Along the Rainfall-Runoff Chain: From Scaling of Greatest Point Rainfall to Global Change Attribution

Abstract:

Processes along the continental rainfall-runoff chain cover a wide range of time and space scales which are presented here combining observations (ranging from minutes to decades) and minimalist concepts. (i) Rainfall, which can be simulated by a censored first-order autoregressive process (vertical moisture fluxes), exhibits 1/f–spectra if presented as binary events (tropics), while extrema world wide increase with duration according to Jennings’ scaling law. (ii) Runoff volatility (Yangtze) shows data collapse which, linked to an intra-annual 1/f–spectrum, is represented by a single function not unlike physical systems at criticality and the short and long return times of extremes are Weibull-distributed. Atmospheric and soil moisture variabilities are also discussed. (iii) Soil moisture (in a bucket), whose variability is interpreted by a biased coinflip Ansatz for rainfall events, adds an equation of state to energy and water flux balances comprising Budyko’s frame work for quasi-stationary watershed analysis. Eco-hydrologic state space presentations in terms of surface flux ratios of energy excess (loss by sensible heat over supply by net radiation) versus water excess (loss by discharge over gain by precipitation) allow attributions of state change to external (or climate) and internal (or anthropogenic) causes. Including the vegetation-greenness index (NDVI) as an active tracer extends the eco-hydrologic state space analysis to supplement the common geographical presentations. Two examples demonstrate the approach combining ERA and MODIS data sets: (a) global geobotanic classification by combining first and second moments of the dryness ratio (net radiation over precipitation) and (b) regional attributions (Tibetan Plateau) of vegetation changes.