Fundamental Principles and Techniques of Landscape Evolution Modeling

Numerical modeling has become an important method for studying landscape evolution, complementing field- and lab-based techniques such as geologic mapping and geochronology. This chapter describes several techniques used to discretize and solve the most fundamental partial differential equations that arise in landscape evolution. Although landscape evolution modeling encompasses all process zones (hillslope, fluvial, aeolian, glacial, and coastal), this chapter draws primarily from examples in hillslope and fluvial systems. The numerical techniques useful for simulating transport- and detachment-limited landscapes, including alternating direction implicit and upwind differencing methods, as well as root-finding techniques such as Newton's method that are useful for solving nonlinear equations, are emphasized. The chapter also reviews some of the challenges associated with sub-grid-scale processes (e.g., modeling erosion in channels that are not resolved in cross section) and combining different types of processes within numerical models.