Issues related to River Basin Modeling - eng.uwo.ca · Issue # 1: Time Step Length There should be...
Transcript of Issues related to River Basin Modeling - eng.uwo.ca · Issue # 1: Time Step Length There should be...
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1. Introduction
2. Some Notes on Stochastic Hydrology
3. Unresolved Issues in River Basin Optimization:
- Time Step Length
- Hydrologic River Routing
- Outflow Constraints on two or more outlets
- Defining Objective Function
- Multiple vs Single Time step Solutions
3. Final Comments
Issues related to River Basin Modeling
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Stochastic Generation of Natural Flows
Goal: Computer generated random series of natural
flows that art statistically similar to historic.
The Ultimate model:
- Works for any time step length (days, weeks or
months);
- Works with any combination of continuious and
intermittent data series;
- Works for large number of stations (50 or more)
Flow monitoring stations
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Significance of Stochastic Natural Flows
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Recent Development in Statistical Science
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Stochastic Generation of Natural Flows
Weekly probability distribution functions;
Weekly mean, standard deviation and skew;
Annual mean, standard deviation, skew;
Annual auto correlation;
Annual cross-correlation between various stations;
Weekly auto correlation; and,
Weekly cross-correlation between various stations.
The relevant weekly statistics to be preserved are:
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Proposed Methodology
Step 1: Generate 1000 years of data for each week using
an Empirical Kernel-type distribution
0
50
100
150
200
250
300
350
400
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Flo
w (
m3/s
)
Probability
Weekly Average Flows for Week 20Raw Data
Empirical
Log-Normal
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Stochastic Generation of Natural Flows
Step 3 consists of re-ordering of the entire rows in a
systematic way until the desired annual lag correlations
and the lag correlations between ending weeks of year i-1
and starting weeks of year i are preserved.
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Stochastic Generation of Natural Flows
a) Step 3 has 1000! combinations
b) Current approach is based on simulated annealing
c) Success rate is acceptable for up to 17 stations
d) There are many possible solutions which are acceptable,
but they are hard to find with the current algorithm.
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Single Time Step Optimization
X1
X2
X5
X6
Y1
Y2
Y3
Y4
X3
X4
Maximize ∑ Yi Ci (objective function)
Reservoir
Irrigation
Y Controlled Flow
X Natural Runoff
i.e. find a set of controlled releases Yi to maximize the
objective function subject to physical flow constraints
related to mass balance and flow limits. Factor Ci is the
pay off function (benefit) for supplying a unit of flow to
user i.
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Typical Seasonal Water Demand
May July Sep
Water
Requirement
Ideal Demand
Achieved Supply (as modelled if STO mode is used)
Best Possible Supply (aprox. 75% of the ideal target in the
above figure; it varies from year to year)
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(MTO) – Model finds demand best demand driver
releases
T 1 T 2 T 3
V initial V final
Maximize ∑ ∑ Yi,t Ci
Y
D
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Issue 1: Time Step Length
1. Assumption of water availability from any source to any
user within a time step. This restricts modeling of large
basins to monthly time steps.
2. Monthly inflow hydrographs are too easy to manage.
The same basins modeled with monthly and weekly time
steps showed up to 28% difference in spills.
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Problems with Channel Routing Constraints
X1
Y1
Y4
X3
River Routing
Effects under
normal
reservoir
release:
River Routing
Effects under
increased
reservoir
release:
Oi = C0Ii + C1Ii-1 + C2Oi-1
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Issue 1: Time Step Length
1. Proper routing requires daily time steps, which has its
own problems:
• model floods the river valley to reduce the time of
travel and consequently downstream deficits (see the
2008 paper in WRR);
• MTO solutions don’t resolve the problem
Ilich, N. 2008. Shortcomings of Linear Programming inOptimizing River Basin Allocation. Water Res. Research, Vol. 44.
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Issue # 1: Time Step Length
There should be guidelines on:
• establishing the proper time step length (not too long
to avoid problem with the spills, not too short to avoid
problems with routing);
• how to model time steps which are shorter than the
total travel time through the basin; and,
• how to model hydrologic river routing within the
optimization framework, can it be done within the LP
framework and if so, how? The routing coefficients
do change with significant flow variations over the
year.
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Issue #2: Modeling of Hydraulic Constraints in LP
Outflow capacity constriants are approximated with linear segments
SVs Ve
Q Q t
1 2
1
Q (m3/s)
Binary variables are required to ensure
proper zone filling from bottom to top
and emptying from top to bottom.
[0, 1]
[0, 1][0, 1]
[0, 1]
Qmax oS
Vs
t
Ve
t( )
1 1
2
V
t
Binary variables significantly slow down the solution process.
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Issue #2: Hydraulic Constraints in LP
SVs Ve
Q Q t
1 2
1
Q (m3/s)
[0, 1]
[0, 1][0, 1]
[0, 1]
Qmax oS
Vs
t
Ve
t( )
1 1
2
V
t
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Min Tech. Specifications: List of Constraints
Storage outlet structure
Diversion at a weir
Return flow channels
Diversion license volume limit per year
Apportionment volume limit per year
Channel routing (?)
Equal deficit constraints:
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Food for thought: Constraints
There should be guidelines on:
• Establishing which constraints are important and by
how much they affect the quality of solutions if they
are not modeled;
• How individual constraints should be formulated and
included in the model; and,
• Problems with constraints should be formulated as
benchmark tests and their solutions should be
published solved in such a way that every model
vendor has ability to verify their model by re-running
the benchmarks.
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Issue # 3: Definition of Objectives
C2
C1
C3
0
1
2
3
4
5
0 2 4 6 8 10
Max.
Div
ers
ion
(m
3/s
)
River Flow (m3/s)
Maximum Diversion vs River Flow
Return=0.3 Div.
C2 > 1.3C1
Israel M.S. and Lund J. 1999. Priority Preserving Unit Penalties inNetwork Flow Modeling. ASCE Journal of Water Resources Planningand Management, Vol. 125 (4), July /August.
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Ele
vation (
m)
Issue # 4: Use of MTO in Development of Rule Curves
Time (days) 365
Solution for year i
Solution for year i+1
20 percentile dry elevations
obtained from all solutions for a
given time step
Solution for year i+2
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Reservoir Operating Zones -- example
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Storage Levels for three Scenarios (1928-1937)
1060
1070
1080
1090
1100
1110
1120
1928 1929 1930 1931 1932 1933
Ele
vation (
m)
Time (years)
STO with proposed rules
MTO solution
STO with no rules
1060
1070
1080
1090
1100
1110
1120
1933 1934 1935 1936 1937 1938
Ele
va
tio
n (
m)
Time (years)
STO with proposed rules
MTO solution
STO with no rules
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Unsolved Issues
• Significance of Time Step Length and STO vs MTO
• Hydrologic Routing
• Reservoir outflow constraints for two or more outlets
• Finding the best set of weight factors
• Agreeing on minimum models’ tech. specifications
• Establishing Benchmarks test problems that should
be accepted in the industry
• Develop procedure for finding and verifying optimal
reservoir operating rules for a range of hydrologic
years; and,
• Develop procedures how to apply the optimal rules in
real time
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The End