Lattice Model for Approximate Self-Affine Soil Profiles

A modeling of the soil structure and surface roughness by means of the concepts of the fractal growth is presented. Two parameters are used to control the model: the fragmentation dimension, $D_f$, and the maximum mass of the deposited aggregates, $M_{max}$. The fragmentation dimension is related to the particle size distribution through the relation $N(r \ge R) \sim R^{D_f}$, where $N(r \ge R)$ is the accumulative number of particles with radius greater than $R$. The size of the deposited aggregates are chose following the power law above, and the morphology of the aggregate is random selected using a bond percolation algorithm. The deposition rules are the same used in the model of solid-on-solid deposition with surface relaxation. A comparison of the model with real data shows that the Hurst exponent, $H$, measured {\it via} semivariogram method and detrended fluctuation analysis, agrees in statistical sense with the simulated profiles.