Equilibrium and time scales in geomorphology: Application to sand‐bed alluvial streams

Equilibrium is defined as a single‐valued, temporally invariant functional relationship between the values of an output variable and the values of the input variable(s) in a geomorphic system. Disequilibrium occurs if the output deviates from the functional relationship by more than a consensual degree. Natural geomorphic variables are characterized by a relaxation time. Output variables are insensitive to cyclical inputs with frequencies much greater than the relaxation time, but can respond completely for sufficiently low frequencies. Rapid trends, recent step changes or pulse inputs, and intermediate frequency inputs can cause disequilibrium. The gradient of sand‐bed alluvial channels (the output variable) is determined by sediment and water delivery from slopes (the input variables), and changes in this hydraulic regime require regrading by erosion and deposition. Initial stages of adjustment to changed regime in a long, unbranched channel with sediment and water delivery only at the upstream end propagate downstream, but later stages of adjustment occur simultaneously throughout the reach. In a dendritic channel network the gradient responds rather uniformly throughout the network to changes in regime during all stages of adjustment. The time scale of adjustment to changed regime depends upon the size of the channel network (or stream length), the sediment and water discharges, and to a lesser degree upon the magnitude of the change. Grade as defined by Mackin (1948) is synonymous with equilibrium as used in this paper if ‘a period of years’ is replaced by ‘a time period commensurate with the relaxation time of the gradient’. The use of the term grade is best restricted to a single‐valued relationship between channel gradient and the hydraulic regime.