A rudimentary mechanistic model for soil formation and landscape development: II. A two-dimensional model incorporating chemical weathering

The necessity for a quantitative analysis of pedogenesis has become more compelling in the last few decades. In part one of this paper we proposed a rudimentary mechanistic model that considers soil formation spatially at the catena scale. This paper extends the model for soil formation in a landscape conditioned by a digital elevation model and further illustrates the application of the model in quantifying pedogenesis. The current model states that the change in soil thickness over time depends on the physical weathering rate of rock, the loss due to chemical weathering and the transport of soil through erosion. The rate of physical weathering or lowering of the bedrock surface is represented as an exponential decline with soil thickness. The chemical weathering rate is modelled as a negative exponential function of both soil thickness and time. Assuming uni-dimensional weathering, the rate of chemical weathering can be expressed as a reduction in soil thickness. The movement of materials in the landscape is characterized by diffusive transport. The model is solved numerically using the finite-difference approach and applied to a digital elevation model. The results for simulation of soil formation in a landscape after 10,000 years shows that the soil accumulates (thickens) in the gullies and erodes (thins) in the ridges. The soil from the upper slope is transported down-slope by the erosion processes and fills the gullies. Soil thickness is highly correlated with the profile curvature. The effect of climate, rock type and land management is illustrated by different combinations of weathering rate and erosive diffusivity. To illustrate the effect of irregularity and randomness on the stability of the solution and the soil development, spatially correlated normally distributed random numbers were added to the initial soil elevation. The small randomness appears to cause instability (chaos) in the system. Dimensionality analysis of the soil thickness as a function of time confirms the non-linear chaotic behaviour of the model rather than merely random noise. A difference plot of the soil thickness time series unveiled the presence of a strange attractor. Alternatively, these results may be a result of numerical instability.