RV R Meander A toolbox for re-meandering of channelized streams

Jorge D Abad alowast and Marcelo H Garcia b

aGraduate Research Assistant Dept of Civil and Environmental Engrg

University of Illinois at Urbana-Champaign Urbana IL 61801 USA

bChester and Helen Siess Professor Dept of Civil and Environmental Engrg

University of Illinois at Urbana-Champaign Urbana IL 61801 USA

Abstract

RV R Meander was developed as a toolbox for modeling restoration and naturalshyization processes in rivers This model includes Windows-based and Geographical Information System-based programs for analyzing and modeling planform migration of streams In the past several rivers have been channelized causing environmental and ecological problems Restoration techniques evolve as natural solutions to chanshynelization therefore the prediction of planform migration in rivers is indispensable for economic and social reasons such as development of urban areas close to rivers prevention of damages to infrastructure reduction of agricultural land losses and for the maintenance of biological diversity in rivers Abad and Garcia (2004) preshysented a conceptual and mathematical model for evolution of meandering rivers that can be used in restoration and naturalization processes In this work the description of RV R Meander is based on the computational characteristics and applicability rather than presenting its theoretical basis RV R Meander is an object oriented user-friendly model for restoration purposes Two modules are included statistical analysis and planform migration of rivers This model has been successfully tested on Microsoft Windows NT 402000XP and on ArcMap 818283

Key words Fluvial geomorphology Restoration Planform migration Software User-friendly model GIS

Program and manuals available at httpvtchluiucedusoftware lowast Corresponding author Fax (217)333-0687

Email address abaduiucedu (Jorge D Abad)

Preprint submitted to Computers amp Geosciences 18 May 2005

1 Introduction

Naturalization processes are phenomena in which an interdisciplinary group of researchers of civil engineers biologists hydrologists geographers and geshyologists among others have been working together in order to obtain a better understanding of rivers A component of this complex environment is called river morphodynamics This is described by planform migration of the river due to erosion of the margins (banks) widening of the river degradation and aggradation of the bed evolution of bedforms variations in suspended concentrations and bar formations Garcia (1999) In the past several rivers have been channelized causing direct 1 and indirect 2 consequences Today restoration techniques have become natural solutions to channelization Sevshyeral general approaches for restoration have been presented in Newbury et al (1992) Miller (1999) Fischenich and Morrow (2000) RRC (2002) Shields et al (2003) among others In this paper the development of a simplified user-friendly model (RV R Meander) for planform analysis (characterization) and migration is presented Similar models for characterization and migration of meandering rivers have been presented in the past such as Hooke (1984) Oneill and Abrahams (1986) Howard and Hemberger (1991) Lagasse et al (2003) and Lagasse et al (2004) The present model for migration and evolushytion of meanders includes two modules The first module determines important parameters (characterization) of natural streams based on statistical analysis by MacDonald (1991) and MacDonald et al (1992) such as sinuosity rate of migration fattening and skewness This module is indispensable when analyzshying a stream qualitatively and quantitatively for future planning The second module presents the planform migration model itself where a bank erosion sub model is applied using the concept of near-bank velocity (Ikeda et al 1981) As previously stated in this work the main objective is to present a description of RV R Meander on computational characteristics and applicashybility rather than presenting its theoretical basis The reader would benefit from three sources a paper under preparation that will present a conceptual methodology to formulate meander designs in restoration processes Abad and Garcia (2005) that contains case studies and user manuals for RV R Meander and Rhoads et al (2005) for the evaluation of the geomorphological perforshymance of Naturalized Rivers

1 increment on bed slope flow velocity sediment transport etc 2 bank erosion damage of protection structures increment of the channel width re-initialization of meandering deposition and erosion on the river bed damage to fish habitat reduction of the capacity of the stream on flood events etc

2

2 Model description

RV R Meander was developed using object oriented programming (OOP) style Figure 1 shows the flowchart of the RV R Meander processes Two versions of the model are available The first is a stand-alone Windows-based version and the second one is a Geographical Information System-based (GISshybased) version (see figures 2 and 3) The main difference between these two versions is the work environment and how the input data are incorporated into the model (river configuration) The different modules are divided into classes and used in the main interface as dll (dynamic link library) This type of structure programing will allow future incorporation of other components into the RV R Meander model (ie pre-processing and post-processing routines) More details about the theoretical approach for each module can be found in Abad and Garcia (2004) The model allows the user to choose either SI units or English units

Fig 1 Flowchart of model processes

3

21 Model versions

211 Stand-alone Windows-based version

The stand-alone version was developed entirely using Microsoft Visual C++ and Microsoft Foundation Classes (MFC) Figure 2 shows the Windows work environment In this version there are three ways to input the coordinates for the river centerlines This can be done by typing the coordinates by copying and pasting them from a spreadsheet or by importing them from an ArcMap-DXF file For the statistical module it is necessary to specify three centerlines for time 1 (t1) time 2 (t2) and for the valley centerlines For the migration module only one centerline is necessary

Fig 2 Stand-alone Windows-based version

212 GIS-based version

The GIS-based version was developed using Microsoft Visual C++ in adshydition to MFC Visual Basic and the ArcObjects Developer Kit (built using Microsoftrsquos Component Object Model (COM) technology) This version allows the user to use existing GIS line data to automatically obtain the river centershyline coordinates from within ESRI ArcMap ArcObjects is the development platform for the ArcGIS family of applications such as ArcMap ArcCatashylog and ArcScene It allows users to increase the functionality available in ArcInfo and ArcView packages ESRI (2004) Figure 3 shows the GIS-based work environment

4

Fig 3 GIS-based version

22 Modules in RV R Meander

These two versions (Windows-based and GIS-based) of the model include both the statistical analysis of stream shift module and the river migration module

221 Statistical analysis of stream shift module

This module is useful for analyzing a stream qualitatively and quantitatively for future planning Stream shift and meander properties can be analyzed using given centerlines for the valley and stream centerlines for at least two different times (t1 and t2) RV R Meander can calculate important composhynents of stream shift such as average normal shift average transverse shift average longitudinal shift average absolute transversal shift average absolute longitudinal shift and shift ratio These are calculated based on statistical analysis Additionally this module can measure meander characteristics such as sinuosity time rate of change of sinuosity average curvature and rate of flood plain area reworked Fig 4 shows the stream variables for the calculation of the sinuosity (S) and

LA S2minusS1the meander growth rate ( S) S and S are calculated as S = and S = Lv t2minust1

respectively where LA is the stream channel length Lv is the valley length dθ S1 and S2 the sinuosities at time t1 and t2 respectively and C = ds

is the

5

stream curvature (θ is the angle between channel centerline and down-valley direction and s is the streamwise coordinate)

Fig 4 Variables and coordinate system (a) 3D view (b) Top view and (c) Cross-section

6

Figure 5 shows the area reworked by the stream The flood plain area worked is the measurement of how much area has been deposited or eroded In general is a measurement of how much land surrounding a stream reach would be affected by meandering (MacDonald et al 1992) It is calculated by an integration of the area conformed by the centerlines corresponding to two different times Then the time rate of area reworked per channel length can be defined by

2|n|Δsr =

Δt Δs

Fig 5 Area reworked by a stream

From figure 5 one can see that the average normal shift is given by n macr = nΔs

Δt Δs

which is the average distance that the stream moves normal to itself per unit time This parameter gives an idea of how much the stream banks have mishygrated due to erosion This average normal shift can be decomposed into the

nSinθΔs nCosθΔsaveraged down-valley and cross-valley shift (x macr = and y ˙ =

Δt Δs Δt Δs

respectively) Moreover the average absolute down-valley and cross-valley |nSinθ|Δs |nCosθ|Δs

shift is given by |x| = and |y| = respectively The avshyΔt Δs Δt Δs

erage absolute cross-valley shift is especially useful because it indicates how much the stream can be expected to shift to either side of the stream centershyline MacDonald (1991) and MacDonald et al (1992)

To run this module only two data are required 1) lag time between t1 and t2 river centerlines and 2) the approximate wavelength of the meanders Several examples are presented in MacDonald (1991) MacDonald et al (1992) besides an application of this module is presented in the case study

7

222 River migration module

RV R Meander can simulate the planform migration of proposed river centershylines The model is valid for erodible streams It makes the assumption that the stream is in quasi-steady condition This means that the flow characterisshytics (ie velocity water depth) develop much faster than the time it takes for the bed elevation to change (Garcia et al 1996) Another assumption is that the channel width is constant throughout the simulation (valid for equilibshyrium streams) therefore the mean width has to be given as input data to the model To model bank erosion the concept of excess velocity near the banks is used where the normal bank erosion rate is proportional to this excess velocshyity times an erosion coefficient (Ikeda et al 1981) This module was applied to several streams in Illinois (Garcia et al 1996) and in a recent project of migration analysis in Poplar Creek a tributary of the Fox River Illinois

Flow field model Some assumptions and restrictions are used to derive the governing equations The continuity equation for sediment is not included and a linear profile of the bed in the transverse direction is assumed The configuration of variables and coordinates can be seen in figure 4

The instantaneous governing equations can be written as Garcia et al (1996)

1 partulowast partulowast Clowast 1 partHlowast τ lowast lowast lowast lowast lowast s u + v + u v = minus g minus (1)

1 + n lowastClowast partslowast partnlowast 1 + n lowastClowast 1 + n lowastClowast partslowast ρDlowast

1 partvlowast partvlowast Clowast partHlowast τ lowast lowast lowast lowast2 n u + v minus u = minusg minus (2)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n partnlowast ρDlowast

1 part(u lowastDlowast) part(v lowastDlowast) Clowast lowast D lowast + + v = 0 (3)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n

where u lowast and v lowast are the velocity components along the streamwise and transshyverse directions respectively Hlowast is the water surface elevation Clowast is the local curvature and Dlowast is the local flow depth (see figure 4) Equations 1 and 2 are the flow momentum equations along the streamwise and normal directions respectively Equation 3 represents the water mass conservation

radic The bed shear stress vector is defined as τ lowast = (τs

lowast τnlowast) = ρCf u lowast2 + v lowast2(u lowast v lowast)

where the friction coefficient is given by the Engelund-Hansen resistance equashytion for a flat bed This equation is stated as Cf = [6 + 25ln( Dlowast

)]minus2 where 25dlowast s

Dlowast and dlowast s(mean sediment diameter) are given in meters A linearization of

the governing equation is performed thus the instantaneous variables are subshy

stituted by the mean value plus a fluctuation over the mean (u lowast = U + u lowast

Dlowast

Hlowast

Clowast

v = v = D + d = H + h = C Cf = Cfo + Cf τs lowast = τs + τs

τn lowast = τn)

8

2 Model description

RV R Meander was developed using object oriented programming (OOP) style Figure 1 shows the flowchart of the RV R Meander processes Two versions of the model are available The first is a stand-alone Windows-based version and the second one is a Geographical Information System-based (GISshybased) version (see figures 2 and 3) The main difference between these two versions is the work environment and how the input data are incorporated into the model (river configuration) The different modules are divided into classes and used in the main interface as dll (dynamic link library) This type of structure programing will allow future incorporation of other components into the RV R Meander model (ie pre-processing and post-processing routines) More details about the theoretical approach for each module can be found in Abad and Garcia (2004) The model allows the user to choose either SI units or English units

Fig 1 Flowchart of model processes

3

21 Model versions

211 Stand-alone Windows-based version

The stand-alone version was developed entirely using Microsoft Visual C++ and Microsoft Foundation Classes (MFC) Figure 2 shows the Windows work environment In this version there are three ways to input the coordinates for the river centerlines This can be done by typing the coordinates by copying and pasting them from a spreadsheet or by importing them from an ArcMap-DXF file For the statistical module it is necessary to specify three centerlines for time 1 (t1) time 2 (t2) and for the valley centerlines For the migration module only one centerline is necessary

Fig 2 Stand-alone Windows-based version

212 GIS-based version

The GIS-based version was developed using Microsoft Visual C++ in adshydition to MFC Visual Basic and the ArcObjects Developer Kit (built using Microsoftrsquos Component Object Model (COM) technology) This version allows the user to use existing GIS line data to automatically obtain the river centershyline coordinates from within ESRI ArcMap ArcObjects is the development platform for the ArcGIS family of applications such as ArcMap ArcCatashylog and ArcScene It allows users to increase the functionality available in ArcInfo and ArcView packages ESRI (2004) Figure 3 shows the GIS-based work environment

4

Fig 3 GIS-based version

22 Modules in RV R Meander

These two versions (Windows-based and GIS-based) of the model include both the statistical analysis of stream shift module and the river migration module

221 Statistical analysis of stream shift module

This module is useful for analyzing a stream qualitatively and quantitatively for future planning Stream shift and meander properties can be analyzed using given centerlines for the valley and stream centerlines for at least two different times (t1 and t2) RV R Meander can calculate important composhynents of stream shift such as average normal shift average transverse shift average longitudinal shift average absolute transversal shift average absolute longitudinal shift and shift ratio These are calculated based on statistical analysis Additionally this module can measure meander characteristics such as sinuosity time rate of change of sinuosity average curvature and rate of flood plain area reworked Fig 4 shows the stream variables for the calculation of the sinuosity (S) and

LA S2minusS1the meander growth rate ( S) S and S are calculated as S = and S = Lv t2minust1

respectively where LA is the stream channel length Lv is the valley length dθ S1 and S2 the sinuosities at time t1 and t2 respectively and C = ds

is the

5

stream curvature (θ is the angle between channel centerline and down-valley direction and s is the streamwise coordinate)

Fig 4 Variables and coordinate system (a) 3D view (b) Top view and (c) Cross-section

6

Figure 5 shows the area reworked by the stream The flood plain area worked is the measurement of how much area has been deposited or eroded In general is a measurement of how much land surrounding a stream reach would be affected by meandering (MacDonald et al 1992) It is calculated by an integration of the area conformed by the centerlines corresponding to two different times Then the time rate of area reworked per channel length can be defined by

2|n|Δsr =

Δt Δs

Fig 5 Area reworked by a stream

From figure 5 one can see that the average normal shift is given by n macr = nΔs

Δt Δs

which is the average distance that the stream moves normal to itself per unit time This parameter gives an idea of how much the stream banks have mishygrated due to erosion This average normal shift can be decomposed into the

nSinθΔs nCosθΔsaveraged down-valley and cross-valley shift (x macr = and y ˙ =

Δt Δs Δt Δs

respectively) Moreover the average absolute down-valley and cross-valley |nSinθ|Δs |nCosθ|Δs

shift is given by |x| = and |y| = respectively The avshyΔt Δs Δt Δs

erage absolute cross-valley shift is especially useful because it indicates how much the stream can be expected to shift to either side of the stream centershyline MacDonald (1991) and MacDonald et al (1992)

To run this module only two data are required 1) lag time between t1 and t2 river centerlines and 2) the approximate wavelength of the meanders Several examples are presented in MacDonald (1991) MacDonald et al (1992) besides an application of this module is presented in the case study

7

222 River migration module

RV R Meander can simulate the planform migration of proposed river centershylines The model is valid for erodible streams It makes the assumption that the stream is in quasi-steady condition This means that the flow characterisshytics (ie velocity water depth) develop much faster than the time it takes for the bed elevation to change (Garcia et al 1996) Another assumption is that the channel width is constant throughout the simulation (valid for equilibshyrium streams) therefore the mean width has to be given as input data to the model To model bank erosion the concept of excess velocity near the banks is used where the normal bank erosion rate is proportional to this excess velocshyity times an erosion coefficient (Ikeda et al 1981) This module was applied to several streams in Illinois (Garcia et al 1996) and in a recent project of migration analysis in Poplar Creek a tributary of the Fox River Illinois

Flow field model Some assumptions and restrictions are used to derive the governing equations The continuity equation for sediment is not included and a linear profile of the bed in the transverse direction is assumed The configuration of variables and coordinates can be seen in figure 4

The instantaneous governing equations can be written as Garcia et al (1996)

1 partulowast partulowast Clowast 1 partHlowast τ lowast lowast lowast lowast lowast s u + v + u v = minus g minus (1)

1 + n lowastClowast partslowast partnlowast 1 + n lowastClowast 1 + n lowastClowast partslowast ρDlowast

1 partvlowast partvlowast Clowast partHlowast τ lowast lowast lowast lowast2 n u + v minus u = minusg minus (2)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n partnlowast ρDlowast

1 part(u lowastDlowast) part(v lowastDlowast) Clowast lowast D lowast + + v = 0 (3)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n

where u lowast and v lowast are the velocity components along the streamwise and transshyverse directions respectively Hlowast is the water surface elevation Clowast is the local curvature and Dlowast is the local flow depth (see figure 4) Equations 1 and 2 are the flow momentum equations along the streamwise and normal directions respectively Equation 3 represents the water mass conservation

radic The bed shear stress vector is defined as τ lowast = (τs

lowast τnlowast) = ρCf u lowast2 + v lowast2(u lowast v lowast)

where the friction coefficient is given by the Engelund-Hansen resistance equashytion for a flat bed This equation is stated as Cf = [6 + 25ln( Dlowast

)]minus2 where 25dlowast s

Dlowast and dlowast s(mean sediment diameter) are given in meters A linearization of

the governing equation is performed thus the instantaneous variables are subshy

stituted by the mean value plus a fluctuation over the mean (u lowast = U + u lowast

Dlowast

Hlowast

Clowast

v = v = D + d = H + h = C Cf = Cfo + Cf τs lowast = τs + τs

τn lowast = τn)

8

21 Model versions

211 Stand-alone Windows-based version

The stand-alone version was developed entirely using Microsoft Visual C++ and Microsoft Foundation Classes (MFC) Figure 2 shows the Windows work environment In this version there are three ways to input the coordinates for the river centerlines This can be done by typing the coordinates by copying and pasting them from a spreadsheet or by importing them from an ArcMap-DXF file For the statistical module it is necessary to specify three centerlines for time 1 (t1) time 2 (t2) and for the valley centerlines For the migration module only one centerline is necessary

Fig 2 Stand-alone Windows-based version

212 GIS-based version

The GIS-based version was developed using Microsoft Visual C++ in adshydition to MFC Visual Basic and the ArcObjects Developer Kit (built using Microsoftrsquos Component Object Model (COM) technology) This version allows the user to use existing GIS line data to automatically obtain the river centershyline coordinates from within ESRI ArcMap ArcObjects is the development platform for the ArcGIS family of applications such as ArcMap ArcCatashylog and ArcScene It allows users to increase the functionality available in ArcInfo and ArcView packages ESRI (2004) Figure 3 shows the GIS-based work environment

4

Fig 3 GIS-based version

22 Modules in RV R Meander

These two versions (Windows-based and GIS-based) of the model include both the statistical analysis of stream shift module and the river migration module

221 Statistical analysis of stream shift module

This module is useful for analyzing a stream qualitatively and quantitatively for future planning Stream shift and meander properties can be analyzed using given centerlines for the valley and stream centerlines for at least two different times (t1 and t2) RV R Meander can calculate important composhynents of stream shift such as average normal shift average transverse shift average longitudinal shift average absolute transversal shift average absolute longitudinal shift and shift ratio These are calculated based on statistical analysis Additionally this module can measure meander characteristics such as sinuosity time rate of change of sinuosity average curvature and rate of flood plain area reworked Fig 4 shows the stream variables for the calculation of the sinuosity (S) and

LA S2minusS1the meander growth rate ( S) S and S are calculated as S = and S = Lv t2minust1

respectively where LA is the stream channel length Lv is the valley length dθ S1 and S2 the sinuosities at time t1 and t2 respectively and C = ds

is the

5

stream curvature (θ is the angle between channel centerline and down-valley direction and s is the streamwise coordinate)

Fig 4 Variables and coordinate system (a) 3D view (b) Top view and (c) Cross-section

6

Figure 5 shows the area reworked by the stream The flood plain area worked is the measurement of how much area has been deposited or eroded In general is a measurement of how much land surrounding a stream reach would be affected by meandering (MacDonald et al 1992) It is calculated by an integration of the area conformed by the centerlines corresponding to two different times Then the time rate of area reworked per channel length can be defined by

2|n|Δsr =

Δt Δs

Fig 5 Area reworked by a stream

From figure 5 one can see that the average normal shift is given by n macr = nΔs

Δt Δs

which is the average distance that the stream moves normal to itself per unit time This parameter gives an idea of how much the stream banks have mishygrated due to erosion This average normal shift can be decomposed into the

nSinθΔs nCosθΔsaveraged down-valley and cross-valley shift (x macr = and y ˙ =

Δt Δs Δt Δs

respectively) Moreover the average absolute down-valley and cross-valley |nSinθ|Δs |nCosθ|Δs

shift is given by |x| = and |y| = respectively The avshyΔt Δs Δt Δs

erage absolute cross-valley shift is especially useful because it indicates how much the stream can be expected to shift to either side of the stream centershyline MacDonald (1991) and MacDonald et al (1992)

To run this module only two data are required 1) lag time between t1 and t2 river centerlines and 2) the approximate wavelength of the meanders Several examples are presented in MacDonald (1991) MacDonald et al (1992) besides an application of this module is presented in the case study

7

222 River migration module

RV R Meander can simulate the planform migration of proposed river centershylines The model is valid for erodible streams It makes the assumption that the stream is in quasi-steady condition This means that the flow characterisshytics (ie velocity water depth) develop much faster than the time it takes for the bed elevation to change (Garcia et al 1996) Another assumption is that the channel width is constant throughout the simulation (valid for equilibshyrium streams) therefore the mean width has to be given as input data to the model To model bank erosion the concept of excess velocity near the banks is used where the normal bank erosion rate is proportional to this excess velocshyity times an erosion coefficient (Ikeda et al 1981) This module was applied to several streams in Illinois (Garcia et al 1996) and in a recent project of migration analysis in Poplar Creek a tributary of the Fox River Illinois

Flow field model Some assumptions and restrictions are used to derive the governing equations The continuity equation for sediment is not included and a linear profile of the bed in the transverse direction is assumed The configuration of variables and coordinates can be seen in figure 4

The instantaneous governing equations can be written as Garcia et al (1996)

1 partulowast partulowast Clowast 1 partHlowast τ lowast lowast lowast lowast lowast s u + v + u v = minus g minus (1)

1 + n lowastClowast partslowast partnlowast 1 + n lowastClowast 1 + n lowastClowast partslowast ρDlowast

1 partvlowast partvlowast Clowast partHlowast τ lowast lowast lowast lowast2 n u + v minus u = minusg minus (2)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n partnlowast ρDlowast

1 part(u lowastDlowast) part(v lowastDlowast) Clowast lowast D lowast + + v = 0 (3)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n

where u lowast and v lowast are the velocity components along the streamwise and transshyverse directions respectively Hlowast is the water surface elevation Clowast is the local curvature and Dlowast is the local flow depth (see figure 4) Equations 1 and 2 are the flow momentum equations along the streamwise and normal directions respectively Equation 3 represents the water mass conservation

radic The bed shear stress vector is defined as τ lowast = (τs

lowast τnlowast) = ρCf u lowast2 + v lowast2(u lowast v lowast)

where the friction coefficient is given by the Engelund-Hansen resistance equashytion for a flat bed This equation is stated as Cf = [6 + 25ln( Dlowast

)]minus2 where 25dlowast s

Dlowast and dlowast s(mean sediment diameter) are given in meters A linearization of

the governing equation is performed thus the instantaneous variables are subshy

stituted by the mean value plus a fluctuation over the mean (u lowast = U + u lowast

Dlowast

Hlowast

Clowast

v = v = D + d = H + h = C Cf = Cfo + Cf τs lowast = τs + τs

τn lowast = τn)

8

Fig 3 GIS-based version

22 Modules in RV R Meander

These two versions (Windows-based and GIS-based) of the model include both the statistical analysis of stream shift module and the river migration module

221 Statistical analysis of stream shift module

This module is useful for analyzing a stream qualitatively and quantitatively for future planning Stream shift and meander properties can be analyzed using given centerlines for the valley and stream centerlines for at least two different times (t1 and t2) RV R Meander can calculate important composhynents of stream shift such as average normal shift average transverse shift average longitudinal shift average absolute transversal shift average absolute longitudinal shift and shift ratio These are calculated based on statistical analysis Additionally this module can measure meander characteristics such as sinuosity time rate of change of sinuosity average curvature and rate of flood plain area reworked Fig 4 shows the stream variables for the calculation of the sinuosity (S) and

LA S2minusS1the meander growth rate ( S) S and S are calculated as S = and S = Lv t2minust1

respectively where LA is the stream channel length Lv is the valley length dθ S1 and S2 the sinuosities at time t1 and t2 respectively and C = ds

is the

5

stream curvature (θ is the angle between channel centerline and down-valley direction and s is the streamwise coordinate)

Fig 4 Variables and coordinate system (a) 3D view (b) Top view and (c) Cross-section

6

Figure 5 shows the area reworked by the stream The flood plain area worked is the measurement of how much area has been deposited or eroded In general is a measurement of how much land surrounding a stream reach would be affected by meandering (MacDonald et al 1992) It is calculated by an integration of the area conformed by the centerlines corresponding to two different times Then the time rate of area reworked per channel length can be defined by

2|n|Δsr =

Δt Δs

Fig 5 Area reworked by a stream

From figure 5 one can see that the average normal shift is given by n macr = nΔs

Δt Δs

which is the average distance that the stream moves normal to itself per unit time This parameter gives an idea of how much the stream banks have mishygrated due to erosion This average normal shift can be decomposed into the

nSinθΔs nCosθΔsaveraged down-valley and cross-valley shift (x macr = and y ˙ =

Δt Δs Δt Δs

respectively) Moreover the average absolute down-valley and cross-valley |nSinθ|Δs |nCosθ|Δs

shift is given by |x| = and |y| = respectively The avshyΔt Δs Δt Δs

erage absolute cross-valley shift is especially useful because it indicates how much the stream can be expected to shift to either side of the stream centershyline MacDonald (1991) and MacDonald et al (1992)

To run this module only two data are required 1) lag time between t1 and t2 river centerlines and 2) the approximate wavelength of the meanders Several examples are presented in MacDonald (1991) MacDonald et al (1992) besides an application of this module is presented in the case study

7

222 River migration module

RV R Meander can simulate the planform migration of proposed river centershylines The model is valid for erodible streams It makes the assumption that the stream is in quasi-steady condition This means that the flow characterisshytics (ie velocity water depth) develop much faster than the time it takes for the bed elevation to change (Garcia et al 1996) Another assumption is that the channel width is constant throughout the simulation (valid for equilibshyrium streams) therefore the mean width has to be given as input data to the model To model bank erosion the concept of excess velocity near the banks is used where the normal bank erosion rate is proportional to this excess velocshyity times an erosion coefficient (Ikeda et al 1981) This module was applied to several streams in Illinois (Garcia et al 1996) and in a recent project of migration analysis in Poplar Creek a tributary of the Fox River Illinois

Flow field model Some assumptions and restrictions are used to derive the governing equations The continuity equation for sediment is not included and a linear profile of the bed in the transverse direction is assumed The configuration of variables and coordinates can be seen in figure 4

The instantaneous governing equations can be written as Garcia et al (1996)

1 partulowast partulowast Clowast 1 partHlowast τ lowast lowast lowast lowast lowast s u + v + u v = minus g minus (1)

1 + n lowastClowast partslowast partnlowast 1 + n lowastClowast 1 + n lowastClowast partslowast ρDlowast

1 partvlowast partvlowast Clowast partHlowast τ lowast lowast lowast lowast2 n u + v minus u = minusg minus (2)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n partnlowast ρDlowast

1 part(u lowastDlowast) part(v lowastDlowast) Clowast lowast D lowast + + v = 0 (3)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n

where u lowast and v lowast are the velocity components along the streamwise and transshyverse directions respectively Hlowast is the water surface elevation Clowast is the local curvature and Dlowast is the local flow depth (see figure 4) Equations 1 and 2 are the flow momentum equations along the streamwise and normal directions respectively Equation 3 represents the water mass conservation

radic The bed shear stress vector is defined as τ lowast = (τs

lowast τnlowast) = ρCf u lowast2 + v lowast2(u lowast v lowast)

where the friction coefficient is given by the Engelund-Hansen resistance equashytion for a flat bed This equation is stated as Cf = [6 + 25ln( Dlowast

)]minus2 where 25dlowast s

Dlowast and dlowast s(mean sediment diameter) are given in meters A linearization of

the governing equation is performed thus the instantaneous variables are subshy

stituted by the mean value plus a fluctuation over the mean (u lowast = U + u lowast

Dlowast

Hlowast

Clowast

v = v = D + d = H + h = C Cf = Cfo + Cf τs lowast = τs + τs

τn lowast = τn)

8

stream curvature (θ is the angle between channel centerline and down-valley direction and s is the streamwise coordinate)

Fig 4 Variables and coordinate system (a) 3D view (b) Top view and (c) Cross-section

6

Figure 5 shows the area reworked by the stream The flood plain area worked is the measurement of how much area has been deposited or eroded In general is a measurement of how much land surrounding a stream reach would be affected by meandering (MacDonald et al 1992) It is calculated by an integration of the area conformed by the centerlines corresponding to two different times Then the time rate of area reworked per channel length can be defined by

2|n|Δsr =

Δt Δs

Fig 5 Area reworked by a stream

From figure 5 one can see that the average normal shift is given by n macr = nΔs

Δt Δs

which is the average distance that the stream moves normal to itself per unit time This parameter gives an idea of how much the stream banks have mishygrated due to erosion This average normal shift can be decomposed into the

nSinθΔs nCosθΔsaveraged down-valley and cross-valley shift (x macr = and y ˙ =

Δt Δs Δt Δs

respectively) Moreover the average absolute down-valley and cross-valley |nSinθ|Δs |nCosθ|Δs

shift is given by |x| = and |y| = respectively The avshyΔt Δs Δt Δs

erage absolute cross-valley shift is especially useful because it indicates how much the stream can be expected to shift to either side of the stream centershyline MacDonald (1991) and MacDonald et al (1992)

To run this module only two data are required 1) lag time between t1 and t2 river centerlines and 2) the approximate wavelength of the meanders Several examples are presented in MacDonald (1991) MacDonald et al (1992) besides an application of this module is presented in the case study

7

222 River migration module

RV R Meander can simulate the planform migration of proposed river centershylines The model is valid for erodible streams It makes the assumption that the stream is in quasi-steady condition This means that the flow characterisshytics (ie velocity water depth) develop much faster than the time it takes for the bed elevation to change (Garcia et al 1996) Another assumption is that the channel width is constant throughout the simulation (valid for equilibshyrium streams) therefore the mean width has to be given as input data to the model To model bank erosion the concept of excess velocity near the banks is used where the normal bank erosion rate is proportional to this excess velocshyity times an erosion coefficient (Ikeda et al 1981) This module was applied to several streams in Illinois (Garcia et al 1996) and in a recent project of migration analysis in Poplar Creek a tributary of the Fox River Illinois

Flow field model Some assumptions and restrictions are used to derive the governing equations The continuity equation for sediment is not included and a linear profile of the bed in the transverse direction is assumed The configuration of variables and coordinates can be seen in figure 4

The instantaneous governing equations can be written as Garcia et al (1996)

1 partulowast partulowast Clowast 1 partHlowast τ lowast lowast lowast lowast lowast s u + v + u v = minus g minus (1)

1 + n lowastClowast partslowast partnlowast 1 + n lowastClowast 1 + n lowastClowast partslowast ρDlowast

1 partvlowast partvlowast Clowast partHlowast τ lowast lowast lowast lowast2 n u + v minus u = minusg minus (2)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n partnlowast ρDlowast

1 part(u lowastDlowast) part(v lowastDlowast) Clowast lowast D lowast + + v = 0 (3)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n

where u lowast and v lowast are the velocity components along the streamwise and transshyverse directions respectively Hlowast is the water surface elevation Clowast is the local curvature and Dlowast is the local flow depth (see figure 4) Equations 1 and 2 are the flow momentum equations along the streamwise and normal directions respectively Equation 3 represents the water mass conservation

radic The bed shear stress vector is defined as τ lowast = (τs

lowast τnlowast) = ρCf u lowast2 + v lowast2(u lowast v lowast)

where the friction coefficient is given by the Engelund-Hansen resistance equashytion for a flat bed This equation is stated as Cf = [6 + 25ln( Dlowast

)]minus2 where 25dlowast s

Dlowast and dlowast s(mean sediment diameter) are given in meters A linearization of

the governing equation is performed thus the instantaneous variables are subshy

stituted by the mean value plus a fluctuation over the mean (u lowast = U + u lowast

Dlowast

Hlowast

Clowast

v = v = D + d = H + h = C Cf = Cfo + Cf τs lowast = τs + τs

τn lowast = τn)

8

Figure 5 shows the area reworked by the stream The flood plain area worked is the measurement of how much area has been deposited or eroded In general is a measurement of how much land surrounding a stream reach would be affected by meandering (MacDonald et al 1992) It is calculated by an integration of the area conformed by the centerlines corresponding to two different times Then the time rate of area reworked per channel length can be defined by

2|n|Δsr =

Δt Δs

Fig 5 Area reworked by a stream

From figure 5 one can see that the average normal shift is given by n macr = nΔs

Δt Δs

which is the average distance that the stream moves normal to itself per unit time This parameter gives an idea of how much the stream banks have mishygrated due to erosion This average normal shift can be decomposed into the

nSinθΔs nCosθΔsaveraged down-valley and cross-valley shift (x macr = and y ˙ =

Δt Δs Δt Δs

respectively) Moreover the average absolute down-valley and cross-valley |nSinθ|Δs |nCosθ|Δs

shift is given by |x| = and |y| = respectively The avshyΔt Δs Δt Δs

erage absolute cross-valley shift is especially useful because it indicates how much the stream can be expected to shift to either side of the stream centershyline MacDonald (1991) and MacDonald et al (1992)

To run this module only two data are required 1) lag time between t1 and t2 river centerlines and 2) the approximate wavelength of the meanders Several examples are presented in MacDonald (1991) MacDonald et al (1992) besides an application of this module is presented in the case study

7

222 River migration module

RV R Meander can simulate the planform migration of proposed river centershylines The model is valid for erodible streams It makes the assumption that the stream is in quasi-steady condition This means that the flow characterisshytics (ie velocity water depth) develop much faster than the time it takes for the bed elevation to change (Garcia et al 1996) Another assumption is that the channel width is constant throughout the simulation (valid for equilibshyrium streams) therefore the mean width has to be given as input data to the model To model bank erosion the concept of excess velocity near the banks is used where the normal bank erosion rate is proportional to this excess velocshyity times an erosion coefficient (Ikeda et al 1981) This module was applied to several streams in Illinois (Garcia et al 1996) and in a recent project of migration analysis in Poplar Creek a tributary of the Fox River Illinois

Flow field model Some assumptions and restrictions are used to derive the governing equations The continuity equation for sediment is not included and a linear profile of the bed in the transverse direction is assumed The configuration of variables and coordinates can be seen in figure 4

The instantaneous governing equations can be written as Garcia et al (1996)

1 partulowast partulowast Clowast 1 partHlowast τ lowast lowast lowast lowast lowast s u + v + u v = minus g minus (1)

1 + n lowastClowast partslowast partnlowast 1 + n lowastClowast 1 + n lowastClowast partslowast ρDlowast

1 partvlowast partvlowast Clowast partHlowast τ lowast lowast lowast lowast2 n u + v minus u = minusg minus (2)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n partnlowast ρDlowast

1 part(u lowastDlowast) part(v lowastDlowast) Clowast lowast D lowast + + v = 0 (3)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n

where u lowast and v lowast are the velocity components along the streamwise and transshyverse directions respectively Hlowast is the water surface elevation Clowast is the local curvature and Dlowast is the local flow depth (see figure 4) Equations 1 and 2 are the flow momentum equations along the streamwise and normal directions respectively Equation 3 represents the water mass conservation

radic The bed shear stress vector is defined as τ lowast = (τs

lowast τnlowast) = ρCf u lowast2 + v lowast2(u lowast v lowast)

where the friction coefficient is given by the Engelund-Hansen resistance equashytion for a flat bed This equation is stated as Cf = [6 + 25ln( Dlowast

)]minus2 where 25dlowast s

Dlowast and dlowast s(mean sediment diameter) are given in meters A linearization of

the governing equation is performed thus the instantaneous variables are subshy

stituted by the mean value plus a fluctuation over the mean (u lowast = U + u lowast

Dlowast

Hlowast

Clowast

v = v = D + d = H + h = C Cf = Cfo + Cf τs lowast = τs + τs

τn lowast = τn)

8

222 River migration module

RV R Meander can simulate the planform migration of proposed river centershylines The model is valid for erodible streams It makes the assumption that the stream is in quasi-steady condition This means that the flow characterisshytics (ie velocity water depth) develop much faster than the time it takes for the bed elevation to change (Garcia et al 1996) Another assumption is that the channel width is constant throughout the simulation (valid for equilibshyrium streams) therefore the mean width has to be given as input data to the model To model bank erosion the concept of excess velocity near the banks is used where the normal bank erosion rate is proportional to this excess velocshyity times an erosion coefficient (Ikeda et al 1981) This module was applied to several streams in Illinois (Garcia et al 1996) and in a recent project of migration analysis in Poplar Creek a tributary of the Fox River Illinois

Flow field model Some assumptions and restrictions are used to derive the governing equations The continuity equation for sediment is not included and a linear profile of the bed in the transverse direction is assumed The configuration of variables and coordinates can be seen in figure 4

The instantaneous governing equations can be written as Garcia et al (1996)

1 partulowast partulowast Clowast 1 partHlowast τ lowast lowast lowast lowast lowast s u + v + u v = minus g minus (1)

1 + n lowastClowast partslowast partnlowast 1 + n lowastClowast 1 + n lowastClowast partslowast ρDlowast

1 partvlowast partvlowast Clowast partHlowast τ lowast lowast lowast lowast2 n u + v minus u = minusg minus (2)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n partnlowast ρDlowast

1 part(u lowastDlowast) part(v lowastDlowast) Clowast lowast D lowast + + v = 0 (3)

lowastClowast lowastClowast1 + n partslowast partnlowast 1 + n

where u lowast and v lowast are the velocity components along the streamwise and transshyverse directions respectively Hlowast is the water surface elevation Clowast is the local curvature and Dlowast is the local flow depth (see figure 4) Equations 1 and 2 are the flow momentum equations along the streamwise and normal directions respectively Equation 3 represents the water mass conservation

radic The bed shear stress vector is defined as τ lowast = (τs

lowast τnlowast) = ρCf u lowast2 + v lowast2(u lowast v lowast)

where the friction coefficient is given by the Engelund-Hansen resistance equashytion for a flat bed This equation is stated as Cf = [6 + 25ln( Dlowast

)]minus2 where 25dlowast s

Dlowast and dlowast s(mean sediment diameter) are given in meters A linearization of

the governing equation is performed thus the instantaneous variables are subshy

stituted by the mean value plus a fluctuation over the mean (u lowast = U + u lowast

Dlowast

Hlowast

Clowast

v = v = D + d = H + h = C Cf = Cfo + Cf τs lowast = τs + τs

τn lowast = τn)

8

The mean bed elevation is expressed as ηlowast = ηo lowast minusSos

lowast + η

After some mathshyematical manipulation see (Garcia et al 1996) the near-bank perturbation velocity ub is found to be

s j

minusa2s minusa2s ub(s) = a1e + a3C(s) + a4e C(s)e a2sds (4) 0

where a1(n) = u(0 n)+χC(0)n = = minusχ a4 = +(α+

a2 2Cfoβχ a3 Cfoβ[χ5Fo 2

1)χ2 + 5 Cfoχ2(α + χ3F 2)] χ = UUo β = BlowastDo lowast and F 2 = Uo

lowast2(gDlowast) o o o

In the above formulations Uo Do refers to uniform flow conditions in an equivalent straight channel

A bank erosion model is incorporated which relates the near-bank perturbation velocity (equation 4) to the bank migration Therefore the normal bank erosion

dnlowast

brate is ζlowast = dtlowast

where ζ was made dimensionless with Uo lowast The total erosion

is computed as ζ = Eoub(s) where Eo is the erosion coefficient that has to be estimated or calibrated empirically

The explanation of the user interface for this module is given in the case study

3 A case study Poplar Creek re-meanderization

The Poplar Creek project involved the re-meandering of Poplar Creek a tribshyutary of the Fox River Illinois Poplar Creek is located in Cook County Il USA An approximated 800 meter long reach of the Poplar Creek was channelshyized in 1938 The objective of the project was to present some alternatives for re-meandering this reach These alternatives took into account changes in the surrounding areas of the reach that have occurred since channelization took place Many of these changes are due to development of residential areas facshytories and civil structures Four alternatives were presented Because Poplar Creek has erodible banks and its channel width was nearly constant over the years the RV R meander model was chosen for planform migration purposes Four possible configurations of centerlines were simulated and the X-Y coordishynates for these configurations were imported from ArcMap-DXF files Because no information about sediment transport was available the channel forming discharge was found by considering the 2-year return interval discharge A frequency analysis was then carried out using the data from USGS station 05550500 (Poplar Creek at Elgin IL) Figure 6 shows the user interface for the input of X-Y coordinates for Poplar Creek

Input parameters Input parameters for the river migration module were as follows

9

Fig 6 User interface to input river centerlines

bull Initial curvature (C0) was given as 00 bull Initial perturbation velocity (UB0) was given as 00 bull Transverse bed slope coefficient (ALF) 3 a value of 6 was used as recomshy

mended by Garcia et al (1996) bull Discharge (Q) the channel-forming discharge was 1334 m3s bull Geometry configuration the width and depth were 12 and 15 m respectively

(based on surveys) bull Erosion coefficient (Eo) the estimated value of Eo was 100x10minus7 This value

was also compared because of the similar conditions to the Eo for the Leaf River found in Garcia et al (1996) where Eo was 700x10minus8

bull Mean sediment diameter (ds) 00030 m bull Number of years (t) 100 years

Using the modules user interface the other required parameters were calcushylated Figure 7 shows the user interface containing the parameters for the Poplar Creek case study

3 This coefficient controls the steepness of the transverse slope of the channel bed see Kikkawa et al (1976) and Zimmerman and Kennedy (1978) for more informashytion

10

Fig 6 User interface to input river centerlines

bull Initial curvature (C0) was given as 00 bull Initial perturbation velocity (UB0) was given as 00 bull Transverse bed slope coefficient (ALF) 3 a value of 6 was used as recomshy

mended by Garcia et al (1996) bull Discharge (Q) the channel-forming discharge was 1334 m3s bull Geometry configuration the width and depth were 12 and 15 m respectively

(based on surveys) bull Erosion coefficient (Eo) the estimated value of Eo was 100x10minus7 This value

was also compared because of the similar conditions to the Eo for the Leaf River found in Garcia et al (1996) where Eo was 700x10minus8

bull Mean sediment diameter (ds) 00030 m bull Number of years (t) 100 years

Using the modules user interface the other required parameters were calcushylated Figure 7 shows the user interface containing the parameters for the Poplar Creek case study

3 This coefficient controls the steepness of the transverse slope of the channel bed see Kikkawa et al (1976) and Zimmerman and Kennedy (1978) for more informashytion

10

Fig 7 User interface to run migration module

Alternative solutions Four different alternatives were simulated for Poplar Creek The input parameters for all the alternatives were the same except for the X-Y coordinates of the river centerline At the downstream end of the reach a straight channel was substituted for the real channel because of the presence of a bridge In this paper only alternative 4 is presented because it has been proved by Abad (2002) that the use of a Kinoshita curve (Parker et al 1983) described a stable configuration Since Poplar Creek has a skewed characteristic the high amplitude bends follow a Kinoshita curve Thus the generalized form of the Kinoshita curve is

θ = θ0Sin(κs) + θ03(JsCos(3κs) minus JfSin(3κs)) (5)

where θ is the angle between channel centerline and down-valley direction θ0 is the reference angle (approx maximum value of θ) κ is the arc-length bend wave number = 2

λπ (where λ is the arclength in a wavelength) Jf is

the fattening coefficient Js is the skewing coefficient and s is the streamwise

11

coordinate (s = 0 at the initial section and s = λ at the end of the curve) Two Kinoshita curves are shown in figure 8 The main characteristics of these curves are given in table 1

Table 1 Alternative 4 Kinoshita curves characteristics

Curve θ0 Js Jf λ X minus Y(initial) X minus Y(end)

1 75 120 1192 30000 (39533797 465205305) (39517847 465214513)

2 -80 130 1192 21000 (39510931 465215961) (39498995 465215961)

Figure 8 shows the planform migration results for alternative 4 and figure 9 shows the user interface for the X-Y output coordinates which could be exported as an ASCII file

Fig 8 Planform migration of alternative 4

12

coordinate (s = 0 at the initial section and s = λ at the end of the curve) Two Kinoshita curves are shown in figure 8 The main characteristics of these curves are given in table 1

Table 1 Alternative 4 Kinoshita curves characteristics

Curve θ0 Js Jf λ X minus Y(initial) X minus Y(end)

1 75 120 1192 30000 (39533797 465205305) (39517847 465214513)

2 -80 130 1192 21000 (39510931 465215961) (39498995 465215961)

Figure 8 shows the planform migration results for alternative 4 and figure 9 shows the user interface for the X-Y output coordinates which could be exported as an ASCII file

Fig 8 Planform migration of alternative 4

12

Fig 9 User interface to see results for migration module

The statistical module was run for the case of Poplar Creek by considering the same input (t1) coordinates as for the migration module (figure 6) and output coordinates (t2) given by the predicted results given by the migration module (figure 8) An additional set of coordinates for the valley centerline has been used Figures 10 and 11 show the user interface to input the data and to output the results where a set of parameters for characterization is presented It is seen from the statistical analysis results that for the alternate 4 (using Kinoshita curves) the rate of shift is very small which means that this configuration is stable after 100 years of simulation

Fig 10 User interface to run the statistical module

13

Fig 11 User interface to see results for the statistical module

4 Discussion

The applicability of RV R Meander represents the first stage (ie evaluation of alternatives in re-meandering of channelized streams) on restoration projects because of its simplicity and practicality allowing this model can be run in any PC computer without any problem of memory or storage capacity This model can be used to characterize meandering rivers in a large planform scale (by using the statistical module) and to predict river migration (by using a simplified 2-D module) The migration module could be easily adapted to any stream by calibrating the bank erosion coefficient (with past river centershylines) and therefore it represents a first evaluation tool rather than describshying the full hydrodynamics sediment transport and bank erosion processes which indeed require more advanced models More sophisticated 2-D models for river migration (with corrections for secondary flows shear stress distrishybutions gravity effects on bedload etc) have been presented in the past such as Mosselman (1998) Nagata et al (2000a) Nagata et al (2000b) Duan et al (2001) Sun et al (2001a) Sun et al (2001b) Sun et al (2001c) Darby and Delbono (2002) Lancaster and Bras (2002) among others Abad (2005) stated that some of the existing 2-D hydrodynamic models also present sevshyeral limitations since they do not capture accurately flow structures such as the bi-cellular secondary pattern the boundary shear distribution and thereshyfore sediment transport pattern which are part of river migration Thus the applicability of any model requires prior knowledge of which is the objective for the project in study therefore the user should be aware of which are the limitations when using a specific model

14

5 Conclusions

RV R Meander (Abad and Garcia 2005) is a simplified river planform mishygration and statistical analysis computer model From this model Windows-based and GIS-based toolkits were developed These toolkits are considered a valuable tool for predicting river morphodynamics processes such as river evoshylution The RV R Meander model was validated in streams in Illinois (Garcia et al 1996) and in a recent project at Poplar Creek Abad (2002) and Abad and Garcia (2004) The toolkits both include two modules The first modshyule of statistical analysis allows the user to characterize meandering rivers The second module the river migration model allows the user to simulate the planform evolution of meandering rivers with time and should be useful for stream naturalization projects However the user should be aware of several limitations of the present migration module such as the width of the channel is treated as constant only one set of sediments is considered the discharge is calculated by using the concept of channel forming discharge no formulation for cut-off occurrence is incorporated

6 Acknowledgments

The support of the Illinois Water Resources Center (Grants USGS Project 04 contract No 14-08-0004-G2017 and 2001IL4321B) and the National Science Foundation (Grant No 0097059) are gratefully acknowledged The authors are grateful to Bruce Rhoads and Rebeca Wade for providing us with the data used in the Poplar Creek study The help provided by Jose F Rodriguez is deeply appreciated Nils Oberg is also gratefully acknowledged for his contributions on the GIS-based version Suggestions and comments by Jose Vasquez and an additional anonymous reviewer helped to improve the final manuscript

References

Abad J D December 2002 2d river models for prediction of sediment transshyport and morphological variations Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign Illinois USA 73 pp

Abad J D 2005 Cfd simulations of asymmetric kinoshita-generated meshyandering bends Submitted to the XXXI International Association of Hyshydraulic Engineering and Research (IAHR) Congress September 11-16 Seoul Korea 10 pp

Abad J D Garcia M H 2004 Conceptual and mathematical model for

15

evolution of meandering rivers in naturalization processes On CD-ROM of Proc Joint Conference on Water Resources Engineering and Water Reshysources Planning and Management ASCE June 27-July 1 Salt Lake City Utah 10 pp

Abad J D Garcia M H 2005 Rvr meander Manual reference Hydrosysshytems Laboratory Department of Civil and Environmental Engineering Unishyversity of Illinois at Urbana-Champaign httpvtchluiucedusoftware 45 pp

Darby S E Delbono I 2002 A model of equilibrium bed topography for meanders Earth Surface Processes and Landforms 27 1057ndash1085

Duan J G Wang S Y Jia Y 2001 The applications of the enhanced cche2d model to study the alluvial channel migration processes Journal of Hydraulic Research 39 (5) 1ndash12

ESRI 2004 Edn documentation library for arcobjects Environmental Sysshytems Research Institute httpedndocesricomarcgisdeveloper

Fischenich C Morrow J V 2000 Reconecction of floodplains with incised channels United States Waterways Experimental Station Vicksburg Misshysissippi ERDC TN-EMRRP-SR-09 1ndash11

Garcia M H 1999 Sedimentation and erosion hydraulics In Mays K (Ed) Hydraulic Design Handbook McGraw-Hill New York pp 61ndash6113

Garcia M H Bittner L Nino Y 1996 Mathematical modeling of meanshydering streams in illinois A tool for stream management and engineering Hydraulic Engineering Series No 43 Department of Civil and Environmenshytal Engineering University of Illinois at Urbana-Champaign 63 pp

Hooke J M 1984 Changes in river meanders Progress in Physical Geograshyphy 8 473ndash508

Howard A D Hemberger A T 1991 Multivariate characterization of meshyandering Geormorphology 4 161ndash186

Ikeda S Parker G Sawai K 1981 Bend theory of river meanders part 1 linear development Journal of Fluid Mechanics 112 363ndash377

Kikkawa H Ikeda S Kitagawa A 1976 Flow and bed topography in curved open channels Journal of the Hydraulics Division 102 (HY9) 1327ndash 1342

Lagasse P F Spitz W J Zevenbergen L W 2003 A methodshyology for arcview tools for predicting channel migration ESRI User Conference Proceedings July 7-11 San Diego California USA httpgisesricomlibraryuserconfproc03abstractsa0251pdf

Lagasse P F Spitz W J Zevenbergen L W Zachmann D W 2004 Handbook for predicting stream meander migration Report 533 National Cooperative Highway Research Program Transportation Research Board of the National Academies Washington DC USA 105 pp

Lancaster S T Bras R L 2002 A simple model of river meandering and its comparison to natural channels Hydrological Processes 16 1ndash26

MacDonald T E 1991 Inventory and analysis of stream meander problems in minnesota Masterrsquos thesis Department of Civil Engineering University

16

Fig 11 User interface to see results for the statistical module

4 Discussion

The applicability of RV R Meander represents the first stage (ie evaluation of alternatives in re-meandering of channelized streams) on restoration projects because of its simplicity and practicality allowing this model can be run in any PC computer without any problem of memory or storage capacity This model can be used to characterize meandering rivers in a large planform scale (by using the statistical module) and to predict river migration (by using a simplified 2-D module) The migration module could be easily adapted to any stream by calibrating the bank erosion coefficient (with past river centershylines) and therefore it represents a first evaluation tool rather than describshying the full hydrodynamics sediment transport and bank erosion processes which indeed require more advanced models More sophisticated 2-D models for river migration (with corrections for secondary flows shear stress distrishybutions gravity effects on bedload etc) have been presented in the past such as Mosselman (1998) Nagata et al (2000a) Nagata et al (2000b) Duan et al (2001) Sun et al (2001a) Sun et al (2001b) Sun et al (2001c) Darby and Delbono (2002) Lancaster and Bras (2002) among others Abad (2005) stated that some of the existing 2-D hydrodynamic models also present sevshyeral limitations since they do not capture accurately flow structures such as the bi-cellular secondary pattern the boundary shear distribution and thereshyfore sediment transport pattern which are part of river migration Thus the applicability of any model requires prior knowledge of which is the objective for the project in study therefore the user should be aware of which are the limitations when using a specific model

14

5 Conclusions

RV R Meander (Abad and Garcia 2005) is a simplified river planform mishygration and statistical analysis computer model From this model Windows-based and GIS-based toolkits were developed These toolkits are considered a valuable tool for predicting river morphodynamics processes such as river evoshylution The RV R Meander model was validated in streams in Illinois (Garcia et al 1996) and in a recent project at Poplar Creek Abad (2002) and Abad and Garcia (2004) The toolkits both include two modules The first modshyule of statistical analysis allows the user to characterize meandering rivers The second module the river migration model allows the user to simulate the planform evolution of meandering rivers with time and should be useful for stream naturalization projects However the user should be aware of several limitations of the present migration module such as the width of the channel is treated as constant only one set of sediments is considered the discharge is calculated by using the concept of channel forming discharge no formulation for cut-off occurrence is incorporated

6 Acknowledgments

The support of the Illinois Water Resources Center (Grants USGS Project 04 contract No 14-08-0004-G2017 and 2001IL4321B) and the National Science Foundation (Grant No 0097059) are gratefully acknowledged The authors are grateful to Bruce Rhoads and Rebeca Wade for providing us with the data used in the Poplar Creek study The help provided by Jose F Rodriguez is deeply appreciated Nils Oberg is also gratefully acknowledged for his contributions on the GIS-based version Suggestions and comments by Jose Vasquez and an additional anonymous reviewer helped to improve the final manuscript

References

Abad J D December 2002 2d river models for prediction of sediment transshyport and morphological variations Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign Illinois USA 73 pp

Abad J D 2005 Cfd simulations of asymmetric kinoshita-generated meshyandering bends Submitted to the XXXI International Association of Hyshydraulic Engineering and Research (IAHR) Congress September 11-16 Seoul Korea 10 pp

Abad J D Garcia M H 2004 Conceptual and mathematical model for

15

evolution of meandering rivers in naturalization processes On CD-ROM of Proc Joint Conference on Water Resources Engineering and Water Reshysources Planning and Management ASCE June 27-July 1 Salt Lake City Utah 10 pp

Abad J D Garcia M H 2005 Rvr meander Manual reference Hydrosysshytems Laboratory Department of Civil and Environmental Engineering Unishyversity of Illinois at Urbana-Champaign httpvtchluiucedusoftware 45 pp

Darby S E Delbono I 2002 A model of equilibrium bed topography for meanders Earth Surface Processes and Landforms 27 1057ndash1085

Duan J G Wang S Y Jia Y 2001 The applications of the enhanced cche2d model to study the alluvial channel migration processes Journal of Hydraulic Research 39 (5) 1ndash12

ESRI 2004 Edn documentation library for arcobjects Environmental Sysshytems Research Institute httpedndocesricomarcgisdeveloper

Fischenich C Morrow J V 2000 Reconecction of floodplains with incised channels United States Waterways Experimental Station Vicksburg Misshysissippi ERDC TN-EMRRP-SR-09 1ndash11

Garcia M H 1999 Sedimentation and erosion hydraulics In Mays K (Ed) Hydraulic Design Handbook McGraw-Hill New York pp 61ndash6113

Garcia M H Bittner L Nino Y 1996 Mathematical modeling of meanshydering streams in illinois A tool for stream management and engineering Hydraulic Engineering Series No 43 Department of Civil and Environmenshytal Engineering University of Illinois at Urbana-Champaign 63 pp

Hooke J M 1984 Changes in river meanders Progress in Physical Geograshyphy 8 473ndash508

Howard A D Hemberger A T 1991 Multivariate characterization of meshyandering Geormorphology 4 161ndash186

Ikeda S Parker G Sawai K 1981 Bend theory of river meanders part 1 linear development Journal of Fluid Mechanics 112 363ndash377

Kikkawa H Ikeda S Kitagawa A 1976 Flow and bed topography in curved open channels Journal of the Hydraulics Division 102 (HY9) 1327ndash 1342

Lagasse P F Spitz W J Zevenbergen L W 2003 A methodshyology for arcview tools for predicting channel migration ESRI User Conference Proceedings July 7-11 San Diego California USA httpgisesricomlibraryuserconfproc03abstractsa0251pdf

Lagasse P F Spitz W J Zevenbergen L W Zachmann D W 2004 Handbook for predicting stream meander migration Report 533 National Cooperative Highway Research Program Transportation Research Board of the National Academies Washington DC USA 105 pp

Lancaster S T Bras R L 2002 A simple model of river meandering and its comparison to natural channels Hydrological Processes 16 1ndash26

MacDonald T E 1991 Inventory and analysis of stream meander problems in minnesota Masterrsquos thesis Department of Civil Engineering University

16

5 Conclusions

RV R Meander (Abad and Garcia 2005) is a simplified river planform mishygration and statistical analysis computer model From this model Windows-based and GIS-based toolkits were developed These toolkits are considered a valuable tool for predicting river morphodynamics processes such as river evoshylution The RV R Meander model was validated in streams in Illinois (Garcia et al 1996) and in a recent project at Poplar Creek Abad (2002) and Abad and Garcia (2004) The toolkits both include two modules The first modshyule of statistical analysis allows the user to characterize meandering rivers The second module the river migration model allows the user to simulate the planform evolution of meandering rivers with time and should be useful for stream naturalization projects However the user should be aware of several limitations of the present migration module such as the width of the channel is treated as constant only one set of sediments is considered the discharge is calculated by using the concept of channel forming discharge no formulation for cut-off occurrence is incorporated

6 Acknowledgments

The support of the Illinois Water Resources Center (Grants USGS Project 04 contract No 14-08-0004-G2017 and 2001IL4321B) and the National Science Foundation (Grant No 0097059) are gratefully acknowledged The authors are grateful to Bruce Rhoads and Rebeca Wade for providing us with the data used in the Poplar Creek study The help provided by Jose F Rodriguez is deeply appreciated Nils Oberg is also gratefully acknowledged for his contributions on the GIS-based version Suggestions and comments by Jose Vasquez and an additional anonymous reviewer helped to improve the final manuscript

References

Abad J D December 2002 2d river models for prediction of sediment transshyport and morphological variations Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign Illinois USA 73 pp

Abad J D 2005 Cfd simulations of asymmetric kinoshita-generated meshyandering bends Submitted to the XXXI International Association of Hyshydraulic Engineering and Research (IAHR) Congress September 11-16 Seoul Korea 10 pp

Abad J D Garcia M H 2004 Conceptual and mathematical model for

15

evolution of meandering rivers in naturalization processes On CD-ROM of Proc Joint Conference on Water Resources Engineering and Water Reshysources Planning and Management ASCE June 27-July 1 Salt Lake City Utah 10 pp

Abad J D Garcia M H 2005 Rvr meander Manual reference Hydrosysshytems Laboratory Department of Civil and Environmental Engineering Unishyversity of Illinois at Urbana-Champaign httpvtchluiucedusoftware 45 pp

Darby S E Delbono I 2002 A model of equilibrium bed topography for meanders Earth Surface Processes and Landforms 27 1057ndash1085

Duan J G Wang S Y Jia Y 2001 The applications of the enhanced cche2d model to study the alluvial channel migration processes Journal of Hydraulic Research 39 (5) 1ndash12

ESRI 2004 Edn documentation library for arcobjects Environmental Sysshytems Research Institute httpedndocesricomarcgisdeveloper

Fischenich C Morrow J V 2000 Reconecction of floodplains with incised channels United States Waterways Experimental Station Vicksburg Misshysissippi ERDC TN-EMRRP-SR-09 1ndash11

Garcia M H 1999 Sedimentation and erosion hydraulics In Mays K (Ed) Hydraulic Design Handbook McGraw-Hill New York pp 61ndash6113

Garcia M H Bittner L Nino Y 1996 Mathematical modeling of meanshydering streams in illinois A tool for stream management and engineering Hydraulic Engineering Series No 43 Department of Civil and Environmenshytal Engineering University of Illinois at Urbana-Champaign 63 pp

Hooke J M 1984 Changes in river meanders Progress in Physical Geograshyphy 8 473ndash508

Howard A D Hemberger A T 1991 Multivariate characterization of meshyandering Geormorphology 4 161ndash186

Ikeda S Parker G Sawai K 1981 Bend theory of river meanders part 1 linear development Journal of Fluid Mechanics 112 363ndash377

Kikkawa H Ikeda S Kitagawa A 1976 Flow and bed topography in curved open channels Journal of the Hydraulics Division 102 (HY9) 1327ndash 1342

Lagasse P F Spitz W J Zevenbergen L W 2003 A methodshyology for arcview tools for predicting channel migration ESRI User Conference Proceedings July 7-11 San Diego California USA httpgisesricomlibraryuserconfproc03abstractsa0251pdf

Lagasse P F Spitz W J Zevenbergen L W Zachmann D W 2004 Handbook for predicting stream meander migration Report 533 National Cooperative Highway Research Program Transportation Research Board of the National Academies Washington DC USA 105 pp

Lancaster S T Bras R L 2002 A simple model of river meandering and its comparison to natural channels Hydrological Processes 16 1ndash26

MacDonald T E 1991 Inventory and analysis of stream meander problems in minnesota Masterrsquos thesis Department of Civil Engineering University

16

evolution of meandering rivers in naturalization processes On CD-ROM of Proc Joint Conference on Water Resources Engineering and Water Reshysources Planning and Management ASCE June 27-July 1 Salt Lake City Utah 10 pp

Abad J D Garcia M H 2005 Rvr meander Manual reference Hydrosysshytems Laboratory Department of Civil and Environmental Engineering Unishyversity of Illinois at Urbana-Champaign httpvtchluiucedusoftware 45 pp

Darby S E Delbono I 2002 A model of equilibrium bed topography for meanders Earth Surface Processes and Landforms 27 1057ndash1085

Duan J G Wang S Y Jia Y 2001 The applications of the enhanced cche2d model to study the alluvial channel migration processes Journal of Hydraulic Research 39 (5) 1ndash12

ESRI 2004 Edn documentation library for arcobjects Environmental Sysshytems Research Institute httpedndocesricomarcgisdeveloper

Fischenich C Morrow J V 2000 Reconecction of floodplains with incised channels United States Waterways Experimental Station Vicksburg Misshysissippi ERDC TN-EMRRP-SR-09 1ndash11

Garcia M H 1999 Sedimentation and erosion hydraulics In Mays K (Ed) Hydraulic Design Handbook McGraw-Hill New York pp 61ndash6113

Garcia M H Bittner L Nino Y 1996 Mathematical modeling of meanshydering streams in illinois A tool for stream management and engineering Hydraulic Engineering Series No 43 Department of Civil and Environmenshytal Engineering University of Illinois at Urbana-Champaign 63 pp

Hooke J M 1984 Changes in river meanders Progress in Physical Geograshyphy 8 473ndash508

Howard A D Hemberger A T 1991 Multivariate characterization of meshyandering Geormorphology 4 161ndash186

Ikeda S Parker G Sawai K 1981 Bend theory of river meanders part 1 linear development Journal of Fluid Mechanics 112 363ndash377

Kikkawa H Ikeda S Kitagawa A 1976 Flow and bed topography in curved open channels Journal of the Hydraulics Division 102 (HY9) 1327ndash 1342

Lagasse P F Spitz W J Zevenbergen L W 2003 A methodshyology for arcview tools for predicting channel migration ESRI User Conference Proceedings July 7-11 San Diego California USA httpgisesricomlibraryuserconfproc03abstractsa0251pdf

Lagasse P F Spitz W J Zevenbergen L W Zachmann D W 2004 Handbook for predicting stream meander migration Report 533 National Cooperative Highway Research Program Transportation Research Board of the National Academies Washington DC USA 105 pp

Lancaster S T Bras R L 2002 A simple model of river meandering and its comparison to natural channels Hydrological Processes 16 1ndash26

MacDonald T E 1991 Inventory and analysis of stream meander problems in minnesota Masterrsquos thesis Department of Civil Engineering University

16

of Minnesota Minneapolis Minnesota USA 152 pp MacDonald T E Parker G Leuthe D 1992 Inventory and analysis of

stream meander problems in minnesota Tech rep Department of Civil Engineering University of Minnesota Minneapolis Minnesota USA 38 pp

Miller D E 1999 Deformable stream banks Can we call it restoration withshyout them Wildland Hydrology 293ndash300

Mosselman E 1998 Morphological modeling of rivers with erodible banks Hydrological Processes 12 1357ndash1370

Nagata N Hosoda T Muramoto Y 2000b Numerical analysis of river channel processes with bank erosion Journal of Hydraulic Engineering 112 (4) 243ndash252

Nagata N Uchikura Y Hosoda T 2000a Numerical study on changes of channel configuration after river improvement work On CD-ROM of Proc of Fourth International Conference on Hydroinformatics July 23-27 Iowa City Iowa USA 8 pp

Newbury R Gaboury M Watson C Roseboom D Hill T Beardsley J Rodsater J Duong L 1992 Field manual of urban stream restorashytion Report to the U S Environmental Protection Agency Conservation Technology Information Center West Lafayette IN USA 144 pp

Oneill M P Abrahams A D 1986 Objective identification of meanders and bends Journal of Hydrology 83 337ndash353

Parker G Diplas P Akiyama J 1983 Meander bends of high amplitude Journal of Hydraulic Engineering 109 (10) 1323ndash1337

Rhoads B L Garcia M H Rodriguez J F Abad J D Bombardelli F A Daniels M 2005 Evaluating the geomorphological performance of naturalized rivers Submitted as a book chapter In Sears D and Darby S (Eds) Uncertainty in River Restoration 44 pp

RRC 2002 Manual of River Restoration Techniques Web edition River Restoration Center Silsoe Campus Silsoe Bedfordshire UK httpwwwtherrccoukmanualphp

Shields F D Copeland R R Klingeman P C Doyle M W Simon A 2003 Design for stream restoration Journal of Hydraulic Engineering 129 (8) 575ndash584

Sun T Meakin P Jossang T 2001a Meander migration and the lateral tilting of floodplains Water Resources Research 37 (5) 1485ndash1502

Sun T Meakin P Jossang T 2001b A computer model for meandering rivers with multiple bed load sediment sizes 1 Theory Water Resources Research 37 (8) 2227ndash2241

Sun T Meakin P Jossang T 2001c A computer model for meandering rivers with multiple bed load sediment sizes 2 Computer simulations Water Resources Research 37 (8) 2243ndash2258

Zimmerman C Kennedy J F 1978 Transverse bed slopes in curved alluvial streams Journal of the Hydraulics Division 104 (HY1) 33ndash48

17