Erodability

Erodability (or erodibility) is the inherent yielding or nonresistance of soils and rocks to erosion. A high erodability implies that the same amount of work exerted by the erosion processes leads to a larger removal of material. Because the mechanics behind erosion depend upon the competence and coherence of the material, erodability is treated in different ways depending on the type of surface that eroded.

Soils

Soil erodibility is a lumped parameter that represents an integrated annual value of the soil profile reaction to the process of soil detachment and transport by raindrops and surface flow.^[1] The most commonly used model for predicting soil loss from water erosion is the Universal Soil Loss Equation (USLE) (also known as the K-factor technique), which estimates the average annual soil loss ${\displaystyle A}$  as:^[2]

${\displaystyle A=RKLSCP}$ 

where R is the , K is the soil erodibility,^[3][4] L and S are topographic factors representing length and slope, and C and P are cropping management factors.

Other factors such as the stone content (referred as stoniness), which acts as protection against soil erosion, are very significant in Mediterranean countries.^[5][6] The K-factor is estimated as following ^[1][4]

K = [(2.1 x 10⁻⁴ M^1.14 (12–OM) + 3.25 (s-2) + 2.5 (p-3))/100] * 0.1317

M: the textural factor with M = (m_silt + m_vfs) * (100 - m_c)

m_c :clay fraction content (b0.002 mm);

m_silt  : silt fraction content (0.002–0.05 mm);

m_vfs : very fine sand fraction content (0.05–0.1 mm);

OM: Organic Matter content (%)

s: soil structure

p: permeability

The K-factor is expressed in the International System of units as t ha h ha⁻¹ MJ⁻¹ mm⁻¹

Rocks

Shear stress model

Geological and experimental studies have shown that the erosion of bedrock by rivers follows in first approach the following expression^[7] known as the shear stress model of stream power erosion:

${\displaystyle {dz \over dt}=-K_{\tau }(\tau \ -\tau \ _{c})^{a}}$ 

where z is the riverbed elevation, t is time, K_\tau is the erodability, ${\displaystyle \tau }$  is the basal shear stress of the water flow, and a is an exponent. For a river channel with a slope S and a water depth D, ${\displaystyle \tau }$  can be expressed as:

${\displaystyle \tau \ =\rho \ gDS}$ 

Note that ${\displaystyle K_{\tau }}$  embeds not only mechanical properties inherent to the rock but also other factors unaccounted in the previous two equations, such as the availability of river tools (pebbles being dragged by the current) that actually produce the abrasion of the riverbed.

${\displaystyle K_{\tau }}$  can be measured in the lab for weak rocks, but river erosion rates in natural geological scenarios are often slower than 0.1 mm/yr, and therefore the river incision must be dated over periods longer than a few thousand years to make accurate measurements. K_e values range between 10⁻⁶ to 10⁺² m yr⁻¹ Pa^−1.5 for a=1.5 and 10⁻⁴ to 10⁺⁴ m yr⁻¹ Pa⁻¹ for a=1.^[8] However, the hydrological conditions in these time scales are usually poorly constrained, impeding a good the quantification of D.

Unit stream power model

An alternative model for bedrock erosion is the unit stream power, which assumes that erosion rates are proportional to the potential energy loss of the water per unit area:

${\displaystyle {dz \over dt}=-K_{\omega }\ \omega \ }$ 

where ${\displaystyle K_{\omega }}$  is the erodability, and ${\displaystyle \omega }$  is the unit stream power, which is easily calculated as:

${\displaystyle \omega \ =\rho \ gQS/W}$ 

where Q is the water discharge of the river [m³/s], and W is the width of the river channel [m].

Relative differences in long-term erodability can be estimated by quantifying the erosion response under similar climatic and topographic conditions with different rock lithology.^[9]

See also

• Erosion
• Stream power
• Stream power law

References

1. Renard, K.G.; Foster, G.R.; Weesies, G.A.; McCool, D.K.; Yoder, D.C. (1997). Predicting soil erosion by water: a guide to conservation planning with the Revised Universal Soil Loss Equation (RUSLE) (PDF). Agricultural Handbook. Vol. 703. United States Department of Agriculture (USDA). ISBN 0-16-048938-5.
2. Ward, Andrew D. & Trimble, Stanley W. (2004). "Soil conservation and sediment budgets". Environmental Hydrology. CRC Press. p. 259. ISBN 978-1-56670-616-2.
3. Soil Erodability (K-Factor) in Europe, European Commission.
4. Panagos, Panos; Meusburger, Katrin; Ballabio, Cristiano; Borrelli, Pasqualle; Alewell, Christine (2014). "Soil erodibility in Europe: A high-resolution dataset based on LUCAS". Science of the Total Environment. 479–480: 189–200. Bibcode:2014ScTEn.479..189P. doi:10.1016/j.scitotenv.2014.02.010. PMID 24561925.
5. Bosco, Claudio; de Rigo, Daniele; Dewitte, Olivier; Poesen, Jean; Panagos, Panos (2015). "Modelling soil erosion at European scale: towards harmonization and reproducibility". Natural Hazards and Earth System Sciences. 15 (2): 225–245. Bibcode:2015NHESS..15..225B. doi:10.5194/nhess-15-225-2015. ISSN 1561-8633.
6. Poesen, Jean; Lavee, Hanoch (1994). "Rock fragments in top soils: significance and processes". CATENA. 23 (1–2): 1–28. Bibcode:1994Caten..23....1P. doi:10.1016/0341-8162(94)90050-7. ISSN 0341-8162.
7. Bagnold, Ralph A. (1977). "Bed load transport by natural rivers". Water Resources Research. 13 (2): 303–312. Bibcode:1977WRR....13..303B. doi:10.1029/WR013i002p00303. ISSN 1944-7973.
8. Garcia-Castellanos, Daniel; Villaseñor, Antonio (2011). "Messinian salinity crisis regulated by competing tectonics and erosion at the Gibraltar arc". Nature. 480 (7377): 359–363. Bibcode:2011Natur.480..359G. doi:10.1038/nature10651. ISSN 1476-4687. PMID 22170684. S2CID 205227033.
9. Hooke, Rohrer, 1977 - Relative erodibility of source-area rock types, as determined from second-order variations in alluvial-fan size, Geological Society of America Bulletin, v. 88, p. 1177-1182, 4 figs., August 1977, Doc. no. 70815