The writer wishes to congratulate the authors for their very interesting development on step-pool streams. Recent advances on stepped channel flows with a fixed bed provide additional information on the topic. The discusser will show that the maximum flow resistance condition implies a characteristic flow pattern.For stepped channel flow above a fixed bed, two types of flow regimes can be distinguished: a succession of free falls at low discharges called a nappe flow regime ( Figure 1) and a skimming flow regime (Figure 2). At very low discharges the flow at each step consists of a free-falling jet impacting on the pool followed by a fully developed hydraulic jump. With increasing flow rates or decreasing step length L, the hydraulic jump is affected by the edge of the downstream step and eventually disappears (Figure 1). For larger discharges or smaller step lengths the flow becomes a skimming flow. In the skimming flow regime the water flows as a coherent stream, skimming over the steps and cushioned by the recirculating fluid trapped between them (Figure 2). In the step corners, recirculating vortices develop and are maintained through the transmission of shear stress from the water flowing past the edge of the steps. The transition between nappe and skimming flow is a function of the discharge and the step geometry. Chanson [1994] showed that skimming flow regime occurs for discharges larger than a critical value defined as (h c) onset •= S(1.057 -0.465 tan 0) (1) (fixed-bed channel with horizontal steps) where L is the step length measured parallel to the mean channel slope and (hc)onse t is the characteristic critical depth. Skimming flow regime occurs for h c > (hc)onset, where h c is the critical flow depth.Let us consider now the concept of "maximum flow resistance" in natural step pools. In a nappe flow regime the presence (or 4not) of hydraulic jumps is a dominant parameter. Hydraulic jumps have a great erosive power [e.g., Chow, 1959;Hager, 1992]. In a nappe flow regime with fully developed hydraulic jumps the jumps will contribute greatly to the erosion of step bottoms (below the jumps), leading to the step destruction. A new step arrangement with smaller step lengths will then take place. The waters will flow as a nappe flow with partially developed jumps or ultimately without hydraulic jumps.In skimming flow down flat-slope streams (i.e., 0 < 30ø), Chanson [1995] showed that maximum flow resistance is

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The study of channel networks has been dominated since 1966 by the random model. However, recent work has shown (1) that although the topological properties of small networks conform to the random model more closely than those of large ones, even small networks exhibit systematic deviations from topological randomness and (2) that the topological and length properties of channel networks are controlled to a large degree by the spatial requirements of subbasins and the need for these subbasins to fit together in space, by the size, sinuosity, and migration rate of valley bends, and by the length and steepness of valley sides. The factors that control the density properties of channel networks vary with the scale of the investigation and the geomorphic processes governing channel initiation. Although progress has been made toward a satisfactory stream junction angle model, further work is needed. The evolution of channel networks has been investigated by a variety of methods, including the development of conceptual and simulation models, the monitoring of small‐scale badland and experimental drainage basins, and the substitution of space for time. The morphology of most channel networks is largely inherited from the past or strongly influenced by inherited forms. Inasmuch as there is no way of ever knowing the origin or complex history of such networks, the use of stochastic models in their study seems unavoidable.

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