Gradation of complexity and predictability of hydrological processes

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 evaluated. 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.