Stream tracer analysis, extrapolation, and modeling
Prediction of downstream arrival and passage times, and peak concentration for a contaminant spill in a river is often of crucial importance for environmental resource managers. Protection of critical habitats for fish and wildlife requires timely actions. Often water supply systems have less than a day's supply of water in storage. Drinking water and industrial water intakes can usually be shut-down for a limited period to allow spill passage, but lengthy shut-downs may result in interruption of drinking water supply, reduced fire protection, interruption of industrial processes, and increased liability for the responsible party. By examining dye tracer data collected by the USGS from 18 Louisiana streams, we extend the distribution number concept beyond the Lower Mississippi River where it was initially applied. Discharge in these streams at the time of study by the USGS ranged from 0.071 m3s-1 to 22,400 m3s-1. A method for prediction of spill duration and peak concentration in streams with limited available data is also developed. It is also observed that, at the time that a point, x, is reached by the leading edge of a tracer cloud, the location of the trailing edge is roughly fixed and insensitive to stream discharge. This implies that the longitudinal dispersion coefficient is proportional to velocity in the advection-dispersion spill model. This also implies that at any fixed location the trailing edge velocity is a constant fraction of the leading edge velocity, and is independent of stream discharge. Application of these methods to a hypothetical spill is discussed.
The Mississippi River is the source of drinking water for more than I million Louisiana residents. The river also is used for transportation of hazardous chemicals and petroleum products, and is the receiving stream for wastewater effluents from numerous industries and municipalities. To minimize the public's risk from contaminant spills and accidental discharges, drinking water providers need timely warning of approaching contaminants. Based on a modified plug-flow (MPF) formulation, a time-of-travel model has been developed to provide projections of the time of arrival, peak arrival time, time of passage, and duration of contaminant spills on the Mississippi River. Estimates of the peak concentrations of contaminants passing downstream locations are calculated from spill mass, discharge, and calculated duration. The model used for this research was calibrated using dye time-of-travel studies. The primary objective of this model is to facilitate the timely warning of drinking water providers. Additionally, this model may be of value in other water quality management applications, including contingency planning, impact assessment, monitoring, enforcement, and surveillance. KEYWORDS: time-of-travel, spill modeling, Mississippi River, modified plug-flow model, unit concentration, dye tracer studies.
For decades, numerous tracer studies have been performed in streams and other waterbodies throughout the world. Typically, these studies involve slug injection of a dye or other soluble tracer at an upstream site, and observation of passage of the tracer at one or more downstream locations by taking discrete water samples or measurements. For applications of tracer study results to spill contingency planning, it is desirable to estimate for these fixed locations the peak tracer concentration and time of occurrence of the peak from each series of measured concentrations at specific sampling times. The author is unaware of any publication within the literature on stream tracer data analysis which describes a simple algorithm for interpolation of the tracer peak. In the past when analyzing newly obtained tracer data, the author has been frustrated by the need to re-derive a consistent method for estimation of peak time and concentration. This note was developed to provide a documented procedure for peak interpolation and to provide a clear explanation of the procedure. The method proposed here does appear to combine simplicity with reasonable results. In specific cases, other interpolation methods may be superior to the method proposed here. This proposed method, or alternative algorithmic methods are not a replacement for judgement, and every dataset should be examined by the analyst. The author welcomes any suggestions of alternatives or improvements of this proposed method. Comments may be submitted through the Researchgate.net page for this note. A small Excel spreadsheet file named Agunwamba-1997-PeakCalc is also available for download from Researchgate.net under the ”Linked Data” selection for this note. That spreadsheet calculates the results presented in this note.