## V

FIGURE 3.22 Energy circuit diagram translation of Manning's equation.

equations have been developed to describe the effect of channel roughness on stream flow such as the Manning's equation (Figure 3.22, see also Equation 3.2). This relationship was developed for conditions of uniform flow to design flood control channels, but it is commonly used for nonuniform flow conditions in natural channels. In this equation velocity (V) is directly proportional to the slope (S) and size of the channel (R) but inversely proportional to the roughness of the channel (n). Manning's n is termed the roughness coefficient, and it is an index of the friction of the channel on the stream flow. Some values of the roughness coefficient have been measured (Chow, 1964; Dunne and Leopold, 1978), and they range from 0.012 ft 1/6 for smooth concrete channels to 0.050 ft 1/6 for streams with rocky beds or dense aquatic vegetation. Manning's equation can be used for ecological engineering design as values of the roughness coefficient become better known. Debris dams have been assigned high values of Manning's n which is a reflection of their role in causing a localized reduction in current velocity and consequent changes in sediment transport (see the Hjulstrom relationship in Figure 3.7).

A diversity of debris dams exists in streams like different species in ecosystems. Figure 3.23 shows a gradient of debris dams ranging from megajams which span 10 times bankfull depth of the channel to microjams and individual log pieces. Table 3.3 describes three kinds of debris dams from a river in the Pacific Northwest of the U.S. Each type of dam has a unique architecture and different influences on stream flow and channel form.

An exciting strategy is the active manipulation of woody debris in streams to control erosion. This action has been done in the context of creating habitat for stream organisms, but its application for erosion control is recent (Streb, 2001). A carefully placed debris dam can divert current away from critical channel locations where erosion is to be controlled, while having several by-product values in the ecology of the stream. This kind of management can be especially important for watersheds in which riparian forests have been cut, thereby removing a natural source of wood to streams. Sedell and Beschta (1991) discuss this strategy in a paper with the compelling title of "Bringing Back the 'Bio' in Bioengineering."

Another important and interesting aspect of debris dams is the self-building behavior that they exhibit. This is the accumulation process in which wood builds up to form a dam. A key feature of the process is a positive feedback relationship

Height r

10 wb

Height r

10 wb

1.0 wb

Height h

Height h

FIGURE 3.23 Examples of different types of debris dams. (A) Megajam. (B) Macrojam. (C) Mesojam. (D) Microjam. (E) Individual jog pieces; hb = bankfull depth; Wb = width of the channel. (From Church, M. 1992. The Rivers Handbook: Hydrological and Ecological Principles. Vol. 1. P. Calow and G. E. Petts (eds.). Blackwell Scientific, Oxford, U.K. With permission.)

b in which the initial pieces of wood in the dam catch increasingly more wood because of the action of the dam in creating a growing obstruction to flow. In this way the dam builds itself through input of wood pieces being carried in the current. The products of the self-building behavior are dams with complexity of architecture and size being determined by wood supply, channel dimensions, and current velocities. In a sense woody debris dams are fascinating structures because they represent complex systems that emerge from simple rules and elements. The self-building behavior of debris dams is a special case of self-organization, which is autocatalytic in creating structure. Other related examples are traffic jams (Edie, 1974), ice jams in rivers (Ashton, 1979; Beltaos, 1995), and even jams of signals in communication systems such as telephone networks (Alfredo Nava, personal communication). A description of autocatalysis is given by H. T. Odum (1983) below:

Many naturally occurring units in the real world store energy and then feed it back internally to facilitate in the inflow of other energy. The feedback acts as a control, often as a multiplier, and catalyzes the inflow. Such units are sometimes termed autocatalytic. The process of storing and using the storage to pump additional energy tends to accelerate growth and maximize power. Such modules are frequent in all kinds of system.

It is suggested here that the wood of the debris dam feeds back upon the current in the stream to bring more wood into the dam and therefore it grows autocatalytically.

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