Reply to the Discussion of “Assessment and review of the hydraulics of storage flood routing 70 years after the presentation of the Muskingum method” by M. Perumal

Koussis, Antonis D.

doi:10.1080/02626667.2010.491261

Cited by 9 publications

(10 citation statements)

References 41 publications

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“…The accuracy of the flood wave model is important too, and, in this respect, the St. Venant equations are superior to storage routing models. However, the latter are efficient, robust and mathematically simple diffusion-wave equivalents with wide applicability range (e.g., Reggiani et al 2014) that can simulate the propagation of flood waves in streams using even sparse hydro-morphological data (Koussis 2009(Koussis , 2010a.…”

Section: Reverse Routing Of Flood Wavesmentioning

confidence: 99%

“…The reservoir releases q(0, t) must be controlled -to the extent feasible-so that the flow at x = L resulting from the flood wave propagation does not exceed a threshold: q(L, t) ≤ q alarm . The discharge-depth correspondence is not unique in transient flow, it depends on the flow dynamics; however, the q-y threshold relationship may be determined approximately through the Jones-Thomas rating formula q = q o [1 + (<c k >S o ) -1 ∂y/∂t] 1/2 by evaluating at-a-section records of water stage or depth (Henderson 1966, Koussis 2010a; q o is a nominal uniform flow rate, in as much as a prismatic channel must be substituted for a natural stream reach to define q o .…”

Section: Downloaded By [Rutgers University] At 08:29 15 August 2015mentioning

confidence: 99%

“…With appropriate parameters, storage routing models are upstream-controlled CDE substitutes (Koussis 2009(Koussis , 2010a, and hence incapable of accommodating a downstream boundary condition. So, storage routing models account for wave diffusion, but integration must proceed from upstream to downstream.…”

Section: Storage Routing Modelsmentioning

confidence: 99%

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Reverse flood and pollution routing with the lag-and-route model

Koussis

Mazi

2016

Hydrological Sciences Journal

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Section: Reverse Routing Of Flood Wavesmentioning

confidence: 99%

Section: Downloaded By [Rutgers University] At 08:29 15 August 2015mentioning

confidence: 99%

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Reverse flood and pollution routing with the lag-and-route model

Koussis

Mazi

2016

Hydrological Sciences Journal

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“…Hence, a numerical scheme that originates in the KW equation yet allows for numerical diffusion that matches the physical diffusion constitutes a promising basis for reversing the wave propagation computationally. First Cunge (1969) analysed such a scheme for flood routing; Koussis (1975Koussis ( , 1978Koussis ( , 2009Koussis ( , 2010) also linked storage routing to the diffusion-wave model. The good performance of Matched Artificial Diffusion (MAD) schemes in forward routing has been verified in flood [e.g., Koussis, 1975;Weinmann, 1977;Perkins and Koussis, 1996] and in pollution routing in streams Koussis et al, 1990).…”

Section: Formulation Of the Reverse Routing Problemmentioning

confidence: 99%

Reverse flood routing with the inverted Muskingum storage routing scheme

Koussis

Mazi

Lykoudis

et al. 2012

Nat. Hazards Earth Syst. Sci.

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Abstract. This work treats reverse flood routing aiming at signal identification: inflows are inferred from observed outflows by orienting the Muskingum scheme against the wave propagation direction. Routing against the wave propagation is an ill-posed, inverse problem (small errors amplify, leading to large spurious responses); therefore, the reverse solution must be smoothness-constrained towards stability and uniqueness (regularised). Theoretical constrains on the coefficients of the reverse routing scheme assist in error control, but optimal grids are derived by numerical experimentation. Exact solutions of the convection-diffusion equation, for a single and a composite wave, are reverse-routed and in both instances the wave is backtracked well for a range of grid parameters. In the arduous test of a square pulse, the result is comparable to those of more complex methods. Seeding outflow data with random errors enhances instability; to cope with the spurious oscillations, the reversed solution is conditioned by smoothing via low-pass filtering or optimisation. Good-quality inflow hydrographs are recovered with either smoothing treatment, yet the computationally demanding optimisation is superior. Finally, the reverse Muskingum routing method is compared to a reverse-solution method of the St. Venant equations of flood wave motion and is found to perform equally well, at a fraction of the computing effort. This study leads us to conclude that the efficiently attained good inflow identification rests on the simplicity of the Muskingum reverse routing scheme that endows it with numerical robustness. Character of the reverse routing problemThe forward calculation of the propagation of a flood wave in an open channel, known as flood routing, is a problem of applied hydrology that has been studied extensively. The relevant methods of solution, all within the framework of one-dimensional free-surface flow, span the spectrum from numerical solutions of the hydraulic equations of Barré de Saint-Venant to storage routing models of the diffusion-wave type (Koussis, 2009), and have utility in such applications as flood warning, river training and urban storm drainage design. On occasion, however, flood related questions are posed in the reverse sense, such as, e.g., in signal identification (hydrologic forensics): "Which inflow created the outflow observed at cross-section X, or the observed flood profile along reach Y?" We may be also interested in operating a reservoir (optimal outflow control) to minimise downstream flood damage (Szöllósi -Nagy, 1987). Bruen and Dooge (2007) point out that reliable solution techniques of the latter problem would be valuable in handling of urban flash flooding.Yet reverse routing is an inverse problem and as such not well posed. A problem is well-posed when its solution exists, is unique and stable (Bronstein and Semendjajew, 1964), that is, small changes in the initial condition (forcing) cause small changes in the response. The reverse routing solution clearly exists, but must be co...

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“…In hourly simulations, routing phenomena are also represented, by re-solving the problem from upstream to downstream. In the case of relatively 15 steep channels, a kinematic-wave model is employed, implementing a temporal transfer of the hydrograph from the upstream to the downstream node, while in the case of mild slopes, a Muskingum diffusive-wave scheme is employed, implementing a non-linear transformation of the input hydrograph (Koussis, 2009(Koussis, , 2010). …”

Section: Hydrogeios Modelling Frameworkmentioning

confidence: 99%