QUANTITATIVELY RELATING STREAM NETWORK EVOLUTION TO GROUNDWATER FLOW

Spatio-temporal scaling of hydrologic/geomorphic processes allows organization of Stommel diagrams linking distinct physical and temporal scales. For such diagrams to be useful, they typically must extend over many orders of magnitude, which means that they are typically graphed biologarithmically. In evaluating the controls of the corresponding physical processes, three factors are important: The form of the scaling relationship (which generates the shape of a curve on the diagram), the fundamental spatial scale, if there is one, and a time scale. The time scale relates the spatial scale and a fundamental velocity. Applied to headward erosion and stream capture events, the result is almost identical to that which describes vegetation growth in the subsurface, and which has been carefully tested over length scales of 30 microns to 10 km, with corresponding time scales that range from tens of seconds to 100kyr. Owing to uncertainties of many kinds, testing of the corresponding geomorphic relationship for drainage evolution is less certain, but it appears that the fundamental length scale is the same for vegetation (at about 30 microns), while the characteristic velocity is a little higher than for vegetation growth (about 30m/yr, rather than a few meters per year). This distinction is in line with the difference in vertical (infiltration) and horizontal (regional flow rates) velocities. Both are known to be proportional to the difference between the precipitation and the evapotranspiration. In our, so far, limited study, the drainage organization rates appear to be mostly consistent across climate regimes, with integration occurring correspondingly faster in wetter climates. Implications for drainage (re)organization in various tectonic and climatic regimes will be discussed in light of competing geomorphic processes that tend to pull apart or fill in drainages.