Gradation of complexity and predictability of hydrological processes
Journal of Geophysical Research - Atmospheres
Quantification of the complexity and predictability of hydrological systems is important for evaluating the impact of climate change on hydrological processes, and for guiding water activities. In the literature, the focus seems to have been on describing the complexity of spatiotemporal distribution of hydrological variables, but little attention has been paid to the study of complexity gradation, because the degree of absolute complexity of hydrological systems cannot be objectively
... Here we show that complexity and predictability of hydrological processes can be graded into three ranks (low, middle, and high). The gradation is based on the difference in the energy distribution of hydrological series and that of white noise under multitemporal scales. It reflects different energy concentration levels and contents of deterministic components of the hydrological series in the three ranks. Higher energy concentration level reflects lower complexity and higher predictability, but scattered energy distribution being similar to white noise has the highest complexity and is almost unpredictable. We conclude that the three ranks (low, middle, and high) approximately correspond to deterministic, stochastic, and random hydrological systems, respectively. The result of complexity gradation can guide hydrological observations and modeling, and identification of similarity patterns among different hydrological systems. Introduction Hydrological processes are highly complex due to the influence of many, often interrelated, physical factors; the complexity is compounded by the influence of climate change [Labat, 2010; Montzka et al., 2008] . Changes in hydrological processes significantly impact the timing, intensity, and duration of hydrological response. These changes are also linked to the amount and distribution of runoff, leading to the changes in water resources availability [Zhang et al., 2009] . Changes in water resources will greatly influence water security, energy security, food security, ecological health, and sustainable socioeconomic development. Evaluation of the complexity and predictability of hydrological processes are therefore important not only to understand the variability of hydrological processes under climate change but also to guide hydrological modeling and forecasting, water disaster control, water resources management, and many other water-related activities [Li and Zhang, 2008] . Generally, complexity reflects the information content of a dynamic system, and predictability reflects the cognitive level of the system. More useful information indicates lower complexity and easier cognition indicates higher predictability. Studies on the complexity of hydrological processes have focused on enumerating the temporal-spatial variability of hydrological variables, and the result is usually the complexity distribution of the concerned variable, described by the contour map of a certain entropy measure, such as Shannon entropy, relative entropy, and mutual entropy [Koutsoyiannis, 2005; Brunsell, 2010; Mishra et al., 2009; Chou, 2011; Singh, 2013 Singh, , 2014 . Complexity measures based on static entropy quantify statistical order in the time series [Varotsos et al., 2004] . However, from the results we cannot ascertain the level of absolute complexity and predictability of hydrological processes, such as runoff, in a watershed. It is, therefore, important to objectively grade the degree of complexity of hydrological processes. This can constitute a basis for gauging the hydrological system's complexity, guiding hydrological observations and modeling, comparing similarity patterns of complexities among different hydrological systems, and especially for guiding the difficult scientific problem of prediction in ungauged basins (PUB).