DSD-INT 2019 Development and Calibration of a Global Tide and Surge Model (GTSM) - Wang
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The document discusses the development and calibration of a global tide and surge model (GTSM) to improve the accuracy of tide and surge forecasts, particularly in light of increasing climate-related risks. It presents a parameter estimation scheme that utilizes a coarse-to-fine strategy to enhance model performance while managing computational costs. Additionally, results from numerical experiments indicate improved accuracy in both coarse and fine grid models, with plans for future work focusing on further refinement of parameter estimation techniques.
![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]](https://image.slidesharecdn.com/dsd-int2019developmentandcalibrationofaglobaltideandsurgemodelgtsm-wang-191218225553/85/DSD-INT-2019-Development-and-Calibration-of-a-Global-Tide-and-Surge-Model-GTSM-Wang-14-320.jpg)
![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.](https://image.slidesharecdn.com/dsd-int2019developmentandcalibrationofaglobaltideandsurgemodelgtsm-wang-191218225553/85/DSD-INT-2019-Development-and-Calibration-of-a-Global-Tide-and-Surge-Model-GTSM-Wang-18-320.jpg)
![2020
Numerical Experiments and Results
4 ➢ Estimation Results Analysis: Jan. 1 to Jan. 14
𝑅𝑀𝑆𝐸 =
σ 𝑡(𝑦𝑜(𝑡) − 𝑦 𝑚 𝑡, 𝑝 )2
𝑁
𝑅𝑀𝑆𝐸 𝑑𝑖𝑓𝑓 = 𝑅𝑀𝑆𝐸𝑖𝑛𝑖𝑡𝑖𝑎𝑙 − 𝑅𝑀𝑆𝐸𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑
Estimated RMSE in fine GTSM [m] RMSE difference [m]](https://image.slidesharecdn.com/dsd-int2019developmentandcalibrationofaglobaltideandsurgemodelgtsm-wang-191218225553/85/DSD-INT-2019-Development-and-Calibration-of-a-Global-Tide-and-Surge-Model-GTSM-Wang-20-320.jpg)
![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](https://image.slidesharecdn.com/dsd-int2019developmentandcalibrationofaglobaltideandsurgemodelgtsm-wang-191218225553/85/DSD-INT-2019-Development-and-Calibration-of-a-Global-Tide-and-Surge-Model-GTSM-Wang-21-320.jpg)
![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]](https://image.slidesharecdn.com/dsd-int2019developmentandcalibrationofaglobaltideandsurgemodelgtsm-wang-191218225553/85/DSD-INT-2019-Development-and-Calibration-of-a-Global-Tide-and-Surge-Model-GTSM-Wang-22-320.jpg)
![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]](https://image.slidesharecdn.com/dsd-int2019developmentandcalibrationofaglobaltideandsurgemodelgtsm-wang-191218225553/85/DSD-INT-2019-Development-and-Calibration-of-a-Global-Tide-and-Surge-Model-GTSM-Wang-23-320.jpg)
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.
- 19. 1919 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
- 20. 2020 Numerical Experiments and Results 4 ➢ Estimation Results Analysis: Jan. 1 to Jan. 14 𝑅𝑀𝑆𝐸 = σ 𝑡(𝑦𝑜(𝑡) − 𝑦 𝑚 𝑡, 𝑝 )2 𝑁 𝑅𝑀𝑆𝐸 𝑑𝑖𝑓𝑓 = 𝑅𝑀𝑆𝐸𝑖𝑛𝑖𝑡𝑖𝑎𝑙 − 𝑅𝑀𝑆𝐸𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 Estimated RMSE in fine GTSM [m] RMSE difference [m]
- 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.
- 26. 2626 Thank You!