Along the rainfall-runoff chain: from greatest point rainfall scaling to global change attribution

Climate regimes of watersheds are determined by the rainfall-runoff chain, which comprises processes of a wide range of time and space scales. They are presented here in geographical and eco-hydrological state spaces combining observations and minimalist concepts. (i) Water supply and demand govern the rainfall-runoff chain: Rainfall provides the water supply, can be simulated by a censored first-order autoregressive process, exhibits flicker noise spectra if presented as binary events (tropics), and its world wide extrema increase with duration according to Jennings? scaling law. Net radiation represents the water demand which, related to water supply, separates water from energy limited regimes and determines the discharge as the probability of rainfall reaching the soil water reservoir. This macrostate of the rainfall-runoff chain is described by an empirical equation of state and derived by a (microstate) biased coin-flip Ansatz. (ii) Eco-hydrologic spaces spanned by water and energy fluxes or flux ratios, embed the states of the rainfall-runoff chain as occurrence probabilities and their time changes as trajectories. Tracers, like vegetation-greenness, can also be included to estimate watershed resilience and, based on trajectories, to attribute the changes to external (or climate) and internal (or anthropogenic) causes. (iii) Geo-morphological patterns like the area ratios of closed lakes (lake/basin), soil moisture storage of watersheds, and drainage densities of river systems, can be functionally related to eco-hydrological climates. Suitable minimalist models of the rainfall-runoff chain provide estimates of regional climate regimes governing the watersheds of the past, present, or future.