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U.S. GEOLOGICAL SURVEY
Scientific Investigation Report 2008–5075

Modeling Water-Surface Elevations and Virtual Shorelines for the Colorado River in Grand Canyon, Arizona

Prepared in cooperation with the
GRAND CANYON MONITORING AND RESEARCH CENTER

By Christopher S. Magirl, Michael J. Breedlove, Robert H. Webb, and Peter G. Griffiths

Abstract

Using widely-available software intended for modeling rivers, a new one-dimensional hydraulic model was developed for the Colorado River through Grand Canyon from Lees Ferry to Diamond Creek. Solving one-dimensional equations of energy and continuity, the model predicts stage for a known steady-state discharge at specific locations, or cross sections, along the river corridor. This model uses 2,680 cross sections built with high-resolution digital topography of ground locations away from the river flowing at a discharge of 227 m³/s; synthetic bathymetry was created for topography submerged below the 227 m³/s water surface. The synthetic bathymetry was created by adjusting the water depth at each cross section up or down until the model’s predicted water-surface elevation closely matched a known water surface. This approach is unorthodox and offers a technique to construct one-dimensional hydraulic models of bedrock-controlled rivers where bathymetric data have not been collected. An analysis of this modeling approach shows that while effective in enabling a useful model, the synthetic bathymetry can differ from the actual bathymetry. The known water-surface profile was measured using elevation data collected in 2000 and 2002, and the model can simulate discharges up to 5,900 m³/s. In addition to the hydraulic model, GIS-based techniques were used to estimate virtual shorelines and construct inundation maps.

The error of the hydraulic model in predicting stage is within 0.4 m for discharges less than 1,300 m³/s. Between 1,300-2,500 m³/s, the model accuracy is about 1.0 m, and for discharges between 2,500-5,900 m³/s, the model accuracy is on the order of 1.5 m.

In the absence of large floods on the flow-regulated Colorado River in Grand Canyon, the new hydraulic model and the accompanying inundation maps are a useful resource for researchers interested in water depths, shorelines, and stage-discharge curves for flows within the river corridor with 2002 topographic conditions.

Contents

Abstract
Introduction
Study Area, Place Names, and Units
Water-Surface Profile Analysis with the Standard Step Method
Hydraulic Model Construction
Estimating Model Accuracy
Virtual Shoreline Construction
Results
Future Model Adaptations
Conclusions
References Cited

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Download the report (PDF, 3.6 MB)

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Send questions or comments about this report to the author, C.S. Magirl, (520) 670-6671 X267.