Intro to Geomorphology (Geos 450/550) Lecture 7: channel geometry and sediment transport power laws in channel geometry bed load sediment transport Rouse number: mode of transport vs. grain size suspended load sediment transport read Pelletier (2012) Leopold and Maddock (1953) found for alluvial channels: w = aA b h = cA f v = kA m S = tA z where b = 0.5, f = 0.4, m = 0.1, z = -0.4 Channel width increases with drainage area because banks widen to convey flow Slope decreases with increasing area because flow depth increases (and both velocity and bed shear stress (which drives bed load sediment transport) are closely related to hS (depth-slope product)) Walnut Gulch field trip wrap-up https://www.youtube.com/user/watershedAZ Flume 6: aka the big dog S = 0.01, w = 20 m Lucky Hills 103: aka the little whipper-snapper S = 0.02, w = 1.5 m Hydraulic relations: Event-rank analysis for flume 6: Q (5 yr) = 70 m 3 /sh (5 yr) = 1.15 m You do: event-rank analysis for flume 103 use S = 0.05, n = 0.05 Also: Predict bed load sediment flux for d = 10 mm in both flumes Bed-load sediment transport formulae: Step 1: calculate threshold of motion well-sorted fine gravel 15 SHIELDS DIAGRAM The silt-sand and sand-gravel borders correspond to the values of Re p computed with R = 1.65, = 0.01 cm 2 /s and D = mm and 2 mm, respectively. no motion motion Bed-load sediment transport formulae: Step 2: calculate bed load transport, q s (units L 2 /T) if threshold of motion is exceeded Wiberg & Smith (1992) Bed-load sediment transport formulae: All its glory: Bed-load sediment transport formulae: Use Dietrich (1982) to compute w s : How to determine bed vs. suspended load? Suspended-sediment load: Langbein-Schumm curve Conceptual model for sediment detachment from hillslopes: Rainsplash is the key mechanism for sediment release from hillslopes. Rainsplash is proportional to rainfall (not precipitation) rate and varies inversely with leaf area index (LAI). LAI varies from 0 to approx. 8. With each increase in LAI value of 0.5, rainsplash disturbance drops by 50%, i.e. Why exponential dependence on LAI? Detachment rate varies nonlinearly with slope: Pelletier (2012) Nearing et al. (1997) based on USLE datasets This model distinguishes detachment and transport. Detachment is primarily a function of rainsplash, which in turn is a function of rainfall intensity and leaf area index (LAI). Transport is a function of slope (at the hillslope scale) and bed shear stress and sediment texture (and the watershed scale). D(x,y,d) = detachment rate (kg m 2 yr 1 ), c 1 is a free parameter (dimensionless) calibrated to measured global sediment discharge data, b is the bulk density of the soil (kg m 3 ), f d is the fraction of the soil within each soil texture bin of grain diameter d (dimensionless), S is slope gradient (dimensionless), R k is the mean monthly rainfall (m yr 1 )), and L k is the mean monthly LAI (dimensionless). The first equation provides a map of the average detachment rate for every month. Sediment is routed downslope in suspension if the Rouse number is smaller than one (the definition of suspended sediment). Input data layers: (5 arcmin or 10 km resolution) Brute-force model calibration: Model results: Model predictions versus observed data: Model reproduces observed relations between sediment delivery ratio and drainage basin area (top), yield and basin area (middle), and yield and average basin slope (bottom).