Mathematical characteristics of the longitudinal profile of rivers

Abstract

Analysis of the form of the longitudinal profile of rivers can be used when making aleogeomorphological reconstructions. Comparing of different equations used for approximation of the longitudinal profiles of rivers showed that most exactly the form of topographical profile is expressed through the logarithmic equasion of the type h=K-d lg l. All other equations: parabolic, lagorithmica, exponent and bilogarithmic equations do not express the form of the actually existing profile, and besides, very often are hard for calculations. Empirically it was established that the parameters of a logarithmic equasion can be defined without knowing the actual profile what is especially important for paleogeomorphological reconstructions. The parameter K is defined by the altitude of the source of the river, correlation coefficient between them is equal to 0.931-0.03. The parameter d is rather well correlated with the difference of altitudes of the source and mouth of the river (H) : d=0.417H, correlation coefficient - 0.91±0.04.