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

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

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

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.

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

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 (?)

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)

Flanagan, 2013

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

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?