I believe hydrologic models like Muskingum method do not have major benefits over full dynamic wave equation (St. Vernant) in terms of prediction accuracy, as they are developed due to the need for simplified routing technique to be applied for large watershed (hydrologic) model. Especially, Muskingum method ignores the momentum equation, and solely is solely based on the continuity equation by considering peak attenuation (diffusive wave) caused by storage effects.

The only advantage is simplicity  and practicality on the account of ignoring other terms of the full dynamic model.

Muskingum-Cunge has comparable accuracy to other hydrological routing models such as PULS or Kinematic Wave. The disadvantage of hydrological routing appears when the free surface becomes too steep and solution is characterized by a moving hydraulic bore. In such conditions, a St. Venant equation solver is recommended, with a non-linear scheme to capture well bore celerity values even when Courant numbers are low.

other advantage of M-C method is that its coefficients are physically based (Cunge,

1969) and the numerical solution is independent of  time and space  intervals when

the latter are  selected within the spatial and temporal resolution criteria  (Ponce, 1981 ; Ponce and Theurer, 1982).

In many existing flood forecasting systems M-C provides reasonable estimates of the routing time and maximum discharges within limited computational time if the flow remains in the main river channel.

If the objective is to forecast water levels and interactions with inundation plains in presence of hydraulic infrastructures an usteady flow solution must be sought.

Storage routing models (Muskingum, Kalinin-Miljukov, Lag & Route etc.; see, e.g., Dooge

1973) are efficient, robust and mathematically simple diffusion wave equivalents with wide applicability range that can simulate the propagation of flood waves in streams using even sparse hydro-morphological data (Koussis 2009, 2010a). Storage routing models are akin to the Convection-Diffusion Equation (CDE), and thus approximate the hydraulic equations well, they have been field-verified and are often used in rainfall-runoff models. The CDE is superior to the kinematic wave model and to the Puls model, but not as powerful as the St Venant equations, which, however, demand dense hydro-morphological data.

The main features of wave propagation are (nonlinear) translation and attenuation, the latter caused by the spreading of the wave due to the pressure gradient (hydraulic diffusion). With appropriate parameters (hydraulically estimated -e.g., Cunge, 1969; Koussis, 1978- and, better, calibrated against observations), storage routing models are upstream-controlled CDE substitutes, hence incapable of accommodating a downstream boundary condition. Thus, storage routing models account for wave diffusion, but integration must proceed from upstream to downstream. If possible, non-linearity should be accounted for in the wave celerity.

The single-reach Muskingum model is prone to causing unphysical results in long reaches (large negative outflow values and distorted hydrograph shape) . However, by dividing the reach in sub-reaches to which the single-reach Muskingum model is applied sequentially with adjusted parameters, specifically, smaller values of the weighting factor due to shorter sub-reaches; the multi-reach Muskingum model essentially rivals the accuracy of the Kalinin-Miljukov model using fewer elements (spurious oscillations remain, but are small). The Lag & Route model is also capable and very efficient.

Transient-flow (looped) rating curves can be also coupled with storage routing (implicit in the Kalinin-Miljukov model) via consideration of, e.g., the Jones-Thomas approximation (Koussis, 2010b).

REFERENCES

Cunge, J. A. (1969) On the subject of a flood propagation computation method (Muskingum method). J. Hydraul. Res. 7(2), 205–230.

Dooge, J.C.I., 1973. Linear theory of hydrologic systems. Washington DC: Agricultural Research Service, US Dept. Agriculture, Tech. Bull. no. 1468.

Koussis, A.D., 1978. Theoretical estimations of flood routing parameters. Journal of the Hydraulics Division ASCE, 104 (HY1), 109–115.

Koussis, A.D., 2009. An assessment review of the hydraulics of storage flood routing 70 years after the presentation of the Muskingum method. Hydrological Sciences Journal, 54

(1), 43–61. doi:10.1623/hysj.54.1.43

Koussis, A.D., 2010a. Reply to the Discussion of “An assessment review of the hydraulics of storage flood routing 70 years after the presentation of the Muskingum method” by M. Perumal. Hydrological Sciences Journal, 55 (8), 1431–1441. doi:10.1080/02626667.2010.491261

Koussis, A.D., 2010b. Comment on “A praxis-oriented perspective of streamflow inference from stage observations – the method of Dottori et al. (2009) and the alternative of the Jones Formula, with the kinematic wave celerity computed on the looped rating curve”. Hydrology and Earth Systems Sciences, 14, 1093–1097. doi:10.5194/hess-14-1093-2010

 Thanks all for your answer.. It really helped me