The geomorphological unit hydrograph from a historical-critical perspective

In this paper we present a brief overview of Geomorphological Instanteneous Unit Hydrograph (GIUH) theories and analyze their successful path without hiding their limitations. The history of the GIUH is subdivided into three major sections The first is based on the milestone works of Rodríguez-Iturbe and Valdés (1979), and Gupta and Waymire (1983), which recognized that a treatment of water discharges with ”travel times” could give a rich interpretation of the theory of the Instantaneous Unit Hydrograph (IUH). We show how this was possible, what assumptions were made, which of these assumptions can be relaxed, and which have become obsolete and been discarded. The second section focuses on the Width Function Based IUH (WFIUH) approach and its achievements in assessing the interplay of the topology and geometry of the network with water dynamics. The limitations of the WFIUH approach are described, and a way to work around them is suggested. Finally, a new formal approach to estimating the water budget by ”travel times”, which derives from a suitable use of the water budget equation and some hypotheses, has been introduced and disentangled.