Practical application of numerical modelling to overbank flows in a compound river channel

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1 Practical application of numerical moelling to overbank flows in a compoun river channel Moreta, P.M. Lecturer, School of Computing an Engineering, University of West Lonon, Ealing, W5 5RF Lonon, UK Rotimi A.J. PhD stuent, School of Computing an Engineering, University of West Lonon, Ealing, W5 5RF Lonon, UK Kawuwa A.S. PhD stuent, Faculty of Engineering an Physical Sciences, University of Surrey, Guilfor, GU 7XH, UK López-Querol, S. Department of Civil, Environmental an Geomatic Engineering, University College of Lonon, Ealing, W5 5RF Lonon, UK, s.lopez-querol@ucl.ac.uk ABSTRACT: Compoun sections forme by a river channel an flooplains, are use in river channels esign to provie aitional conveyance capacity uring high ischarge perios. When the overbank flow occurs, the flow in the river channel is affecte by the momentum transfer between the main channel an flooplains, which moifies water levels an velocity istributions given by traitional methos. One-imensional (D) moels using the Single Channel Metho (SCM) an the Divie Channel metho (DCM) have been proven to be not accurate enough in compoun channel flows. New more avance moels have been evelope in orer to accurately estimate ischarge flows an epth-average velocity istributions. The quasi-two imensional moel Conveyance Estimation System (CES) estimates ischarges an velocities in a cross-section base on the Lateral Distribution Metho (LDM). Two-imensional (D) moelling solves the epth-average Navier-Stokes equations in a iscretize reach of a river. In this work, publishe fiel measurements of the (UK) are analyze via D, CES an D moelling, in orer to fin a practical solution to give goo preictions of water levels an velocity istributions in overbank flows in river channels with flooplains. The results show that D moelling combine with CES gives reasonable accurate values an is a complementary tool for avance D moels in real conitions. INTRODUCTION Worl population growth has graually resulte in increase human settlements, evelopments an activities aroun the flooplains of rivers which lea to isastrous effects uring flooing of natural rivers. River floos result in huge losses in human lives an economic losses. A thir of the worl s losses ue to natural isasters is cause by floo isasters, flooing also accounts for half the loss of life with analyses of the tren showing that this figures have significantly increase (Berz, 000). Accurate estimation of flow rate in channels is of enormous significance for floo prevention. Flooing occurs when the quantity of water flowing along a channel is higher than its carrying capacity. Hence the nee for accurate preiction of river ischarges uring floo conitions to mitigate the impact, thereby saving lives an properties has rawn greater attention of researchers an engineers in recent times. There are numerous methos an approaches that have been employe in recent times to facilitate accurate estimation an preiction of ischarge, conveyance an water surface level of rivers uring overbank flow. Previous work in compoun open channels has been mainly focuse on moelling uniform flow conitions an compare with experimental ata in laboratory flumes. Shiono an Knight (99) evelope a quasi-two imensional moel (base on lateral istribution metho) to moel conveyance in compoun cross sections. This approach has been use in the Environment Agency s Conveyance Estimation System (CES). Mc Gahey et al (008) emonstrate the ability of CES to accurately estimate lateral velocity istribution an ischarges assuming uniform conitions in real rivers. The aim of this work is to valiate the application of one-imensional Lateral Distribution Metho (LDM) via the use of Conveyance Estimation System (CES) which is a commercial software for the estimation of ischarge/conveyance capacity of compoun channels an compare the results to that of the traitional one-imensional methos, Single Channel Metho (SCM) an Divie Channel

2 Metho (DCM) using Hyrological Engineering Centre River Analysis System (HEC-RAS) software. The two-imensional SRH-D (Seimentation an River Hyraulics Dimensional) moel is also use for comparison of velocity istributions. The ata that were utilize for successfully carrying out the simulation in this research work were obtaine from the previous work of Martin an Myers (99), Myers an Lyness (994); Lyness an Myers (994a) an Lyness an Myers (994b), conucte on river Main, Northern Irelan. The aim of the project was achieve by simulation of the stuy reach of river Main (which is a reconstructe prototype river reach in Northern Irelan, Unite Kingom) on both CES an HEC-RAS computational moelling software an the two-imensional coe SRHD. The three coes have been applie by using the same bounary conitions, cross-section ata an flow parameters in orer to have the same criteria for comparison an valiation. Finally the water surface level an velocity istribution results obtaine from this software were analyse an compare with available fiel ata to valiate an verify the results. A great effort has been mae over the last ecaes to improve calculation of water levels an velocities in real rivers by the use of D an 3D moelling. However some important uncertainties are still unsolve. In this context, an accurate D moel easy to calibrate an with the support of the CES can be an improve tool for comparison. LITERATURE REVIEW In compoun channels, the velocity graient between the main channel an flooplain flows generates shear forces in the main channel-flooplain interfaces. Sellin (964) presente photographic evience of the bank horizontal vortices acting along the interface an together with Zheleznyakov (97) emonstrate a ecrease in the main channel ischarge after overbank flow occurs, only partially compensate by some ischarge increase on the flooplain. The physics of floo hyraulics has been wiely stuie uring the last 30 years (Knight an Shiono, 996; Sellin, 996 an Wormleaton et al 004), concluing in a eep knowlege an unerstaning of the phenomenon involve. Commercial moels, such as HEC-RAS an MIKE, use calculation methos like SCM an DCM. The SCM consiers the same velocity for the whole section. The DCM separates the cross-section into areas of ifferent flow characteristics, such as the main channel an flooplains. Wormleaton et al. (98) emonstrate that the SCM unerestimates the conveyance capacity an the DCM overestimates compoun channel. In the following years, several researchers presente some improve methos for compoun channel flow estimation, Wormleaton an Merret (990) propose a simple moification that improves the DCM estimation an the DCM was empirically correcte by Ackers (99). An alternative an more avance metho was evelope in those years, the lateral istribution metho (LDM) formulate by Wark et al. (990) an the metho by Shiono an Knight (99). These two methos are base on the same equations an calculate the lateral velocity istribution in the cross section, like a quasi-d moel. This paper aims to iscuss refinements in D moelling that are able to cope with such complexities in a straightforwar way. The research focuses on the preiction of the velocity istribution across the river. While the free surface profile is compute reasonably well by D numerical moels, the same oes not hol for the velocities unless the appropriate term at the interface is use. The methoology presente herein uses the HEC-RAS an the CES in orer to improve D numerical moelling. The interaction between the main channel an the flooplain is moelle by using the lateral istribution of velocities given by CES. This metho is applie to previously publishe fiel ata from. Moreover, the results given by wiely use D moels (SRHD), will be use for comparison. 3 RIVER MAIN FIELD DATASET The river ata uner stuy consist of a reach of the river Main, in Northern Irelan, which has some length of its reach reconstructe an realigne (between 98 an 986). This reach of the river comprises a trapezoial compoun channel with a centralise eep main channel borere by one or two sie berms. Numerous number of research works have been carrie out on this river reach (Martin an Myers, 99; Myers an Lyness, 994; Lyness an Myers, 994; Defra /Environmental Agency, 003), with the aim of having a better unerstaning of the hyraulic behaviour of two-stage waterways. The measure stuy reach is foun to have a longituinal length of 800 meters from upstream (section 4) to ownstream (section 6) with an average longituinal of or :50 with floo plains slope towars the main channel having a graient of :5. It

3 is ivie into nine cross sections, situate at equal intervals of 00 meters apart. The plan view, upstream an the ownstream cross sections of the river Main reach uner investigation are shown in Figures an. view of the compoun river channel an the materials in flooplains an river banks. Table. Main geometric an hyraulic parameters in the stuy reach. Upstream s4 Downstream s06 Long.. Be slope Bankfull flow 0. - Manning n (m.c.) Manning n (f.p.) Be with.. Lateral slope (f.p.) :5 :0 Figure. plan view. Location of cross-sections from upstream (s4) to ownstream (s6). Cross sections Sect4-upstream Sect4-comparison Sec6-ownstream Figure. Upstream (ote) an ownstream (full line) cross sections, numbers 4 an 6 respectively, of reach of stuy. The river material comprises of a very coarse gravel with a D50 size ranging between 00 an 00 mm. Quarrie stones of up to 0.5 tonne in weight an having a size up to m in iameter are use as a rip-rap to protect the sie slopes of the main channel. The grass an wee that cover the berms are maintaine regularly by keeping them short (Martin an Myers 99). Figure 3 shows a cross-sectional Figure 3. : river channel an flooplains. Main channel is covere by cobbles, with meium rip-rap stones for the bank slopes an flooplains with natural grass. Some typical water surface profiles measurements obtaine using steay flow computation for the ischarges of 0.5, 0. an 5.3 m3/s were shown by Myers an Lyness 994 an reprouce in figures 5 an 6 in the next section. The 0.5 m3/s ischarge correspons to an inbank flow an the two higher ischarges (0. an 5.3 m3/s) are overbank flows, the lower uner the top flooplain level an the higher full covering the flooplains. Martin an Myers (99), Lyness an Myers (994b) an Lyness et al (987) inicate that SCM unerestimate ischarges, while that of DCM overestimates it, revealing there is an exchange of momentum between flooplains an main channel, in overbank flow situation. Table. Geometry in sections. Upstream S4 Downstream S06 Y (m) Z (m) Y (m) Z (m)

4 Roughness Manning s n coefficients were estimate by using uniform flow conitions in upstream cross-section 4 by Martin an Myers (99) an Myers an Lyness (994a). These stuies foun that using Manning s formula the inbank roughness ecrease between n = for low epths an n = for bankfull. However the Manning s n for the gravels/cobbles in the varies between n = , an the Manning s n for the riprap on the bank is higher than n = This means that as the water epth increases the main channel mean roughness shoul be greater, which oes not fit the estimation of Manning s roughness by using the mean slope an fiel rating curves. Table 3. Slope an istance between cross-sections. Section Distance Be Level Be slope F Figure 4. profile an water level profiles measure in fielworks for inbank (0.5), an overbank (0. an 50.3) flows (after Myers an Lyness 994). 4 NUMERICAL MODELS Q0.5 ata Q0. ata Q50.3 ata In the next subsections the moels use in the present work are briefly escri. The D HEC-RAS moel (USACE, 008), the CES moel (Environment Agency, 004), an the SRHD (Lai, 008) 4. HEC-RAS D Moel The results obtaine with D moelling base on the energy or Bernoulli equation (HEC-RAS) are compare here with the fiel measurements in terms of free surface profile an velocity istributions. The DCM an SCM were use by applying the HEC- RAS moel, as well as CES in backwater computation moe. Uner steay conitions, the one imensional hyraulic equations to be solve are the conservation of mass: Q = 0 an the conservation of energy: ( Q A) H + ga ( ) = 0 + ga S o S f () () where A = cross-sectional area normal to the flow; Q = ischarge; g = acceleration ue to gravity; H = elevation of the water surface above a specifie atum, also calle stage; S o = slope; S f = energy slope; x = longituinal coorinate. Equations () an () are solve using the well known four-point implicit box finite ifference scheme (USACE, 008). HEC-RAS solves these equations using the stanar step metho as follows: α V V Y + Z + α = Y + Z + + h e g g (3) where Y i = epth of water at cross-sections; Z i = elevation of the ; V i = average velocities at crosssections; α i = velocity weighting coefficients; h e = energy hea loss. The energy hea loss can be calculate multiplying the length between the crosssections times the friction slope, S f. HEC-RAS uses two methos for computing the value of S f, epening on whether the cross-section is treate as a unique compoun section (SCM) or it is ivie in sub-sections (DCM). The equations for the SCM are: Q S f = (4) K AR 3 K = (5) n

5 where R = hyraulic raius of the whole section, K = hyraulic conveyance, an n = Manning s roughness coefficient for the whole section. The DCM ivies the cross-section into a main channel an two lateral flooplains applying eq. (3) for each subivision an calculating the friction slope separately: Q i S f = (6) Ki K i 3 i AR = (7) n i where the subscript i ifferentiate the three subsections. The total K = Σ K i an the total Q = Σ Q i. HEC-RAS software implements the Flow Distribution Option in orer to compute the lateral velocity istribution V i by iviing the cross-section into a number of slices an then calculating the V i as: Q si V i = (8) Asi where A si = cross-sectional area for each slice; Q si = ischarge for each of the slice. 4. CES quasi-d Moel The Environment Agency s CES moel is base on the LDM (Wark et al, 988; Shiono an Knight, 99, Ervine et al, 000), an it combines the continuity an momentum epth-average equations of motion for steay conitions an in the stream-wise component. The general equation of the moel for a straight river (sinuosity equal.0) is obtaine: gs Y o f q 8 + S y + y ( q Y ) f λ Y q = Γ (9) 8 where f = Darcy s friction factor; q = streamwise unit flow rate (=Y U ); U = epth-average velocity; S y = lateral slope; λ = non-imensional Boussinesq ey viscosity; y = lateral horizontal coorinate; an Γ = seconary flow parameter. The first term in eq. (3) is the hyrostatic pressure, the secon is the bounary friction term, the thir is the turbulence ue to lateral shear stress an the last term in the right sie represents the seconary circulations. The recommene values for the ifferent variables an the Finite Element Coe for solution of Equation 3 can be foun in Defra/EA 003. Once the velocity in each slice, U, is obtaine, the total ischarge, Q t, in the cross section can be calculate as sum of unit ischarges as: ( y y ) Q (0) t = q i i where y i an y i- are the horizontal coorinates in transverse irection for both sies of the slice. 4.3 SRHD Moel The two imensional epth-average moel SRH- D is a free-use available numerical coe evelope by Yong G. Lai, from U.S. Bureau of Reclamation (Lai, 00). The coe is base on the finite-volume approach an it can be assume that provies an acceptable solution of the D equations in a variety of river flows (Lai, 000; an Lai et al, 006). The moel solves the shallow water equations of flow: = = Continuity equation: H t + ( HU ) ( HV ) + = 0 () Momentum equations in x an y : ( HU ) ( HU ) ( HU V ) + + = t ( Hτ ) ( Hτ xy ) H xx + gh ( HV ) ( HU V ) ( HV ) + + = t ( Hτ ) ( Hτ ) xy + yy zb τ xb + ρ () (3) H z τ b yb gh + ρ where, x an y are horizontal Cartesian coorinates; z b is elevation, t is time; H is water epth; U an V b are epth-average velocity components in x an y irections, respectively, τ xx, τ xy an τ yy are epth-average stresses ue to turbulence as well as ispersion, ρ is the water ensity, an τ xb, τ yb, are the shear stresses. These stresses are obtaine using the Manning s resistance equation as follows: b τ = ρc U x f ( U + V ) zb + zb + (4a)

6 b τ y = ρc V gn C f = 3 H f ( U + V ) zb + zb + (4b) (4c) where C f is a friction coefficient that is mainly epening on n, the Manning s roughness coefficient. The turbulence stresses are compute with Boussinesq equation as: τ τ τ xx xy yy U U = ρ υt 3 U V = τ yx = ρ( υ + υt ) + V V = ρ( υ + υt ) + k 3 ( υ + ) + k (5) where υ is kinematic viscosity of water an υ t is ey viscosity. The ey viscosity is calculate with the k-ε turbulence moel (Roi 993), an the ey viscosity is calculate as: k t = C (0) ε υ µ with two aitional equations for the turbulent kinetic energy, k, an its issipation rate, ε. Launer an Spaling (974) ae two transport equations to solve the new two unknown variables. Figure 5., mesh iscretization (5680 elements). The mesh is enser in the main channel banks, incline, an less ense where the is flat. The numerical solution of the SRHD equations is implemente in a finite-volume metho with quarilateral elements. The stanar conjugate graient solver with ILU preconitioning is use (Lai 000) for spatial integration in an iterative process. The computational omain is iscretize in 5939 noes an 5680 quarilateral elements, 99 in crossstream irection an 60 in streamwise, as it is shown in Fig. 5. The bounary conitions are total ischarge at the upstream section an a unique mean water level for the ownstream cross-section. SRHD calculates a istribution of the velocity along the upstream conition in such a way that the total ischarge is satisfie. The approach use in this work is the conveyance istribution, which at the inlet is istribute across the upstream section following the conveyance proportion, eq. (7), so then the velocity in each element is proportional to epth an inversely proportional to Manning s n. This approach overestimates velocities in the main channel an unerestimates them in the flooplain. These bounary conitions are the same than the D moel, so the ifferences in results are only epenent on moelling equations. 5 MODELLING APPROACH The first step in a river moelling work once the topography an geometry is efine is to ientify the hyraulic variables involve. The most important one is the hyraulic resistance to flow, efine in terms of Manning s roughness coefficient in this work. In orer to reuce the uncertainty explaine in previous sections about the Manning s n value, this is calibrate with the 800 m longituinal water level profile in the 0.5 m3/s inbank ischarge. The HEC- RAS D moel is use for iterating ifferent Manning s n an to obtain the bankfull n by fitting the compute water profiles with the fiel profiles. Figure 6 shows the compute profile obtaine with a mean Manning s n = 0.04 in the main channel, which is the roughness that best fits the fiel ata. Accoring to the variation of roughness with epth, the Manning s n in the shoul be an in the banks. These values will be use as the main channel roughness coefficients in the overbank ischarges. The water levels obtaine with HEC-RAS for the two overbank ischarges (0. an 5.3 m3/s) are shown in Fig. 7. The bank stations are locate on the top of the main channel (DCM) or on the top of the flooplain walls (SCM) an two separate solutions are obtaine. The results illustrate the main ifferences between both methos. The DCM gives lower

7 water levels than the SCM for the same ischarge. In general the water levels measure in the fiel works are foun between the two numerical solutions (DCM an SCM). Some small iscrepancies appear, probably ue to roughness variation with epth an/or local changes in slope or section area DCM-nEST DCM-nCAL Fiel ata Figure 6. Fiel (9 full ots) an compute water surface profiles by using HEC-RAS with the estimate (DCM-nEST) an calibrate Manning coefficients (Manual) for the inbank flow Q50.3-DCM Q50.3 ata Q50.3-SCM Q0.-DCM Q0. ata Q0.-SCM Figure 7. Compute water surface profiles by using HEC-RAS (DCM an SCM) for the two overbank ischarges. Comparison with fiel ata (Myers an Lyness, 994). Previous stuies in compoun channel flows emonstrate that DCM an SCM are not proviing goo results uner uniform flow conitions. In this paper, Fig. 7 emonstrates that for graually variable flow conitions DCM an SCM maintain iscrepancies in water levels with real ata an give ifferent results. In terms of velocity istribution across the section, the SCM gives a uniform velocity for the whole section an the DCM is not proviing a real istribution. For overbank flow the velocities given by HEC-RAS are ifferent to the real istribution, especially in the main channel. Fig. 8 shows the velocity istribution obtaine with HEC-RAS for the inbank flow Q0.5 an for the overbank flow Q5.3, together with the values measure for Q5.3. The moel overestimates velocities in main river banks. Velocity (m/s) Velocity Distribution for Q0.5 an Q5.3 (s4) DCM vel Q0.5 water level Q0.5 DCM vel Q5.3 water level Q5.3 vel ata Q0.5 Vel ata Q Cross Chainages (m) Figure 8. Fiel measure an D compute velocities in section s4 for inbank an overbank ischarges, Q0.5 an Q5.3. In orer to unerstan the flow behaviour in this graually varie flow river, the SRHD was applie to the computational omain in Figure 5. The way the D moel estimates total energy is a combination of friction (through a roughness coefficient) an turbulence stresses (through a issipation coefficient). This is an important avantage with respect to D moelling that only inclues friction losses an the velocity istribution only epens on water epth an Manning s coefficient. The results obtaine with SRHD moel are shown in Figs 9 an 0. The water level profiles obtaine with D moelling (k-ε turbulence moel) are lower than those obtaine with the DCM for all the ischarges. The Manning s coefficients are the same in both moels, as well as the bounary conitions. The ifference in water levels between D an D solution are smaller for overbank flows than for the inbank one. This result confirms the conclusions by Moreta (04) who emonstrate that for uniform flow in straight compoun channels, D moelling gives lower water levels than D moelling if the roughness an bounary conitions are the same Q0.5 ata Q0.5-DCM Q0.5-SRHD 33.5 Figure 9. Water level fiel ata an D compute water surface (W.S.) compare with D values (DCM). Inbank ischarge Q0.5.

8 Q0. ata Q0.-DCM Q0.-SRHD Q5.3 ata Q5.3-DCM Q5.3-SRHD water profiles obtaine by D moel are better than the D moel. However, the istribution of epthaverage velocity can be obviously improve. The CES is applie to section 4, using the same slope an Manning s coefficient of roughness than in D moelling. CES precise a water level to estimate the velocity istribution an total ischarge. The water epth use for estimating the velocity is that obtaine from the D moelling. Figures an show that the velocity istribution obtaine with CES fit better with the ata than the istribution given by D moel Figure 0. Water level fiel ata an D compute water surface (W.S.) compare with D values (DCM). Overbank ischarges Q0. an Q5.3. However D moelling has some avantages over D moelling. First, the changes in main channel an flooplain sinuosity are taken into account, secon, it consiers internal energy losses ue to flow turbulence an thir, consequently the velocity irection an istribution must be better simulate. In Figures an the velocity istribution obtaine with D (DCM) an D moels for the inbank, Q0.5, an overbank, Q5.3, ischarges are compare with fiel measurements. The velocities given by SRHD improve slightly the velocities obtaine by DCM. Velocity (m/s) Velocity Distribution for Q0.5 (s4) vel ata Q0.5 DCM vel Q0.5 D vel Q0.5 CES vel Q Cross Chainages (m) Figure. Velocities of fiel ata (Martin an Myers, 99) an compute with D (DCM), D (SRH) an CES for overbank ischarge Q IMPROVING D MODELLING In orer to improve D moelling (with DCM), the results obtaine with CES are iscusse in this paragraph. The first step is that for straight river channels with moerate roughene flooplains, the Velocity (m/s) Velocity Distribution for Q5.3 (s4) Vel ata Q5.3 DCM vel Q5.3 SRHD vel Q5.3 CES vel Q Cross Chainages (m) Figure. Velocities of fiel ata (Martin an Myers, 99) an compute with D (DCM), D (SRH) an CES for overbank ischarge Q CONCLUSIONS The numerical analysis of this work is base on previously publishe fiel ata an illustrates some of the problems that affect common D numerical moel in reproucing overbank flow. HEC-RAS moel is not able to yiel an accurate velocity istribution across the section of a straight compoun channel. Seconly, the comparison between the fiel ata an the SRHD moel shows the nee to take into account that the Manning s coefficients vali for D moelling are not enough accurate for D simulations. Therefore, some uncertainties rising from the use of D moels can provie uncertain results respect to better preictable estimations obtaine by D moelling. The analysis an comparison of flow velocities measure in fiel works an compute by numerical moels has shown that the preiction of accurate velocity istributions in compoun channel flow is a major challenge in numerical moelling. Typical D finite volume coes base on k-ε turbulence moel tren to uner preict main channel an flooplain interaction. These D moels slightly improve the epth-average velocities obtaine with D moel

9 for the straight river case analyse herein. In orer to better simulate velocities, the CES base on Lateral Distribution Metho is propose for comparison. The CES gives a better representation of momentum interaction between main channel an flooplains an of the velocity istribution across the section. This methoology has been contraste with fiel river ata uner graually varie conitions, confirming the results of some previously publishe works on the topic uner ifferente conitions (Weber an Menenez, 004, an Vionnet et al, 004). 8 REFERENCES Ackers, P. (99). Hyraulic esign of two-stage channels. Proc. ICE, Water Maritime an Energy, Lonon 96(4), pp Babaeyan-Koopaei, K. Ervine, D.A., Sellin, R.H.J. (00). Development of a UK ata base for preicting floo levelsfor overbank flows. Environment Agency of UK. +Berz, G. (000) 'Floo Disasters: Lessons from the pastworries for the future'. Proc. Inst. Of Civil Engineers: Water, Maritime an Energy, Lonon, March, 4 (). Knight D.W. an Shiono K. (996). River channel an flooplain hyraulics. In Flooplain Processes, (Es. Anerson, Walling & Bates), Chapter 5: J Wiley. Defra/Environment Agency (003) Reucing uncertainty in river floo conveyance, Interim report Review of methos for Estimating Conveyance. Project W5A-057, HR Wallingfor, UK. Lai, Y.G. (November, 008) Theory an user manual for SRH- D. Denver, Colorao: U.S. Bureau of Reclamation. Lai, Y.G. (009) Two-Dimensional Depth-Average Flow Moeling with an Unstructure Hybri Mesh. Denver, Colorao: U.S. Bureau of Reclamation. Lai, Y.G. (008) Seimentation an River Hyraulics software (SRH-D). Version- e. Denver, Colorao: U.S. Bureau of Reclamation. Lyness, F.J. & Myers, W.R.C. (994a). Velocity coefficients for overbank flows in a compact compoun channel an their effects on the use of one imensional flow moel. n Int. Conf. on River Floo Hyraulics, York, UK, -5 March, John Wiley & Sons Lt. p Lyness, J.F. an Myers, R.C. (994b). Comparisons between measure an numerically moelle unsteay flows in a compoun channel using ifferent representation of friction slope. n Int. Conf. on River Floo Hyraulics, York, UK, -5 March, John Wiley & Sons Lt. Martin L. A. an Myers, W.R.C. (99) Measurement of overbank flow in a compoun river channel. Proc. ICE, Water Maritime an Energy,, p Martín-Moreta, P. (00). -D moel for vegetate rivers; calibration with Besòs river ata. (in Spanish) PhD thesis, UPC, Barcelona, Spain. McGahey, C., Samuels, P.G. an Knight D.W. (006). A practical approach to estimating the flow capacity of rivers application an analysis. Proc. River Flow 006, Lisbon, September, : Myers, W.R. an Lyness, F.J. (994). Hyraulic stuy of a two-stage river channel. Regulate Rivers Research an Management, 9(4), p.5-. Sellin, R.H.J. (964). A laboratory investigation into the interaction between the flow in the channel of a river an that over its floo plain. La Houille Blanche. 7, pp Shiono, K., Knight, D.W. (99). Turbulent open channel flows with variable epth across the channel. J. Flui Mechanics,, pp US Army Corps of Engineers, HEC-RAS, Hyraulic Reference Manual, Hyrologic Engineering Center, Davis Version 4.0, 008. Vionnet, C., Tassi, P., Martín-Vie, J.P. (004). Estimates of flow resistance an ey-viscosity coefficients for D moelling on vegetate flooplains. Hyrological processes, Vol. 8, Issue 5, pp Wark, J.B., Samuels, P.C., Ervine, D.A. (990). A practical metho of estimating velocity an ischarge in compoun channels. Proc. River Floo Hyraulics pp Weber, J.F. & Menénez, A.N. (004) Performance of lateral velocity istribution moels for compoun channel sections. International Conference on Fluvial Hyraulics,. Wormleaton, P.R. Allen J., Hajipanos P. (98). Discharge assessment in compoun channel flow. Journal of Hyraulics Division, ASCE, 08(9), pp Wormleaton, P.R., Merrett, D.J. (990). An improve metho of the calculation for steay uniform flow in prismatic main channel/floo plain sections. Journal of Hyraulic Research, Vol. 8, nº, pp Wormleaton, P.R., Sellin, R.H.J., Bryant, T., Loveless, J.H., Hey, R.D., Catmur, S.E. (004). Flow structures in a twostage channel with a mobile. Journal of Hyraulic Research, Vol. 4(), pp Zheleznyakov G.V. (97). Interaction of Channel an Flooplain Streams. Proc. 4 th IAHR congress, Paris, vol. 5, pp