Landscapes posses many scales of variability, from hillslopes to the river network structure, and have been the subject of intense research over the past three decades. Despite this tremendous variability, it has been well documented by now that scale-invariances do exist in several landscape attributes reflecting the natural organization of processes responsible for the formation of those landscapes. The availability of very high resolution (sub-meter scale) digital topography data from laser altimetry (LiDAR) offers an unprecedented opportunity to probe into the structure of landscapes at scales never imagined before and extract properties useful for modeling water, sediment, and nutrient fluxes in a watershed. In this work, we take advantage of these high resolution topography data to introduce new metrics for quantifying landscape organization and explore scaling laws across the continuum of hillslope-fluvial regimes. The innovations we introduce rely on: (1) adapting a new scale parameter which we call ``directed distance from the divide'' which allows examining divergent and convergent parts of the landscape under a single framework; (2) using this new scale parameter to identify the signature of landslides on a landscape allowing thus an objective mapping of those landslides; (3) introduction of the ``incremental drainage area'' function along the mainstream to quantify the hierarchy and clustering of tributaries; and (4) introduction of an non-traditional horizontal function that measures ``valley width''as one fills up the channels beyond their banks and maps the left and right extend of the landscape.
A common theme in all of the above developments is the quest for mapping the complex three dimensional structure of landscapes onto simpler, preferably one dimensional, functions that reflect different aspects of the landscape organization. Once this is accomplished, our common method of analysis relies on the theory of multi-scaling using wavelets, i.e., in quantifying how the statistical structure of the extracted attributes changes when one sees them at different scales.
University of Minnesota Ph.D. dissertation. October 2009. Major: Civil Engineering. Advisor: Efi Foufoula. 1 computer file (PDF); xvi, 132 pages. Ill. (some col.)
Scale invariance and scaling breaks - new metrics for inferring process signature from high resolution LiDAR topography..
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