The concentration of dissolved solids and river flow

Abstract

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...

The effects of antecedent moisture conditions on the relationship of hydrology to hydrochemistry in a small forested watershed

“…Data have been bulked to derive regression relationships ( power functions) between solute concentration and discharge (Foster, 1978;Walling and Webb, 1986;Webb and Walling, 1992), sometimes distinguishing seasonal trends (Foster, 1978;Walling and Webb, 1986). There is much scatter in these relationships, however, and power functions are perhaps not the most appropriate technique to describe solute response to changing stream¯ow (O'Connor, 1976). Furthermore, it is generally recognized that very dierent responses are to be expected from event to event owing to both storm characteristics (rainfall amount and intensity) and antecedent moisture conditions (Muscutt et al, 1990;A Â vila et al, 1992;Jenkins et al, 1994;Soulsby, 1995).…”

Nutrient and metal loads estimated by using discrete, automated, and continuous water-quality monitoring techniques for the Blackstone River at the Massachusetts-Rhode Island State line, water years 2013–14

“…Furthermore, moderate to semistrong negative correlations between the explanatory variable of discharge and total nitrogen (rho = −0.662), dissolved nitrogen (rho = −0.759), and nitrate (rho = −0.866) indicate dilution with increasing flow (table 9). These negative correlations indicate that the primary source of nitrogen may be from groundwater discharge or a relatively constant point source (O'Connor, 1976;Albek, 2003;Granato, 2006;Granato and others, 2009). Total organic nitrogen, particulate nitrogen, and particulate carbon have semistrong to strong relations with each other (table 10).…”

“…The remaining correlations are weak to moderate, indicating that two or more explanatory variables are needed to describe the variability in estimates of trace metal concentration. Several dissolved trace metals have negative correlations to discharge and (or) antecedent precipitation, which may indicate that the dissolved species are from point sources that are diluted by runoff (O'Connor, 1976) or perhaps from groundwater discharge. Many of these correlations are weak, however, and many of the correlations to antecedent precipitation are not statistically significant at the 95-percent confidence limit.…”

“…This is not to say, however, that measured flow is not an important variable for consideration in the development of regression equations for estimating concentrations. Equations that use streamflow to estimate concentration, known as water-quality transport curves, can be the best way to accurately estimate concentrations if the relations are strong and other near realtime measurements are not readily available (O'Connor, 1976;Glysson, 1987;Granato, 2006;Granato and others, 2009). Therefore, measured flows and estimated concentrations provide the best possible load estimates with meaningful prediction-interval estimates.…”

Computer programs for obtaining and analyzing daily mean streamflow data from the U.S. Geological Survey National Water Information System web site

“…Streamflow statistics also may be used to indicate receiving-water quality because concentrations of water-quality constituents commonly vary naturally with streamflow. For example, concentrations of suspended sediment and sedimentassociated constituents (such as nutrients, trace elements, and many organic compounds) commonly increase with increasing flows, and concentrations of many dissolved constituents commonly decrease with increasing flows in streams and rivers (O'Connor, 1976;Glysson, 1987;others, 2003, 2005).…”