1 2 3 4 The Concept of Transport Capacity 5 in Geomorphology 6 7 8 John Wainwright, 9 Durham University, Department of Geography, Science Laboratories, South Road, 10 Durham, DH1 3LE, UK ([email protected]) 11 12 Anthony J Parsons 13 Department of Geography, University of Sheffield, Winter Street, Sheffield S10 2TN, 14 UK ([email protected]) 15 16 James R Cooper 17 Department of Geography and Planning, School of Environmental Sciences, 18 University of Liverpool, Liverpool L69 7ZT, UK ([email protected]) 19 20 Peng Gao, 21 Department of Geography, SUNY Syracuse, 144 Eggers Hall, Syracuse, New York 22 13244, USA ([email protected]) 23 24 John A Gillies, 25 Division of Atmospheric Sciences, Desert Research Institute, 2215 Raggio Parkway, 26 Reno, NV 89512, USA ([email protected]) 27 28 Luca Mao, 29 Department of Ecosystems and Environment, Pontificia Universidad Católica de 30 Chile, Avenida Vicuña Mackenna 4860, Santiago de Chile, Chile ([email protected]) 31 32 Julian D Orford 33 School of Geography, Archaeology and Palaeoecology, Queen’s University Belfast, 34 Belfast, BT7 1NN, Northern Ireland, UK ([email protected]) 35 36 Peter G Knight 37 School of Physical and Geographical Sciences 38 William Smith Building, Keele University, ST5 5BG. UK ([email protected]) 39 40 Abstract 41 The concept of sediment-transport capacity has been engrained in geomorphological literature 42 for >50 years, although the earliest explicit definition is Gilbert’s work in fluvial 43 geomorphology in the 1870s with implicit versions found in 18th - 19th century engineering. 44 We review the development of transport capacity in the fluvial, aeolian, coastal, hillslope, 45 débris flow and glacial process domains. Despite cross-fertilization between different process 46 domains, there seem to have been independent inventions of the idea in aeolian and hillslope 47 geomorphology. We demonstrate how different definitions have been used, which makes it 48 both a difficult concept to test, and one that may lead to poor communications between those 49 working in different domains. 50 The original relation between the power of a flow and its ability to transport sediment 51 can be challenged for three reasons. First, as sediment becomes entrained in a flow, the nature 52 of the flow changes and so it is unreasonable to link the capacity of the water or wind only to 53 the ability of the fluid to move sediment. Secondly, the range of processes involved in most 54 movements means that simple relations are unlikely to hold, not least because the movement 55 of sediment often changes the substrate, which in turn affects the flow conditions. Thirdly, the 56 inherently stochastic nature of sediment transport means that any capacity relationships do not 57 scale either in time or in space. Consequently, new theories of sediment transport are needed 58 to improve understanding and prediction, and guide measurement and management of all 59 geomorphic systems. 60 61 Keywords: sediment transport; geomorphology; turbulence; complex systems; models; 62 management 1 63 Introduction 64 The notion of sediment-transport capacity has been engrained in geomorphological and related 65 geophysical literature for over 50 years. However, the definition has not always been 66 consistent across the discipline. One reason for this inconsistency has been the tendency in 67 recent decades for increasing specialization in studies relating to particular process domains. 68 Together with the proliferation of literature, specialization means that only rarely are 69 evaluations made of linkages between concepts in different process domains. This trend 70 towards increasingly focussed specialization, however, contrasts with developments in 71 complexity theory, Earth-Systems Science and integrated management of the environment that 72 all emphasize the benefits of integrated approaches. In this review, we will first examine how 73 the notion of transport capacity has been developed and applied in the various branches of 74 geomorphology in order to evaluate commonalities and divergences in approach, in relation to 75 conceptual developments and empirical support. In doing so, we assess the effectiveness of 76 the concept by using advances across the different process domains to inform and interpret 77 each other and thereby provide an overall critique of the concept. We take a critical realist 78 approach (Richards, 1990; Sayer, 2000) to assess whether the use of the concept, both within 79 a single process domain and between different process domains, enables the explanation of 80 observations both in the field and laboratory. In other words, if the definitions of transport 81 capacity that have been developed are real – mechanistic – characterizations of how sediment 82 is transported in geomorphic systems, they should be able to explain observed phenomena. If 83 not, there needs to be a reëvluation of whether it is the concept (or concepts) that are 84 problematic, or the experimental approaches and data that are flawed. 85 86 GK Gilbert was central to the development of the concept of transport capacity in 87 geomorphology. In his Report on the Geology of the Henry Mountains [1877] he noted: 88 89 Transportation is favored by increasing water supply as greatly as by increasing 90 declivity. When the volume of a storm increases, it becomes at the same time more 91 rapid, and its transporting capacity gains by the increment to velocity as by the 92 increment to volume. Hence the increase in power of transportation is more than 93 proportional to the increase in volume. 94 [Gilbert 1877: 98] 95 2 96 Based on a steady-state conceptualization of river form, and an early formulation of a concept 97 of stream power, he goes on to suggest: 98 99 Let us suppose that a stream endowed with a constant volume of water, is at some 100 point continuously supplied with as great a load as it is capable of carrying. For so 101 great a distance as its velocity remains the same, it will neither corrade (downward) 102 nor deposit, but will leave the grade of its bed unchanged. But if in its progress it 103 reaches a place where a less declivity of bed gives a diminished velocity, its 104 capacity for transportation will become less than the load and part of the load will 105 be deposited. Or if in its progress it reaches a place where a greater declivity of bed 106 gives an increased velocity, the capacity for transportation will become greater than 107 the load and there will be corrasion of the bed. In this way a stream which has a 108 supply of débris equal to its capacity, tends to build up the gentler slopes of its bed 109 and cut away the steeper. It tends to establish a single, uniform grade. 110 [Gilbert 1877: 106] 111 112 Implicit in this definition is the idea of supply limitation, that a channel will convey as much 113 sediment as its capacity allows, unless there is insufficient material to be transported. More 114 widely influential was Gilbert’s seminal USGS Professional Paper The Transportation of 115 Débris by Running Water, published in 1914. It is this work that seems to provide the first 116 formal definition of transport capacity in the English literature: 117 118 The maximum load a stream can carry is its capacity. ... Capacity is a function of 119 various conditions, such as slope and discharge, .... When a fully loaded stream 120 undergoes some change of condition affecting its capacity, it becomes thereby 121 overloaded or underloaded. If overloaded, it drops part of its load, making a 122 deposit. If underloaded, it takes on more load, thereby eroding its bed. 123 [Gilbert 1914: 35] 124 125 He goes on to say that capacity is a function of discharge, slope, débris size and channel-form 126 (channel depth / width) ratio. While the concept of transport capacity is asserted without 127 support from further reference in the 1877 report, his statement that “the maximum particles 128 which streams are able to move are proportioned to the sixth powers of their velocities” 3 129 [Gilbert, 1877: 104] shows that he was at least aware of the work of Leslie [1823] or more 130 likely Hopkins [1844] on entrainment by this time. In 1914, however, Gilbert suggests that the 131 idea can be traced at least as far back as 1786 in the work of Dubuat, who demonstrated 132 experimentally that the sediment discharge in a water flow was proportional to a square of 133 excess velocity (flow velocity minus the flow velocity required for entrainment). These results 134 were certainly still in use almost a century later, for example in the study of Lechalas [1871]. 135 Both of these authors were working in a tradition of applied hydraulics, interested in the 136 navigation of rivers and the building of canals. 137 138 Although Gilbert [1877, 1914] provides the first uses of the term in the 139 geomorphological/geophysical literature, it was largely ignored or misunderstood by this 140 community until championed by Strahler’s advocacy of a process-based geomorphology in his 141 papers of the early 1950s [1950, 1952] (see, for example, Holmes’ review of 1915 in which he 142 suggests the wide variability in observed rates mean that these sorts of observation are unlikely 143 to be useful in dating geological deposits and thus unlikely to be of broader use. But, by contrast 144 that “experiments of these kinds, while of considerable theoretical interest, serve only as a 145 check to undue speculation” [1915: 134] and what is needed is more field study). However, 146 the engineering aspects of his work meant that Gilbert influenced the hydraulic engineering 147 literature more directly, for example being cited in the work of Hans Einstein [1942: 567], 148 originally working in the Zürich school, but then later for the US Department of Agriculture 149 (e.g., Meyer-Peter et al.