I2. On the Brutsaert Baseflow Recessions and Their Geomorphic Origins
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Rinaldo, Andrea; Parlange, Marc; Mutzner, Raphael; Tomasic, Nevena; Ceola, Serena; Bertuzzo, Enrico; Rodriguez-Iturbe, Ignacio
Moving from a classic study on the base flow characteristics of six basins in the Finger Lakes region , a set of Brutsaert recession curves (the lower envelope of available records of |dQ/dt| as a function of Q, where Q is at-a-station gauged flow rate) has been constructed from Swiss streamflow data relatively unaffected by snowmelt. The Lecture builds on the functional dependences found in  (chiefly through Boussinesq’ nonlinear solution of free-surface groundwater flow, yielding a specific relation to local drainage area and total stream length) and on the expedient avoidance of proper time references, to apply and generalize recent results aimed at the geomorphic origins of recession curves , that is, fully integrating sizable geometric and topologic complexity. In particular, such results propose a link between river network morphology and the parametrization in , in particular by assimilating the basic scaling exponent a (i.e. |dQ/dt|µQa) to that characterizing the empirical relation N(x) µ G(x)a (where x is the downstream distance from the channel heads, N(x) is the number of channel reaches exactly located at distance x from their heads, and G(x) is the total drainage network length at a distance greater or equal to x down to the gauging station where Q is recorded ). Application of the method, originally tested on DTMs and daily discharge observations in 67 US basins, suggests a definite linkage of active drainage and source functions with the basic features of the Brutsaert envelopes. The possible morphological predictability of base flow features is central to transport processes at catchment scales, not least for its implications on our understanding of the geomorphic structure of the hydrologic response  and of the stationarity of the ensuing travel time distributions leading to the so-called old water paradox . These issues are briefly discussed in the Lecture. Here, through a broad survey of Swiss field data, we go on suggest that the method  provides excellent results only in catchments where drainage density (roughly defined as the ratio of total channel network length to its drainage area [L-1], defined at a station) can be regarded as spatially constant. When uneven drainage densities are observed, chiefly in our test cases for high mountainous areas where drainage density varies significantly owing to complex cryosphere dynamics and geologic or pedologic constraints, the method’s assumptions do not hold. In the Lecture a detailed reexamination of the premises of the approaches [1,2] is proposed. A revision is then proposed, which includes geomorphic corrections based on a proper description of the drainage density seen as a random space function . Such corrections properly vanish should drainage density become spatially constant. Overall, it is recognized a definite geomorphic origin for Brutsaert recessions, with notable implications. REFERENCES  W. Brutsaert & J.L. Nieber, Regionalized drought flow hydrograph from a mature glaciated plateau, Water Resources Research, 13(3), 637-643, 1977  B. Basudev & M. Marani, Geomorphological origin of recession curves, Geophysical Research Letters, 37, L24403, 2010  I. Rodriguez-Iturbe and J.B. Valdes, The geomorphologic structure of the hydrologic response, Water Resources Research, 15(6), 1409-1420, 1979  G. Botter, E. Bertuzzo, A. Rinaldo, Transport in the hydrologic response: Travel time distributions, soil moisture dynamics, and the old water paradox, Water Resources Research, 46, W03514, 2010  G. Tucker, F. Catani and R.L. Bras, Statistical analysis of drainage density from digital terrain data, Geomorphology, 36, 187-202, 2001
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