hanoi, january 28 th 2015 quang dinh deib – politecnico di milano imrr project emulators of the...
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Hanoi, January 28th 2015
Quang DinhDEIB – Politecnico di Milano
IMRR Project
7 – Emulators of the Delta model
INTEGRATED AND SUSTAINABLE WATER MANAGEMENT OF RED-THAI BINH RIVER SYSTEM
IN A CHANGING CLIMATE
IMRR phases
econnaissance
odeling the system
ndicators identification
cenarios definition
lternative design
valuation
RMISAE
omparisonC
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Delta model 320 Rivers & canals with 4200 km ~ 8000 Cross sections 29 Bridges 148 Drainage culverts 89 Sluice gates 160 Pumping stations from main river 303 Pumping stations from 11 irrigation
districts
complete description of the system at each time step
~ 2 days for 16 years simulation
MIKE11
More than 16000 state varia
bles!
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• point to point information is required
• ~ 350 million years simulation for 1 policy
The model simulation must be extremely fast (1 yr in few milliseconds)
In the IMRR Project
Lumped model, computationally
efficient
Emulators
MIKE11
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Emulators
Reference: S. Galelli and A.Castelletti (2013), Tree-based iterative input variable selection for hydrological modeling, Water Resources Research, 49(7), 4295-4310.
Select among the PB model (Delta model) output components, one component y, the dynamic of which we like to emulate
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EmulatorsStep 0: Output selection
Evaluation of other indicators• qST: daily flow at Son Tay control station (for the
environmental indicators)
• hPL & hTQ: daily water level in Pha Lai & Tuyen Quang (for the flood indicators)
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Choose: hHN, d, qST, hPL & hTQ
htHN
Dt
qtST
htTQ
htPL
rHB, rTB, rTQ
qHY , qYB
minor & lat. flows
tt
wt
Vt
dt
EmulatorsStep 1: Sample dataset
t, t-1,t-2,…
• Dataset plays a critical role in building the emulator
• constituted by N tuples {inputs, output}
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10. Các sự kiện thủ văn cực đoanTomorrow 9:00-10:00
EmulatorsStep 1: Sample dataset
List of experiments:
• Exp1: 17 yrs (Oct,1994-Oct, 2010), using historical flows
• Exp2: 17 yrs (Oct,1994-Oct, 2010), using natural flows (the case in which
reservoirs were not presented)
• Exp3: 2 yrs in which big flood occurred (1969 & 1971)
• Exp4: 1969, 1971, 1996 with 300 & 500 yrs return periods
• Exp5: 10 yrs, corresponding to 10 extreme yrs (5 floods + 5 droughts)
• Exp6: 10 yrs with 100, 200, 300 & 500 yrs return period
More than 22,630 tu
ples!
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EmulatorsStep 1: Sample dataset
List of experiments:
• Exp1: 17 yrs (Oct,1994-Oct, 2010), using historical flows
• Exp2: 17 yrs (Oct,1994-Oct, 2010), using natural flows (the case in which
reservoirs were not presented)
• Exp3: 2 yrs in which big flood occurred (1969 & 1971)
• Exp4: 1969, 1971, 1996 with 300 & 500 yrs return periods
• Exp5: 10 yrs, corresponding to 10 extreme yrs (5 floods + 5 droughts)
• Exp6: 10 yrs with 100, 200, 300 & 500 yrs return period
Data set was splitted in two sub-sets: trainings & validation (cross-validation)
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Emulators
•model is identified (but extra-tree)
adopt ANN to emulate this model to, later on, embed it into MO optimization framework
•The input that are most relevant in explaining I-O behavior of the PB model, with respect to y, are recursively selected, until all the selected state variables are given a dynamic description
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EmulatorsHow to choose the number n of its neurons?
• n too low reduces the accuracy, but the ANN computation is faster
• n too high: opposite
the identification was repeated for different values of n
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Emulators Step 2-4: Iterative Input variable Selection & Emulator Building
• Water level at Ha Noi
• Total supply deficit
• Flow at Son Tay
• Water level at Tuyen
Quang & Pha Lai
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Emulators Step 2-4: IIS & EB – Water level at Ha Noi
Order Variable ΔR2 R2
1 QtD 0.98521 0.98521
2 htHN 0.0105 0.99571
3 tt 0.00002 0.99573
• htHN: the daily mean water level at Ha Noi section between [t-1,t)
• tt: daily maximum tide at river mouth
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5 neurons 1 output
wlt+1HN
3 inputs
QtD
htHN
tt
Emulators Step 2-4: IIS & EB – Water level at Ha Noi
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Emulators Step 2-4: IIS & EB – Water level at Ha Noi
Statistic Monolithic emulator
R2 0.9923
mean err [%] 4.2707
st. dev. err [%] 8.7666
max err [m] 2.4752
min err [m] -2.0242
max(err99) [m] 1.6474
μ(|err99|) [m] 0.3658
min(err47) [m] -1.4580
μ(|err47|) [m] 0.0996
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Emulators Step 2-4: IIS & EB – Water level at Ha Noi
• dry season: interested in the effects of low water levels
• flood season: interested in the effects of the high water levels
would it not be better to consider specialized emulators in the different seasons?
• Build a cluster of 3 different emulators:
- dry season (15/11 - 15/5)
- flood season (1/7 – 15/9)
- two intermediate seasons
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Emulators Step 2-4: IIS & EB – Water level at Ha Noi
• dry season: 7 neurons
• flood & intermediate seasons: 5 neurons
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Emulators Step 2-4: IIS & EB – Water level at Ha Noi
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Dynamic emulator:
Quy hoạch động ngẫu nhiênStochastic Dynamic Programming (SDP)
Giải thuật di truyền Genetic Algorithm (GA)
Emulators Step 2-4: IIS & EB – Water level at Ha Noi
Non-dynamic emulator: by excluding water level at Hanoi
• we identified an ANN emulator with 5 neurons
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Dynamic emulator:
Emulators Step 2-4: Iterative Input variable Selection & Emulator Building
• Water level at Ha Noi
• Total supply deficit
• Flow at Son Tay
• Water level at Tuyen
Quang & Pha Lai
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Emulators Step 2-4: IIS & EB – Total supply deficit
Order Variable ΔR2 R2
1 wt 0.6983 0.6983
2 Vt0.1377 0.8360
3 QtD 0.0494 0.8854
4 tt0.0049 0.8903
! Canals system behaves like a reservoir:
•store water when it can be withdrawn from the river
•supply it to the fields when the water demand requires it.
• We identified an ANN emulator with 5 neurons
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Emulators Step 2-4: IIS & EB – Total supply deficit
Order Variable ΔR2 R2
1 Vt 0.9850 0.9850
2 tt0.0030 0.9880
3 wt0.0021 0.9901
4 QtD 0.0023 0.9924
• we identified an ANN emulator with 5 neurons
• Vt would not be known without the Delta model identify one more emulator to evaluate it
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Emulators Step 2-4: IIS & EB – Total supply deficit
Order Variable ΔR2 R2
1 wt 0.7752 0.7752
2 QtD 0.1218 0.8970
3 tt0.0308 0.9278
• we identified an ANN emulator with 5 neurons
Non-dynamic V emulator: by removing the water volume V stored in the canals from the possible inputs
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Emulators Step 2-4: Iterative Input variable Selection & Emulator Building
• Water level at Ha Noi
• Total supply deficit
• Flow at Son Tay
• Water level at Tuyen
Quang & Pha Lai
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Emulators Step 2-4: IIS & EB – Flow at Son Tay
•network has to be dynamic & we consider qST among inputs
•• tide & water demand are not relevant in Son Tay
•sum QD of the upstream flows (releases + unregulated flows)
can be used instead of using each single output
•Delay time is generally lower than 1 day considered 2 cases
1 day delay
no delay
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Emulators Step 2-4: IIS & EB – Flow at Son Tay
• qST is used to evaluate the environmental indicators
the emulator has to fit well especially for low flows
•training & validation dataset only flows below 5400 m3/s (75th
quantile of the historical time series of flows at ST)
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Emulators Step 2-4: IIS & EB – Flow at Son Tay
• All have high performances in term of R2
• the last one gives better fitting (also considering errors on the
extremes)
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Emulators Step 2-4: Iterative Input variable Selection & Emulator Building
• Water level at Ha Noi
• Total supply deficit
• Flow at Son Tay
• Water level at Tuyen
Quang & Pha Lai
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