1. Hanoi, January 28 th 2015 Quang Dinh DEIB – Politecnico di Milano IMRR Project Emulators of the Delta model 7 – Emulators of the Delta model INTEGRATED AND SUSTAINABLE WATER MANAGEMENT OF RED-THAI BINH RIVER SYSTEM IN A CHANGING CLIMATE

2. IMRR phases econnaissance odeling the system ndicators identification cenarios definition lternative design valuation R M I S A E omparison C 2

3. 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 variables! 3

4. 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 efficientEmulators MIKE11 4

5. 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 5

6. 6 JSJS JHJH JFJF Emulators Step 0: Output selection

7. 7 JSJS JHJH JFJF h t HN – mực nước ngày tại Hà Nội Emulators Step 0: Output selection

8. 8 JSJS JHJH JFJF d t : tổng lượng nước thiếu vùng đồng bằng trong ngày t Emulators Step 0: Output selection

9. Evaluation of other indicators q ST : daily flow at Son Tay control station (for the environmental indicators) h PL & h TQ : daily water level in Pha Lai & Tuyen Quang (for the flood indicators) 9  Choose: h HN, d, q ST, h PL & h TQ

10. Emulators Prepare a sample data set 10

11. h t HN D t q t ST h t TQ h t PL  r HB, r TB, r TQ  q HY, q YB  minor & lat. flows   t   t   V t  d t Emulators Step 1: Sample dataset t, t-1,t-2,… Dataset plays a critical role in building the emulator constituted by N tuples {inputs, output} 11

12. 10. Các sự kiện thủ văn cực đoan Tomorrow 9:00-10:00 Emulators Step 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 tuples! 12

13. Emulators Step 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) 13

14. 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 14

15. ANN: Artificial Neural NetworkEmulators inputs neurons output 15

16. Emulators How 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 16

17. Emulators Step 2-4: 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 17

18. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Water level at Ha Noi OrderVariable ΔR2 ΔR2 R2R2 1QtDQtD 0.98521 2h t HN 0.01050.99571 3 tt 0.000020.99573 h t HN : the daily mean water level at Ha Noi section between [t- 1,t)  t : daily maximum tide at river mouth 18

19. 5 neurons 1 output wl t+1 HN 3 inputs  Q t D  h t HN   t Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Water level at Ha Noi 19

20. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Water level at Ha Noi StatisticMonolithic emulator R2R2 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 20

21. Emulators Step 2-4: 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 21

22. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Water level at Ha Noi dry season: 7 neurons flood & intermediate seasons: 5 neurons 22

23. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Water level at Ha Noi 23 Dynamic emulator: Quy hoạch động ngẫu nhiên Stochastic Dynamic Programming (SDP) Giải thuật di truyền Genetic Algorithm (GA)

24. Emulators Step 2-4: 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 23 Dynamic emulator:

25. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Water level at Ha Noi Dynamic Non-dynamic 24

26. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Water level at Ha Noi Dynamic Non-dynamic 25

27. Emulators Step 2-4: 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 26

28. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Total supply deficit OrderVariable ΔR2 ΔR2 R2R2 1 tt 0.6983 2VtVt 0.13770.8360 3QtDQtD 0.04940.8854 4 tt 0.00490.8903 ! 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 27

29. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Total supply deficit OrderVariable ΔR2 ΔR2 R2R2 1 VtVt 0.9850 2 tt 0.00300.9880 3 tt 0.00210.9901 4QtDQtD 0.00230.9924 we identified an ANN emulator with 5 neurons V t would not be known without the Delta model  identify one more emulator to evaluate it 28

30. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Total supply deficit Delta model Emulator 29

31. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Total supply deficit Delta model Emulator 30

32. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Total supply deficit 31

33. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Total supply deficit OrderVariable ΔR2 ΔR2 R2R2 1 tt 0.7752 2QtDQtD 0.12180.8970 3 tt 0.03080.9278 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 32

34. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Total supply deficit Non-dynamic V emulator 33

35. Emulators Step 2-4: 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 34

36. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Flow at Son Tay network has to be dynamic & we consider q ST among inputs tide & water demand are not relevant in Son Tay sum Q D 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 35

37. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Flow at Son Tay we identified an ANN emulator with 5 neurons 36

38. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Flow at Son Tay 1971 37

39. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Flow at Son Tay 1996 38

40. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Flow at Son Tay q ST is used to evaluate the environmental indicators  the emulator has to fit well especially for low flows training & validation dataset only flows below 5400 m 3 /s (75 th quantile of the historical time series of flows at ST) 39

41. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Flow at Son Tay All have high performances in term of R 2 the last one gives better fitting (also considering errors on the extremes) 40

42. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Flow at Son Tay 1997 41

43. Emulators Step 2-4: Emulators Step 2-4: IIS & EB – Flow at Son Tay 2003 42

44. Emulators Step 2-4: 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 43

45. Thanks for your attention XIN CẢM ƠN 41