Linear diffusion-wave channel routing using a discrete Hayami convolution method

Wang, Li; Wu, Ji; Elliot, William J.; Fiedler, Fritz; Lapin, Sergey

doi:10.1016/j.jhydrol.2013.11.046

Cited by 27 publications

(13 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, this sensitivity test illustrates the impact of both parameters on the propagation velocity and the shape of the flood peaks: increasing C Q values yield more rapidly propagating and higher flood peaks, whereas increasing D Q values lead to flattened peaks. These observations are in agreement with the literature (Moussa and Bocquillon, 1996;Yu et al, 2000;Chahinian et al, 2006;Charlier et al, 2009) and confirm that the lower the C Q and the higher the D Q , the lower the peak flow intensity and the transfer velocity. Figure 5a' and b' illustrate the simulation of lateral flows using the solution of the inverse problem when input and output signals are known.…”

Section: Sensitivity Analysissupporting

confidence: 93%

“…In most practical applications, the acceleration terms in the Saint-Venant equations can be neglected, and consequently by combining the differential continuity equation and the simplified momentum equation, the Saint-Venant system is reduced to a single parabolic equation: the diffusive wave equation (DWE;Moussa, 1996;Fan and Li, 2006;Wang et al, 2014). The two parameters of the equation, celerity and diffusivity, are usually taken as functions of the discharge.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection–diffusion equation

Cholet

Charlier²,

Moussa

et al. 2017

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

Abstract. The aim of this study is to present a framework that provides new ways to characterize the spatio-temporal variability of lateral exchanges for water flow and solute transport in a karst conduit network during flood events, treating both the diffusive wave equation and the advection–diffusion equation with the same mathematical approach, assuming uniform lateral flow and solute transport. A solution to the inverse problem for the advection–diffusion equations is then applied to data from two successive gauging stations to simulate flows and solute exchange dynamics after recharge. The study site is the karst conduit network of the Fourbanne aquifer in the French Jura Mountains, which includes two reaches characterizing the network from sinkhole to cave stream to the spring. The model is applied, after separation of the base from the flood components, on discharge and total dissolved solids (TDSs) in order to assess lateral flows and solute concentrations and compare them to help identify water origin. The results showed various lateral contributions in space – between the two reaches located in the unsaturated zone (R1), and in the zone that is both unsaturated and saturated (R2) – as well as in time, according to hydrological conditions. Globally, the two reaches show a distinct response to flood routing, with important lateral inflows on R1 and large outflows on R2. By combining these results with solute exchanges and the analysis of flood routing parameters distribution, we showed that lateral inflows on R1 are the addition of diffuse infiltration (observed whatever the hydrological conditions) and localized infiltration in the secondary conduit network (tributaries) in the unsaturated zone, except in extreme dry periods. On R2, despite inflows on the base component, lateral outflows are observed during floods. This pattern was attributed to the concept of reversal flows of conduit–matrix exchanges, inducing a complex water mixing effect in the saturated zone. From our results we build the functional scheme of the karst system. It demonstrates the impact of the saturated zone on matrix–conduit exchanges in this shallow phreatic aquifer and highlights the important role of the unsaturated zone on storage and transfer functions of the system.

show abstract

Section: Sensitivity Analysissupporting

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection–diffusion equation

Cholet

Charlier²,

Moussa

et al. 2017

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

show abstract

“…(7) (Singh, 2001(Singh, , 2002. The diffusive wave in the historic formulations (Cunge, 1969;Akan and Yen, 1981) or in more recent works (Rutschmann and Hager, 1996;Wang et al, 2006Wang et al, , 2014Swain and Sahoo, 2015) can thus be considered a higher-order approximation than the kinematic wave approximation (Katopodes, 1982;Zoppou and O'Neill, 1982;Daluz Vieira, 1983;Ferrick, 1985;Ponce, 1990). Both have been largely studied (since Wooding, 1965a, b;Singh, 1975;Lane and Woolhiser, 1977;Ponce, 1991) until more recently (Szymkiewicz and Gasiorowski, 2012;Yu and Duan, 2014) and have proven very useful for canal control algorithms or flood routing procedures, with lateral inflow , in rectangular channels (Keskin and Agiralioglu, 1997), for real-time forecast (Todini and Bossi, 1986), in lowland catchments , for overland flows (Pearson, 1989;Chua et al, 2008;Wong, 2010, 2011), on urban catchments (Gironás et al, 2009;Elga et al, 2015), for small catchments Chahinian et al, 2005;Charlier, 2007), for mountainous catchments , for medium-size catchments (Emmanuel et al, 2015) or tropical catchments , at the largest scale of the Amazon basin Paiva et al, 2013), for anthropogenic hillslopes (Hallema and Moussa, 2013), to address backwater effects , stormwater runoff on impervious surfaces (Singh, 1975;Pearson, 1989;Blandford and Meadows, 1990;, stream-aquifer interactions (Perkins and Koussis, 1996), or volume and mass conservatio...…”

Section: Water Flowmentioning

confidence: 99%

Determinants of modelling choices for 1-D free-surface flow and morphodynamics in hydrology and hydraulics: a review

Cheviron

Moussa²

2016

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

Abstract. This review paper investigates the determinants of modelling choices, for numerous applications of 1-D freesurface flow and morphodynamic equations in hydrology and hydraulics, across multiple spatiotemporal scales. We aim to characterize each case study by its signature composed of model refinement (Navier-Stokes: NS; Reynolds-averaged Navier-Stokes: RANS; Saint-Venant: SV; or approximations to Saint-Venant: ASV), spatiotemporal scales and subscales (domain length: L from 1 cm to 1000 km; temporal scale: T from 1 s to 1 year; flow depth: H from 1 mm to 10 m; spatial step for modelling: δL; temporal step: δT ), flow typology (Overland: O; High gradient: Hg; Bedforms: B; Fluvial: F), and dimensionless numbers (dimensionless time period T * , Reynolds number Re, Froude number Fr, slope S, inundation ratio z , Shields number θ ). The determinants of modelling choices are therefore sought in the interplay between flow characteristics and cross-scale and scale-independent views. The influence of spatiotemporal scales on modelling choices is first quantified through the expected correlation between increasing scales and decreasing model refinements (though modelling objectives also show through the chosen spatial and temporal subscales). Then flow typology appears a secondary but important determinant in the choice of model refinement. This finding is confirmed by the discriminating values of several dimensionless numbers, which prove preferential associations between model refinements and flow typologies. This review is intended to help modellers in positioning their choices with respect to the most frequent practices, within a generic, normative procedure possibly enriched by the community for a larger, comprehensive and updated image of modelling strategies.

show abstract

“…Recently, an analytical expression of the Green's function of linearized Saint Venant equations for shallow water waves was derived to analyse the propagation of a perturbation superposed to uniform flow (Di Cristo, Iervolino, & Vacca, 2012). Wang, Wu, Elliot, Fiedler, and Lapin (2014) analysed the characteristics of the kernel function for the Hayami convolution solution to the linear diffusionwave channel routing. Although there have been a few works proposing new types of function or modifications to get different representations of the linearized Saint Venant equations (Di Cristo et al, 2012;Dooge et al, 1987;Strupczewski & Dooge, 1995, 1996Wang et al, 2014), the issues solving the dilemma of assigning adequate parameters in practical applications and the treatment of multiple inputs from lateral flow along the main channel are still lacking.…”

Section: Introductionmentioning

confidence: 99%

Refinement of the channel response system by considering time‐varying parameters for flood prediction

Huang

Lee

2020

Hydrological Processes

View full text Add to dashboard Cite

Impulse response functions derived from different types of flood wave equations (simplified shallow water equations) are continuously developed to conduct the linear channel routing (LCR), which is based on the linearized Saint Venant equation and has been widely applied to avoid any possibility of numerical instability. The impulse response function proposed by Dooge, Napiórkowski, and Strupczewski (1987) and derived from the dynamic wave equation with complete force terms has been acknowledged as a classic work to establish a good physical interpretation for the LCR model; however, the flexibility of altering the shape of impulse response still needs to be improved. Based on the concept of this work, this study intends to introduce the time‐varying parameters in the model, so the values of parameters can be adjusted according to the inflow condition, flood stage, and the cross‐sectional shape. Moreover, an integrated routing procedure is proposed to formulate the impulse response function for lateral‐flow inputs and then to connect multiple inputs from subwatersheds or alongside the main channel with the impulse response function of each channel segment to reflect the spatial variation of hydraulic characteristics among different segments. In the discussion of this article, the impulse response function is analysed to show its sensitivity to hydraulic variables with spatial and temporary variations. Flood‐event simulations of a studied watershed are also provided to verify the applicability of the proposed channel routing system.

show abstract

Linear diffusion-wave channel routing using a discrete Hayami convolution method

Cited by 27 publications

References 25 publications

Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection–diffusion equation

Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection–diffusion equation

Determinants of modelling choices for 1-D free-surface flow and morphodynamics in hydrology and hydraulics: a review

Refinement of the channel response system by considering time‐varying parameters for flood prediction

Contact Info

Product

Resources

About