Correlation Structure of Morphometric Properties of Drainage Systems and Their Controlling Agents

To facilitate analysis of quantitative data obtained by measurements of many elements in nature, variables are mapped onto plane sets of points to form variable systems, within which (1) each variable is fairly highly correlated with every other, (2) the direction of causality, if any, is given, and (3) one or more variables is correlated with a variable not contained in the system. Variable systems are classified by the presence and direction of feedback among the variables. Variable systems may be infinite, and constitute hypotheses about the contained variables. Fifteen variables of geomorphic, surficial, and climatic elements are arranged into two related variable systems on the basis of correlation coefficients for every possible pair in the study. One system contains variables that measure and determine scale of topography; the other contains variables that measure and determine scale-free elements of topography, i.e., the appearance of the landscape. On the basis of the feedback that possibly exists in nature, there is some tendency for geomorphic elements to control the processes of erosion that shape them, but the control does not extend to the external elements of climate, geology, etc., and therefore the condition of maturity (which is perhaps a shifting equilibrium) is not stable but depends on constancy of climate and other governing factors. A change in some governing factor results in changes in the topography that neither return the governing factor to its original condition nor affect the processes of erosion in the particular way necessary to restore the original form of the land. Drainage density and valley-side slope angle, in particular, are by-products of the rates of energy expenditure on the land surface by running water and the rates of restoration of soil and vegetal cover in relation to the resistance of the surface to erosion. Valley-side slope, however, may exert control over internal erosive and depositional processes to maintain a steady angle consistent with external controlling factors.