About This Calculator

This calculator estimates river depth based on measured river width by using width to estimate discharge, and then using discharge to estimate depth. The functional form of these relationships was first described by Leopold and Maddock in 1953 (Link) as:

w = a * Q^b

and

d = c * Q^f

where w is river width, d is river depth, Q is discharge, and a, b, c, and f are coefficients.

In 2002, Moody and Troutman (Link), published a study which used field measurements to define coefficients for these relationships.

In this tool we allow the user to input (or measure) one or more river widths. The average width value is then used, with the coefficients from Moody and Troutman, to calculate the discharge, and then subsequently the depth of the river. The width range is determined using the minimum and maximum values of the width numbers provided. The depth uncertainty values are calculated using the minimum and maximum width values, and the coefficients corresponding to the edges of the 95% confidence interval from Moody and Troutman. The coefficients are chosen to provide the largest uncertainty range possible (i.e., the minimum width and corresponding coefficients are used to generate the smallest possible depth value, and vise versa for the maximum).

References:

Leopold, Luna Bergere, and Thomas Maddock. The hydraulic geometry of stream channels and some physiographic implications. Vol. 252. US Government Printing Office, 1953.

Moody, John A., and Brent M. Troutman. "Characterization of the spatial variability of channel morphology." Earth Surface Processes and Landforms: The Journal of the British Geomorphological Research Group 27.12 (2002): 1251-1266.

Please note that these depth estimates are highly generalized and may not be accurate for all river types or locations. Local factors such as geology, climate, and human modifications can influence the actual depth-width relationship.