Barotropic and Baroclinic Tide Models for SWOTEdward D. Zaron, Portland State University & Richard D. Ray, NASA/Goddard Space Flight Center & Gary D. Egbert, Oregon State University

Assessment of SWOT Mission Requirements Related to Tides1. SWOT will require improved models of coastal tides. Pre-launch work consists of

developing improved models (already underway by several international groups).More specifically for SWOT, pre-launch work should involve developing thealgorithms to merge nested regional and global fields for routine SWOT dataprocessing.

2. SWOT will require improved models of high-latitude tides. Although efforts alongthese lines are ongoing and will continue, most progress will occur once theSWOT data themselves are available.

3. SWOT will require models of deep-ocean internal tides.

4. For certain rivers subject to significant upstream tidal propagation from theocean, the precision of SWOT elevation and discharge estimates will beimproved by correcting for tides. For many isolated rivers SWOT may provide theonly information available for determining the tidal effects.

Models of the Stationary TideEmpirical Mapping of Along-Track Harmonic Constants

Figure 1: The in-phase component of the internal M2 tide, obtained from harmonicanalysis of exact-repeat mission altimetry. Color scale ranges from -2 cm to +2 cm.

Model Validation and Assessment

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Figure 2: CryoSat-2 variance reduction (cm2) with empirical M2 correction from Fig-ure 1. Throughout much of the ocean, and especially in regions of strong internal-tide generation, the variance reduction is positive (red). Regions where varianceis not reduced are mostly near boundary currents where mesoscale variability hascorrupted the tidal estimates (blue). Mesoscale variability also likely causes signif-icant loss of coherence in the tide itself, to such an extent that there may well belittle coherent signal to map in those locations.

Data Assimilative Modeling with Reduced Gravity Dynamics

M2 [cm]

K1 [cm]

Figure 3: We have developed a reduced gravity (RG) data assimilation schemefor mapping low-mode coherent internal tides, and applied this to a multi-missiondataset to produce preliminary global first-mode M2 (top) and K1 (bottom) solu-tions. Vertical dependence of the flow variables are described using flat-bottommodes (which depend on the local depth H(x,y)), yielding a coupled system of (2-dimensional) PDEs for the modal coefficients for surface elevation and horizontalvelocity.

Non-Stationary Baroclinic Tides

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ctra

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sity

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10-4 10-3 10-2 10-1

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North Pacificmode-1: 1.19 cm2 total0.23 cm2 non-stationary

mode-2: 0.26 cm2 total0.12 cm2 non-stationary.

Amazon Plume

Mode-1: 1.07 cm2 total0.47 cm2 non-stationary

Figure 4: Along-track wavenumber spectra of sea-surface heights as measuredover 18 years by the T/P and Jason satellites. Black curve is the spectrum afterapplying a standard barotropic ocean tide correction. Red curve shows the samespectrum, but after estimating and removing residual tides point-by-point along eachtrack; by this approach the temporally coherent internal tides are removed. In bothpanels the large peak near wavenumber 0.008 cycles/km is caused by mode-1 in-ternal tides.

High-Latitude Barotropic Tides

Figure 5: Valid ocean altimeter returns for 35-day periods in late summer (left toright) 1996, 2003, and 2008, over the Chukchi Sea and adjoining Arctic Ocean. The1996 data were collected by ERS-2; the other years by Envisat. The large loss ofsummer ice in more recent years in striking, which can be exploited for improvedsampling of Arctic tides.

Coastal and River Tides

Figure 6: Tide-gauge water elevation for thePotomac River at Washington, D.C., showinghourly measurements (blue) and daily mean(red). To recover mean river stage oversub-monthly intervals at decimeter precision,the infrequent altimeter measurements will re-quire correction for tidal variability even at thisstation located 280 km from the Atlantic.

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HRET

IT

Figure 7: Explained variance asa function of distance from coastfor the model in Figure 1 (IT) andanother model (HRET) which uti-lizes spatially-coupled harmonicanalysis.

Summary of Key Activities1. Design and implement a protocol for testing coastal tide models, relying primarily

on independent satellite data.

2. Work with the SWOT tide teams to prioritize regions for improved modeldevelopment, with highest priority given to regions overflown by SWOTs initial1-day sampling phase.

3. Develop nested tide-prediction algorithms for SWOT tide corrections, includingcorrections provided by other groups.

4. Utilize improved data for both modeling and testing, e.g., improved bathymetrydatasets, improved altimeter data and path-delay corrections, and better editingand flagging criteria.

5. Continue to refine coastal tide models via data assimilation of altimetry.

2016 SWOT Science Team MeetingPasadena, CAJune 13-16, 2016

Edward D. ZaronDepartment of Civil and Environmental Engineering

Portland State Universityezaron@pdx.edu