Mutual information is useful for investigating the dependence between two experimental time series. It is often used to establish an appropriate time delay in phase-portrait reconstruction from time-series data. A histogram based approach has been used so far to estimate the probabilities. It is shown here that kernel density estimation of the probability density functions needed in estimating the average mutual information across two coordinates can be more effective than the histogram method of Fraser and Swinney [Phys. Rev. A 33, 1134 (1986)].

Flood estimation and flood management have traditionally been the domain of hydrologists, water resources engineers and statisticians, and disciplinary approaches abound. Dominant views have been shaped; one example is the catchment perspective: floods are formed and influenced by the interaction of local, catchment-specific characteristics, such as meteorology, topography and geology. These traditional views have been beneficial, but they have a narrow framing. In this paper we contrast traditional views with broader perspectives that are emerging from an improved understanding of the climatic context of floods. We come to the following conclusions: (1) extending the traditional system boundaries (local catchment, recent decades, hydrological/hydraulic processes) opens up exciting possibilities for better understanding and improved tools for flood risk assessment and management. (2) Statistical approaches in flood estimation need to be complemented by the search for the causal mechanisms and dominant processes in the atmosphere, catchment and river system that leave their fingerprints on flood characteristics. (3) Natural climate variability leads to time-varying flood characteristics, and this variation may be partially quantifiable and predictable, with the perspective of dynamic, climate-informed flood risk management. (4) Efforts are needed to fully account for factors that contribute to changes in all three risk components (hazard, exposure, vulnerability) and to better understand the interactions between society and floods. (5) Given the global scale and societal importance, we call for the organization of an international multidisciplinary collaboration and data-sharing initiative to further understand the links between climate and flooding and to advance flood research.