for Daily Streamflows
Abstract
The time generalized (Tsallis) q-entropy, Sq(T), has recently been introduced for rainfall as a function of both order q and aggregation time, T, (Poveda, G., 2011, Adv. Water Res., 34(2), 243-256). Here we quantify the time generalized q-entropy for daily streamflows records in Colombia, USA, and the Amazon River basin. All results show that Sq(T) consists of a set of continuous power laws of T, whose scaling exponents vary with q (Figures 1a and 1c), implying that the generalized q-entropy exhibits multiscaling in time. Also, Sq(T) exhibits a monotonic decrease with q for all T (Figure 1b). Mathematically, Sq(T) ∼ Tβ (q), with β (q)=kq for q≤ 0, and k a positive constant, and β (q)≃ 0 for q > 0 (Figure 1d). It is shown that Sq(T)|q=1 recovers the standard Shannon entropy for all T. Differences between the estimated Sq(T) functions and scaling exponents, and the value of T to reach maximum entropy in rainfall and streamflows records are discussed.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2011
- Bibcode:
- 2011AGUFMNG51E1682P
- Keywords:
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- 4400 NONLINEAR GEOPHYSICS;
- 4430 NONLINEAR GEOPHYSICS / Complex systems;
- 4435 NONLINEAR GEOPHYSICS / Emergent phenomena;
- 4475 NONLINEAR GEOPHYSICS / Scaling: spatial and temporal