INTRODUCTION Historically, the idea of a static erosional net- work with uplift everywhere balanced by erosion has deep roots. Playfair (1802) described drainage basins as trees, each stream delicately adjusted such that at each joining of streams, the slopes were delicately balanced. The systematic change of slope within landscapes suggested to Playfair that an equilibrium existed between erosion and sediment transport over the entire basin, and a stable geometry resulted from this balance. Gilbert (1877) noted that erosional landforms have convergent stream networks and divergent ridge networks, and proposed that the typical concave-up profile of streams is due to the in- creased volume of water moving through down- stream sections in the drainage network. He pos- tulated that divides between adjacent streams must migrate toward the stream with a shallower gradient; stable channel networks are achieved once gradients in adjacent streams are similar. In- stability of drainage lines could be explained in terms of differential resistance to erosion, differ- ential uplift, time, and possibly the interaction be- tween stream transport capacity and availability of sediment for transport. For Gilbert, the net- work of streams and hillslopes is a strongly inter- active system, delicately adjusted at dynamic equilibrium to a stable form. Strahler (1950) characterized erosional land- scapes as open mass-transport systems that adjust their morphology to attain a time-independent form. He measured valley-side slope angles from several completely dissected natural drainages, and showed that a given area maintains a charac- teristic slope with a narrow range of values. The presence of a characteristic slope lends support to the hypothesis of a stable landform. Hack (1960) hypothesized that every stream- hillslope pair is adjusted one to the other, and given constant forcing conditions, all elements of the landscape erode at the same rate, similar to Gilbert’s dynamic equilibrium. Differences in form could, under those conditions, be related only to differences in resistance to flow, such as variable lithology and vegetation. Changes in the form could also result from changes in the forc- ing conditions, but responses to perturbations were fast enough to restore a dynamic steady state adjusted to the new boundary conditions. He explicitly viewed landscapes as spatial struc- tures with time-independent forms. NUMERICAL FORMULATIONS OF LANDSCAPE EROSION In general, erosion is controlled by the re- sistance of the substrate to surface and body forces. The resistance is set by rock properties (crystal structure and chemistry, rock strength or cohesion, grain size), vegetative cover, and degree of saturation. Applied forces vary widely across natural landscapes: the scratching paws of burrowing animals; the pounding impact of rain drops; the torque of bending trees under the wind’s impulse; soil expansion and contraction during saturating events and freeze-thaw; epi- sodic failures of oversteepened slopes; the thrash- ing torrents of streams; and the grinding mass of a sliding glacier, to name a few. The rate of disin- tegration of crystalline bedrock to smaller parti- cles also sets a limit on the availability of trans- portable material. For modeling purposes, sim- plification is required at some level to obtain so- lutions to mass transport across the landscape. Several landscape erosion models have been developed in recent years (Willgoose et al., 1991; Kramer and Marder, 1992; Chase, 1992; Leheny and Nagel, 1993; Howard, 1994; Tucker and Bras, 1998, for overview of models), and they differ in the means and degree of simplification of erosional processes that they employ. However, all of the models assume that forces applied by surface runoff dominate erosional processes in landscapes, and thus are based on routing water down the steepest slope in a numerical grid. Runoff is treated as steady, uniform flow, and this assumption allows the use of upstream drainage through a point as a proxy for stream flow at that point. Calculation of erosion depends on assump- tions concerning the availability and transporta- bility of sediment, but in general erosion rate is a function of local slope, discharge, uplift rate, and substrate resistance. The models develop land- scapes with branching stream networks similar to natural drainage patterns (Chase, 1992; Leheny and Nagel, 1993), and even capture transient evo- lutionary features of the network such as exten- sion and abstraction of streams (Glock, 1931; Kramer and Marder, 1992). Models based solely on stream erosion, how- ever, develop slopes approaching infinity near drainage divides. While some natural landscapes have near vertical slopes, most hillslopes flatten near ridge crests. If a diffusive short-length scale process is added to the models, the resultant land- Geology; December 2000; v. 28; no. 12; p. 1067–1070; 6 figures. 1067 Landscape instability in an experimental drainage basin Leslie E. Hasbargen Chris Paola Department of Geology and Geophysics, University of Minnesota, Twin Cities, 310 Pillsbury Drive S.E., Minneapolis, Minnesota 55455-0219, USA ABSTRACT Do drainage basins develop static river networks when subject to steady forcing? While cur- rent landscape evolution models differ in formulation and implementation, they have the com- mon characteristic that when run for long times at constant forcing, they evolve to a static steady- state configuration in which erosion everywhere balances uplift rate. This results in temporally stationary ridge and valley networks. We have constructed a physical model of a drainage basin in which we can impose constant rainfall and uplift conditions. The model landscapes never be- come static, and they are not sensitive to initial surface conditions. Ridges migrate laterally, change length, and undergo topographic inversion (streams occupy former ridge locations). Lat- eral stream migration can also produce strath terraces. This occurs without any change in exter- nal forcing, so the terraces must be considered autocyclic. The experimental drainage basin also exhibits autocyclic (internally generated) oscillations in erosion rate over a variety of time scales, despite constant forcing. The experimental landforms are clearly not perfect analogs of natural erosional networks, but the results raise the possibility that natural systems may be more dynamic than the current models would suggest, and that features like strath terraces that are generally interpreted in terms of external forcing may arise autocyclically as well. Keywords: landscape evolution, strath, topographic inversion, autocyclic.