Transcript A simulation-optimization-based decision support system for water

A simulation-optimization-based
decision support system
for water allocation
14. Workshop
Modellierung und Simulation von Ökosystemen
27.10-29.10.2010
Divas Karimanzira
• Goals
• Problem situation
• Structure of the decision support system
• Selected results
• Benefits and applications
• Conclusions
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Goals
• Provide Descision Support (DSS) for comprehensive
Water Management: Surface Water (SW) Resources
and Groundwater (GW) Resources
• Support Water Management through
comprehensive Water Models for SIMULATION and
Model Based OPTIMIZATION
• Support Water Management through SCENARIOS
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Total area [sq. km]
Beijing vs Thuringia
16.800
16.172
Inhabitants, 2003
14.560.000
2.373.000
Beijing
Province
Per capita water consumption [l/d], 2003
248
87
Precipitation, annual mean [mm], 1993-2003
Beijing
City
509
626
Average monthly values (1993-2003)
Thuringia
Erfurt
Precipitation [mm])
180
Beijing
Thuringia
160
140
120
100
80
60
40
20
0
jan feb mar apr may jun jul aug sep oct nov dec
Month
4
Yongding river downstream
of the Sanjiadin-Sluice
Miyun
Largest drinking
water reservoir
o
Max. storage 4,37 bn m³.
o
03.2004, 30m below the highest
admissible level,
o
Corresponds to a storage volume of only
0,8 bn. m³ water.
o
o
Dry since 1998
Water directed to Beijing.
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Sources
Huairou
Miyun
Baihebao
Guanting
Transport systems
BeijingMiyunChannel
Bai river
Guishui river
Waterworks
Customers
WW 9
Tianchunsan
Households
&
Industry
Changxindian
Chengzi
Yongding r.
Industry
Yanhua
...
Pipeline
groundwater
Agriculture
WW 8
Aggr. WW
Live
environment
6
• Groundwater is the most important source of water for the
Beijing region covering 50-70%
• Almost all available groundwater resources are already
developed.
• Beijing has suffered from over exploitation of this source.
• Surface water supply in the Beijing region depend mainly
on upstream inflows (Chaobai, North Grand Canal,
Yongding)
Problems:
• excessive withdrawal
• lack of regional coordination leads to issues such as
– uncoordinated withdrawals
– and upstream water contamination.
7
8
• Data to identify and describe the physical, social, legal, economic, and
institutional factors that affect water resources management.
•
Climatic factors such as temperature, wind, solar radiation, and rainfall
•
Water quantity and quality demands over time and space
• Land-use and geomorphic information (e.g., slopes, drainage density,
geology, Soils, land covers, channel cross-sections, and groundwater
depths);
• Hydrologic data that include flows, water levels, depths, and velocities;
• Pollutant loads from point sources (e.g., cities, industries, and wastewater
• Treatment plants that discharge their wastes into surface waters and
• Pollutant loads from nonpoint sources that enter surface waters along an
entire stretch of the river, channel or reservoir.
Datatypes: static and dynamic data, numbers, time series, text, and images
that characterize the quantity, quality, and spatial and temporal
distributions
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Chaobai River
Miyun-Inflow Huai
Chaobai River
Inflow Huai-Xiangyang Sluice
Data source
TS_Q_ChaobaiFinalFlowStation
ChaobaiFinalFlowStation
Wenyu River
TS_Q_Miy un_FROM_OtherRiv ers
0
Other rivers
Huai River
River /
Channel /
Pipeline
TS_Q_Xiahui
Qing River
Catchment area
Miyun
TS_Q_Zhangjiaf en
Catchment
area
TS_Q_Chaobai_FROM_Bai
Catchment area
Bai river
Miyun Reservoir
Bai River
Pipeline
Miyun-9th Waterworks
Huairou-WW9
TS_Q_Koutou
Jing Mi-Tuancheng
Huairou Reservoir
TS_Q_Xiapu
Water Tunnel
Catchment area
Huairou
XXX Sluice
Yongding-Yuyuantan
Reservoir
Guishui River
SNWT-Tuancheng
TS_Q_Guanting_FROM_Guishui
Initial states:
Hucheng + Tonghui River
Jing Mi Channel
Huairou-Tuancheng
TS_Q_Qianxinzhuan
Baihebao Reservoir
WenyuFinalFlowStation
Miyun-WW9
Pipeline
Huairou-9th Waterworks
Split
Jing Mi Channel
Bai River
Jing Mi Channel
Miyun-Huairou
Catchment area
Baihebao
TS_Q_Weny uFinalFlowStation
Wenyu River
Qing-Tonghui
South-North
Water Transfer
Yongding Channel
Sluice
IS_H_Miyun
IS_H_Baihebao
IS_H_Guanting
IS_H_Huairou
Beijing
City
Demand
TS_Q_Sanjiadian_TO_YongdingChannel
TS_Q_Sanjiadian_FROM_Yongding
TS_Q_Xiangshuibao
TS_Q_Sanjiadian_TO_Yongding
Yongding River
Guanting-Zhaitang
TS_Q_Shixiali
Defines initial
states
Catchment area
Guanting
Guanting Reservoir
Yongding River
Zhaitang-Sanjiadian
Sanjiadian Sluice
TS_Q_Yongding_FROM_MiddleWatershed
Water from middle watershed
Confluence
Groundwater
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Summary:
• Consists of important surface water elements:
–
–
–
–
–
–
5 catchment areas (sub-catchments neglected)
4 reservoirs
2 lakes
11 rivers and channels
7 waterworks
1 reduced groundwater model or interface to FEFLOW simulation
• Fast simulation (≈ 0.5 minute per year simulation time) allows simulation
horizons of 10 years or more
• Possibility to control different outflows manually
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Integration of GW and SW-Models
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13
 Finite Element models are computationally expensive!
 But: For optimization GW model has to be started > 1000 times!
3D-Model: ~100.000 nodes, simulation of 5 years: ~15 Minutes
Optimization time: 250 hours ~ 10 days !
 Reduction of complexity of Groundwater Model necessary!
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• Inputs:
– Groundwater recharge,
– Withdrawal rates, water supply
• Output:
– Hydraulic heads of representative points
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•
The water resources allocation problem is formulated as a discrete-time optimal
control problem:
K 1

K
k
k
k
k 
min
F
x

f
x
,
u
,
z



0
u k , k 1,, K
k 0


 
•
subject to


x0  xt0 
Initial state (reservoir level,
groundwater head …)
xk 1  f k xk , uk , z k 
Process equations (balance of reservoir
and groundwater storages …)
Equality constraints (balance of nonhk xk , uk , z k   0
storage nodes …)
g k xk , uk , z k  0 Inequality constraints (min (max)
reservoir level …)
Optimization horizon
K


•
The equality and inequality constraints of the full discrete-time optimal control
problem are composed of the constraints of the individual elements of the
network definition.
•
The overall objective function is the sum of all objectives of the network elements.
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Example objective function:
A
maximize supply to customers
T
n
max WS ij
i 1 j 1
B
minimize demand deficit
T
min
n

i 1 j 1
WDi , j  WS i , j
WDi , j
; WS i , j  WDi , j
C
maximize level at Miyun reservoir at final time
max H T , Miyun
D
maximize groundwater head at final time
max H T ,GW
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Numerical Solver HQP
• Efficient and fast solution of time discrete optimal control
problems,
• Special interface to support the formulation of optimal
control problems,
• Sequential Quadratic Programming (SQP),
• Interior-Point method for the quadratic subproblems within
the SQP method,
• Gradient calculation by means of Automatic differentiation
(software package Adol-C),
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Reservoir water levels
Groundwater hydraulic head
Consumed water
Result
evaluation
Desired management policies
Groundwater
Surface water
(hydrology, optimization, decision maker)
Simulation
inputs
Human experts
Balance at surface level
Definition of the optimal
control problem
Objective functions, constraints,
initial state and prediction of
external influences
Model transfer
Optimization
Node-Link
Network
q Reservoir outflows
q Groundwater withdrawal
Decision proposal for water allocation
(Management plans)
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Discharge
Simulation
Land use
Climate
Flow rates
Surface water
model
Water demand
Groundwater
model
Exploitation
Flow rates
Hydraulic heads
Recharge
Discharge
Optimization
Water levels
Land use
Objective function
Flow rates
Climate
Model-based
optimizer
Water demand
Water levels
Flow rates
Hydraulic heads
Exploitation
Recharge
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...
Land use
economic
climate
Model parameters(e.g Volume characteristics)
Environment data(e.g.evaporation,land use )
Water demand (e.g. consumption policies )
Control strategies for reservoirs(e.g. timeseries)
Simulation control data(e.g. horizont, resolution )
Scenarios
Database management system
(TIMESERIES GENERATOR)
Population
Fi x, y, z, t 
Model
Parameters
Model
Structures
Surface water
model
Prognosis
Water
demand
Modell
Prognosis
Groundwater
model
Prognosis
Optimization
relevant data
OPTIMIZATION
Objectives,
constraints
Reporting tools:
Plots,
Spreadsheet
Presentation of relevant Information
HUMAN MACHINE INTERFACE (HMI)
DSS-WIZARD
Semi-automatic model update
Information system
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Scenario - Wizard
Report
SW-Model
(Matlab)
Network
Editor
(Java)
GW-Model
(FeFlow) Report
Water Demand
Model
(Matlab)
Reduced GW
Model
Report
(Matlab)
Optimizer
(C++)
SIM
OPT
Both
Report
SW-Model
Report (Matlab)
GW-Model
(FeFlow)
Report
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Attributes
Initial stage:
Scenario of year 2006
Assumed impact:
Precipitation drop from 600mm in year
2006 to 400mm in year 2007
Possible reactions: Increased exploitation of groundwater,
Increased waste water reuse,
Increased water use from water transfers,
Increased prices for household water use,
Decreased agricultural irrigation, etc.
Procedure:
For each possibility, a scenario has to be
formulated to derive the input for
simulations and running simulations for
the possibilities of the reaction
Decision support:
Comparison of the simulation results and
finding an optimum between the
possibilities for a given goal function
Goal function:
e.g., No limitations in water supply of the
households and minimal costs.
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Catchment area outflow [m3/h]
Cost Value
90
10
perfect Modell
simulation
80
8
measured
Simulation
Nash-Sutcliffe: 0.73135
Bias: 1.6612
6
70
4
60
2
50
Bias
0
40
-2
30
-4
20
-6
10
-8
-10
-0.4
0
1982/01/01
1984/01/01
1986/01/01
1988/01/01
1990/01/01
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Nash-Sutcliffe
Date
Catchment area outflow [m3/h]
45
Nash-Sutcliffe: 0.67845
• Results of modeling a
selected catchment area as
an example.
simulation
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measured
35
30
• Figures show good training
and validation Nash-Sutcliffe
values of 0.73135 and
0.67845, respectively.
25
20
15
10
5
0
2007/01/01
2011/01/01
2013/01/01
2015/01/01
Date
24
Inflow Guanting Reservior [m3/s]
250
• Figures show the
simulated/meas’d
water inflow into
the Guanting
reservoir and
Q_In_Guanting
Overall inflow (computed)
200
150
100
50
0
1995/01/01
1995/04/01
1995/07/01
1995/10/01
1996/01/01
Date
Guanting water level [m]
479
478.5
• the corresponding
water level for a
period of a year.
h_Guanting
Water_level (computed)
478
477.5
477
476.5
476
475.5
475
474.5
474
1995/01/01
1995/04/01
1995/07/01
1995/10/01
1996/01/01
Date
25
FEM vs. Reduced model (Output Nr. 5 - Scenario1)
37
Red. model
36
FEM model
35
h
[m]
34
33
32
31
30
29
28
0
1
2
3
4
• The performance of
the drastically red.
groundwater model is
good, reflecting the
fact that the original
FEM model with more
than 100.000 nodes
has been reduced to a
state space model
with 36 states.
Time [yr]
1.8
Measured
Model (1)
Model (2)
Model (3)
1.6
Water demand (100 mil m 3)
1.4
1.2
•
Yearly domestic water
demand:
Different model types:
– Model(1) – Kalman
predictor- based model
– Model(2)-multiple
regression model
– Model(3)- neural
network –based model
1
0.8
0.6
0.4
0.2
0
•
1997
1998
1999
2000
Year
2001
2002
2003
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• The proposed concept for optimal water
management is evaluated for several sets of
experiments.
• The first set of experiments compares two
scenarios.
• Scenario 1:
– minimize demand deficit and keep demand constant
for the next 10 years and
• Scenario 2
– minimize demand deficit and increase demand 5%
yearly for the next 10 years. The results of the two
scenarios are illustrated in the Figures 4 to 5.
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Beijing Water System - global demand and supply [m3/s]
300
global demand
global supply
250
200
150
100
50
Scenario 1
0
0
1
2
3
4
5
6
7
8
9
10
Time [y]
Beijing Water System - global demand and supply [m3/s]
350
• Scenario 1 shows
that the demand
can be fulfilled for
the ten years, but
without considering
sustainability, the
Miyun reservoir and
the Groundwater are
overexploited.
global demand
• By increasing in
Scenario 2 the
demand yearly, then
we can see that the
demand won’t be
fulfilled anymore
global supply
300
250
200
150
100
50
Scenario 2
0
0
1
2
3
4
5
6
7
8
9
10
28
Average head of global groundwater storage
30
• Within 1.5 years
Miyun has already
reached its
minimum and
28
26
Scenario 1
24
22
20
18
16
Scenario 2
14
12
10
0
2
3
4
5
6
7
8
9
10
6
7
8
9
10
• at the end of the 10
years, the systems
groundwater level
has sunk rapidly.
Water level of Miyun reservoir
160
max
155
150
145
Scenario 1
140
135
Scenario 2
130
min
125
0
1
2
3
4
5
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Use Case
Short-term Horizon
Time
Horizon
< 1 year
Scenario / Main Objectives
Result
Satisfy water supply of households,
industry, agriculture
- optimal withdrawal
strategies for reservoirs and
waterworks
Consideration of trends in
precipitation and consumption;
Reduce groundwater
overexploitation
Consideration of climatic changes,
new resources, consumption;
Stop groundwater overexploitation
- optimal withdrawal
strategies
- optimal resources
allocation
- simulation scenarios
Medium-term Horizon
1 ... 5
years
Long-term Horizon
5 ... 20
years
Extraordinary Events
< 1 year
Decision support e.g. for
- optimal withdrawal
environmental catastrophes;
strategies
objective function depends on the event - simulation scenarios
Structural Changes
1 ... 20
years
Prediction of impact of new elements
of the water system (e.g. new
channels or reservoires)
- simulation scenarios
30
•
•
•
•
Management of water supply based on optimization
–
optimized management of water resources
–
optimized supply in periods of increased demand
–
priority management in water scarcity periods
Emergency management and water resources protection in case of
–
natural disasters, terroristic attacks, accidents,
–
water resources pollution
Optimized adaptation of the water supply system to trends and changes
–
evaluation and implementation of political decisions
–
adaptation to changes in economy, population and agriculture
–
handling climate changes and water quality degradation
–
evaluation of increased waste water reuse
–
strategies for sustainability of water use
4. Support for planning tasks
–
simulation and optimization of future technical structures
–
simulation and evaluation of resource recharge strategies
–
simulation and evaluation of strategies of demand reduction
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• Developed to meet the growing demands and pressures on water
resources managers.
• Approach is state of the art and generic
• Based on a node-link network representation of the water resource
system being simulated
• Include scenario planning in combination with state-of-the-art large-scale
network flow optimization algorithm
• Places demand-side issues and water allocation schemes on an equal
footing with supply-side topics
• Integrated approach to simulating both natural and man-made
components of water systems
• Planner access to a more comprehensive view of the broad range of
factors for sustainable water management
• GUI that facilitate user interaction and stresses out user sovereignty
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Thank you for your attention !
Questions?
33