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.

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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