In the mid-1970s, I was pursuing a Ph.D. at Colorado State University, and I was fortunate to be at the right time at the right place. There, I had the honor and pleasure of close association with a select crop of students from all over the world. One of these students was Fred Theurer, who, in 1975, completed a Ph.D. under the supervision of Dr. Everett Richardson, "Rich" to his many students.

After graduation, Fred returned to his employment with the Natural Resources Conservation Service, the former Soil Conservation Service (SCS), in Washington, D.C. He told his bosses that the convex method was no good, and that it had to be replaced by a better routing tool, still to be developed. Indeed, the convex method, developed by SCS in the mid-1950s, was a linear kinematic wave model featuring built-in, uncontrolled numerical diffusion. In practice, this meant that it lacked consistency, i.e., that a routed hydrograph could not be reproduced by substepping the reach length. In other words, the convex method was grid-dependent; two choices for grid size (time step and space step) would invariably give two different answers.

Seeking a proper replacement, in the late 1970s, SCS developed the Att-Kin model, which stands for "Attenuation-Kinematic." The Att-Kin method divided the routing into two sequential steps: the first designed to provide reservoir attenuation, and the second to provide pure kinematic translation. While the model fared well in tests designed to prove consistency, it was not without its pitfalls. The matter was clarified in the 1990s, when the Muskingum-Cunge method was further developed and tested.1 It is now generally agreed that the Muskingum-Cunge method is the only hydrologic channel routing method that is stable, convergent, and consistent (i.e., grid independent), when used within its recommended parameter ranges. This is because the Muskingum-Cunge method simulates not the kinematic wave model, but the diffusion wave model.2

1 Ponce, V. M., A. K. Lohani, and C. Scheyhing. 1996. Analytical verification of Muskingum-Cunge routing. Journal of Hydrology, 174(1996), 235-241.
2 Ponce, V. M., and D. B. Simons. 1977. Shallow wave propagation in open channel flow. Journal of the Hydraulics Division, ASCE, 103(HY12), 1461-1476.

The Crooked river upstream of Elliott Lane Bridge, Prineville, Oregon.