水系密度の変化に関する理論的考察

Abstract

A theoretical equation which shows the temporal change of drainage density is ex-pressed as follows;D, (t, T)=-_exp~j3~(v)_dv}(v)/~ ? exp{ 5 j3, (~) d4dvｱ1/Dswhere Di, (t, T) is the drainage density at time T on the I-th basin or geomorphic surfacewhich was formed at time t: jβi(τ) is the coefficient concerning the process which causesthe development of river at time τ:γi(τ) is the maximum drainage density at time τ andDi is the initial drainage density on the I-th geomorphic surface or basin. The equation isbased on the assumption that drainage density increases with time until it reaches thespecific upper limit, the maximum drainage density, which concerns some physical propertiesof the basin.It is possible to modify the equations into what shows the temporal change of drainagedensities in various basins or on geomorphic surfaces. The equation is;19(1, T)- exP{5>?_dr}5~p?/r?expt5 ~3(~e) d~1 dv +1/Dowith Do the initial drainage density, where it is assumed that the process is single and thephysical properties are not changed in the basins.By employing this equation, we obtain that the influence of the variation in the processto the change of the drainage density becomes smaller with time as the absolute value ofthe function concerning the process becomes larger, if we set the function is expressed asthe non-negative one where periodic variation and invariable term are combined.