Differential equation model for river water with Hydrogen and Oxygen’ s stable isotope composition

First,the widely used Rayleigh-Model founded by predecessor is introduced and its merits and drawbacks are pointed out.Having noticed its drawbacks and made some assumptions and simplifications,the following two models are deduced based on basic law of hydraulics and Rayleigh fractional principle: (1) the differential equation model for the stable isotope composition that varies with time in static water body,which discloses the relationship among stable isotope composition in static water body,the fractional factor and the evaporation rate,and (2) the differential equation model for stable isotope composition that varies with time and space of the kinetic water body in the river,which describes the quantitative relations among the flowing river water's hydrogen and oxygen's stable isotope composition,the fractionation factor,the fluid velocity and flux.In the end,the inner link among these three models is presented through the mathematical deduction.The proposal of these models makes it possible to simulate the river water's stable isotope composition quantitatively and gives help to interpret more objectively and more sufficiently the information included in the stable isotope data of water.