1. Review: overland water erosion
PROCESSES
INFLUENCES
Generate runoff
Saturation excess
Infiltration excess
Hydraulic soil properties
Conductivity
Compaction/use history
Ground cover (interception)
Antecedent conditions
Existing moisture
Seasonal barriers

2. Review: overland water erosion, cont’d
PROCESS
INFLUENCES
Raindrop impact
Detachment makes particles available to overland flow
Overland flow
Sheet/interrill flow
Rill flow
Requires overcoming threshold for erosion
Ground cover/canopy
Roughness/resistance
Grain roughness
Form roughness, from furrows, veg., etc.
Slope length, steepness and shape
Convergent slopes collect water, focus water/soil energy dissipation

3. Review: overland water erosion, cont’d
PROCESS
INFLUENCES
Runoff entrainment
Grains (cohesionless)
Aggregates (cohesive)
Threshold behavior
Flow depth, Re smaller than in rivers: different dynamics
Soil texture, structure
Relative exposure
Cohesion agents
Clay minerals
Roots/hyphae
Flow depth, slope, velocity
Depth often increases downslope

4. Review: overland water erosion, cont’d
PROCESS
INFLUENCES
Transport capacity
Bedload
Suspended load
Dissolved load?
Flow depth, slope, velocity
Critical shear stress
Critical stream power
Critical unit stream power
Capacity not necessarily the same as supply
A flow may carry less than its transport capacity, but not more.

5. Review: overland water erosion, cont’d
PROCESS
INFLUENCES
Deposition/storage
Bedload
threshold
Suspended load
Deposition by settling, may lag changes in fluid motion
Flow depth, slope, velocity
Critical shear stress
Critical stream power
Critical unit stream power
Along-slope changes in slope, velocity, can promote deposition
Increased roughness, footslope

6. Modeling soil erosion EMPIRICAL PHYSICAL/THEORETICAL *USLE
Easy for end-user
Possibly accurate predictions
Broadly used, promoted
Not spatially-explicit
Limitations to time and space scale
WEPP, LISEM, MIKE-SHE
Not as intuitive
Difficult to constrain, capture complexity
Research tool
Spatially-explicit, event or long-term basis
Physically sound (?)

7. WEPP overview Fundamental unit = hillslope Computes rainfall-runoff
Simulates two erosion processes: rainsplash (interrill) and rill erosion
Defines erosion and deposition by comparing transport capacity (x,t) with mass flux (x,t)

8. Flanagan, 2013

9. WEPP erosion component
Interrill
𝐷 𝑖 = 𝐾 𝑖 𝐼 2 𝑆 𝑓 𝐶 𝑒 𝐶 𝑐 𝑆 𝑟 𝑤 𝑟
Rill erosion
𝐷 𝑟,𝑚𝑎𝑥 = 𝐾 𝑟 𝜏− 𝜏 𝑐
𝐷 𝑟 = 𝐷 𝑟,𝑚𝑎𝑥 1− 𝑞 𝑠 𝑇 , or
𝐷 𝑟 = 𝑣 𝑠 /𝑞(𝑇− 𝑞 𝑠 )
𝑇= 𝑘 𝑡 𝜏 𝑏
𝑑 𝑞 𝑠 𝑑𝑥 = 𝐷 𝑖 + 𝐷 𝑟

10. WEPP erosion component
Interrill
𝐷 𝑖 = 𝐾 𝑖 𝐼 2 𝑆 𝑖 𝐶 𝑒 𝐶 𝑐 𝑠 𝑟 𝑤 𝑟
Rill erosion
𝐷 𝑟,𝑚𝑎𝑥 = 𝐾 𝑟 𝜏− 𝜏 𝑐
𝐷 𝑟 = 𝐷 𝑟,𝑚𝑎𝑥 1− 𝑞 𝑠 𝑇 , or
𝐷 𝑟 = 𝑣 𝑠 /𝑞(𝑇− 𝑞 𝑠 )
𝑇= 𝑘 𝑡 𝜏 𝑏
𝑑 𝑞 𝑠 𝑑𝑥 = 𝐷 𝑖 + 𝐷 𝑟
How does erosion vary in space and time?
What parameters may vary with conservation practices?