On the mathematics of storage routing

Some mathematical aspects of storage routing are investigated analytically and through numerical simulation. The minimum size of the time interval required to eliminate computed values at the beginning of the outflow hydrograph falling below the initial steady flow rate is given for two routing schemes. The stability behavior of a refined Muskingum scheme is explored; it is found that values of the weighting coefficient up to 1.0 may be used with appropriately specified time intervals. The concept of “relative” storage is analyzed and it is shown that it is unnecessary when the correct initial condition of the storage is considered. The classical best straight-line fit procedure between storage and weighted discharge is investigated. In an example case, it is demonstrated that this method of system identification is not reliable. The possibility of using discharge-dependent parameters is discussed.