sediment velocity (u), mean particle activity ( – see equation 38) and mean sediment 3150
flux (q) for: a. flow dominated by coarse particles moving near to the substrate; b. 3151
99 flow dominated by fine particles moving throughout the flow column; and c. 3152
hyperconcentrated or débris flows where the velocities of the fluid and the sediment 3153
converge. In moving from condition a. to condition c., the upstream effects of flow 3154
variability cause both u(z) and (z to become more variable because of anisotropy in 3155
the turbulent flow. 3156
Figure 13: Spatial and temporal scales of measurement of sediment transport and their implicit
3157
or explicit uses. The area shaded in blue has been the one typically used to infer 3158
transport-capacity rates. Measurements at other scales and for other purposes have 3159
come to challenge the underlying concept of transport capacity. 3160
100
Tables
3161
Table I: A list of commonly used models that employ sediment-transport-capacity relations across 3162
different process domains. 3163
Model Transport-capacity equations Reference HEC-RAS (Hydrologic
Engineering Center’s River Analysis System)
Fluvial erosion:
Ackers and White (1973) England and Hansen (1967) Laursen (1968)
Meyer-Peter and Müller (1948) Toffaleti (1968)
Yang (1973, 1984) Wilcock (2001)
Brunner (2010)
ISIS: river and floodplain modelling
Fluvial transport:
Ackers and White (1973)
CH2MHILL (2015) DELFT3D: 3D modeling suite
to investigate hydrodynamics, sediment transport and morphology and water quality for fluvial, estuarine and coastal environments Wave erosion: Bijker (1971) Soulsby (1997) van Rijn (1993) Current erosion:
Ashida and Michiue (1974) Engelund and Hansen (1967) Meyer-Peter and Müller (1948) Wilcock and Crowe (2003)
Deltares (2014)
MIKE21: simulation of physical, chemical and biological processes in coastal and marine envrionments
Current erosion: van Rijn (1993)
Engelund and Fredsøe (1976) Engelund and Hansen (1967) Meyer-Peter and Müller (1948)
DHI (2013)
WEPP (Water Erosion Prediction Project)
Hillslope erosion:
Foster (1982) based on Yalin (1963)
USDA (1995)
TOPMODEL (TOPography based hydrological MODEL
Hillslope erosion: Kirkby (1993)
Kirkby (1997) EUROSEM (European Soil
Erosion Model)
Splash erosion: Poesen (1985) Govers (1991) Everaert (1992)
Poesen and Torri (1988) Rill erosion: Govers (1990) Interrill erosion: Everaert (1991) Fluvial erosion: Govers (1990) Morgan et al. (1998)
KINEROS (Kinematic Runoff and Erosion Model)
Hillslope and channel erosion: Ackers and White (1973) Engelund and Hansen (1967) Kilinc and Richardson (1973) Meyer and Wischmeier (1969) Yalin (1963)
Yang (1973)
101
Figures
3164
3165
Figure 1: Comparisons between observed and calculated bedload transport in Elbow
3166
River, Alberta, Canada data for different bedload formulae, illustrating each formula
3167
produces contrasting estimates. (HRS: a group of formulae developed by researchers
3168
associated with the United Kingdom Hydraulics Research) [from Gomez and Church,
3169
1989].
102 3171
3172
Figure 2: Measured submerged bedload transport rate, ib versus predicted values using 3173
equation 3. The data were compiled from Johnson (1943), Smart and Jaeggi (1983), Gomez 3174
and Church (1988), Recking (2006), and those compiled by Gao (2003). These data include 3175
all of the available experiments to date that transport bed load of homogeneous grains under 3176
the ideal condition and cover the full range of both the saltation and sheetflow régimes. 3177
103 3178
Figure 3: Schematic illustration of grain-size changes in the bed-surface (Ds50) and 3179
transported (D50) sediment. In (a), a feed flume, only the bed surface changes, while in a 3180
recirculating flume (b), the change is primarily in the transported sediment. In both cases (c), 3181
transport coarsens relative to the bed surface. Thus, the same ratio of D50/Ds50 may be caused 3182
by (1) a low transport rate with small D50 or (2) a high transport rate with big D50 (after 3183
Wilcock and DeTemple, 2005). 3184
104 3185
Figure 4: The modified two-phase model. The two solid curves represent equation 5 with
3186
c = 0.03 and 0.06, respectively. The two dashed lines denote the boundary between the two 3187
regimes for the same two c values. The areas between these curves and lines reflect the 3188
influence of the uncertainties in the determination of c values. The dots are the bedload data 3189
reported in Hayes (1999) from a gravel-bed river significantly affected by a recent volcanic 3190
eruption (the data that have values of B greater than 1 are not included). Régime I is the area 3191
below the horizontal zone that includes two parts, the narrow area bounded by the two solid 3192
curves and the one on the right representing bed load transported at and below capacities, 3193
respectively. In the below-capacity area, bedload transport rate is relatively low for a given 3194
flow meaning the transport efficiency is relatively low and the median size of bed load D50 is 3195
small comparing to that of the bed surface, Ds50 and substrate, Dsub50. In the at-capacity area, 3196
the transport rate is relatively high for the same flow suggesting the relatively high transport 3197
efficiency and D50 is between Ds50 and Dsub50. Régime II is the area above the dashed 3198
horizontal zone. It also has below-capacity and at-capacity areas. Flows in the former have a 3199
bed with an armour layer, while in the latter do not. D50 in the former is relatively small, 3200
while in the latter is equivalent to both Ds50 and Dsub50. 3201
105 3202
Figure 5: Plot of surface-based fractional transport rates (qbi/fi) against grain size fractions, 3203
D. Each curve represents a flow transporting bed load at capacity in one of four gravel-bed
3204
rivers in Idaho, USA. 3205
106 3206
3207
Figure 6: Schematic of the streamlines above a low amplitude undulation of a sand surface
3208
in an aeolian setting. The maximum u* is located at a distance upwind from the crest 3209
(maximum ) proportional to the wavelength . The sand flux maximum qsat is located at a 3210
distance Lsat downwind, which separates the zones of erosion and deposition (after Durán et 3211
al., 2011).
107 3213
Figure 7: Saturation length Lsat, rescaled by the drag length (𝐿𝑑𝑟𝑎𝑔 = 𝜌𝑝
𝜌𝑓 𝑑), as a function
3214
of the wind shear velocity u*a, rescaled by the threshold u*at. Direct measurements, 3215
performed in a wind tunnel () and in the field (△), are compared to those 3216
determined from the initial dune wavelength (storms: (☆) and slipfaceless dunes 3217
(○)) (after Andreotti et al., 2010). 3218
108 3219
Figure 8: Different equations used to predict sediment transport under longshore conditions,
3220
showing the wide range of potential values for a specific wave energy (after Komar, 1999). 3221
109 3222
3223
Figure 9: Conceptual model of soil erosion derived by Meyer and Wischmeier (1969) from
3224
Ellison (1947) and other sources. 3225
110 3226
Figure 10: Comparison of experimental data with derived transport capacity and detachment
3227
capacity of overland flow on bare soil without sediment input at the top of the slope, but with 3228
flow addition at the rates specified (after Schiettecatte et al., 2008). 3229
111 3230
Figure 11
: Schematic diagram of possible subglacial conditions, showing a plan view of the
3231bed of an active ice sheet or glacier flowing from the top to the bottom of the page. The key 3232
sediment-transport mechanisms are illustrated. The thicknesses of the curves on the left 3233
represent the ice flux (linear scale), the water flux (logarithmic scale), and total flux of débris 3234
in the ice plus deforming or stream-transported sediment below the ice (logarithmic scale) 3235
(after Alley et al., 1997). 3236
112 3238
3239
Figure 12