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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

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Outline • Introduction

o Tide reduction using Tidal Constituent And Residual Interpolation (TCARI) o The challenges faced

• Methodo 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


Corrections to Echo Soundings-

Tide Reduction is CriticalSurveying at this time?

Difference =10.37m (34.02ft)

Or at this time?


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 inputso Systematic

• The accuracy relies on data availability and spatial distribution.


Define shoreline & choose stations

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Stations within the domain that have accepted tidal datums or harmonics are used.


TriangulationTriangular mesh created between station points where each triangle is populated with weighted interpolation solution. Uses Delaunay triangulation method.


Water Level Information


Weighting SolutionsAreas in RED represent 100% influence from the station of interest.

Areas of BLACK represent 0% influence.


Correctors


The Challenges• Complex tidal characteristics

o Diurnal and semidiurnal amphidromes o Variable tidal ranges (20cm ~ 6m)o Mixing tide types

• Limited coastal tide observationso Example: 4 NWLON stations in the Bering Sea

• Open interpolation boundary (extrapolation)o TCARI is an interpolation tool


Complex Tidal Regime - Amphidromes

Pearson et al., 1981

K1 Constituent Amplitude and Phase ContoursM2 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.


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


Evaluation for AlaskaComparing 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

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122

1/2 ))cos(22

( omomom

KM hhAAAA

RMSE

oARMSErRMSE KM /1/2


Model Evaluation - Coastal

2

122

2

122

0 ))cos(22

()))cos()cos((2

1( omom

omoomme hhAA

AAdthtAhtAA

• 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).


Model Evlauation - OffshoreThird Party Historical Data

2 studies with PMEL

Pearson et al. 1981 Mofjeld 1986CombinedThird-party Data Locations


• Model Point Distributions of 4 Scenarios

335 Points (G50 D25)

81 points (G100 D30)

117 Points (G80 D50)

129 Points (Cluster)


Six Scenarios For Comparison

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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)


M2 Phase Contours

TCARI+129 pts ClusteredForeman model only

TCARI + Obs Only TCARI + 81 pts TCARI + 117 pts

TCARI + 335 pts


K1 Phase Contours

TCARI + obs only TCARI + 81 pts TCARI + 117 pts

TCARI + 335 pts TCARI + 129 pts ClusteredForeman Model only


(BERING SEA)


Sensitivity Test (AK)

Wang, 2014

Third-party offshore evaluations


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.]

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Chesapeake Bay (Ongoing)

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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

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Different Interpolation Environment

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59 Stations contributing either/both accepted harmonics or accepted tidal datums


Uncorrected Model Evaluation – Coastal Comparison of M2 & K1 RRMSE

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Uncorrected amplitude and K-prime differences at the 59 stations

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Stations with > 1σ M2 phase difference (uncorrected)

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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.


Stations with > 1σ M2 phase difference (uncorrected)

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• 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.


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.

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Blending -The different scenarios

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• 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.


Clean HWI Contours

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Drawn by HPTGenerated by TCARI Using Accepted Stations


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• 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


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

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Spot Checks RMSE

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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?)

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TCARI Limitation

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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 dramaticallyImproved the HWI contours generated by TCARI and these blended contours arevery similar to our cotidal line distribution.


Spot Checks in the Potomac

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Unblended SolutionLarge phase offset and differences larger than the tide

Blended SolutionPhase offset disappears as does the error.


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.

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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)

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References• NOAA, 1999. NOS CS4 Tidal Constituent and Residual Interpolation (TCARI)

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

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The Questions?

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