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DSD-INT 2019 Development and Calibration of a Global Tide and Surge Model (GTSM) - Wang
1. 11
Development and Calibration of a Global
Tide and Surge Model (GTSM)
Xiaohui Wang1 , Martin Verlaan1,2 ,
Maialen Irazoqui Apecechea2,,Hai Xiang Lin1
(X.Wang-13@tudelft.nl)
1.Delft University of Technology
2.Deltares
2. 22
Outline
➢ Research Motivation
➢ Global Tide and Surge Model
➢ Parameter Estimation Scheme
➢ Numerical Experiments and results
➢ Conclusions
3. 33
Outline
➢ Research Motivation
➢ Global Tide and Surge Model
➢ Parameter Estimation Scheme
➢ Numerical Experiments and results
➢ Conclusions
4. 44
Research Motivation
1
Why to do parameter estimation/calibration?
• The requirement of high accurate forecast of tide and surge
✓ Global climate changes are increasing the risk from storm surges
✓ Accurate forecast can help evaluate the risk
• Global Tide and Surge model is developed to deal with this
global problem.
How to get accurate global forecast results of tide and surges?
Data Assimilation
5. 55
Research Motivation
1
Model forecastparameters model
Physical processes
Data Assimilation
Observations
+/-
Correction
• Model contains uncertain parameters
• Observation is available to validate model output
Research Objective:
• Parameter estimation/Calibration for GTSM
6. 66
Outline
➢ Research Motivation
➢ Global Tide and Surge Model
➢ Parameter Estimation Scheme
➢ Numerical Experiments and results
➢ Conclusions
7. 77
Global Tide and Surge Model
2
𝜕u
𝜕𝑡
+
1
ℎ
(𝛻 ∙ (ℎuu − u𝛻 ∙ (ℎu))=−g𝛻(𝜉 − 𝜉 𝐸𝑄 − 𝜉 𝑆𝐴𝐿) + 𝛻 ∙ (𝜈(𝛻u𝛻u 𝑇
)) +
𝜏
ℎ
𝜏 = −
𝑔
𝐶 𝐷
2 ∥ u ∥ u
𝜏𝐼𝑇 = −𝐶𝐼𝑇 𝑁(𝛻ℎu)𝛻ℎ
Tides
➢ Delft3D Flexible Mesh (unstructured mesh)
➢ A combined tide and surge model
Surges: forced by wind and pressure
Bathymetry, coefficient of bottom friction and
internal tides friction are often identified as three
types of parameters with large uncertainties to
estimate.
8. 88
Global Tide and Surge Model
2
Model GTSM with coarse grid GTSM with fine grid
Mesh ~2 million ~5 million
resolution
50km in deep ocean, 5km in
coastal area
25km in deep ocean, 2.5km in
coastal area, 1.25km in European
Computational cost
(45 days simulation, 20
cores)
3 hours 10 hours
➢ Model settings:
❖ Time steps: 600s
❖ Spin-up time: 20131217 to 20131231
❖ Simulation time: 20140101 to 20140131
High resolution, high accuracy but expensive computational cost.
How to reduce computational cost in parameter estimation scheme?
9. 99
Outline
➢ Research Motivation
➢ Global Tide and Surge Model
➢ Parameter Estimation Scheme
➢ Numerical Experiments and results
➢ Conclusions
10. 1010
Parameter Estimation Scheme
3 ➢ Parameter estimation framework
Calibration with OpenDA:
❖ OpenDA is generic toolbox for data-assimilation
❖ Dud
➢ Run with single perturbation of parameters
➢ Linearize the model and solve it
➢ If improved, update parameters
➢ If not, do line-search
𝐽 =
𝑡
(𝑦𝑜(𝑡) − 𝑦 𝑚 𝑡, 𝑝 )2
𝜎𝑜
2 𝐽 𝑚𝑖𝑛 =
𝑡
(𝑦𝑜(𝑡) − 𝑦 𝑚 𝑡, Ƹ𝑝 )2
𝜎𝑜
2
Observations: 𝑦0 𝑡 Estimated output: 𝑦 𝑚 𝑡, Ƹ𝑝Model output: 𝑦 𝑚 𝑡, 𝑝
11. 1111
Parameter Estimation Scheme
3 ➢ Key issues:
✓ Coarse-to-fine parameter estimation:
Apply parameter estimation in coarse model and set as input in fine model
✓ Parameter dimension reduction:
Parameter selection
Sensitivity test
❖ Huge computational cost
• Computing time increases quickly for high resolution global model.
• Large parameter dimension leads to large number of perturbed model simulations.
❖ Storage memory problem
• Model output can be huge for a long simulation.
• Large parameter and observation dimension.
➢ Solutions:
12. 1212
Parameter Estimation Scheme
3 ➢ Coarse-to-fine strategy
Coarse Incremental Calibration:
Using coarse model to replace the difference (𝛿𝑦) between the initial output
and adjusted output in fine model.
𝐽 𝑛𝑒𝑤 =
𝑡
(𝑦𝑜(𝑡) − 𝑦 𝑚2
𝑡, 𝑝 )2
𝜎𝑜
2 =
𝑡
(𝑦𝑜(𝑡) − 𝑦 𝑚2
𝑡, 𝑝0 + 𝑦 𝑚1
𝑡, 𝑝0 − 𝑦 𝑚1
𝑡, 𝑝 )2
𝜎𝑜
2
Only one initial simulation of GTSM fine model
𝑦 𝑚2
𝑡, 𝑝 ≈ 𝑦 𝑚2
𝑡, 𝑝0 − 𝑦 𝑚1
𝑡, 𝑝0 + 𝑦 𝑚1
𝑡, 𝑝൝
𝑦 𝑚2
𝑡, 𝑝 = 𝑦 𝑚2
𝑡, 𝑝0 + 𝛿𝑦
𝛿𝑦 ≈ 𝑦 𝑚1
𝑡, 𝑝 − 𝑦 𝑚1
𝑡, 𝑝0
𝐺𝑇𝑆𝑀𝑐𝑜𝑎𝑟𝑠𝑒: 𝑦 𝑚1
𝑡, 𝑝0 , GTSMfine: 𝑦 𝑚2
𝑡, 𝑝0 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑜𝑢𝑡𝑝𝑢𝑡: 𝑦 𝑚2
𝑡, Ƹ𝑝
13. 1313
Parameter Estimation Scheme
3
Bathymetry & Internal tides friction: Deep Ocean & global
Bottom friction: coastal area
From Deep Ocean & global to coastal area
➢ Parameter Selection
FES2014 database
Tide gauge data
14. 1414
Parameter Estimation Scheme
3 ➢ Observation: FES2014 database
✓ 1973 time series, from Jan. 1 to Jan. 14, 10 minutes interval
✓ Nearly distance equally
✓ Remove SA, SSA 𝑅𝑀𝑆𝐸 =
σ 𝑡(𝑦𝑜(𝑡) − 𝑦 𝑚 𝑡, 𝑝 )2
𝑁
➢ Accuracy before calibration with GEBCO 2014 & GEBCO 2019
Initial model: GTSM with GEBCO 2019
RMSE distribution in [m] Regional RMSE in [cm]
15. 1515
Parameter Estimation Scheme
3 ➢ Parameter estimation framework
Parameter Dimension
reduction
Bathymetry
OpenDA:
Dud
Observation:
FES2014
Results analysis &
model validation
Coarse-to-fine
Bathymetry Estimation
Further work on BF
and IT estimation……
Observation
investigation
Parameter
selection
Sensitivity
test
Observation:
UHSLC
16. 1616
Outline
➢ Research Motivation
➢ Global Tide and Surge Model
➢ Parameter Estimation Scheme
➢ Numerical Experiments and results
➢ Conclusions
17. 1717
Numerical Experiments and Results
4 ➢ Parameter dimension reduction by sensitivity test
How does the observation error affect the sensitivity?
❖ Set-up
➢ Spin-up: 2 weeks
➢ Simulation: Jan. 1 to 14
❖ Specify parameter sections as adaption
parameters 𝟏𝟎° × 𝟏𝟎°
➢ Not all parameters in every grid can
be estimated in practically.
➢ Limited observations
➢ Expensive computational cost
❖ Sensitivity test
285 boxes
𝑝∗
= 1 + 𝑚 𝑝 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 =
𝐽 𝑝 − 𝐽 𝑜
𝐽0
Dimension reduced from 𝒐 𝟏𝟎 𝟔
to 𝒐 𝟏𝟎 𝟐
18. 1818
Numerical Experiments and Results
4 ➢ Propagation length with bathymetry perturbation
Length scale based on M2 amplitude [km]
Parameter sections cannot be too small
M2 in GTSM in [m]
• When the tide propagates from one location to this position, the perturbation
of bathymetry in this position could lead to a water-level difference.
• The propagation length can be calculated when we assume the water-level
difference is the same as the observation error.
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Numerical Experiments and Results
4
110 boxes
➢ Parameter dimension reduction
❖ Combine sections with same directions nearby
➢ Directions:
• Negative: sensitivity<0
• Positive: Sensitivity >0
❖ Re-sensitivity test
❖ Parameter estimation
Bathymetry difference after estimation
21. 2121
Numerical Experiments and Results
4 ➢ Estimation Results Analysis: Jan. 1 to Jan. 14
❖ Both coarse and fine model have been improved
❖ GTSM with fine grid has a higher accuracy than coarse model
RMSE [cm] GTSM with coarse grid GTSM with fine grid
Initial Estimated Initial Estimated
Arctic 7.00 5.75 5.22 4.33
Indian Ocean 6.46 3.80 5.43 3.54
North Atlantic 6.96 4.50 5.58 3.48
South Atlantic 6.02 4.05 4.98 3.44
North Pacific 4.53 3.51 3.93 3.09
South Pacific 6.18 3.79 4.91 3.17
South Ocean 4.89 3.51 3.95 2.90
Total 5.94 3.91 4.85 3.30
22. 2222
Numerical Experiments and Results
4 ➢ Model Validation—RMSE difference in fine GTSM
Jan. 15 to Jan. 31 July 1 to July 31
RMSE[cm] GTSM with coarse grid GTSM with fine grid
Initial Estimated Initial Estimated
Jan. 15 to 31 6.72 4.96 5.54 4.12
July 1 to 31 6.13 4.24 4.94 3.45
RMSE difference in fine GTSM [m] RMSE difference in fine GTSM [m]
23. 2323
Numerical Experiments and Results
4 ➢ Model Validation—UHSLC dataset (230 time series)
RMSE[cm] GTSM with coarse grid GTSM with fine grid
Initial Estimated Initial Estimated
Jan.1 to 14 16.31 13.48 12.21 10.23
Jan. 15 to 31 16.73 13.87 12.74 10.42
July 1 to 31 16.15 13.32 12.11 9.95
Estimated RMSE in Jan.1 to 14[m] RMSE difference in Jan.1 to 14[m]
24. 2424
Outline
➢ Research Motivation
➢ Global Tide and Surge Model
➢ Parameter Estimation Scheme
➢ Numerical Experiments and results
➢ Conclusions
25. 2525
Conclusions & Future work
5 ➢ The coarse grid parameter estimation for the high
resolution GTSM is efficient.
➢ The accuracy of output in both coarse and fine model are
increased, which can be used for long term forecast.
➢ Future work will continue on:
• Model order reduction for the parameter estimation in
time patterns, because parameter estimation should be
implemented in a longer simulation time but storage
memory is limited.
• Further estimate bottom friction and internal tides
friction.