Hydrologic channel routing predicts the changes in shape, magnitude, and velocity of a flood wave as it propagates down a river reach. The Muskingum Method models reach storage $(S)$ as a combination of prism storage (proportional to outflow $O$) and wedge storage (proportional to inflow-outflow difference $I - O$): $$S = K \cdot [X \cdot I + (1 - X) \cdot O]$$ Where $K$ is travel time of the flood wave through the reach, and $X$ is a dimensionless weighting factor $(0 \le X \le 0.5).$ The discharge at the downstream end at time step $t + \Delta t$ is computed via: $$O_2 = C_0 \cdot I_2 + C_1 \cdot I_1 + C_2 \cdot O_1$$ Where routing coefficients must satisfy $C_0 + C_1 + C_2 = 1:$ $$C_0 = \frac{-KX + 0.5\Delta t}{K(1-X) + 0.5\Delta t},$$ $$\quad C_1 = \frac{KX + 0.5\Delta t}{K(1-X) + 0.5\Delta t},$$ $$\quad C_2 = \frac{K(1-X) - 0.5\Delta t}{K(1-X) + 0.5\Delta t}$$ Managing downstream river discharge during emergency floodgate releases at major dams (such as Hirakud or Ukai Dam...