35th IAHR World Congress, September 8-13,2013, Chengdu, China
Optimal Control of Flow and Sediment in River and Watershed
National Center for Computational Hydroscience and Engineering (NCCHE)The University of Mississippi
Presented in 35th IAHR World Congress, September 8-13,2013, Chengdu, China
Yan Ding1, Moustafa Elgohry2, Mustafa Altinakar4, and Sam S. Y. Wang3
1. Ph.D. Dr. Eng., Research Associate Professor, UM-NCCHE2. Graduate Student, UM-NCCHE3. Ph.D., Research Professor and Director, UM-NCCHE4. Ph.D., P.E., F. ASCE, Frederick A. P. Barnard Distinguished Professor Emeritus&, Director Emeritus, UM-
NCCHE
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Flood and Channel Degradation/Aggredation
Flooded Street, Mississippi River Flood of 1927 River Bank Erosion
Levee Failure, 1993 flood. Missouri. Cedar Rapids, Iowa, June 14, 2008
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Flooding and Flood Control
Flood Gate, West Atchafalaya Basin, Charenton Floodgate, LA
The Bonnet Carré Spillway, the southern-most floodway in the Mississippi River and Tributaries system, has historically been the first floodway in the Lower Mississippi River Valley opened during floods. The USACE’s hydraulic engineers rely on discharge and gauge readings at Red River Landing, about 200 miles above New Orleans, to determine when to open the spillway. The discharge takes two days to reach the city from the landing. As flows increase, bays are opened at Bonnet Carré to divert them.
The spillway (highlighted in green)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Sediment Control
Reservoir Sediment Release at 9:00am, Clear Water Release at 10:00am, 6/19/2010
Xiao Land Di Reservoir, Yellow River, China Yellow River
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Flow and Sediment Transport Control Problems
• Perform an optimally-scheduled water delivery for irrigation to meet the demand of water resources in irrigation canals
Optimal Water Resource Management (only flow control)
• Prevent levee of river from overflowing or breaching during flood season by using the most secure or efficient approach, e.g., operating dam discharge, diverting flood, etc.
Optimal Flood Flow Control (probably with sediment transport)
• To release reservoir sediments to river reaches downstream for managing sediment transport and morphological changes
Best Sediment Release Management
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Difficulties in Optimal Control of Flow and Sediments
• Temporally/spatially non-uniform flow and morphodynamics Requires a forecasting model which can accurately predict complex water flows
and morphodynamic processes in space and time in rivers and watersheds
• Nonlinearity of flow and sediment control Nonlinear process control, Nonlinear optimization Difficulties to establish the relationship between control actions and responses of the
hydrodynamic and morphodynamic variables
• Requirement of Efficient Simulation and optimization In case of fast propagation of flood wave, a very short time is available for predicting
the flood flow at downstream. Due to the limited time for making decision of flood mitigation, it is crucial for decision makers to have an efficient forecasting model and a control model.
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Objectives
Theoretically, • Through adjoint sensitivity analysis, make nonlinear optimization capable of
flow control in complex channel shape and channel network in watershed Optimal Nonlinear Adaptive Control Applicable to unsteady river flows
• Establish a general simulation-based optimization model for controlling hazardous floods so as to make it applicable to a variety of control scenarios
Flexible Control System; and a general tool for real-time flow control
• Sediment Control: Minimize morphological changes due to flood control actions
Optimal Control with multiple constraints and objectives
For Engineering Applications,• Integrate the control model with the CCHE1D flow model, • Apply to practical problems
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Integrated Watershed & Channel Network Modeling with CCHE1D
Digital ElevationModel (DEM)
Rainfall-Runoff Simulation
Upland Soil Erosion(AGNPS or SWAT)
Channel Network Flow and Sediment Routing
(CCHE1D)
Channel Network andSub-basin Definition
(TOPAZ)
01
qxQ
tAL
02 2
2
2
fgSxZg
AQ
xAQ
tL
3/42
2 ||RA
QQnS f
Dynamic Wave Model for Flood Wave Prediction
A=Cross-sectional Area; q=Lateral outflow;=correction factor; R=hydraulic radius n = Manning’s roughness
where Q = discharge; Z=water stage;
• Boundary Conditions• Initial Conditions (Base Flows)• Internal Flow Conditions for Channel
Network
Hydrodynamic Modeling in Channel Network Non-uniform Total-Load Transport Non-equilibrium Transport Model Coupled Sediment Transport Equations Solution Bank Erosion and Mass Failure Several Methods for Determination of Sediment-Related
Parameters
Principal Features
35th IAHR World Congress, September 8-13,2013, Chengdu, China
CCHE1D Sediment Transport ModelNon-equilibrium transport of non-uniform sediments
*
1tk tktk lkt k
t tk s
Q Q Q Q qt U x L
/tk tk t tkC Q A U
*' 11 bk
tk t ks
Ap Q Qt L
*
1tk tktk lkt k
s
AC Q Q Q qt x L
**
bk tkt kQ p Q
A= cross-section area; Ctk= section-averaged sediment concentration of size class k; Qtk= actual sediment transport rate; Qt*k= sediment transport capacity; Ls= adaptation length and Qlk = lateral inflow or outflow sediment discharge per unit channel length; Ut=section averaged velocity of sediment
Non-uniform Total-Load Transport Non-equilibrium SedTran Model Coupled SedTran Equations Solution
(Direct Solution Technique) Bank Erosion and Mass Failure Several Methods for Determination of
Sediment-Related Parameters
Principal Features
35th IAHR World Congress, September 8-13,2013, Chengdu, China
+2.0m
+0.0m
20m
70m
Zobj
Objective Function for Flood Control
To evaluate the discrepancy between predicted and maximum allowable stages, a weighted form is defined as
where T=control duration; L = channel length; t=time; x=distance along channel; Z=predicted water stage; Zobj(x) =maximum allowable water stage in river bank (levee) (or objective water stage); x0= target location where the water stage is protective; = Dirac delta function
40 0 0
0 0
[ ( , ) ( )] ( ), ( ) ( )
0, ( ) ( )
obj objZ
obj
W Z x t Z x x x if Z x Z xr LT
if Z x Z x
0 0( , , , , )
T LFJ r Z Q q x t dxdt
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Sensitivity Analysis- Establishing A Relationship between Control Actions and System Variables
• Compute the gradient of objective function with respect to control variable
1. Influence Coefficient Method (Yeh, 1986): Parameter perturbation trial-and-error; lower accuracy
2. Sensitivity Equation Method (Ding, Jia, & Wang, 2004) Directly compute the sensitivity ∂X/∂q by solving the sensitivity equations Drawback: different control variables have different forms in the equations, no general
measures for system perturbations; The number of sensitivity equations = the number of control variables.
Merit: Forward computation, no worry about the storage of codes
3. Adjoint Sensitivity Method (Ding and Wang, 2003) Solve the governing equations and their associated adjoint equations sequentially. Merit: general measures for sensitivity, limited number of the adjoint equations
(=number of the governing equations) regardless of the number of control variables. Drawback: Backward computation, has to save the time histories of physical variables
before the computation of the adjoint equations.
35th IAHR World Congress, September 8-13,2013, Chengdu, China
x
t
A B
CD
O L
T
Variational Analysis- to Obtain Adjoint Equations
Extended Objective Function
*1 20 0
( )T L
F F A QJ J L L dxdt where A and Q are the Lagrangian multipliers
Fig. 1: Solution domain
Necessary Condition* 0F FJ J
on the conditions that
1
2
( , ) 0( , ) 0{L Q Z
L Q Z
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Adjoint Equations for the Full Nonlinear Saint Venant Equations
* 2
2 (1 ) | |Q QA A g AV Vg r Q rVt x B x K A A Q
2
2
2Q QAQ
gA V rA Vt x x K Q
According to the extremum condition, all terms multiplied by A and Q can be set to zero, respectively, so as to obtain the equations of the two Lagrangian multipliers, i.e, adjoint equations (Ding & Wang 2003)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Adjoint Equations: Linear, Hyperbolic, and of First-Order
The obtained adjoint equations are first-order partial differential equations, which can be rewritten into a compact vector form
0
PNUUMU
xt
Q
A
U
VABgV
*M
2
2
2
||20
||20
KVgA
KVAVg
Nwhere
P represents the source term related to the objective function
This adjoint model has two characteristic lines with the following two real and distinct eigenvalues:
*2
2
2,1 4)1(
21
BAgVV
*2,1 BAgV
In the case of a flow in a prismatic open channel, β=1, therefore
Wave celerity is the same as the open channel flow. But propagation direction in time is opposite (i.e. backward in time)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Variations of J with Respect to Control Variables – Formulations of Sensitivities
00
( (0, )) ( ) (0, )T
Ax
rJ Q t Q t dtQ
ndxdtnK
QgQnrnJ
T L Q
0 0 2
||2)(
dttLAAQ
Bg
ArtLAJ
Lx
T
Q ),()()),((0 3
2
*
dxdttxqqrtxqJ
T L
A ),()),((0 0
Lateral Outflow
Upstream Discharge
Downstream Section Area or Stage
Bed Roughness
Remarks: Control actions for open channel flows may rely on one control variable or a rational combination of these variables. Therefore, a variety of control scenarios principally can be integrated into a general control model of open channel flow.
Q(0,t)
Q(L,t)
q(x,t)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Optimal Control of Sediment Transport and Morphological Changes
The developed model is coupling an adjoint sensitivity model with a sediment transport simulation model (CCHE1D) to mitigate morphological changes.
Different optimization algorithms have been used to estimate the value of the diverted or imposed sediment along river reach (control actions) to minimize the morphological changes under different practices and applications.
Optimization Model
Adjoint sensitivity model
Sediment Transport Simulation Model
CCHE1D
Sediment Control Model
35th IAHR World Congress, September 8-13,2013, Chengdu, China
A Nonuniform/nonequilibrium Sediment Transport Model: CCHE1D
1tk tktk t k k
s
AC Q Q Q qt x L
/ ( )tk tk t tkC Q AU
In which the depth-average concentration and the sediment transport rate can be expressed as
and Eq. (1) becomes,
The bed deformation is determined with
' 11 bktk t k
s
Ap Q Q
t L
* 0bktk t k
AQ Qt
If
Governing equation for the nonequilibrium transport of nonuniform sediment is
3 *1( ) ( ) 0t t
t t t ls
Q QL Q Q Q qt U x L
(1)
(2)
(3)
(4)
(5)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Objective Function for Sediment Control and Minimization of Morphological Changes (Strong Control Condition)
To evaluate the bed area change, a weighted form is defined as
0 0
( , , , )T L
S b lJ f A q x t dxdt
2
0b
SW Af x xLT t
(6)
(7)
where f is a measuring function and can be defined as,
The optimization is to find the control variable q satisfying a dynamic system such that
where Abis satisfied with the sediment continuity equation
Local minimum theory : Necessary Condition: If q is the true value, then JS(q)=0; Sufficient Condition: If the Hessian matrix 2JS(q) is positive definite,
then ql is a local minimizer of fS.
( ) min( ( , )),S b lf q J A q (8)
21
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Optimization Model
objtQ can be taken equal to *tQ
The objective function for control of morphological changes can be written as
and measuring function as,
0 0
( , , , )T L
S S t lJ f Q q x t dxdt
2
02 2
1 , ,(1 ')
objS t t
s
Wf Q x t Q x t x xLT p L
(9)
(10)
22
where i.e. the sediment transport capacity.
' 11 bt t
s
Ap Q Qt L
Consider the equation of morphological change:
It means that for minimizing morphological change in a cross section, it is needed to make sediment transport rate in the section close to the sediment transport capacity.
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Adjoint Equation for Sediment Control
*3
0 0
T L
S S SJ f L dxdt
S SS t l
t l
f fdf Q qQ q
31 1 0t t
t t ls
Q QL Q Q qU t x L
*
0 0 0 0 0 0
T L T L T LS S S S S S t
S t l t S l S tt l s
f f QJ Q q dxdt Q dxdt q dxdt dx Q dtQ q U t x L U
Taking the first variation of the augmented objective function, i.e.
By using Green’s theorem and the variation operator δ in time-space domain shown in Fig. (1), the first variation of the augmented function can be obtained
For minimizing J* , δJ* must be equal zero which means all terms multiplied by δQt must be set to zero which leads to the following equation,
which is the adjoint equation for the Lagrangian multiplier λS
(14)
(15)
(16)
(17)
(18) 02 2
2 1 ,(1 ')
objS S St t
s s
W Q x t Q x x xU t x L LT p L
24
Figure 1. Solution domain
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Sediment Transport Control Actions and Sensitivity
00
( (0, )) ( ) (0, )T
SS t S t
t x
fJ Q t Q t dtQ
Lateral Sediment Discharge
Upstream Sediment Discharge
0 0( ( , )) ( , )
T LS
S l S ll
fJ q x t q x t dxdtq
In this study, fS is not a function in ql, thus the sensitivity is based on the values of λS.26
0( ( , )) ( ) ( , )
TS
S t S tt x L
fJ Q L t Q L t dtQ
Downstream Sediment Discharge
Lateral Outflow ql
Qt(0,t)
Qt(L,t)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Minimization Procedures
• Limited-Memory Quasi-Newton Method (LMQN) Newton-like method, applicable for large-scale computation
(with a large number of control parameters), considering the second order derivative of objective function (the approximate Hessian matrix)
Algorithms: BFGS (named after its inventors, Broyden, Fletcher,
Goldfarb, and Shanno) L-BFGS (unconstrained optimization) L-BFGS-B (bound constrained optimization)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Application
Optimal Flood Control in Alluvial Rivers and Watersheds(with sediment transport but no sediment control)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Optimal Control of Flood Diversion Rate A Hypothetic Single Channel
Time
Dis
char
ge
Tp Td
Qp
Qb
+2.0m
+0.0m
20m
70m
1:2
1:1.
5
Storm Event: A Triangular Hydrograph
x (km)
Elev
atio
n(m
)
0 2 4 6 8 100
1
2
3
4
5
6 Zobj(x) = 4.75-0.025x
Bed slope = 1:40000; d50=0.127mm
q(t)Divert clear waterq(t)=?
Cross Section
100m3/s
48 hours16 hours
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Hours
Dis
char
ge(m
3 /s)
0 12 24 36 48
-100
-50
0
50
100
Iteration= 1Iteration= 4Iteration= 5Iteration= 6Iteration= 10Iteration= 30Iteration= 70
Inflow Hydrograph at inlet
Optimal q(t)
Optimal Lateral Outflow and Objective Function (Case 1)
Iterations of L-BFGS-BO
bjec
tive
Func
tion
Nor
mof
Gra
dien
t
0 10 20 30 40 50 60 7010-3
10-2
10-1
100
101
102
103
104
105
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Objective FunctionNorm of Gradient
Iterations of optimal lateral outflowObjective function and Norm of
gradient of the function
Optimal Outflow q
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Thalweg Change after Storm
x (km)
Thalweg(m)
ThalwegChange(m)
0 2 4 6 8 10-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Initial thalwegThalweg after eventThalweg change
q
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Water Stage and Lateral Discharge
Hours
Wat
erSt
age
(m)
0 12 24 36 481.5
2.5
3.5
4.5
5.5
Without sediment transportWith sediment transport
Zobj=4.57m
HoursD
isch
arge
(m3 /s
)0 12 24 36 48
-80
-60
-40
-20
0
Without sediment transportWith sediment transport
The water stage comparison for with and without sediment transport consideration at bed slope
The lateral discharge comparison for with and without sediment transport consideration at bed slope 32.5 10
32.5 10
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Optimal Control of Lateral Outflows – Multiple Lateral Outflows (Case 3)
Suppose that there are three flood gates (or spillways) in upstream, middle reach, and downstream.
Condition of control:
Z0=3.5m
q1 q2q3
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Optimal Discharges for Multiple Floodgates
Hours
Discharge(m
3 /s)
0 12 24 36 48-100
-75
-50
-25
0
25
50
75
100
125
q2
q3
q1
Discharge withdrawn by single floodgate
Total discharge = q1 + q2 + q3
Hydrograph at inlet
Z0=3.5m
q1 q2 q3
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Comparison of Thalweg Changes after Storm
x (km)
Thalwegchange(m)
0 2 4 6 8 10-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Three floodgatesOne floodgate
q2q1 q3(or q)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
L3 = 13,000m
L2 = 4,500m
L 1=
4,00
0m
1
2
3
Channel No.
Optimal Control of Multiple Lateral Outflows in a Channel Network
Channel No.
QP (m3/s)
Qb (m3/s)
Tp (hour)
Td (hour)
Z0 (m)
1 50.0 2.0 16.0 48.0 3.5 2 50.0 2.0 16.0 48.0 3.5 3 60.0 6.0 16.0 48.0 3.5
+2.0m
+0.0m
20m
70m
1:2
1:1.
5
Z0=3.5m
q3(t)=?
Compound Channel Section
Time
Dis
char
ge
Tp Td
Qp
Qb
Time
Dis
char
ge
Tp Td
Qp
Qb
Time
Dis
char
ge
Tp Td
Qp
Qb
q2(t)=?
q1(t)=?
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Optimal Lateral Outflow Rates and Objective Function
Iterations of L-BFGS-B
Obj
ectiv
eFu
nctio
n0 20 40 60 80 100
10-6
10-4
10-2
100
102Case 5Case 6
Optimal lateral outflow rates at three diversions
Comparison of objective function
One Diversion
Three Diversions
Hours
Dis
char
ge(m
3 /s)
0 12 24 36 48-50
-40
-30
-20
-10
0
10
20
30
40
50
60
q1q2q3
Hydrograph of inlfow at main stem
Hydrograph at two branches
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Comparison of Thalweg along Main Channel
Distance [k m]
Th
alw
eg[m
]
0 1 2 3 4 5 6 7 8 9 10 11 12 130.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Initial ThalwegNo ControlCase 1 (Gate 1 at 1.5 k m ds)Case 2 (Gate 1 at 2.5 k m ds)Case 3 (Gate 1 at 3.5 k m ds)Case 4 (Gate 1 at 4.5 k m ds)
Case 3
Gate 2
Gate 3
C ase 1C ase 2
Jun
cti o
n
Jun c
tion
4.5 k m
1.5 k m
2.5 k m
Case 4
3.5 k m
Distance [km]
Tha
lwe g
[m]
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.51.9
2.1
2.3
2.5
2.7
2.9
3.1
3.3
Initial ThalwegNo ControlCase 1 (Gate 1 at 1.5 km ds)Case 2 (Gate 1 at 2.5 km ds)Case 3 (Gate 1 at 3.5 km ds)Case 4 (Gate 1 at 4.5 km ds)
Case 3
Case 1
Case 2
4.5 km
1.5 km
2.5 km
case 43.5 km
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Application
Optimal Control of Sediment Transport and Morphological Changes in Alluvial Rivers and Watersheds
(No Flow Control)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Hypothetical Case (2): Reservoir Sediment Release
L=7 km
S0=0.5 %
Given Q = Q(t)
1:2 1:2
10 m
20 m
Qs= ?
52
Control Objective: To minimize morphological change downstream
Simulation time = 1 yearSediment Properties: Uniform sediment of d = 20 mmBed load adaptation length = 125 m, suspended load adaptation coefficient = 0.1, and mixing-layer thickness = 0.05 m.
Excess Erosion Problem
Downstream
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Hypothetical Case (2): Conotrol Reservoir Sediment Release
This case has been tested under three different scenarios:
1. Regular operating conditions: The dam release discharge was assumed to be 10 m3/s.
2. Stage operating conditions: The case has been again tested under stage dam release flow discharge
3. Storm operating conditions: the case has been again tested under storm dam release flow discharge
Time (days)
Upstreamflowdischarge(m3/s)
0 50 100 150 200 250 300 350 4000
5
10
15
20
25
30
35
40
45
50
55
60
Figure (2) Stage reservoir water release Figure (3) Stage reservoir water releaseTime (hour)
Upstreamflowdischarge(m3/s)
0 5 10 15 20 25 30 35 40 450
5
10
15
20
25
30
35
40
45
50
55
60
Scenario 2 Scenario 3
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Hypothetical Case (2) – Scenario (1): Model Results
54
Clear water release rate at upstream Q(t) = 10 m3/s
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Hypothetical Case (2) – Scenario (2): Model Results
55Time (days)
Upstreamsedimentdischarge(kg/s)
0 50 100 150 200 250 300 350 4000
5
10
15
20
Distance downstream (km)
Thalwegchange(m)
0 1 2 3 4 5 6 7-10
-8
-6
-4
-2
0
2
No control (clear water)With control
Time (days)
Upstreamflowdischarge(m3/s)
0 50 100 150 200 250 300 350 4000
5
10
15
20
25
30
35
40
45
50
55
60
Flow Release Condition
Optimal Sediment Release Solution
Morphological Changes after one year
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Hypothetical Case (2) – Scenario (3): Model Results
56
Time (hours)
Upstreamsedimentdischarge(kg/s)
0 10 20 30 400
5
10
15
20
25
30
35
No limit on reservior release capacityReservior release capacity = 15 kg/s
Distance downstream (km)
Thalwegchange(m)
0 1 2 3 4 5 6 7-0.4
-0.2
0
0.2
No control (clear water)With control
Time (hour)
Upstreamflowdischarge(m3/s)
0 5 10 15 20 25 30 35 40 450
5
10
15
20
25
30
35
40
45
50
55
60
Upstream flood flow (given)
Morphological changes after storm
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Case (3): Sandy River Reach and Marmot Dam Removal
Source: Stillwater Science, 1999
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Dam Removal Impacts
59
The impacts of removal have been addressed by different studies. Generally they can be divided into main categories.
(1) Short-Term Ecological Impacts of Dam Removal Sediment Release, Increased Sediment Concentration and Contaminated Sediment, and
(2) Long-Term Impacts of Dam Removal (Flow change regimes, temperature, sediment transport and water quality)
Objective of control in this case:
Minimize the morphological changes (erosion and deposition) at downstream by diverting extra sediments from the reservoir (dredging?)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Case Study - Overview
Reservoir deposition profile (Source: PGE photogrametry, 1999)
Reservoir sediment size composition (Stillwater Science, 1999)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Bed Material Properties and Model Parameters
Parameter Value
Roughness Coefficient (Manning’s n) 0.03-0.06 upstream and 0.04-0.06 downstream
Sediment transport equation Wu-Wang-Jia’s formula (Wu et al. 2000)
SEDTRA module (Garbrecht et al. 1995)
Modified Ackers-White formula (Proffit & Sutherland 1983)
Engelund and Hansen’s formula (Engelund and Hansen 1967)Bed load adaptation length 250, 350, 500 and 1000m
Suspended load adaptation coefficient 0.25, 0.5 and 1.0
Mixing-layer thickness 0.05, 0.1 and 0.2mPorosity
0.25Simulation time step, Δt
0.5, 1, 3 and 6 minutesCross sections spacing, Δx
Varying (12m-325m)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Sediment size classes used in the simulations
Number of size
Representative size (mm)
Lower limit (mm)
Upper limit (mm)
1 0.09196 0.0625 0.1252 0.18393 0.125 0.253 0.36785 0.25 0.54 0.73570 0.5 1.05 1.47140 1.0 2.06 2.94281 2.0 4.07 5.88562 4.0 8.08 11.77124 8.0 16.09 23.54247 16.0 32.0
10 47.08494 32.0 64.011 94.16989 64.0 128.012 188.33980 128.0 256.0
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Upstream Discharge Hydrograph
Simulation Period 10/19/2007 – 09/30/2008
Averagedailydischarge(m
3 /s)
10/15 11/15 12/16 01/16 02/16 03/18 04/18 05/19 06/19 07/20 08/20 09/200
50
100
150
200
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Simulation Results: Bed load adaptation length (1/3)
Parameter ValueRoughness Coefficient (Manning’s n)
0.04 upstream and 0.06 downstream
Sediment transport equation
Wu-Wang-Jia’s formula (Wu et al. 2000)
Bed load adaptation length 350 m
Suspended load adaptation coefficient 0.5
Mixing-layer thickness 0.05 m
Simulation time step 0.5 minuteSediment Size Class 12
Simulation parameters and associated values
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Simulation Results: Bed Evolution
Distance From Marmot Dam (km)
Average
Bed
ElevationChange(m)
-2.5 -2 -1.5 -1 -0.5 0-12
-10
-8
-6
-4
-2
0
2
Observations after 1 year15 Days3 months6 months9 months1 year
Dam
Location
(a)
Distance From Marmot Dam (km)
Average
Bed
ElevationChange(m)
0 2 4 6 8 10 12 14 16 18-2
0
2
4
6
8
Observations after 1 year15 Days3 months6 months9 months1 year
Dam
Location
(b)
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Application of Developed Model after Dam Removal
Calculate the required diverted sediment after Marmot dam removal at the location of the dam to mitigate the excess deposition downstream. Simulating period is one year immediately after dam removal.
Date
SedimentDischarge(m3/s)
12-04-2007 03-03-2008 06-01-2008 08-30-20080
0.1
0.2
0.3
0.4Natural sediment flushDiverted sediment under optimal control
Engineering difficulty: how to divert the sediments based on the optimal schedule?Distance Downstream from Marmot Dam (km)
AverageBed
ElevationChange(m)
0 2 4 6 8 10 12 14 16 18-1
0
1
2
3
4
5
Without ControlWith Control
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Optimal sediment diversion after Dam Removal
Date
SedimentDischarge(m3/s)
12-04-2007 03-03-2008 06-01-2008 08-30-20080
0.1
0.2
0.3
0.4Natural sediment flushDiverted sediment under optimal control
Engineering difficulty: how to divert the sediments based on the optimal schedule?
Distance Downstream from Marmot Dam (km)
AverageBed
ElevationChange(m)
0 2 4 6 8 10 12 14 16 18-1
0
1
2
3
4
5
Without ControlWith Control
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Application of the Simulation-based Optimization Model To Channel Network – Problem Setup
+2.0m
+0.0m
20m
70m
1:2
1:1.
5
Compound Channel Section
L3 = 13,000m
L2 = 4,500m
L 1=
4,00
0m
1
2
3
Channel No.
qs(t)=?
Time
Dis
char
ge
Tp Td
Qp
Qb
Time
Dis
char
ge
Tp Td
Qp
Qb
Time
Dis
char
ge
Tp Td
Qp
Qb
Confluence
Channel No.
QP (m3/s)
Qb (m3/s)
Tp (hour)
Td (hour)
1 50.0 2.0 16.0 48.0 2 50.0 2.0 16.0 48.0 3 60.0 6.0 16.0 48.0
Parameters for a 2-day Storm
Sediment Properties: Uniform sediment of d = 20 mm
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Application of Developed Model To Channel Network – Internal Condition at a Confluence
Internal Boundary Condition
21
3 1 20 0 0
T T T
S t S t S tx x xQ dt Q dt Q dt
3 1 2t t tQ Q Q
1 2 3
0
0T
S t S t S tx x xQ Q Q dt
3
3 1 2t t tx x x
Q Q Q
1 2 3 1 3 2
0
0T
S t S t S t S tx x x x x xQ Q Q Q dt
1 3 2 3
0
0T
S S S Sx x x xdt 1 2 3
S S Sx x x
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Optimal Results for Controlling Morphological Changes in Channel Network
Results after 70 iterations
Time [hours]
Upstreamsedimentdischarge[kg/s]
0 4 8 12 16 20 24 28 32 36 40 44 480
0.01
0.02
0.03
0.04
0.05
0.06
Distance [km]
Thalwegchange[m]
0 2 4 6 8 10 12-0.02
-0.015
-0.01
-0.005
0
0.005
Without ControlWith ControlOptimal Solution of Sediment Release
Comparison of Thalweg Changes along the main channel
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Conclusions
79
An optimal procedure to minimize bed changes in open-channels was developed. It is based on adjoint sensitivity analysis for a one-dimensional sediment transport model, CCHE1D. The optimization module includes a numerical solver for the adjoint equation and an optimization procedure.
The model has been validated and applied to different sediment problems in alluvial rivers under different scenarios. The model has the flexibility to control the rate of bed deformation cross-sectional area under different control variables i.e. side inflow/outflow, upstream or downstream sediment discharge conditions.
Different optimization algorithms has been tested and a Limited Memory Quasi-Newton (L-BFGS-B) algorithm was the fastest convergent one.
The model has been applied to sedimentation problems and the results demonstrated that the model is able to mitigate the morphological changes effectively. The developed approach for real world cases such as optimal sediment diversion after dam removal has been elaborated.
35th IAHR World Congress, September 8-13,2013, Chengdu, China
Acknowledgements
This work was a result of research sponsored by the USDA Agriculture Research Service under Specific Research Agreement No. 58-6408-7-236 (monitored by the USDA-ARS National Sedimentation Laboratory) and The University of Mississippi.