Steven C. Chapra

Long-term phenomenological model of phosphorus and oxygen for stratified lakes

Abstract A budget model is developed to predict the long-term response of a lake to changes in its phosphorus loading. This model computes total phosphorus and hypolimnetic oxygen concentrations, taking sediment-water interactions into account. The lake is treated as two segments: the water and a surface sediment layer. A total phosphorus budget for the water accounts for inputs due to external loading and recycle from the sediments. It reflects losses due to flushing and settling. The sediment layer gains total phosphorus by settling and loses total phosphorus by recycle and burial. The recycle from the sediments to the water is dependent on the levels of sediment total phosphorus and hypolimnetic oxygen. Hypolimnetic oxygen concentration is estimated with a semi-empirical model. The model is applied to Shagawa Lake. An analysis is performed to demonstrate how its predictions replicate in-lake changes not possible with simpler phosphorus budget models.

An efficient numerical solution of the transient storage equations for solute transport in small streams

Several investigators have proposed solute transport models that incorporate the effects of transient storage. Transient storage occurs in small streams when portions of the transported solute become isolated in zones of water that are immobile relative to water in the main channel (e.g., pools, gravel beds). Transient storage is modeled by adding a storage term to the advection-dispersion equation describing conservation of mass for the main channel. In addition, a separate mass balance equation is written for the storage zone. Although numerous applications of the transient storage equations may be found in the literature, little attention has been paid to the numerical aspects of the approach. Of particular interest is the coupled nature of the equations describing mass conservation for the main channel and the storage zone. In the work described herein, an implicit finite difference technique is developed that allows for a decoupling of the governing differential equations. This decoupling method may be applied to other sets of coupled equations such as those describing sediment-water interactions for toxic contaminants. For the case at hand, decoupling leads to a 50% reduction in simulation run time. Computational costs may be further reduced through efficient application of the Thomas algorithm. These techniques may be easily incorporated into existing codes and new applications in which simulation run time is of concern.

Sewage contamination in the upper Mississippi River as measured by the fecal sterol, coprostanol

Abstract The molecular sewage indicator, coprostanol, was measured in bed sediments of the Mississippi River for the purpose of determining sewage contamination. Coprostanol is a non-ionic, non-polar, organic molecule that associates with sediments in surface waters, and concentrations of corpostanol in bed sediments provide an indication of long-term sewage loads. Because coprostanol concentrations are dependent on particle size and percent organic carbon, a ratio between coprostanol (sewage sources) and cholestanol + cholesterol (sewage and non-sewage sources) was used to remove the biases related to particle size and percent organic carbon. The dynamics of contaminant transport in the Upper Mississippi River are influenced by both hydrologic and geochemical parameters. A mass balance model incorporating environmental parameters such as river and tributary discharge, suspended sediment concentration, fraction of organic carbon, sedimentation rates, municipal discharges and coprostanol decay rates was developed that describes coprostanol concentrations and therefore, expected patterns of municipal sewage effects on the Upper Mississippi River. Comparison of the computed and the measured coprostanol concentrations provides insight into the complex hydrologic and geochemical processes of contaminant transport and the ability to link measured chemical concentrations with hydrologic characteristics of the Mississippi River.

Reactive Solute Transport in Streams: 1. Development of an Equilibrium‐Based Model

An equilibrium-based solute transport model is developed for the simulation of trace metal fate and transport in streams. The model is formed by coupling a solute transport model with a chemical equilibrium submodel based on MINTEQ. The solute transport model considers the physical processes of advection, dispersion, lateral inflow, and transient storage, while the equilibrium submodel considers the speciation and complexation of aqueous species, precipitation/dissolution and sorption. Within the model, reactions in the water column may result in the formation of solid phases (precipitates and sorbed species) that are subject to downstream transport and settling processes. Solid phases on the streambed may also interact with the water column through dissolution and sorption/desorption reactions. Consideration of both mobile (water-borne) and immobile (streambed) solid phases requires a unique set of governing differential equations and solution techniques that are developed herein. The partial differential equations describing physical transport and the algebraic equations describing chemical equilibria are coupled using the sequential iteration approach.

Reactive Solute Transport in Streams: 2. Simulation of a pH Modification Experiment

We present an application of an equilibrium-based solute transport model to a pH-modification experiment conducted on the Snake River, an acidic, metal-rich stream located in the Rocky Mountains of Colorado. During the experiment, instream pH decreased from 4.2 to 3.2, causing a marked increase in dissolved iron concentrations. Model application requires specification of several parameters that are estimated using tracer techniques, mass balance calculations, and geochemical data. Two basic questions are addressed through model application: (1) What are the processes responsible for the observed increase in dissolved iron concentrations? (2) Can the identified processes be represented within the equilibrium-based transport model? Simulation results indicate that the increase in iron was due to the dissolution of hydrous iron oxides and the photoreduction of ferric iron. Dissolution from the streambed is represented by considering a trace compartment consisting of freshly precipitated hydrous iron oxide and an abundant compartment consisting of aged precipitates that are less soluble. Spatial variability in the solubility of hydrous iron oxide is attributed to heterogeneity in the streambed sediments, temperature effects, and/or variability in the effects of photoreduction. Solubility products estimated via simulation fall within a narrow range (pKsp from 40.2 to 40.8) relative to the 6 order of magnitude variation reported for laboratory experiments (pKsp from 37.3 to 43.3). Results also support the use of an equilibrium-based transport model as the predominate features of the iron and pH profiles are reproduced. The model provides a valuable tool for quantifying the nature and extent of pH-dependent processes within the context of hydrologic transport.