River Time-of-Travel Model:

Michael Gene Waldon, Ph.D., P.E.

University of Southwestern Louisiana

Center for Louisiana Inland Water Studies


Following a spill of potentially toxic material into a river, rapid management decisions must be made in order to protect human health and safeguard threatened resources. Often, municipal and industrial water intakes must be shut down during spill passage. Water storage for drinking and fire protection are limited. Water control structures may also need to be operated, or other protective measures taken to avoid or minimize damage to resources, plant and animal communities, and ecosystems. In support of this decision making, knowledge of the time of arrival and time of passage of water-borne contaminants is vital.

A time-of-travel model (R-TOT) has been developed for the Mississippi River. Recently, a version of this program was extended to include Bayou Lafourche, a controlled distributary of the Mississippi River. More than a million people are provided drinking water from the Mississippi River below Baton Rouge, and a quarter million people obtain their drinking water from Bayou Lafourche. The model predicts time of arrival and duration of passage. Additionally, if quantity of material spilled is known, the model predicts peak concentration at any downstream location.

Model Development and Calibration

The R-TOT model uses a stream flow relationship to predict leading edge, peak, and trailing edge velocity at any rivermile location, and integrates velocity through the stream reach for travel time estimates. Based on an extension of the unit-concentration concept, peak concentration at a downstream rivermile location is predicted from stream flow, predicted duration, and mass of spilled material.

A simple expert advisor is built into the time-of-travel program. This program section provides the user with information classified into 3 categories: error, warning, and note. Error messages provide the user with specific information on erroneous input information. Warnings inform the user of possible input error conditions. Notes advise the user of potential model conditions which may affect the model appropriateness or accuracy. Help is also provided in stream flow estimation.

Results of thousands of fluorescent dye time-of-travel studies performed on streams throughout the U.S. are available from the U.S. Geological Survey, and other agencies. For the Mississippi River model, nine dye studies were applied in model calibration. The model has been tested using data from a number of Mississippi River spills, and is used in early warning of downstream users.

Current versions of R-TOT are written in the BASIC language, and are designed to provide a simple user interface and rapid computational results. The user enters the location of the spill, a downstream rivermile location of interest, and stream flow. Optionally, the user also enters the mass of the spill. Time of arrival, in hours after the spill, is predicted for the leading edge, peak, and trailing edge. If initial mass is entered, peak contaminant concentration is also predicted.

Current versions of the Mississippi River and Bayou Lafourche R-TOT models are available. Requests for copies may be addressed through the OSRADP.

Current Research

Under OSRADP sponsorship, a number of enhancements and improvements are being added to the R-TOT model. These include:

  1. Update and enhance current computer programs - source code and data within the program will be separated into a water body specific module and a separate generic code section. This will enhance the efficiency of developing applications for additional streams.
  2. Extend the programs to additional streams and identify data gaps and needs - data sources will be assessed to identify Louisiana streams for which appropriate data are currently available.
  3. Augment the program to project the complete time-concentration curve for a spill passing a downstream location - a computer program is being written which uses arrival times and peak concentration provided by the R-TOT program to predict the time-concentration curve for a more general class of spills.

Following completion of these tasks, efforts will be directed at training, technology transfer, and program distribution. In addition to the traditional publications and training workshops, support and distribution through the internet will also be established.

Project personnel

Michael Gene Waldon, Ph.D., P.E., waldon@usl.edu, is an Associate Professor-Research in the Center for Louisiana Inland Water Studies and Civil Engineering at USL. His research centers on water quality modeling and monitoring in inland and coastal streams and lakes.

Louis Landesman is a doctoral candidate in Biology at USL. He has experience in aquaculture, and has done fisheries related research in Southeast Asia. In addition to assisting in the development of spill models, he is presently doing work on resource recovery in natural wastewater treatment systems.

Sarah Kuchipudi is a graduate student pursuing her master's degree in environmental engineering within the department of civil engineering. Currently she is assisting in time-of-travel research studies and the development of spill models.

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Sponsored by OSRADP
The Louisiana Applied Oil Spill Research and Development Program/
Office of the Governor