Analysis and Modeling of Landscape Topography: Statistical Description and Evolution Under Natural and Disturbed Conditions

Abstract

<p>The topographical properties of a landscape and their time evolution are key features of the Earth's surface, regulating ecosystem functioning in terms of soil properties as well as water and energy budgets, and creating visually diverse and striking patterns across various spatial scales. Furthermore, the natural evolution of a topography under the influence of geologic erosion can be greatly altered by anthropogenic disturbances (e.g., through agriculture, mining, deforestation), with the potential of accelerating soil erosion, causing land degradation and soil fertility losses. Hence, understanding the geomorphological processes driving the evolution of landscapes under natural and disturbed conditions is key not only to define the main factors and feedbacks shaping the Earth's topography, but also to foresee the consequences of intensive land use and implement optimal strategies of land management and recovery. </p><p>This dissertation addresses some key aspects of landscape evolution and stability, with a focus on the statistical description and modeling of hillslope morphologies under natural and disturbed conditions, the theoretical definition of drainage area at regular and non-regular points of the watershed, and the formation of spatially organized ridge and valley patterns.</p><p>We start from the analysis of topographic slopes under natural and accelerated soil erosion. Using large topographic datasets from mountain ranges worldwide, we show that the approximate age of a landscape is fingerprinted in the tails of its slope distributions. We then explore the role of the different processes driving this dynamic smoothing over geologic time scales by means of numerical experiments, showing that the relaxation process is mainly dominated by diffusion. The effect of agricultural-driven soil erosion on hillslope morphology is then investigated, highlighting how the natural aging process can be altered by intensive land use which, at smaller scales, produces key differences in the slope distribution tails. Furthermore, theoretical solutions are derived for the hillslope profile and the associated soil creep and runoff erosion fluxes, and used to link the observed differences in the morphological features of disturbed and undisturbed areas to a disruption of the natural balance between soil creep and runoff erosion mechanisms.</p><p>We then move the analysis to the drainage area, an important nonlocal morphometric variable used in a large number of geomorphological and ecohydrological applications. A nonlinear differential equation whose validity is limited to regular points of the watershed is obtained from a continuity equation, and the theory is then extended to critical and singular points by means of both Gauss' theorem and dynamical systems concepts. Such a link between the drainage area and a continuity equation sets the basis for the subsequent analysis of organized ridge and valley patterns and channel forming instability. The formation of ridge/valley patterns is analyzed by means of numerical experiments in detachment limited conditions, with the identification of various regimes as a function of diffusive soil creep, runoff erosion, and tectonic uplift as well as the specific geomorphic transport law assumed. Lastly, a linear stability analysis of the coupled water and landscape evolution dynamics is outlined to investigate the critical conditions triggering channel formation and the emergence of characteristic valley spacings in relation to the main geomorphological processes involved.</p>