1. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Integrating Hydrodynamic Model Output and TCARI Interpolation David Wolcott, Lijuan Huang Hydrographic Planning Team August 20, 2014 1

2. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Outline Introduction o Tide reduction using Tidal Constituent And Residual Interpolation (TCARI) o The challenges faced Method o Integrating the offshore HCs from high resolution tide models into the TCARI interpolation  Hydrodynamic model evaluation - onshore  Hydrodynamic model output inclusion sensitivity tests - offshore Results –Alaska –Chesapeake Bay Conclusions, Recommendations, Next Steps

3. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Corrections to Echo Soundings- Tide Reduction is Critical Surveying at this time? Difference = 10.37m (34.02ft) Or at this time?

4. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Tidal Constituent And Residual Interpolation (TCARI) Uses formal mathematics to interpolate tidal constituents, residual water levels, and vertical datums across the survey area. o Solutions follow Laplace’s equation, two-dimensional second order partial differential equation. Mathematical interpolation only, no tidal physics. o Weighting functions for point inputs o Systematic The accuracy relies on data availability and spatial distribution.

5. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Define shoreline & choose stations 5 Stations within the domain that have accepted tidal datums or harmonics are used.

6. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Triangulation Triangular mesh created between station points where each triangle is populated with weighted interpolation solution. Uses Delaunay triangulation method.

7. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Water Level Information

8. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Weighting Solutions Areas in RED represent 100% influence from the station of interest. Areas of BLACK represent 0% influence.

9. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Correctors

10. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES The Challenges Complex tidal characteristics o Diurnal and semidiurnal amphidromes o Variable tidal ranges (20cm ~ 6m) o Mixing tide types Limited coastal tide observations o Example: 4 NWLON stations in the Bering Sea Open interpolation boundary (extrapolation) o TCARI is an interpolation tool

11. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Complex Tidal Regime - Amphidromes Pearson et al., 1981 K1 Constituent Amplitude and Phase Contours M2 Constituent Amplitude and Phase Contours Amphidromic points complicate the generation of tide reduction schemes that are based upon the spatial interpolation/extrapolation of shore-based water level data. The “bullseyes” in the graphics from the 1981 Pearson, et al. paper show the locations of suspected amphidromic points.

12. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Variable Tidal Range and Tide Types One-month comparison of tides, February 2014 GT – Diurnal Range Diurnal Range (GT) at Stations in the Bering Sea

13. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Evaluation for Alaska Comparing the PMEL data with Foreman’s model output, TCARI Obs output, and 4 TCARI + model scenarios Retrieve harmonic constants (HCs) from each scenario (TCARI Obs, Model only, 4 Obs+Model Cases) Evaluate the model at coastal locations with Accepted HCs Calculate RMSE relative to observed HCs from Pearson and Mofjeld’s papers using the equation Normalize RMSE values by dividing them to the amplitude of constituents Export amplitude and phase contours for comparison

14. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Model Evaluation - Coastal The modeled tidal constituents are from a finite element model: FUNDY5SP (Foreman et al., 2006). The relative RMSE values range from ~3% to more than 100% in some locations. Given the discrepancies, accurate hydrographic surveys cannot rely only on the model results in some nearshore regions. The relative RMSE (%), Ae/Ao measures the relative model performance for individual tidal constituent (Shi, et. al, 2014).

15. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Model Evlauation - Offshore Third Party Historical Data 2 studies with PMEL Pearson et al. 1981 Mofjeld 1986 Combined Third-party Data Locations

16. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Model Point Distributions of 4 Scenarios 335 Points (G50 D25) 81 points (G100 D30) 117 Points (G80 D50) 129 Points (Cluster)

17. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Six Scenarios For Comparison 17 All four blended solutions that incorporate the model points used the same TCARI grid. In total we compared 6 scenarios: * Model only * TCARI only * TCARI + Model (4 blended scenarios)

18. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES M2 Phase Contours TCARI+129 pts ClusteredForeman model only TCARI + Obs Only TCARI + 81 ptsTCARI + 117 pts TCARI + 335 pts

19. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES K1 Phase Contours TCARI + obs only TCARI + 81 ptsTCARI + 117 pts TCARI + 335 pts TCARI + 129 pts Clustered Foreman Model only

20. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES (BERING SEA)

21. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Sensitivity Test (AK) Wang, 2014 Third-party offshore evaluations

22. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES General Conclusions – Bering Sea In general, the inclusion of model points improves the offshore interpolation results. Given the same number of model points, the clustered solution works better than the evenly distributed solution. However, the evenly distributed method is operationally more efficient and objective. We want to preserve the influence of coastal observations; in a gridded distribution this is done by buffering the distance between a model point and coastal station. [However, the buffer distance should not be so large that complex nearshore features cannot be resolved.] 22

23. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Chesapeake Bay (Ongoing) 23

24. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Evaluation Use Chesapeake Bay VDATUM model output Compare raw constituents at our stations with accepted constituents Apply interpolated correction surface to all VDATUM nodes Generate blended solutions and evaluate the results 24

25. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Different Interpolation Environment 25 59 Stations contributing either/both accepted harmonics or accepted tidal datums

26. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Uncorrected Model Evaluation – Coastal Comparison of M2 & K1 RRMSE 26

27. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Uncorrected amplitude and K-prime differences at the 59 stations 27

28. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Stations with > 1σ M2 phase difference (uncorrected) 28 The stations with the biggest phase difference (prior to the application of a correction field) are not isolated geographically but tend to be found upstream.

29. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Stations with > 1σ M2 phase difference (uncorrected) 29 There are 16 stations with M2 K’ differences greater than one standard deviation On average those 16 locations are 33% more semi- diurnal than the average of all 59 stations On average those 16 locations have 60% more of a shallow water influence We will continue to explore the reasons for the differences in the phases and amplitudes.

30. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Correction Field Before Evaluation CSDL generated a TCARI solution that interpolated the differences between the modeled constituents and the accepted constituents and applied that surface to all of the model nodes. This is the same step taken to adjust the ADCIRC tidal datum solution with our accepted datum values for the published VDATUM grids. 30

31. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Blending -The different scenarios 31 59 Stations with Accepted harmonics adn/or Accepted tidal datums 202 Model points included 3 Different scenarios TCARI only (DI) Model Blended (MB) – This blended solution uses the raw VDATUM harmonic constituents Model Blended Corrected (MBC) – This blended solution uses harmonic constituents from the model after a correction field was applied to the raw harmonics.

32. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Clean HWI Contours 32 Drawn by HPT Generated by TCARI Using Accepted Stations

33. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES 33 The HWI lines are spaced at 30 minutes In general there is consistency between the three scenarios as there aren’t many locations that dramatically change the phase of tide so all three show a fairly uniform propagation of tide up the bay. The biggest differences are seen near the mouth of the bay. HWI Contours

34. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Spot Checks of the Output The tide curves generated by all three scenarios were compared against historical data at seven locations. –Jacknifing for those stations with accepted information –Direct comparison with unaccepted data at the other locations 34

35. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Spot Checks RMSE 35

36. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Using the model in the rivers The effect of adding model points in the Chesapeake Bay is largely negligible Limitations of TCARI solutions might warrant the use of the model: –Lack of data –Complex tide regimes –Narrowing rivers (Huh?) 36

37. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES TCARI Limitation 37 Cotidal Lines drawn by HPT HWI Contours generated by TCARI-only solution. The dramatic narrowing of the shoreline just south of Mt Vernon forces forces TCARI to put all of the changes in a 13km strip of the river. Inclusion of 21 model points dramatically Improved the HWI contours generated by TCARI and these blended contours are very similar to our cotidal line distribution.

38. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Spot Checks in the Potomac 38 Unblended Solution Large phase offset and differences larger than the tide Blended Solution Phase offset disappears as does the error.

39. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Conclusions The inclusion of model points generally improves the offshore interpolation results. The goal is to fill critical data gap for TCARI interpolation and to do it efficiently (200 points is excessive for the improvement in results) The Bering Sea case study tells us that this tool works due to open boundary, complex tidal regime and lack of data. The Chesapeake Bay, itself, is not a good candidate because we have a solid closed boundary, sufficient data, good spatial distribution, and simple tidal propagation. The Potomac River is a good candidate because of a limitation in the TCARI algorithm. 39

40. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES Future Work and Recommendations Future work: –Complete Chesapeake Evaluation Report –Standardize the procedures for evaluating the modeled constituents –Develop an SOP for operational implementation –Work with CSDL to create a simple database of corrected and uncorrected harmonic constituents from our published VDATUM grids Recommendations: –It is recommended that this procedure be considered for operational use in areas with limited data, offshore regions, complex tides, or big tide ranges (eg. Bering Sea, Cook Inlet, offshore anywhere, Maine) 40

41. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES References NOAA, 1999. NOS CS4 Tidal Constituent and Residual Interpolation (TCARI) http://www.nauticalcharts.noaa.gov/staff/docs/TCARI_CS4.pdf http://www.nauticalcharts.noaa.gov/staff/docs/TCARI_CS4.pdf Foreman, M.G.G., Cummins, P.F., Cherniawsky, J.Y., Stabeno, P., Tidal Energy in the Bering Sea. J. Mar. Res. 2006, 64, 797-818 Mofjeld, H.O., Observed Tides on the Northeastern Bering Sea Shelf. J. Geophys. Res. 1986, 91:2593-2606 Pearson, C.A., Mofjeld, H.O. and Tripp, R.B., 1981. Tides of the Eastern Bering Sea Shelf. The Eastern Bering Sea Shelf: Oceanography and Resources USDCS/NOAA/OMPA Huang, L., Wolcott, D., Licate, L., Wang, J., Gallagher, B., Myers, E., Shi, L., Integrating Offshore Hydrodynamic Model Output with Onshore Observations to Improve Correctors to Hydrographic Survey Soundings 2014 Canadian Hydrographic Conference Proceedings Shi, L., Wang, J., Myers, E., Huang, L., 2014 Development and Use of Tide Models in Alaska Supporting VDATUM and Hydrographic Surveying J. Marine Science and Engineering, 2077- 1312 41

42. NOAA’s CENTER for OPERATIONAL OCEANOGRAPHIC PRODUCTS and SERVICES The Questions? 42 ?? ??