Storage Routing links model the storage and movement of water through a length of a river (drainage link) using a hydrologic routing method. They can represent the travel time of water through a reach, the attenuation of flow rates due to channel shape, and roughness and reach processes.
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Extending the method for variable K
For the convenience of the model users (it being easier to think in terms of the wave travel times) MUSICX defines a variable K which uses the wave travel time interpretation. Combined with the assumption that the flow rate in the reach is represented by the index flow q:
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The criterion expressed in Equation 18 is enforced is enforced as follows:
- For the power function with m=1, the function K(
) is in fact a fixed value of K and the original version of the Muskingum method is being used. A check is made to enforce the requirement that K ≤ dt/x; or - For the power function with m≠1 (and x>0), the value of K() can range between zero and infinity, presenting a potential stability problem. The flow/storage relationship must be modified to avoid this problem and the point at which this should be done is at the largest allowed slope dt/x. This gives:
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Reiterating the section on "Form of the Routing Equation", by choosing the appropriate functional form and appropriate values of m and x, the following hydrologic routing methods can be replicated:
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Clark, M.P. and Kavetski, D. (2010) Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes, Water Resources Research, 46, W10510, doi:10.1029/2009WR0088942009WR008896.
Koussis, A.D. (1978) Theoretical estimation of flood routing parameters. J. Hydraul. Div. Am. Soc. Civ. Eng., 104(HY1): 109-115.
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Laurenson, E.M. (1959) Storage analysis and flood routing in long rivers. Journal of Geophysical Research, 64(12): 2423-2431, doi:10.1029/JZ064i012p02423.
Linsley, R.K., Kohler, M.A. and Paulhus, J.L.H. (1949) Applied Hydrology. McGraw Hill, New York.
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Perumal, M. (2010) Discussion of "Assessment and review of the hydraulics of storage flood routing 70 years after the presentation of the Muskingum method". Hydrological Sciences Journal, 55(8): 1427-1430, doi:10.1080/02626667.2010.491260.
Bibliography
Gill, M.A. (1978) Flood routing by the Muskingum method. Journal of Hydrology, 36: 353-363.
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