1. Overland flow hydraulics https://youtu.be/3TgQ06Z3q0I

2. Runoff
Saturation-excess runoff when water table meets the ground surface
Infiltration-excess runoff when precipitation rate exceeds infiltration rate

3. Horton’s conceptual hillslope model
Mass conservation and overland flow hydraulics suggest zonation of erosion, transport, and deposition on idealized hillslope.
What determines where erosion begins?

4. Shallow overland flow hydraulics
For steady flow, momentum balance requires driving and resisting stresses to be equal Driving stress: 𝜏 𝐷 =𝜌𝑔𝑅𝑆, where 𝑅~ℎ is the hydraulic radius Resisting stress: 𝜏 𝑅 =𝜌 𝑢 ∗ 2 from experiments on fixed roughness Here 𝑢 ∗ is shear velocity, not the same as 𝑢. Setting 𝜏 𝐷 = 𝜏 𝑅 , 𝑢 ∗ = 𝑔𝑅𝑆 If we define 𝑢 𝑢 ∗ = 8 𝑓 , the result is the Darcy-Weisbach formula: 𝑢 = 8𝑔𝑅𝑆 𝑓

5. Are overland flows laminar or tubulent?

6. Gilley and Kottwitz, 1994, Transactions ASAE