Estimate depth from discharge and hydraulic geometry coefficients

Uses the relationship d = c × Qᶠ (parameter names and definitions as in Leopold and Maddock, 1953; default values for c and f as in Raymond et al. 2012)

Usage

calc_depth(Q, c = 0.409, f = 0.294)

Arguments

Q

Discharge (m^3 s^-1).

c

Coefficient representing depth at unit discharge (usually m).

f

Exponent in depth-discharge relation (unitless).

Value

D, stream depth, in the same units as c.

References

Raymond, Peter A., Christopher J. Zappa, David Butman, Thomas L. Bott, Jody Potter, Patrick Mulholland, Andrew E. Laursen, William H. McDowell, and Denis Newbold. Scaling the gas transfer velocity and hydraulic geometry in streams and small rivers. Limnology & Oceanography: Fluids & Environments 2 (2012): 41-53.

Leopold, L.B., and Thomas Maddock Jr. The Hydraulic Geometry of Stream Channels and Some Physiographic Implications. Report. Professional Paper, 1953. USGS Publications Warehouse. https://pubs.er.usgs.gov/publication/pp252.

Examples

Qs <- seq(1,9,2)
calc_depth(Q=Qs)
#> [1] 0.4090000 0.5649330 0.6564785 0.7247398 0.7803162
calc_depth(Q=Qs, f=0.4)
#> [1] 0.4090000 0.6347048 0.7785945 0.8907637 0.9849639