Convex

The Soils Conservation Service (U.S Department of Agriculture, 1971) developed a routing algorithm known as the convex method. It is similar to the Muskingum method in that it involves inflow and outflow hydrograph relationships. Unlike the Muskingum method, the continuity equation is not directly involved. The routing equation is:

Where C is a constant between zero (0) and 1. It is estimated from

Where v is the average flow velocity of the reach. Typically, it is computed at the bank full discharge or 75% of the peak hydrograph flow rate. The determination of average velocity appears to be somewhat subjective (engineering judgment). The value of C is usually approximated at 2x, where x is the Muskingum x. The convex method is somewhat sensitive to the routing interval. The routing interval can be computed from:

where is the desired time interval. Some additional guidelines are that the ratio should be a close to unity as possible and that should be limited to tp/5.

This method is slowly falling out of favor, the SCS in 1983 replaced the method in its TR-20 application with a method knows as Att-Kin.