Scale-dependence of landscape pattern: Interactions among climate, topography, and latitudinal gradients

From the ground, Earth's surface is rough and featured with mountains and valleys. From space, Earth appears to be a smooth sphere. These contrasting perspectives change with an observer's viewpoint along a spectrum of scales, from local to global. The transition or crossover from rough to smooth is controlled by the interplay of interacting gradients of the landscape and tectonics. Climate dynamics and coupled fluxes of energy and water on terrain create patterns on landscapes that manifest as drainage networks. Landscape patterns are driven by dynamics that are typically invariant to changes in scale. The objective of this dissertation is to explain the scale-dependence of the relationship between climate and landscape pattern. First, the generality of a classic relationship between drainage network density (D d) and a climate index (I) reveals that the pattern between Dd and I is spurious, a finding corroborated with digital data over 25 large basins in the U.S. Second, an algorithm, the Binary Link Address (BLA) is developed to capture the structure of drainage networks. The BLA reveals that spatial distributions of some properties of basins are related to network structure, where correlations between network structure and climatic variables are a function of topography. The BLA reconciles the conflict between linear stream paradigms, e.g., the River Continuum Concept (Vannote et al. 1980), and discrete representations of streams, i.e., Horton-Strahler order (Horton 1945, Strahler 1952, 1957). Third, latitudinal and topographic gradients, which quantify the change of a parameter over space, differentiate basins into two groups: (1) where basins are dominated by topography, climate is significantly correlated to BLA and (2) flat basins dominated by latitudinal gradients have no overall pattern between BLA and climate. The theory of biased random walks gives a recipe for separating basins into two universality classes, which suggests that basins are controlled by different processes and dynamics depending on internal topographic gradients, latitudinal gradient, and temporal variability.