Geometry and Topology of Estuary and Braided River Channel Networks Automatically Extracted From Topographic Data.

Automatic extraction of channel networks from topography in systems with multiple interconnected channels, like braided rivers and estuaries, remains a major challenge in hydrology and geomorphology. Representing channelized systems as networks provides a mathematical framework for analyzing transport and geomorphology. In this paper, we introduce a mathematically rigorous methodology and software for extracting channel network topology and geometry from digital elevation models (DEMs) and analyze such channel networks in estuaries and braided rivers. Channels are represented as network links, while channel confluences and bifurcations are represented as network nodes. We analyze and compare DEMs from the field and those generated by numerical modeling. We use a metric called the volume parameter that characterizes the volume of deposited material separating channels to quantify the volume of reworkable sediment deposited between links, which is a measure for the spatial scale associated with each network link. Scale asymmetry is observed in most links downstream of bifurcations, indicating geometric asymmetry and bifurcation stability. The length of links relative to system size scales with volume parameter value to the power of 0.24-0.35, while the number of links decreases and does not exhibit power law behavior. Link depth distributions indicate that the estuaries studied tend to organize around a deep main channel that exists at the largest scale while braided rivers have channel depths that are more evenly distributed across scales. The methods and results presented establish a benchmark for quantifying the topology and geometry of multichannel networks from DEMs with a new automatic extraction tool.

Ecological validity of virtual environments to assess human navigation ability.

Route memory is frequently assessed in virtual environments. These environments can be presented in a fully controlled manner and are easy to use. Yet they lack the physical involvement that participants have when navigating real environments. For some aspects of route memory this may result in reduced performance in virtual environments. We assessed route memory performance in four different environments: real, virtual, virtual with directional information (compass), and hybrid. In the hybrid environment, participants walked the route outside on an open field, while all route information (i.e., path, landmarks) was shown simultaneously on a handheld tablet computer. Results indicate that performance in the real life environment was better than in the virtual conditions for tasks relying on survey knowledge, like pointing to start and end point, and map drawing. Performance in the hybrid condition however, hardly differed from real life performance. Performance in the virtual environment did not benefit from directional information. Given these findings, the hybrid condition may offer the best of both worlds: the performance level is comparable to that of real life for route memory, yet it offers full control of visual input during route learning.

Blocking Delaunay triangulations.

Given a set B of n black points in general position, we say that a set of white points W blocks B if in the Delaunay triangulation of [Formula: see text] there is no edge connecting two black points. We give the following bounds for the size of the smallest set W blocking B: (i) [Formula: see text] white points are always sufficient to block a set of n black points, (ii) if B is in convex position, [Formula: see text] white points are always sufficient to block it, and (iii) at least [Formula: see text] white points are always necessary to block a set of n black points.