Model help:AgDegNormGravMixPW: Difference between revisions

Revision as of 15:53, 10 May 2011

AgDegNormGravMixPW

This is the calculator for aggradation and degradation of sediment mixtures in gravel-bed streams.

Model introduction

The program AgDegNormGravMixPW is an extension of AgDegNormal for sediment mixtures in gravel bed rivers where the channel bed material is transported as bedload only.

Model parameters

Parameter	Description	Unit
Input directory	path to input files
Site prefix	Site prefix for Input/Output files
Case prefix	Case prefix for Input/Output files

Parameter	Description	Unit
Chezy Or Manning, Chezy-1 or Manning-2
Bedload relation, Parker or Wilock, Parker-1 or Wilock-2

Parameter	Description	Unit
Flood discharge		m³ / s
gravel input		m² / s
Intermittency		-
base level		m
initial bed slope		-
reach length		m
Time step		days
no. of intervals(100 or less)		-
Number of printouts		-
Iterations per each printout		-
factor by which Ds90 is multiplied for roughness height		-
factor by which Ds90 is multiplied for active layer thickness		-
Manning-Strickler coefficient r
Submerged specific gravity of sediment
bed porosity, gravel
upwinding coefficient for load spatial derivatives in Exner equation (> 0.5 suggested)
coefficient for material transferred to substrate as bed aggrades
Chezy resistance coefficient		-

Parameter	Description	Unit
Model name	name of the model	-
Author name	name of the model author	-

Uses ports

This will be something that the CSDMS facility will add

Provides ports

This will be something that the CSDMS facility will add

Main equations

Characteristic diameter for the ith size range

[math]\displaystyle{ D_{i} = \left ( D_{b,i} \ast D_{b,i+1} \right ) ^ \left ( {\frac{1}{2}} \right ) }[/math]

(1)

The fraction of sample in the ith size range

[math]\displaystyle{ f_{i} = f_{f,i+1} - f_{f,i} }[/math]

(2)

The conservation of sediment in each grain size range (based on Exner equation)

[math]\displaystyle{ \left ( 1 - \lambda _{p} \right ) [L_{a} {\frac{\partial F_{i}}{\partial t}} + \left ( F_{i} - f_{li} \right ) {\frac{\partial L_{a}}{\partial t}}] = -I_{f} {\frac{\partial q_{bT} p_{i}}{\partial x}} + I_{f} f_{li} {\frac{\partial q_{bT}}{\partial x}} }[/math]

(3)

Fraction of sediment in the ith grain size range at the active-layer substrate interface (if ∂η / ∂t > 0)

[math]\displaystyle{ f_{li} = \left\{\begin{matrix} \alpha F_{i} + \left ( 1 - \alpha \right ) p_{i} & {\frac{\partial \eta}{\partial t}} \gt 0 \\ f_{sub,i} & {\frac{\partial \eta}{\partial t}} \lt 0 }[/math]

(4)

Roughness height due to skin friction

[math]\displaystyle{ k_{s} = n_{k} D_{s90} }[/math]

(5)

Thickness of the active layer

[math]\displaystyle{ L_{a} = n_{a} D_{s90} }[/math]

(6)

Nomenclature

Symbol	Description	Unit
Q	flood discharge	m ³ / s
x	streamwise coordinate	m
η	river bed elevation	m
t	time step	year
B	river width	m
D	grain size of the bed sediment	mm
D_bi	bound diameter	mm
λ_p	bed porosity	-
α	the parameter that governs the grain size distribution of the sediment at the active layer-substrate interface during bed aggredation	-
F_fi	grain size distribution of the active layer for initial condition	-
F_i	fraction of sediment in the ith grain size range in the active layer	-
f_subfi	fraction of sediment in the ith grain size range in the substrate layer for initial condition	-
F_fli	percent finer than ith grain size range for the bed surface for initial condition	-
F_subfli	percent finer than ith grain size range for the substrate layer for initial condition	-
f_li	fraction of sediment in the ith grain size range in the active-layer substrate interface	-
p_i	fraction of sediment in the ith grain size range in the bedload	-
F_sub,i	fraction of substrate material in the ith size range	-
D_s90	the diameter of the bed surface such that the 90% of the sediment is finer	-
n_a	user specified order-one non dimensional constant	-
p_ffi	the percent that is finer than the ith size range for upstream boundary conditon	-
η_d	fixed bed elevation at the downstream end of the modeled reach	m
R	submerged specific gravity	-
ξ_d	downstream water surface elevation	m
q_w	water discharge per unit width	m² / s
k_c	composite roughness height	m
G	imposed annual sediment transfer rate from upstream	tons / annum
G_tf	upstream sediment feed rate	-
ξ_d	downstream water surface elevation	m
L	length of reach under consideration	m
q_w	water discharge per unit width	m² / s
i	number of time steps per printout	-
p	number of printouts desired	-
M	number of spatial intervals	-
R	submerged specific gravity of sediment	-
S_f	friction slope	-
F_r	Froude number	-
U	flow velocity	m / s
C_f	bed friction coefficient	-
g	acceleration of gravity	m/ s^2
α_r	coefficient in Manning-Stricker, dimensionless coefficient between 8 and 9	-
k_s	grain roughness	m
n_k	dimensionless coefficient typically between 2 and 5	-
τ^*	Shield number	-
ρ	fluid density	kg / m³
ρ_s	sediment density	kg / m³
τ_c	critical Shields number for the onset of sediment motion	-
ψ_s	the fraction of bed shear stress	-
q_t ^*	Einstein number	-
q_t	volume sediment transport rate per unit width	-
I_f	flood intermittency	-
t_f	cumulative time the river has been in flood	s
G_t	the annual sediment yield	tone/yr
t_a	the number of seconds in a year	-
Q_f	sediment transport rate during flood discharge
α_t	dimensionless coefficient in the sediment transport equation, equals to 8	-
n_t	exponent in sediment transport relation, equals to 1.5	-
τ_c ^*	reference Shields number in sediment transport relation, equals to 0.047
C_f	bed friction coefficient, equals to τ_b / (ρ U² )	-
C_Z	dimensionless Chezy resistance coefficient.
S_l	initial bed slope of the river	-
η_i	initial bed elevation	-
D_sub50	median size of the substrate layer	m
D_subg	geometric mean size of the substrate layer	m
L_a	thickness of the active layer	m
x	downstream coordinate	m
τ	shear stress on bed surface	N / m²
q_b	bed material load	tons / year
Δx	spatial step length, equals to L / M	m
Q_w	flood discharge	m³ / s
Δt	time step	year
Ntoprint	number of time steps to printout	-
Nprint	number of printouts	-
a_U	upwinding coefficient (1=full upwind, 0.5=central difference)	-
α_s	coefficient in sediment transport relation	-

Output

Symbol	Description	Unit
η	bed surface elevatioon	m
H	water depth	m
ξ	water surface elevation	m
τ_b	bed shear stress	kg / (s^2 m)
S	bed slope	-
q_t	total bed material load	m² / s

Notes

This program computes the time evolution of the long profile of a river of constant width carrying a mixture of gravel sizes, the downstream end of which has a prescribed elevation. In particular, the program computes the time evolution of the spatial profiles of bed elevation, total gravel bedload transport rate and grain size distribution of the surface (active) layer of the bed.

Gravel-bed rivers tend to be poorly-sorted. During floods, bed material load consists almost exclusively of bedload. (Sand is often transported in copious quantities as washload during floods.) The surface material (armor or pavement) tends to be coarser than the substrate. By definition the median size or geometric mean size of the substrate is in the gravel range, but the substrate may contain up to 30% sand in the interstices of an otherwise clast-supported deposit.

The grain size distribution of the bed material is specified in terms of 12 size bounds, Dbi with i = 1 …12, such that f_fi denotes the mass fraction of the sample that is finer than D_bi. The 12 bound diameters specify 11 grain size ranges defined by (D_b,i, D_b,i+1) and (f_f,i, f_f,i+1). For each size range the model computes the characteristic diameter and the fraction of sample in the ith size range.

The flow is assumed normal and the water depth can be computed with either a Manning-Strickler or a Chezy formulation can be used.

The exchange of sediment between the bedload and the bed deposit is modeled with a two-layer model for the channel bed. The bed deposit is divided in two regions, 1) the substrate and 2) the active (or surface or armor) layer.

The grain size distribution of the active layer is assumed to be constant in the vertical and it may vary in the streamwise direction and in time, i.e. the active layer is assumed well-mixed. The grain size distribution of the substrate, in principle, may vary in both streamwise and vertical direction, but it is constant in time. The only way the grain size distribution of the substrate may vary in time is by creating new substrate via bed aggradation. In the present model, the grain size distribution of the substrate is assumed to be constant in space and in time, therefore it works only for the cases of aggradation always and everywhere or degradation always and everywhere. In the case of aggradation followed by degradation, it is necessary to modify the code so that the vertical variation of the grain size distribution of the new substrate created by aggradation is stored in memory.

No attempt is made in this code to decompose the bed resistance into skin friction and form drag. The constant to convert total boundary shear stress to that due to skin friction, ψ_s, is set equal to 1 and consequently the composite roughness height for the Manning-Strickler formulation, k_c, is equal to the roughness height due to skin friction k_s. The roughness height and the thickness of the active layer are computed with the liner functions of the diameter of the bed surface such that the 90% of the sediment is finer.

To compute the bedload transport rate the user can choose from two surface-based bedload transport formulations; those of Parker (1990) and Wilcock and Crowe (2003). In the relation of Parker (1990) the surface grain size distributions need to be renormalized to exclude sand before specification as input to the program. This step is neither necessary nor desirable in the case of the relation of Wilcock and Crowe (2003), where the sand plays an important role in mediating the gravel bedload transport.

The program does not store the vertical and streamwise structure of the new substrate created as the bed aggrades.It is assumed in the model that the grain size distribution of the sediment feed rate does not change in time, the initial grain size distribution of the surface material is the same at every node, the grain size distribution of the substrate is the same at every node and does not vary in the vertical.

The flow is calculated using the normal flow (local equilibrium) approximation.

Note on model running

In the case of the load relation due to Parker (1990), the grain size distributions are automatically renormalized because the relation is for the transport of gravel only in the case of the load relation due to Wilcock-Crowe (2003), the sand and the fine sediment are retained for the computation

The user will be prompted by the program as to which bedload relation he would like to use.

The input grain size distributions may be on a 0-100% or a 0.00-1.00 scale, and the program will automatically scale.

The input grain size distributions must have bounds at 0% and 100% (1.00) to properly perform the calculation. If the user does not input the bounds the program will automatically interpolate upper and lower bounds D_bU and D_bL such that f_fU = 100 (1.00) and f_fL = 0

The water depth is calculated using a Chézy formulation, when only the Chézy coefficient is specified in the input text file. The Manning-Strickler formulation is implemented, when only the coefficients αr and nk are given in the inputfile. When all the three parameters are present, the program will ask the user which formulation they would like to use.

Examples

An example run with input parameters, BLD files, as well as a figure / movie of the output

Follow the next steps to include images / movies of simulations:

Upload file: http://csdms.colorado.edu/wiki/Special:Upload
Create link to the file on your page: [[Image:<file name>]].

Developer(s)

Gary Parker

References

Parker, G., 1990, Surface-based bedload transport relation for gravel rivers, Journal of Hydraulic Research, 28(4): 417-436.

Wilcock, P. R., and Crowe, J. C., 2003, Surface-based transport model for mixed-size sediment, Journal of Hydraulic Engineering, 129(2), 120-128.

Links

@@ Line 17: / Line 17: @@
 ==Model introduction==
-This program computes the time evolution of the long profile of a river of constant width carrying a mixture of gravel sizes, the downstream end of which has a prescribed elevation. In particular, the program computes the time evolution of the spatial profiles of bed elevation, total gravel bedload transport rate and grain size distribution of the surface (active) layer of the bed. The river has constant width. The upstream point, at which sediment is fed, is fixed in the horizontal to be at x = 0. The vertical elevation of the upstream point may change freely as the bed aggrades or degrades. The reach has constant length L, so that the downstream point is fixed in the horizontal at x = L. This downstream point has a user-specified initial elevation hdI.
+The program AgDegNormGravMixPW is an extension of AgDegNormal for sediment mixtures in gravel bed rivers where the channel bed material is transported as bedload only.
-Gravel bedload transport of mixtures is computed with a user-specified selection of the Parker (1990), or Wilcock-Crowe (2003) surface-based formulations for gravel transport. Sand and finer material must first be excluded from the grain size distributions, which then must be renormalized for gravel content only, in the case of the Parker (1990) relation. In the case of the Wilcock-Crowe (2003) relation, the sand is retained in the computation.
 <div id=CMT_MODEL_PARAMETERS>
@@ Line 159: / Line 157: @@
 ==Main equations==
-* Exner equation of conservation of channel bed sediment
+* Characteristic diameter for the ith size range
 ::::{|
-|width=530px|<math> \left ( 1 - \lambda _{p} \right ) {\frac{\partial \eta}{\partial t}} = - I_{f} {\frac{\partial q_{bT}}{\partial x}} </math>
+|width=530px|<math> D_{i} = \left ( D_{b,i} \ast D_{b,i+1} \right ) ^ \left ( {\frac{1}{2}} \right ) </math>
 |width=50p=x align="right"|(1)
 |}
-* Characteristic diameter
+* The fraction of sample in the ith size range
 ::::{|
-|width=530px|<math> D_{i} = \left ( D_{b,i} \ast D_{b,i+1} \right ) ^ \left ( {\frac{1}{2}} \right ) </math>
+|width=530px|<math> f_{i} = f_{f,i+1} - f_{f,i} </math>
 |width=50p=x align="right"|(2)
 |}
+* The conservation of sediment in each grain size range (based on Exner equation)
 ::::{|
-|width=530px|<math> f_{i} = f_{f,i+1} - f_{f,i} </math>
+|width=530px|<math> \left ( 1 - \lambda _{p} \right ) [L_{a} {\frac{\partial F_{i}}{\partial t}} + \left ( F_{i} - f_{li} \right ) {\frac{\partial L_{a}}{\partial t}}] = -I_{f} {\frac{\partial q_{bT} p_{i}}{\partial x}} + I_{f} f_{li} {\frac{\partial q_{bT}}{\partial x}} </math>
 |width=50p=x align="right"|(3)
 |}
-* The conservation of sediment in each grain size range
+* Fraction of sediment in the ith grain size range at the active-layer substrate interface (if ∂η / ∂t > 0)
 ::::{|
-|width=530px|<math> \left ( 1 - \lambda _{p} \right ) [L_{a} {\frac{\partial F_{i}}{\partial t}} + \left ( F_{i} - f_{li} \right ) {\frac{\partial L_{a}}{\partial t}}] = -I_{f} {\frac{\partial q_{bT} p_{i}}{\partial x}} + I_{f} f_{li} {\frac{\partial q_{bT}}{\partial x}} </math>
+|width=530px|<math> f_{li} = \left\{\begin{matrix} \alpha F_{i} + \left ( 1 - \alpha \right ) p_{i} & {\frac{\partial \eta}{\partial t}} > 0 \\ f_{sub,i} & {\frac{\partial \eta}{\partial t}} < 0 </math>
 |width=50p=x align="right"|(4)
-|}
-* Fraction of sediment in the ith grain size range at the active-layer substrate interface (if ∂η / ∂t > 0)
-::::{|
-|width=530px|<math> f_{li} = \alpha F_{i} + \left ( 1 - \alpha \right ) p_{i}  </math>
-|width=50p=x align="right"|(5)
-|}
-* Fraction of sediment in the ith grain size range at the active-layer substrate interface (if ∂η / ∂t < 0)
-::::{|
-|width=530px|<math> f_{li} = f_{sub,i}  </math>
-|width=50p=x align="right"|(6)
 |}
 * Roughness height due to skin friction
 ::::{|
 |width=530px|<math> k_{s} = n_{k} D_{s90}  </math>
-|width=50p=x align="right"|(7)
+|width=50p=x align="right"|(5)
 |}
+* Thickness of the active layer
 ::::{|
 |width=530px|<math> L_{a} = n_{a} D_{s90}  </math>
-|width=50p=x align="right"|(8)
+|width=50p=x align="right"|(6)
-|}
-* Non-dimensional bed shear stress
-::::{|
-|width=530px|<math> \tau _{sg} ^* = {\frac{\tau_{b}}{\left ( \rho _{s} - \rho \right ) g D_{sg}}}  </math>
-|width=50p=x align="right"|(9)
 |}
@@ Line 209: / Line 194: @@
 !Symbol!!Description!!Unit
 |-
-| q
+| Q
-| water discharge / width
+| flood discharge
-| m<sup>2</sup> / s
+| m <sup>3</sup> / s
 |-
-| T
+| x
-| gravel input
+| streamwise coordinate
-| m<sup>2</sup> / s
+| m
 |-
-| I
+| η
-| intermittency
+| river bed elevation
-| -
-|-
-| e
-| base level
 | m
 |-
-| S
+| t
-| initial bed slope
+| time step
-| -
+| year
 |-
-| L
+| B
-| reach length
+| river width
 | m
 |-
-| t
+| D
-| time step
+| grain size of the bed sediment
-| days
+| mm
+|-
+| D<sub>bi</sub>
+| bound diameter
+| mm
 |-
-| M
+| λ<sub>p</sub>
-| no. of intervals
+| bed porosity
 | -
 |-
-| p
+| α
-| no. of prints
+| the parameter that governs the grain size distribution of the sediment at the active layer-substrate interface during bed aggredation
 | -
 |-
-| i
+| F<sub>fi</sub>
-| no. of iterations per print
+| grain size distribution of the active layer for initial condition
 | -
 |-
-| k
+| F<sub>i</sub>
-| factor by which Ds90 is multiplied for roughness height
+| fraction of sediment in the ith grain size range in the active layer
 | -
 |-
-| n
+| f<sub>subfi</sub>
-| factor by which Ds90 is multiplied for active layer thickness
+| fraction of sediment in the ith grain size range in the substrate layer for initial condition
 | -
 |-
-| r
+| F<sub>fli</sub>
-| coefficient in Manning-Strickler relation
+| percent finer than ith grain size range for the bed surface for initial condition
 | -
 |-
-| R
+| F<sub>subfli</sub>
-| submerged specific gravity of gravel
+| percent finer than ith grain size range for the substrate layer for initial condition
 | -
 |-
-| l
+| f<sub>li</sub>
-| bed porosity, gravel
+| fraction of sediment in the ith grain size range in the active-layer substrate interface
 | -
 |-
-| u
+| p<sub>i</sub>
-| upwinding coefficient for load spatial deviations in Exner equation (> 0.5 suggested)
+| fraction of sediment in the ith grain size range in the bedload
 | -
 |-
-| a
+| F<sub>sub,i</sub>
-| coefficient for material transferred to substrate as bed aggrades
+| fraction of substrate material in the ith size range
 | -
 |-
-| C
+| D<sub>s90</sub>
-| coefficient, Cf, in the Chezy formulation
+| the diameter of the bed surface such that the 90% of the sediment is finer
 | -
 |-
-| q<sub>w</sub>
+| n<sub>a</sub>
-| the characteristic flood discharge per unit channel width
+| user specified order-one non dimensional constant
-| -
-|-
-| I<sub>f</sub>
-| flood intermittency
 | -
 |-
-| q<sub>bTf</sub>
+| p<sub>ffi</sub>
-| the volumetric gravel input rate per unit channel width
+| the percent that is finer than the ith size range for upstream boundary conditon
 | -
 |-
 | η<sub>d</sub>
-| the downstream bed elevation
+| fixed bed elevation at the downstream end of the modeled reach
 | m
 |-
-| λ<sub>p</sub>
+| R
-| the bed porosity
+| submerged specific gravity
 | -
 |-
-| S<sub>l</sub>
+| ξ<sub>d</sub>
-| the initial bed slope
+| downstream water surface elevation
+| m
+|-
+| q<sub>w</sub>
+| water discharge per unit width
+| m<sup>2</sup> / s
+|-
+| k<sub>c</sub>
+| composite roughness height
+| m
+|-
+| G
+| imposed annual sediment transfer rate from upstream
+| tons / annum
+|-
+| G<sub>tf</sub>
+| upstream sediment feed rate
 | -
 |-
-| D<sub>bi</sub>
+| ξ<sub>d</sub>
-| the bound diameter
+| downstream water surface elevation
+| m
+|-
+| L
+| length of reach under consideration
+| m
+|-
+| q<sub>w</sub>
+| water discharge per unit width
+| m<sup>2</sup> / s
+|-
+| i
+| number of time steps per printout
 | -
 |-
-| n<sub>k</sub>
+| p
-| dimensionless coefficient typically between 2 and 5
+| number of printouts desired
 | -
-|-
-| Δt
-| time step
-| year
 |-
-| Ntoprint
+| M
-| number of time steps to printout
+| number of spatial intervals
 | -
 |-
-| Nprint
+| R
-| number of printouts
+| submerged specific gravity of sediment
 | -
 |-
-| a<sub>U</sub>
+| S<sub>f</sub>
-| upwinding coefficient (1=full upwind, 0.5=central difference)
+| friction slope
 | -
 |-
-| α<sub>r</sub>
+| F<sub>r</sub>
-| coefficient to compute the roughness height
+| Froude number
 | -
 |-
-| n<sub>a</sub>
+| U
-| coefficient to compute the thickness of the active layer
+| flow velocity
+| m / s
+|-
+| C<sub>f</sub>
+| bed friction coefficient
 | -
 |-
-| α
+| g
-| the parameter that governs the grain size distribution of the sediment at the active layer-substrate interface during bed aggradation
+| acceleration of gravity
+| m/ s^2
+|-
+| α<sub>r</sub>
+| coefficient in Manning-Stricker, dimensionless coefficient between 8 and 9
 | -
 |-
-| x
+| k<sub>s</sub>
-| downstream coordinate
+| grain roughness
 | m
+|-
+| n<sub>k</sub>
+| dimensionless coefficient typically between 2 and 5
+| -
+|-
+| τ<sup>*</sup>
+| Shield number
+| -
+|-
+| ρ
+| fluid density
+| kg / m<sup>3</sup>
+|-
+| ρ<sub>s</sub>
+| sediment density
+| kg / m<sup>3</sup>
+|-
+| τ<sub>c</sub>
+| critical Shields number for the onset of sediment motion
+| -
 |-
-| Sl
+| ψ<sub>s</sub>
-| slope of the bed surface
+| the fraction of bed shear stress
 | -
 |-
-| u<sub>*</sub>
+| q<sub>t</sub> <sup>*</sup>
-| shear velocity
+| Einstein number
-| m / s
+| -
 |-
-| p<sub>feed</sub>
+| q<sub>t</sub>
-| GSD of the feed
+| volume sediment transport rate per unit width
-| tons / year
+| -
 |-
-| F<sub>fs</sub>
+| I<sub>f</sub>
-| GSD of the substrate
+| flood intermittency
 | -
 |-
-| F<sub>f</sub>
+| t<sub>f</sub>
-| GSD of the final surface
+| cumulative time the river has been in flood
+| s
+|-
+| G<sub>t</sub>
+| the annual sediment yield
+| tone/yr
+|-
+| t<sub>a</sub>
+| the number of seconds in a year
 | -
 |-
-| η
+| Q<sub>f</sub>
-| bed elevation
+| sediment transport rate during flood discharge
-| m
 |-
-| f<sub>fi</sub>
+| α<sub>t</sub>
-| the mass fraction of the sample that is finer than D<sub>bi</sub>
+| dimensionless coefficient in the sediment transport equation, equals to 8
 | -
 |-
-| f<sub>i</sub>
+| n<sub>t</sub>
-| the fraction of sample in the ith size range
+| exponent in sediment transport relation, equals to 1.5
 | -
 |-
-| p<sub>i</sub>
+| τ<sub>c</sub> <sup>*</sup>
-| the fraction of sediment in the ith grain size range in the bedload
+| reference Shields number in sediment transport relation, equals to 0.047
+|-
+| C<sub>f</sub>
+| bed friction coefficient, equals to τ<sub>b</sub> / (ρ U<sup>2</sup> )
 | -
 |-
-| α
+| C<sub>Z</sub>
-| a user specified parameter
+| dimensionless Chezy resistance coefficient.
+|-
+| S<sub>l</sub>
+| initial bed slope of the river
 | -
 |-
-| f<sub>sub,i</sub>
+| η<sub>i</sub>
-| the fraction of substrate material in the ith range
+| initial bed elevation
 | -
 |-
-| ψ<sub>s</sub>
+| D<sub>sub50</sub>
-| boundary shear stress due to skin friction
+| median size of the substrate layer
+| m
+|-
+| D<sub>subg</sub>
+| geometric mean size of the substrate layer
+| m
+|-
+| L<sub>a</sub>
+| thickness of the active layer
+| m
+|-
+| x
+| downstream coordinate
+| m
+|-
+| τ
+| shear stress on bed surface
+| N / m<sup>2</sup>
+|-
+| q<sub>b</sub>
+| bed material load
+| tons / year
+|-
+| Δx
+| spatial step length, equals to L / M
+| m
+|-
+| Q<sub>w</sub>
+| flood discharge
+| m<sup>3</sup> / s
+|-
+| Δt
+| time step
+| year
+|-
+| Ntoprint
+| number of time steps to printout
 | -
 |-
-| k<sub>c</sub>
+| Nprint
-| composite roughness height for the Manning-Strickler formulation
+| number of printouts
 | -
 |-
-| k<sub>s</sub>
+| a<sub>U</sub>
-| roughness height due to skin friction
+| upwinding coefficient (1=full upwind, 0.5=central difference)
 | -
 |-
-| F<sub>fi</sub>
+| α<sub>s</sub>
-| grain size distributions of the active layer
+| coefficient in sediment transport relation
 | -
 |-
@@ Line 410: / Line 492: @@
 {| {{Prettytable}} class="wikitable sortable"
 !Symbol!!Description!!Unit
+|-
+| η
+| bed surface elevatioon
+| m
 |-
 | H
@@ Line 415: / Line 501: @@
 | m
 |-
-| τ<sub>sg</sub>
+| ξ
-| shear stress on the bed surface
+| water surface elevation
-| N / m<sup>2</sup>
-|-
-| η
-| bed surface elevation
 | m
 |-
-| q<sub>bT</sub>
+| τ<sub>b</sub>
-| bedload transport rate
+| bed shear stress
-| m<sup>2</sup> / s
+| kg / (s^2 m)
 |-
-| q<sub>bTf</sub>
+| S
-| upstream feed rate
+| bed slope
-| tons / year
+| -
 |-
-| D<sub>sg</sub>
+| q<sub>t</sub>
-| geometric mean grain size on the bed surface
+| total bed material load
-| mm
+| m<sup>2</sup> / s
-|-
-| D<sub>s90</sub>
-| the diameter such that 90% of the bed surface is finer
-| mm
 |-
 |}
@@ Line 444: / Line 522: @@
 ==Notes==
-The program AgDegNormGravMixPW is an extension of AgDegNormal for sediment mixtures in gravel bed rivers where the channel bed material is transported as bedload only.  Gravel-bed rivers tend to be poorly-sorted.  During floods, bed material load consists almost exclusively of bedload.  (Sand is often transported in copious quantities as washload during floods.)  The surface material (armor or pavement) tends to be coarser than the substrate.  By definition the median size D<sub>sub50</sub> or geometric mean size D<sub>subg</sub> of the substrate is in the gravel range, but the substrate may contain up to 30% sand in the interstices of an otherwise clast-supported deposit.
+This program computes the time evolution of the long profile of a river of constant width carrying a mixture of gravel sizes, the downstream end of which has a prescribed elevation. In particular, the program computes the time evolution of the spatial profiles of bed elevation, total gravel bedload transport rate and grain size distribution of the surface (active) layer of the bed.
-The grain size distributions of the sediment feed, initial surface material and substrate material must be specified. It is assumed that the grain size distribution of the sediment feed rate does not change in time, the initial grain size distribution of the surface material is the same at every node, the grain size distribution of the substrate is the same at every node and does not vary in the vertical. These constraints are easy to relax.
+Gravel-bed rivers tend to be poorly-sorted.  During floods, bed material load consists almost exclusively of bedload.  (Sand is often transported in copious quantities as washload during floods.)  The surface material (armor or pavement) tends to be coarser than the substrate.  By definition the median size or geometric mean size of the substrate is in the gravel range, but the substrate may contain up to 30% sand in the interstices of an otherwise clast-supported deposit.
-The program does not store the vertical and streamwise structure of the new substrate created as the bed aggrades. It is assumed that the grain size distribution of the sediment feed rate does not change in time, the initial grain size distribution of the surface material is the same at every node,  the grain size distribution of the substrate is the same at every node and does notvary in the vertical.  These constraints are easy to relax.
+The grain size distribution of the bed material is specified in terms of 12 size bounds, Dbi with i = 1 …12, such that f<sub>fi</sub> denotes the mass fraction of the sample that is finer than D<sub>bi</sub>.  The 12 bound diameters specify 11 grain size ranges defined by (D<sub>b,i</sub>, D<sub>b,i+1</sub>) and (f<sub>f,i</sub>, f<sub>f,i+1</sub>).  For each size range the model computes the characteristic diameter and the fraction of sample in the ith size range.
-The program does not store the vertical and streamwise structure of the new substrate created as the bed aggrades. As a result, is cannot capture the case of aggradation followed by degradation.  Again, the constraint is easy to relax, but at the price of increased memory requirements for storing the newly-created substrate.
+The flow is assumed normal and the water depth can be computed with either a Manning-Strickler or a Chezy formulation can be used.
+The exchange of sediment between the bedload and the bed deposit is modeled with a two-layer model for the channel bed.  The bed deposit is divided in two regions, 1) the substrate and 2) the active (or surface or armor) layer.
+The grain size distribution of the active layer is assumed to be constant in the vertical and it may vary in the streamwise direction and in time, i.e. the active layer is assumed well-mixed.  The grain size distribution of the substrate, in principle, may vary in both streamwise and vertical direction, but it is constant in time.  The only way the grain size distribution of the substrate may vary in time is by creating new substrate via bed aggradation.  In the present model, the grain size distribution of the substrate is assumed to be constant in space and in time, therefore it works only for the cases of aggradation always and everywhere or degradation always and everywhere.  In the case of aggradation followed by degradation, it is necessary to modify the code so that the vertical variation of the grain size distribution of the new substrate created by aggradation is stored in memory.
+No attempt is made in this code to decompose the bed resistance into skin friction and form drag.  The constant to convert total boundary shear stress to that due to skin friction, ψ<sub>s</sub>, is set equal to 1 and consequently the composite roughness height for the Manning-Strickler formulation, k<sub>c</sub>, is equal to the roughness height due to skin friction k<sub>s</sub>.  The roughness height and the thickness of the active layer are computed with the liner functions of the diameter of the bed surface such that the 90% of the sediment is finer.
+To compute the bedload transport rate the user can choose from two surface-based bedload transport formulations; those of Parker (1990) and Wilcock and Crowe (2003).  In the relation of Parker (1990) the surface grain size distributions need to be renormalized to exclude sand before specification as input to the program.  This step is neither necessary nor desirable in the case of the relation of Wilcock and Crowe (2003), where the sand plays an important role in mediating the gravel bedload transport.
-The flow is calculated using the normal flow (local equilibrium) approximation.
-The river is assumed to be morphologically active only intermittently (during floods); this condition is specified in terms of an intermittency If < 1 expressing the fraction of time the river is in flood.
+The program does not store the vertical and streamwise structure of the new substrate created as the bed aggrades.It is assumed in the model that the grain size distribution of the sediment feed rate does not change in time, the initial grain size distribution of the surface material is the same at every node, the grain size distribution of the substrate is the same at every node and does not vary in the vertical.
-In performing the calculation, the following control parameters must be specified:
+The flow is calculated using the normal flow (local equilibrium) approximation.
-M = number of spatial intervals, so that the spatial step length = L/M; dt = time step length; Ntoprint = number of time steps to a printout; Nprint = number of printouts in the calculation.
 * Note on model running
@@ Line 490: / Line 574: @@
 ==Links==
 * [[http://csdms.colorado.edu/wiki/Model:AgDegNormGravMixPW Model:AgDegNormGravMixPW]]
+* [[http://csdms.colorado.edu/wiki/Model_help:AgDegNormal Model_help:AgDegNormal]]
 [[Category:Utility components]]