Many fluvially eroded terrains display an intimate interaction of their patterns of channel and ridge lines. Under the assumption that there is exactly one outer ridge link positioned between any two neighboring outer channel links, the paper analyzes such interlocking networks by investigating their dual graphs. Several formal relationships are established which translate into a set of both existing and new theorems describing the close interdependency of channel and ridge parameters: Interlocking networks are of equal magnitude, the link numbers of the ridge and channel paths enclosing channel and ridge subnetworks have the same mean value, the link number of the boundary path enclosing a subnetwork is equal to the number of boundary paths passing through the root of the subnetwork, there exists a one‐to‐one correspondence between the inner nodes of the two networks as well as between their paths, and every such pair of corresponding ridge and channel paths delineates an area that is closed with regard to slope runoff. Copyright 1991 by the American Geophysical Union.

Abstract: Some new methods for the topologic classification of channel networks are proposed. These methods are all based on the concept of topologic path length, or number of links from the network outlet to a junction or source. Two parameters, the total path length (sum of all path lengths) and the diameter (largest path length) are shown to be useful in network analysis. Some advantages of these parameters are that they are easy to measure, have straightforward topologic interpretations, and are closely related to important geometric measures. Moreover, they are capable of explaining various empirical geomorphic “laws,” such as the 0.6 power relation between mainstream length and area.

Abstract: The random model of drainage basin composition is founded on the assumptions that (a) natural channels are topologically random in the absence of geological controls and (b) for channel networks developed in similar environments, the exterior and interior link lengths are independent random variables with a common distribution for each type. The effectiveness of this model in estimating the values of geomorphic variables and in explaining and predicting geomorphic relationships is illustrated by several examples. The data required for these examples were obtained from map studies of 30 channel networks, comprising a total of about 8700 links, in eastern Kentucky. A common factor in the success of all three applications of the model is the way in which the planimetric features of drainage basins are determined by their underlying topologic structure.

Despite the known biochemical production of a range of aromatic compounds by plants and the presence of benzenoids in floral scents, the emissions of only a few benzenoid compounds have been reported from the biosphere to the atmosphere. Here, using evidence from measurements at aircraft, ecosystem, tree, branch and leaf scales, with complementary isotopic labeling experiments, we show that vegetation (leaves, flowers, and phytoplankton) emits a wide variety of benzenoid compounds to the atmosphere at substantial rates. Controlled environment experiments show that plants are able to alter their metabolism to produce and release many benzenoids under stress conditions. The functions of these compounds remain unclear but may be related to chemical communication and protection against stress. We estimate the total global secondary organic aerosol potential from biogenic benzenoids to be similar to that from anthropogenic benzenoids (~10 Tg y(-1)), pointing to the importance of these natural emissions in atmospheric physics and chemistry.