SCALE PROBLEMS IN HYDROLOGY

SCALE PROBLEMS IN HYDROLOGY

WATER SCIENCE AND TECHNOLOGY LIBRARY Editorial Advisory Board: J. BEAR, Haifa, Israel CHEN MENGXIONG, Beijing, P.R. China v. COTECCHIA, Bari, Italy E. CUSTODIO, Barcelona, Spain R. A. FEDDES, Wageningen, The Netherlands R. FERNANDEZ-RUBIO, Granada, Spain J. J. FRIED, Strasbourg, France G. KovAcs, Budapest, Hungary R. LETOLLE, Paris, France H. J. LIEBSCHER,Koblenz, FR.G. v. v. N. MURTY, Punjab, India S. P. NEUMAN, Tucson, U.S.A. A. 1. PECK, Wembley, Australia G. F. PINDER, Princeton, U.S.A. 1. C. RODDA, Wallingford, U.K. I. RODRfGUEZ ITURBE, Caracas, Venezuela J. C. V AN DAM, Delft, The Netherlands J. VAN SCHILFGAARDE, Riverside, U.S.A. D. VISCHER, Zurich, Switzerland J. T. WILSON, Ada, U.S.A.

SCALE PROBLEMS IN HYDROLOGY Runoff Generation and Basin Response Edited by V.K.GUPTA Department of Civil Engineering, University of Mississippi I. RODRIGUEZ-ITURBE Graduate Program in Hydrology and Water Resources, Universidad Simon Bolivar, and lnstituto lnternacional de Estudios Avanzados, Caracas, Venezuela and E. F. WOOD Director, Water Resources Program, Princeton University D. REIDEL PUBLISHING COMPANY A MEMBER OF THE KLUWER ACADEMIC PUBLISHERS GROUP DORDRECHT / BOSTON / LANCASTER / TOKYO

library of Congress Cataloging in Publication Data Scale problems in hydrology. (Water science and technology library) Includes index. 1. Watersheds-Measurement-Congresses. 2. Runoff-Measurement- Congress.es. 3. Slopes (Physical geography)-measurement-congresses. I. Gupta, Vijay K. II. Rodrfguez-Iturbe, Ignacio. III. Wood, Eric F. IV. Series. GB980.S27 1986 551.48 86--13781 ISBN-13: 978-94-010-8579-3 e-isbn-13: 978-94-009-4678-1 DOl: 10.1007/978-94-009-4678-1 Published by D. Reidel Publishing Company, P.O. Box 17,3300 AA Dordrecht, Holland. Sold and distributed in the U.S.A. and Canada by Kluwer Academic PUblishers, 101 Philip Drive, Assinippi Park, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.o. Box 322, 3300 AH Dordrecht, Holland. 02-0993- 75-t8 All Rights Reserved 1986 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover 1 st edition 1986 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner

TABLE OF CONTENTS Preface VII 1. On the Relative Role of Hillslope and Network Geometry in Hydrologic Response 0.1. Mesa and E. R. Mifflin 2. Nonlinearity and Time-Variance of the Hydrologic Response of a Small Mountain Creek E. Caroni, R. Rosso and F. Siccardi 19 3. A Runoff Simulation Model Based on Hillslope Topography Mike Kirkby 39 4. A Geomorphologic Approach to Synthesis of Direct Runoff Hydrograph from the Upper Tiber River Basin, Italy C. Corradini, F. Melone, L. Ubertini and V. P. Singh 57 5. Spatial Heterogeneity and Scale in the Infiltration Response of Catchments M. Sivapalan and E. F. Wood 81 6. Runoff Production and Flood Frequency in Catchments of Order n: An Alternative Approach Keith Beven 107 7. A Study of Scale Effects in Flood Frequency Response C. S. Hebson and E. F. Wood 133 8. On Scales, Gravity and Network Structure in Basin Runoff V. K. Gupta, E. Waymire and I. Rodrfguez-Iturbe 159 9. Averaging Properties of Channel Networks Using Methods in Stochastic Branching Theory B. M. Troutman and M. R. Karlinger 185

vi 10. Incorporation of Channel Losses in the Geomorphologic IUH M. Diaz-Granados, R. L. Bras andj. B. Valdes List of Authors TABLE OF CONTENTS 217 245

PREFACE A special workshop on scale problems in hydrology was held at Princeton University, Princeton, New Jersey, during October 31-November 3, 1984. This workshop was the second in a series on this general topic. The proceedings of the first workshop, held in Caracas, Venezuela, in January 1982, appeared in the Journal of Hydrology (Volume 65:1/3, 1983). This book contains the papers presented at the second workshop. The scale problems in hydrology and other geophysical sciences stem from the recognition that the mathematical relationships describing a physical phenomenon are mostly scale dependent in the sense that different relationships manifest at different space-time scales. The broad scientific problem then is to identify and formulate suitable relationships at the scales of practical interest, test them experimentally and seek consistent analytical connections between these relationships and those known at other scales. For example, the current hydrologic theories of evaporation, infiltration, subsurface water transport and water sediment transport overland and in channels etc. derive mostly from laboratory experiments and therefore generally apply at "small" space-time scales. A rigorous extrapolation of these theories to large spatial and temporal basin scales, as mandated by practical considerations, appears very difficult. Consequently, analytical formulations of suitable hydrologic theories at basin wide space-time scales and their experimental verification is currently being perceived to be an exciting and challenging area of scientific research in hydrology. In order to successfully meet these challenges in the future, this series of workshops was initiated. Even though the scale problems described above can be safely speculated to manifest themselves in most, if not all, components of the hydrologic cycles, the papers in this book mostly concern themselves with process of runoff generation and structure of the runoff hydrographs from different subbasins of a basin, including the basin itself. Typically the various papers presented in this book consider one or more aspects of spatial variability in river basins due to ~eology, channel network geomorphology, soil and vegetation and space-time variability in the climate via rainfall in formulating and testing relationships at large scales, governing runoff generation from hillslopes and the structure of basin hydrographs. vii

viii PREFACE New theoretical advances in the descriptions of hydrologic processes at large scales require developing testable hypotheses and performing suitable experiments for testing these hypotheses. These issues pose problems whose solutions mandate that a group of scientists of some critical size from all over the world participate in both experimental and theoretical aspects of the scale problems and meet periodically in taking stock of the progress as well as identifying outstanding problems. We hope that these workshops will motivate a greater interdisciplinary participation from the international scientific community in this very important area of hydrologic science. The four days of workshop provided an opportunity for an exciting and free exchange of ideas and long useful discussions. We thank Princeton University for its hospitality and the University of Mississippi for its administrative support. The hospitality and help extended by the Utah Water Research Laboratory at Utah State University during the final stages of preparation of this book are gratefully acknowledged. This workshop was supported by the National Science Foundation through grant CEE-84-17682 and by the Army Research Office through grant 22323-GS-CF. Sincere gratitude is expressed to these two agencies for without their support this workshop would not have been possible. Vijay K. Gupta (University of Mississippi) Ignacio Rodrfguez-Iturbe (Caracas, Venezuela) Eric F. Wood (Princeton University)