Graf (1977)1 proposed that after initiation, gullies approach a new equilibrium extent at an exponentially decreasing rate over time. Dendrochronological evidence was provided as field support for the rate law from 70 - 150 y old gullies in Colorado, and laboratory experiments on channel network growth have produced qualitatively similar results. The rate law is an intuitive and appealing concept that is included in many descriptions of geomorphic adjustment to change, however the age of many gullies precludes investigation of the processes responsible for gully growth and the physical meaning of the rate law.
Gully formation over the last 10 y in SE Australia has presented an opportunity to investigate the rate law in more detail. An exponential growth model fits the data well, with a half-life of only 0.7 - 3.5 y. Gullies have extended by only 10s of cm over the last 3 y of monitoring, and gully widening now dominates over headward growth. Closer examination and monitoring of erosion processes reveals a change in process dominance from overland flow during gully initiation to seepage erosion in the latter stages of network growth. It is proposed that the relative efficacy of these processes produces the rapid exponential decline in network growth observed. In some situations, initial rapid growth of gullies is a result of multiple points of scour which later merge by headcut retreat, rather than migration of a single headcut up through a valley.
1 Graf, W. L. (1977) The rate law and fluvial geomorphology, Am. J. Sci. 277:178-191.