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DSD-INT 2018 A Methodology Study for Model Build and Calibration of 2D Hydrodynamic Models at Estuaries - Shen

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Presentation by Edward Shen, Ove ARUP & Partners, Hong Kong, at the Delft3D - User Days (Day 2: Hydrodynamics), during Delft Software Days - Edition 2018. Tuesday, 13 November 2018, Delft.

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DSD-INT 2018 A Methodology Study for Model Build and Calibration of 2D Hydrodynamic Models at Estuaries - Shen

  1. 1. A Methodology Study for Model Build and Calibration of 2D Hydrodynamic Models at Estuaries - Location of Open Boundary and its effects on Model Quality Ir. Edward Shen, MASCE, MHKIE, Hong Kong correspondence: edward.qiang.shen@gmail.com
  2. 2. Problem: The confidence in use of numerical models much depends on the effectiveness of model calibration and validation. This, however, in most cases is only carried out locally with limited data for a specified period. Location of Open Boundary and its effects on Model Quality How far is it offshore ? Location of open sea boundary Objective: How to secure the model reliability by building a healthy skeleton is the purpose of this methodology study. This presentation, Location of Open Boundary and Its Effects on Model Quality is part of the methodology study for the purpose. Fact: A model is a replica of an entity in the nature, it shall have its skeleton, consisting of grid, boundary, bathymetry, seabed roughness and river inflow at estuaries. - Have we valued enough this issue?
  3. 3. D50 50m-Depth Ratio A new parameter named as 50m-depth ratio (D50) is introduced in the study. The D50 is the ratio of the length of model boundary at water depth of 50m or above to the total length of model boundary at open sea. The D50 is found effective and hence brought into play in discussion of model quality for models with varying boundary location. Length where water depth > 50m Location of Open Boundary and its effects on Model Quality D50 = A+B50+C50 A+B+C
  4. 4. Fr – Froude Number U – Depth-averaged velocity (m/s) H – Total water depth (m) Location of Open Boundary and its effects on Model Quality 50m Depth H Fr Water Depth vs Fr * assume U=1 m/s Open boundaries are artificial “water- water” boundaries. To get a well-posed mathematical problem with a unique solution, a set of initial and boundary conditions for water levels and horizontal velocities must be specified. The flow at the open boundaries must be sub-critical (Fr<1) such that upstream water levels and velocities are controlled by downstream boundary conditions. <1 Theoretical Background – Froude Number vs Water Depth Effects of dynamic forcing at open boundaries decrease rapidly 10 times less with increasing water depth from 0 to 50m. This implies that at water depth deeper than 50m:  upstream effects of uncertainties in velocities at open boundary is insignificant;  water levels at open boundary dominate upstream water levels and velocities. Dynamic Force Gravity Force Froude Number (Fr) =
  5. 5. 50m Depth For 2D depth-averaged flow the shear- stress at the bed induced by a turbulent flow is assumed to be given by a quadratic friction law: H – Total water depth, varying n - Manning Coefficient, n=0.02 H 1/C2 CD Water Depth vs Shear Stress Location of Open Boundary and its effects on Model Quality Theoretical Background – Shear Stress vs Water Depth Seabed shear stress at open boundary reduces rapidly 3~4 times less with increasing water depth from 0 to 50m. This implies that at water depth deeper than 50m:  reflection due to numerical disturbance at open boundary decreases significantly  therefore secure the model solution on the specified boundary conditions
  6. 6. BC Brunei A Brunei B Brunei C Brunei D Case 1 Brunei Models Model Area (km2) Volume (m3) Average Depth (m) D50 (%) Offshore Length (km) Alongshore Length (km) Brunei A 17,865 1.92518E+12 108 78 100 185 Brunei B 13,509 5.83641E+11 43 72 84 160 Brunei C 9,882 2.71418E+11 28 52 60 160 Brunei D 9,422 2.48072E+11 26 38 56 160  Four models with varying domains: 56- 100km offshore; 160km to 185km alongshore.  Delft3D modeling systems, default physical and numerical parameters.  Astronomical tide forcing (TPXO7.2) on open sea boundary.  Grid resolution: 100m x 100m within the estuary, 500m x 500m offshore.  Manning roughness coefficient of 0.02.  No river flows are incorporated at estuaries.  Model runs for a complete neap-spring- neap tide cycle Location of Open Boundary and its effects on Model Quality
  7. 7. Current A Current B Tajung Brunei Channel 3 Limbang Channel 1 Kitang Case 1 Brunei Models – Difference in Water Level and Tidal Range time  elevation(m) Kitang 20 Jul 27 Jul 3 Aug 10 Aug 0 0.5 1 1.5 2 2.5 3 Location of Open Boundary and its effects on Model Quality Findings  models with a larger D50 have the predicted water level better matched with the recorded.  Models with a larger D50 also exhibit a higher tidal range.  A unstable run with a smaller D50 = 38%Water level comparison plot: Model C (blue), Model D (red) Station Model RMS Error(%) Max Tide Range (m) Tide Range Error (%) D50 (%) Tanjung Brunei A 4.3 2.32 -2 78 Brunei B 4.5 2.28 -4 72 Brunei C 4.5 2.24 -6 52 Brunei D 5.1 Jagged n/a 38 Kitang Brunei A 4.4 2.33 -1 78 Brunei B 4.6 2.29 -2 72 Brunei C 4.6 2.25 -4 52 Brunei D 5.4 Jagged n/a 38
  8. 8. Station Model Max Tide Speed (m/s) Difference (%) D50 (%) Ebb Flood Ebb Flood Current A Brunei A 0.23 0.2 4 5 78 Brunei B 0.22 0.19 2 2 72 Brunei C 0.22 0.18 0 0 52 Brunei D unstable Unstable N/A N/A 38 Current B Brunei A 0.69 0.59 1 2 78 Brunei B 0.69 0.59 1 2 72 Brunei C 0.68 0.58 0 0 52 Brunei D unstable unstable N/A N/A 38 Current A Current B Tajung Brunei Channel 3 Limbang Channel 1 Kitang Difference in max Tidal Speed (m/s) Station - Current B Unstable current speed in Model D time  depthaveragedvelocity,mcomponent(m/s) Current B 22 Jul 29 Jul 5 Aug -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Current B A B C 78 72 52 Model A B C D50 (%) 78 72 52 Ebb Tide Flood Tide Location of Open Boundary and its effects on Model Quality Case 1 Brunei Models – Difference in Maximum Tidal Speed Findings  Max ebb and flood tidal speed increase with increasing D50 in a neap-spring-neap cycle.  Difference is around 5%.  A unstable run with a smaller D50 = 38%  Ebb tide stronger than flood tide
  9. 9. Models B, D: Instantaneous Discharge Transection – BruneiBay 2 time  instantaneousdischarge(m3 /s) BruneiBay_2a 20 Jul 27 Jul 3 Aug 10 Aug -4 -3 -2 -1 0 1 2 3 4 x 10 4 Current A Tajung Brunei Channel 3 Limbang Channel 1 Kitang Current B Case 1 Brunei Models – Difference in Maximum Tidal Flux Transect Model Max Tide Flux (103 m3/s) Difference (%) D50 (%) Ebb Flood Ebb Flood BruneiBay 1 Brunei A 11.4 11.4 -1 4 78 Brunei B 11.5 11.3 0 3 72 Brunei C 11.5 10.9 0 0 52 Brunei D Unstable Unstable N/A N/A 38 BruneiBay 2 Brunei A 30.6 26.6 0 4 78 Brunei B 30.7 26.2 0 3 72 Brunei C 30.6 25.5 0 0 52 Brunei D Unstable Unstable N/A N/A 38 Difference in max Tidal Flux (103 m3/s) Transection - BruneiBay 2 Unstable results found in Model D A B C 78 72 52 Model A B C D50 (%) 78 72 52 Ebb Tide Flood Tide Location of Open Boundary and its effects on Model Quality Findings  Maximum tidal flux increase with increasing D50 in the range of 0< D50 < 50%.  A unstable run with a D50 = 38% <50%  Ebb tide stronger than flood tide
  10. 10. Current A Tajung Brunei Channel 3 Limbang Channel 1 Kitang Current B Case 1 Brunei Models – Difference in Averaged Tidal Flux Transection Model Ave Tide Flux (103 m3/s) Difference (%) D50 (%) Ebb Flood Ebb Flood BruneiBay 1 Brunei A 5.4 5.19 4.2 3.1 78 Brunei B 5.27 5.08 1.7 1.0 72 Brunei C 5.19 5.03 0 0 52 Brunei D Unstable Unstable N/A N/A 38 BruneiBay 2 Brunei A 13.7 12.0 4.5 3.0 78 Brunei B 13.4 11.8 2.1 0.9 72 Brunei C 13.1 11.7 0 0 52 Brunei D Unstable Unstable N/A N/A 38 Difference in Averaged Tidal Flux (103 m3/s) BruneiBay 2 Ebb Tide Flood Tide A B C 78 72 52 Model A B C D50 (%) 78 72 52 Ebb Tide Flood Tide A B C 78 72 52 A B C 78 72 52 Location of Open Boundary and its effects on Model Quality Findings  Averaged tidal flux increase with increasing D50  Difference around 4%  A unstable run with D50=38% <50%  Ebb tide stronger than flood tide Transection - BruneiBay 1
  11. 11. Location of Open Boundary and its effects on Model Quality Case 1 Brunei Models – Difference in Computing Time Model Grid Size (M x N) Computing Time (Hours) Saved Time (%) D50 (%) Brunei A 644 x 518 7.9 0 78 Brunei B 598 x 494 6.8 14 72 Brunei C 598 x 448 5.7 28 52 Brunei D 598 x 441 5.8 27 38 Simulation period: a complete neap-spring-neap tide cycle 2011.07.20 – 2011.08.10 Computer system: Intel ® Core ™ i5-8400 CPU @ 2.8 GHz RAM: 16.0 GB
  12. 12. PRE D PRE C PRE B PRE A1 PRE A Model Area (km2) Volume (m3) Average Depth (m) D50 (%) Offshore Length (km) Alongshore Length (km) PRE A 73,655 4.21554E+12 57 81 160 460 PRE A1 37,576 1.47761E+12 39 74 92 340 PRE B 29,986 9.50903E+11 32 52 72 330 PRE C 16,578 3.89657E+11 24 22 50 230 PRE D 7,441 9.10545E+10 12 0 20 185 Location of Open Boundary and its effects on Model Quality Case 2 PRE Models  Five models with varying domains: 20- 160km offshore; 185km to 460km alongshore.  Delft3D modeling systems, default physical and numerical parameters.  Astronomical tide forcing (TPXO7.2) on open sea boundary.  Grid resolution: 200m x 300m in estuary, 1.5km x 1.5km offshore.  Manning roughness coefficient of 0.02.  No river flows are incorporated at estuaries.  Model runs for a complete neap-spring- neap tide cycle.
  13. 13. TBT Macau QUB WAG PRD1 PRD2a PRD2b PRD3 Station Model RMS Error (%) Max Tide Range (m) Tide Range Error (%) D50 (%) Macau PRE18A 4.3 2.22 -1 81 PRE18A1 3.5 2.18 -2 74 PRE18B 3.2 2.19 -2 52 PRE18C 3.1 2.16 -3 22 PRE18D 3.3 2.11 -5 0 TBT PRE18A 3.9 2.59 -1 81 PRE18A1 4.1 2.55 -3 74 PRE18B 4.3 2.56 -3 52 PRE18C 4.7 2.52 -4 22 PRE18D 5.9 2.42 -8 0 QUB PRE18A 3.4 1.96 -4 81 PRE18A1 3.5 1.89 -7 74 PRE18B 3.8 1.86 -9 52 PRE18C 4.2 1.81 -11 22 PRE18D 5.1 1.72 -15 0 Location of Open Boundary and its effects on Model Quality Case 2 PRE Models – Difference in Water Level and Tidal Range Findings  In general, models with a larger D50 have better calibrated results.  Models with a larger D50 also exhibit a higher tidal range.  Difference found in tide range up to 15%
  14. 14. time  depthaveragedvelocity,mcomponent(m/s) PRD_2b 10 Feb 17 Feb 24 Feb 3 Mar 10 Mar -1.5 -1 -0.5 0 0.5 1 1.5 TBT Macau QUB WAG PRD1 PRD2a PRD2b PRD3 Models A, A1,D Case 2 PRE Models – Difference in Maximum Tidal Speed Location of Open Boundary and its effects on Model Quality Findings  Max ebb and flood tidal speed increase with increasing D50 in 0<D50 <50%.  Difference found in tidal speed is above 10%.  A larger D50 doesn’t ensure a higher tidal speed, if D50>50%.  Ebb tide stronger than flood tide (PRD2b) Model A A1 B C D D50 (%) 81 72 52 22 0 A A1 B C D 81 72 52 22 0 Flood Tide Ebb Tide Flood Tide Station Model Max Tide Speed (m/s) Difference (%) D50 (%) Ebb Flood Ebb Flood PRD2a PRE18A 1.0 1.22 6 12 81 PRE18A1 1.02 1.18 8 8 74 PRE18B 1.0 1.15 7 6 52 PRE18C 0.98 1.15 5 5 22 PRE18D 0.94 1.09 0 0 0 PRD2b PRE18A 1.33 1.13 10 11 81 PRE18A1 1.36 1.05 12 3 74 PTE18B 1.34 1.05 11 3 52 PRE18C 1.31 1.05 8 4 22 PRE18D 1.21 1.02 0 0 0 Difference in max Tidal Speed (m/s) Station PRD2b Effects of D50 on tidal strength show signs of nonlinear feature
  15. 15. time  instantaneousdischarge(m3 /s) PRD_2 10 Feb 17 Feb 24 Feb 3 Mar 10 Mar -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x 10 5 Transect Model Max Tide Flux (103 m3/s) Difference (%) D50 (%) Ebb Flood Ebb Flood PRD1 PRE18A 35.2 45.0 6 11 81 PRE18A1 33.9 43.4 3 7 74 PRE18B 34.8 42.5 5 5 52 PRE18C 33.9 41.5 2 2 22 PRE18D 33.1 40.6 0 0 0 PRD2 PRE18A 196 192 6 13 81 PRE18A1 198 176 8 3 74 PRE18B 197 176 7 3 52 PRE18C 193 177 5 4 22 PRE18D 184 170 0 0 0 Difference in max Tidal Flux (103 m3/s) Model A A1 B C D D50 (%) 81 72 52 22 0 A A1 B C D 81 72 52 22 0 Ebb Tide Flood TideEbb Tide Case 2 PRE Models – Difference in Maximum Tidal Flux Location of Open Boundary and its effects on Model Quality Transection PRD2 Findings  Max ebb and flood tidal flux increase with increasing D50 in 0<D50 <50%.  Difference found in tidal flux is above 10%.  A larger D50 doesn’t ensure a stronger tidal flux, if D50>50%.  Ebb tide stronger than flood tide (PRD2) TBT Macau QUB WAG PRD1 PRD2a PRD2b PRD3 PRD2
  16. 16. Transect Model Averaged Tide Flux (103 m3/s) Difference (%) D50 (%) Ebb Flood Ebb Flood PRD1 PRE18A 17.98 20.83 8.9 10.2 81 PRE18A1 18.18 19.57 10.1 3.5 74 PRE18B 18.03 19.64 9.2 3.8 52 PRE18C 17.67 19.25 7.0 1.8 22 PRE18D 16.52 18.91 0 0 0 PRD2 PRE18A 89.07 86.98 8.6 9.7 81 PRE18A1 90.47 82.13 10.3 3.6 74 PRE18B 90.41 81.10 10.2 2.3 52 PRE18C 86.96 80.95 6.0 2.1 22 PRE18D 82.01 79.29 0 0 0 TBT Macau QUB WAG PRD1 PRD2a PRD2b PRD3 PRD2 Difference in Averaged Tidal Flux (103 m3/s) Transection – PRD2 Ebb Tide Model A A1 B C D D50 (%) 81 72 52 22 0 Flood Tide A A1 B C D 81 72 52 22 0 Ebb Tide A A1 B C D 81 72 52 22 0 Flood Tide A A1 B C D 81 72 52 22 0 Case 2 PRE Models – Difference in Averaged Tidal Flux Location of Open Boundary and its effects on Model Quality Findings  Averaged ebb and flood tidal flux increase with increasing D50 in 0<D50 <50%.  Difference found in tidal flux is above 10%.  A larger D50 doesn’t ensure a stronger tidal flux, if D50>50%.Transection – PRD1
  17. 17. Location of Open Boundary and its effects on Model Quality Case 2 PRE Models – Difference in Computing Time Model Grid Size (M x N) Computing time (Hours) Saved Time (%) D50 (%) PRE A 460 x 702 9.4 0 81 PRE A1 415 x 639 7.2 23 74 PRE B 396 x 639 6.8 28 52 PRE C 368 x 574 5.5 42 22 PRE D 320 x 518 4.1 56 0 Simulation period: a complete neap-spring-neap tide cycle 2011.02.10 – 2011.03.10 Computer system: Intel ® Core ™ i5-8400 CPU @ 2.8 GHz RAM 16.0 GB
  18. 18. Modaomen Humen Jiaomen Hengmen Hongqimen Application of D50 Practice Location of Open Boundary and its effects on Model Quality Station RMS Error (%) ARMAE Spring Neap Spring Neap Humen 13.1 17.9 0.22 0.42 Jiaomen 12.6 16.9 0.22 0.4 Hongqimen 12.0 18.6 0.17 0.54 Hengmen 12.8 16.5 0.19 0.24 Modaommen 13.8 17.8 0.24 0.35 Jitimen 9.7 16.9 0.14 0.34 Hutiaomen 17.0 18.6 0.33 0.53 Yamen 13.5 19.3 0.31 0.54 All RMS Error (%) <20% commercial criteria 0.1< ARMAE < 0.6 excellent to reasonable Model PRE18A1 with D50=74% is selected for further flow calibration at eight river outlets in PRE. The results show overall integrity and quality.
  19. 19. Conclusions and Summary Location of Open Boundary and its effects on Model Quality Models with a larger D50 (D50>50%) have the predicted water level better matched with the recorded. The larger the D50, the higher the tidal range is. The difference for model with varying D50 can be around 10%. For models with D50 > 50%, a larger D50 may not ensure a higher tidal speed and/or stronger tidal flux. This give an opportunity to find the optimal D50 in terms of tidal strength. D50 > 50% is recommended for 2D hydrodynamic regional model builds at estuaries. This shall enable to secure an overall quality model. Model A A1 B C D D50 (%) 81 72 52 22 0 Both tidal speed and tidal flux increase in models with increasing D50 in D50 < 50%. The Difference can be above 10%. The effect is overall rather than local. 1 2 3 4 5 Tidal Flux

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