In order to quantify soil erosion in the model it is necessary to calculate the sediment yield (S_y). To do this, the MUSLE equation (equation 1) is a modification of the original USLE which included soil erodibility (K), cover and management (C), practice (P) topography (LS) and a coarse fragment factor (F). 

\(S_{y}=(q_{surfQ_{peak}A})^{0.56}.K_{USLE}.C_{USLE}.P_{USLE}.LS_{USLE}.F_{USLE}\) [Equation 1]

                
The modification involved representing the USLE rainfall erosivity factor (R) with surrogate information from runoff (q_surfQ_peak and A). Q_surf is the surface runoff (mm day-1), Q_peak is the peak runoff discharge and A is the area for sediment yield calculation.
Alternatively, the rainfall erosivity term in R_USLE is defined in MJ mm ha^-1 hr^-1. It represents the product of rainfall kinetic energy and the maximum rainfall in a 30 minute period (KE x I30). As highly dependent on detailed records I30 is not well defined but is widely used in model applications. 
However, Davison et al. (2005) propose a power law relationship (KE = aPb) to define KE on a daily resolution from daily rainfall totals (Equation 2). Across the UK no significant geographic variation was found for this relationship (Davison et al. (2005). 

\(KE_{DT}={a_{1}+a_{2}}\cos[D_{J}(\frac{2\pi }{365}+a_{3})]P^{b}\)                  [Equation 2]

where: KE_DT is daily kinetic energy of rainfall as direct throughfall (J m-2), P is daily rainfall (mm) and DJ is Julian Day; parameter values for UK: α₁ = 6.608, α₂ = 0.519, α₃ = 2.727, b =1.204.
Total kinetic energy is the sum of the leaf drainage and direct throughfall components. Kinetic energy of leaf drainage is related to plant height (PH in m: leaf drainage from plants lower than 0.15 m contribute no kinetic energy) (Equation 3). The relative size of the components is defined by crop cover fraction (CC holding a value between 0 and 1) (Equation 4).

\(KE_{LD} = 15.8.PH^{0.5}-5.87\)                  [Equation 3]

\(KE = (1-CC).KE_{DT}+CC.KE_{LD}\)         [Equation 4]

As the variation of rainfall erosivity across Europe (Panagos et al., 2015) strongly reflects hydro-climatic classification it was decided to estimate R based on the rainfall kinetic energy calculation (Equation 2) for which the fitting parameters (α,b) are related to the Koppen climatic classification.
Therefore the equation adopted here (Equation 5) is a modification of R_USLE.

\(S_{y}=KE.K_{MMF}.C_{USLE}. P_{USLE}.LS_{USLE}.F_{CFRG}\)           [Equation 5]

The soil erodibility parameter (K) adopted differs from those originally used in the USLE family of models (based on textural composition and organic matter content) by using the simpler formulation related to textural composition as used by Morgan and Duzant (2008). Units of K_mmf are g j_-1 whose value is determined by the particle size fractions (F_clay, F_silt and F_sand which hold values between 0 and 1) and coefficients related to those fractions (Equation 6).

\(K_{MMF}=F_{clay}.0.1+F_{silt}.0.5+F_{sand}.0.3 \)       [Equation 6]

The cover and management factor C_USLE is defined as the ratio of soil loss from land cropped under specified conditions to the corresponding loss from clean-tilled, continuous fallow. Though data exists for temporally-averaged C_USLE factors in Europe (Panagos, Borrelli, Meusburger, Alewell, et al., 2015), these do not take into account daily variation in plant cover, and daily C_USLE factors are calculated empirically (Neitsch et al., 2011):

\(C_{USLE}=exp((ln(0.8) -ln(C_{min}))exp(-0.00115\cdot r_{surf})+ln(C_{min}))\) [Equation 7]

where r_surf is the crop residue on the soil surface [kg/ha] and C_min is a minimum C_USLE calculated as follows:

\(C_{min}=1.463\cdot ln(C_{av})+0.1034\)                   [Equation 8]

where C_av is the average annual C_USLE factor.

The support practice factor P_USLE is defined as the ratio of soil loss with a specific support practice (e.g. contour ploughing) to the corresponding soil loss with up-and-down slope culture. Spatially-resolved data to 1-km resolution are available for Europe (Panagos, Borrelli, Meusburger, van der Zanden, et al., 2015).
The topographic factor LS_USLE takes into account the steepness and slope of the hillslope on which erosion is occurring. It can be calculated from hillslope length and slope angle (Neitsch et al., 2011) and spatially-resolved data are available at 25- and 100-m resolution (Panagos, Borrelli, & Meusburger, 2015).
The coarse fragment factor F_CFRG takes into account the amount of rock in the soil profile, and is calculated as:
         

\(F_{CFRG} = exp(-0.053\cdot rock)\)             [Equation 9]

where rock is the percentage of rock in the first soil layer. Thus, F_CFRG =1  when no rock is present.

 

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Soil Model

Soil                                                                 Water

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Consult the NanoFASE Library to see abstracts of these deliverable reports: NanoFASE Report D2.2 Spatial transport framework

Davison PS, Withers PJA, Lord EI, Betson MJ, Strömqvist J. PSYCHIC – A process-based model of phosphorus and sediment mobilisation and delivery within agricultural catchments. Part 1: Model description and parameterisation. Journal of Hydrology. 2008 Feb; 350(3-4):290–302. Morgan R, Duzant J. Modified MMF (Morgan-Morgan-Finney) model for evaluating effects of crops and vegetation cover on soil erosion. Earth Surface Processes and Landforms. 2008; 32:90–106. Neitsch S, Arnold J, Kiniry J and Williams J. Soil and Water Assessment Tool – theoretical documentation. Texas Water Resources Institute Technical Report 406 Texas A&M University System, College Station Texas US. 2011. Panagos P, Ballabio C, Borrelli P, Meusburger K, Klik A, Rousseva S, et al. Rainfall erosivity in Europe. Science of the Total Environment. 2015 Apr 1; 511:801–814. Panagos, P., Borrelli, P., Meusburger, K., Alewell, C., Lugato, E., & Montanarella, L. (2015). Estimating the soil erosion cover-management factor at the European scale. Land Use Policy, 48 (Supplement C), 38-50. doi: 10.1016/j.landusepol.2015.05.021 Panagos, P., Borrelli, P., Meusburger, K., van der Zanden, E. H., Poesen, J., & Alewell, C. (2015). Modelling the effect of support practices (P-factor) on the reduction of soil erosion by water at European scale. Environmental Science & Policy, 51 (Supplement C), 23-34. doi: 10.1016/j.envsci.2015.03.012 Panagos, P., Borrelli, P., & Meusburger, K. (2015). A New European Slope Length and Steepness Factor (LS-Factor) for Modeling Soil Erosion by Water. Geosciences, 5(2), 117-126. doi: 10.3390/geosciences5020117 Мodelling: Science of the Total Environment, v. 650, p. 530-540.

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  Mike Hutchins

  Centre for Ecology and Hydrology (CEH)