Erosion

Erosion is the suite of physical and biogeochemical surface processes by which flowing water, wind, glacial ice, waves, and gravity detach clastic particles or bedrock blocks from their point of origin, entrain them into a moving medium, and transport them downslope toward depositional basins. In geological analysis, erosion is distinguished from weathering: weathering is the in situ mechanical disaggregation (such as frost wedging or salt crystallization) and chemical alteration (such as silicate hydrolysis by carbonic acid, H₂CO₃, or carbonate dissolution of CaCO₃) of rock with no net lateral movement, whereas erosion requires detachment plus translational transport driven by fluid shear stress or gravitational potential energy conversion into translational kinetic energy.

Across continental surfaces, the competition between endogenic tectonic rock uplift (U) and exogenic erosional denudation (E) governs the topographic evolution of mountain belts, incises fluvial drainage networks, exposes deep plutonic and metamorphic basement terrains across stratigraphic unconformities, and supplies the detrital clasts and dissolved ions that lithify into sedimentary rock successions (such as the Morrison Formation and Cedar Mountain Formation). Over multimillion-year timescales, physical erosion in active orogens continually exposes fresh unweathered calcium- and magnesium-silicate minerals to atmospheric CO₂ and H₂O, regulating Earth's long-term greenhouse climate thermostat and driving secular shifts in marine ⁸⁷Sr/⁸⁶Sr ratios tracked by strontium isotope stratigraphy.

Boundary Shear Stress and the Dimensionless Shields Parameter (τ*_c)

Fluvial rivers are the dominant global agent of continental erosion, delivering ~15 to 20 billion metric tons (Gt) of suspended and bedload sediment and ~4 Gt of dissolved solutes to the global oceans each year. For a steady, uniform open-channel flow of water density ρ_f (≈ 1,000 kg/m³), flow depth h (or hydraulic radius R_h), and channel bed slope S = tan θ, the downslope component of gravitational weight is balanced by the boundary shear stress τ_b exerted by the turbulent flow on the channel bed:

τ_b = ρ_f · g · h · S

where g = 9.81 m/s² is gravitational acceleration. Whether τ_b is sufficient to entrain a non-cohesive sediment grain of diameter D and density ρ_s (≈ 2,650 kg/m³ for quartz) depends on the ratio of hydrodynamic fluid drag and lift forces to the submerged gravitational weight of the grain. In 1936, Albert Shields formulated the dimensionless Shields stress τ*:

τ* = τ_b / [ (ρ_s − ρ_f) · g · D ]

Incipient motion (detachment and bedload rolling, sliding, or saltation) begins when τ* exceeds the critical Shields parameter τ*_c, which typically ranges from τ*_c ≈ 0.030 to 0.060 (commonly ~0.045 for rough turbulent boundary layers over well-sorted sand and gravel beds). As captured on the empirical Hjulström-Sundborg diagram, the flow velocity required for entrainment is lowest for fine-to-medium sand (D ≈ 0.1–0.5 mm); coarser gravels require higher velocity to overcome grain weight (τ_b ∝ D), while finer cohesive silts and clays (D < 0.0625 mm) also require higher velocity to overcome electrostatic van der Waals attraction and burial within the viscous laminar sublayer.

Stream-Power Bedrock Incision Law and Hack's Drainage Scaling

In uplifting mountain channels where bedrock is exposed directly to turbulent water and saltating sediment tools (abrasion by suspended and bedload impacts, hydraulic plucking along joints, and cavitation), the vertical rate of fluvial bedrock incision E (in m/yr or mm/yr) is modeled by the stream-power incision law (Howard and Kerby, 1983; Whipple and Tucker, 1999):

E = K · A^m · Sⁿ

Here A is the upstream contributing drainage area (which serves as a proxy for water discharge Q ∝ A^c), S = −dz/dx is the local channel gradient, K is the dimensional erodibility coefficient (encoding bedrock tensile strength, joint spacing, climate runoff variability, and bedload tool supply), and m and n are positive exponents linked to the physics of shear stress or unit stream power. When incision is proportional to boundary shear stress τ_b, dimensional analysis yields m ≈ 1/3 and n ≈ 2/3; when incision is proportional to unit stream power ω = ρ_f g Q S / W (power dissipated per unit bed area across channel width W ∝ Q^0.5), m ≈ 0.45–0.50 and n ≈ 1.0, maintaining a characteristic concavity index θ = m / n ≈ 0.45 ± 0.10 across graded bedrock rivers worldwide.

Combining the stream-power law with continuity of rock mass in a mountain belt experiencing steady tectonic uplift rate U gives the partial differential equation for river longitudinal profile evolution:

∂z / ∂t = U − K · A^m · (|∂z / ∂x|)ⁿ

At topographic steady state (∂z/∂t = 0, where erosion balances rock uplift E = U), solving for local channel slope S yields Flint's law:

S = (U / K)^1/n · A^−(m/n) = k_s · A^−θ

where k_s = (U / K)^1/n is the normalized channel steepness index, used globally in tectonic geomorphology to map active fault uplift rates from digital elevation models.

Hillslope Linear/Nonlinear Diffusion, Glacial Buzzsaws, and Aeolian Saltation

Outside river channels, landscape denudation is partitioned among hillslope transport, glacial ice flow, and wind shear:

1. Hillslope Diffusive Creep and Threshold Landsliding: On soil-mantled hillslopes, freeze-thaw cycles, wetting-drying expansion, and biological burrowing (bioturbation) drive downslope regolith flux q_s proportional to local topographic gradient: q_s = −D_h ∇z, where D_h (in m²/yr) is the hillslope diffusivity. Conservation of mass (∂z/∂t = U − ∇·q_s = U + D_h ∇²z) predicts parabolic, convex-upward ridge crests with hilltop curvature C = −∇²z = U / D_h. As tectonic uplift steepens slopes toward the critical internal friction angle of rock/regolith (S_c ≈ 30°–35°), transport transitions to a non-linear flux q_s = −D_h ∇z / [1 − (|∇z|/S_c)²] dominated by shallow debris flows and bedrock landslides.
2. Glacial Abrasion and Quarrying (Plucking): Temperate alpine glaciers sliding over bedrock at basal velocity u_b erode via two mechanisms: glacial abrasion (in which rock clasts frozen into basal ice score bedrock with parallel striations and generate silt-sized glacial flour at a rate proportional to contact pressure and u_b, Hallet, 1979) and glacial quarrying (plucking) (in which fluctuating subglacial meltwater pressures propagate subcritical fractures on the low-pressure lee side of bedrock bumps and dislodge joint-bounded blocks). Operating near the equilibrium-line altitude (ELA), this "glacial buzzsaw" excavates amphitheater-like cirques, knife-edge arêtes, pyramidal horns, and parabolic U-shaped glacial troughs at rates of 1 to > 20 mm/yr.
3. Aeolian Saltation, Reptation, and Deflation: Because air density (ρ_a ≈ 1.22 kg/m³) is ~800-fold lower than water density, wind entrains sand grains via ballistic saltation once the friction velocity u* = √(τ_b/ρ_a) exceeds Ralph Bagnold's (1941) fluid threshold u*_t ≈ 0.1 · √[(ρ_s − ρ_a)gD / ρ_a]. Returning saltating grains strike the bed with high translational kinetic energy at 10°–16° impact angles, splashing neighbouring grains into short hops (reptation) and ejecting < 62.5 μm silt dust into turbulent suspension across thousands of kilometers (depositing blankets of loess), while wind-driven sand abrasion sculpts streamlined bedrock ridges (yardangs) and multi-faceted cobbles (ventifacts).

Cosmogenic Nuclide Erosion Rates and the Silicate Weathering Thermostat

To measure integrated catchment-wide erosion rates over 10³ to 10⁵ year timescales (bridging the gap between decadal stream-gauge sediment traps and 10⁶-year low-temperature thermochronology), geomorphologists measure in situ terrestrial cosmogenic nuclides—chiefly ¹⁰Be (half-life 1.387 Myr) and ²⁶Al (half-life 0.705 Myr)—produced within quartz (SiO₂) grains by secondary cosmic-ray spallation in the upper ~1–2 meters of the crust. Because cosmic-ray production P(z) = P₀ exp(−ρz / Λ) attenuates exponentially with mass depth ρz (attenuation length Λ ≈ 160 g/cm², corresponding to ~60 cm in bedrock of density ρ ≈ 2.65 g/cm³), the steady-state concentration N (in atoms/g of quartz) in river sand leaving a catchment is inversely proportional to the mean catchment erosion rate E:

N = P₀ / [ λ + (ρ · E / Λ) ] ⟹ E ≈ (Λ / ρ) · (P₀ / N) (when ρE / Λ ≫ λ)

Slowly eroding cratonic shields (such as Australia or the Canadian Shield, E ≈ 1–10 m/Myr) accumulate high ¹⁰Be concentrations in river quartz, whereas rapidly eroding active mountain belts (such as the Himalayas, Southern Alps of New Zealand, and Taiwan, E ≈ 1,000–10,000 m/Myr) flush quartz quickly through the upper 60 cm cosmic-ray zone and yield low ¹⁰Be concentrations.

By stripping away weathered regolith and supplying fresh calc-silicate minerals (represented by wollastonite, CaSiO₃) to the critical zone, physical erosion fuels the Urey silicate-weathering reaction (Berner, Lasaga, and Garrels, 1983; Raymo and Ruddiman, 1992):

CaSiO₃(s) + 2CO₂(g) + H₂O(l) → Ca²⁺(aq) + 2HCO₃⁻(aq) + SiO₂(aq) → CaCO₃(s) + SiO₂(s) + CO₂(g) + H₂O(l)

Each mole of calcium silicate weathered on land and precipitated as marine limestone (CaCO₃) sequesters one net mole of atmospheric CO₂ into the lithosphere, coupling tectonic mountain building and physical erosion directly to Earth's long-term carbon cycle.

Why does fine sand erode at a lower flow velocity than either cohesive clay or coarse gravel?

On the Hjulström-Sundborg curve, fine-to-medium sand grains (D ≈ 0.1–0.5 mm) are detached at the lowest current velocity (~15–20 cm/s). Particles larger than 0.5 mm (coarse sand, pebbles, cobbles) are non-cohesive, so the fluid shear stress needed to lift them scales linearly with grain weight and diameter (τ_b ∝ D). Conversely, particles smaller than 0.0625 mm (silt and clay) sit entirely inside the viscous laminar boundary sublayer and bind together via electrostatic surface forces and extracellular biofilms, requiring much higher flow velocities (often > 100 cm/s) to rip cohesive mud clasts from the bed.

Why does carbonate dissolution not act as a net sink for atmospheric CO₂ over multimillion-year timescales?

During karst chemical weathering of limestone, one mole of atmospheric CO₂ and one mole of H₂O dissolve one mole of CaCO₃ into soluble Ca²⁺ and 2HCO₃⁻: CaCO₃ + CO₂ + H₂O ⇌ Ca²⁺ + 2HCO₃⁻. However, when those ions reach the ocean within 10⁴–10⁵ years and marine organisms precipitate CaCO₃ shells, the exact reverse reaction occurs, releasing that same mole of CO₂ back to the ocean-atmosphere system. Only calcium- and magnesium-silicate weathering (which converts 2 moles of CO₂ into 1 mole of CaCO₃ and releases only 1 mole of CO₂) provides a permanent net geological sink for volcanic CO₂.

How can researchers tell from a topographic map whether a valley was carved by a river or a glacier?

A bedrock river concentrates its boundary shear stress along a narrow channel thalweg (representing < 1% of the valley width), incising vertically while hillslopes fail by landsliding at their angle of repose to form a V-shaped cross-sectional valley with interlocking spurs. By contrast, an alpine glacier fills the entire valley floor to depths of hundreds of meters, distributing basal sliding and quarrying across the bed and valley walls simultaneously to carve a broad, parabolic U-shaped trough with truncated spurs and hanging tributary valleys.

1. Shields, A. (1936). Anwendung der Ähnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung (Mitteilungen der Preußischen Versuchsanstalt für Wasserbau und Schiffbau, Heft 26). Berlin. https://doi.org/10.1007/978-3-662-09886-8
2. Bagnold, R. A. (1941). The Physics of Blown Sand and Desert Dunes. Methuen & Co. https://doi.org/10.1007/978-94-009-5682-7
3. Raymo, M. E., & Ruddiman, W. F. (1992). "Tectonic forcing of late Cenozoic climate." Nature, 359(6391), 117–122. https://doi.org/10.1038/359117a0
4. Whipple, K. X., & Tucker, G. E. (1999). "Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs." Journal of Geophysical Research: Solid Earth, 104(B8), 17661–17674. https://doi.org/10.1029/1999JB900120