1. Channel shape

2. Alluvial channel cross-sectional shape
Reflects sediment supply rate, sediment size distribution, vegetation, flow variability and recurrence, etc.
In stable channel, cross-section contains 1.5-year (RI) flood
sustained by balance between sediment supply, floodplain aggradation, and lateral migration

3. Alluvial channel cross-sectional shape
How do open-channel hydraulics influence erosion at the channel boundary?

4. Velocity distribution in a cross-section
TRAPEZOIDAL
RECTANGULAR
PARABOLIC
NATURAL MEANDERING

5. Shear stress ∝ velocity gradient

6. What flow conditions determine channel dimensions?

7. Hydraulic geometry
Recall macroscopic flow continuity relationship: 𝑄=𝑉𝑑𝑤 How do 𝑉, 𝑑, and 𝑤 vary as 𝑄 varies? At a station (𝑄(𝑡)) and downstream (𝑄(𝑥)) hydraulic geometry relations: 𝑤=𝑎 𝑄 𝑏 𝑑=𝑐 𝑄 𝑓 𝑉=𝑘 𝑄 𝑚 𝑏+𝑓+𝑚=1, 𝑎𝑐𝑘=1

8. Hydraulic geometry 𝑤=𝑎 𝑄 𝑏 𝑑=𝑐 𝑄 𝑓 𝑉=𝑘 𝑄 𝑚 𝑏+𝑓+𝑚=1, 𝑎𝑐𝑘=1 exponent AASDS 𝑏
0.26
0.5 𝑓
0.4 𝑚
0.34
0.1

9. Flow duration Daily or yearly discharge data Ranked by discharge value
Assigned exceedence probability based on ranking and number of records:
𝑃=100× 𝑚 𝑛+1
Exceedence probability for daily streamflow is the probability on any given day that discharge will be higher. Reciprocal 1/𝑃 is recurrence interval.

10. Sediment Rating Curves
Bedload transport relationship
𝑄 𝑠 =𝑓(𝑄)
Multiply 𝑃(𝑄) by 𝑄 𝑠 (𝑄) to get weighted distribution of sediment transport
Peak of sediment rating curve is “effective discharge”