A general expression for the spatial and temporal distribution of conservative dissolved solids in freshwater rivers which incorporates the contribution of both the groundwater and surface water components of river flow is presented. The first part of this paper deals with the steady state conditions. With certain simplifying assumptions the correlation between concentration of dissolved solids and flow is developed for both spatially uniform and nonuniform conditions. The analysis includes the effect of both geophysical discontinuities and point sources. Examples from a number of rivers throughout the country are presented to indicate the utility of the analysis. The second part addresses the temporal variation of the dissolved solids concentration for two time scales. One describes the annual variation in concentration due to the time variable components of the river flow, and the second the variation over a semimonthly period due to a time variable point input. Applications to a variety of river conditions are also presented for the time variable analysis. INTRODUCTION: STEADY STATE ANALYSIS Many factors affect the concentration of total dissolved solids in natural water systems. These solids are the result of both natural phenomena and man's activity and may enter the stream as either distributed or point sources. In freshwater streams and rivers one of the most sign!ficant factors which affects the concentration of dissolved solids is the spatial and/or temporal variation of flow. It is the purpose of this paper to present an analytical framework relating the river flow to the concentration of dissolved solids for both steady state and time variable conditions. The correlation between flow and concentration of dissolved solids has long been recognized [Lenz and Sawyer, 1944; Hem, 1959; Toler. 1965]. Various forms of inverse relationships have been presented: hyperbolic [Durum, 1953] and logarithmic [Gunnerson, 1967; Pionke and Nicks, 1970]. In some cases, consideration of antecedent flow conditions has improved the correlation [Ledbetter and Gloyna, 1964; Hall, 1971; Pionke et al., 1972]. The inclusion of interflow, in addition to surface and base flow, has been suggested to provide a more realistic basis of analysis [Hart et al., 1964]. The groundwater and surface water components of the total flow have been analyzed according to the respective concentrations of various constituents [La $ala, 1967; Pinder and Jones, 1969]. Development of Equations The basic equation is developed by applying the principle of conservation of mass. A mass balance is taken about an elemental volume of streams A V along the longitudinal axis of the channel of cross-sectional area A and length Ax. It is assumed that vertical and lateral-uniformity exists and that longitudinal dispersion is small by contrast to the advective component of the flow. The dissolved constituent enters the stream from both surface runoff Qs and groundwater inflow Qg with concentrations cs and cg, respectively. The mass balance of the dissolved solids yi...
