Robust methods for high accuracy tidal modelling

in coastal and shelf seasF. Lyard, L. Roblou1

M. Lux, C. Penard, J. Lamouroux2

E. Bronner3

1LEGOS, CNRS, Toulouse2Noveltis, Toulouse3CNESS, Toulouse

Florent.Lyard@legos.obs-mip.fr

Regional modelling approach

Completed in COMAPI/PISTACH project (CNES/Noveltis/CLS) :

n North-East Atlanticn Mediterranean Sea

Completed as Pilot configurationn Persian Gulf

On-going investigation stagen Amazon estuary/shelfn Kerguelen Plateaun West Indian Shelf

Preliminary investigation stagen Bering Sean China/indonesian Sean Solomon Sean Patagonian Shelfn Caspian Sean Black Sea…

Objectives :n Investigate the shelf and coastal seas HF dynamicsn Improve regional de-aliasing corrections for altimetry

coastal applications (extended tidal spectrum, data-controled accuracy)

Approachn Regional tidal modelling and data assimilationn Regional storm surges simulationsn T-UGOm FE/FV model (SW 2D module)

Data assimilation approachObjectives :

n Robust modeling and assimilation methodologyn Feed-back to the hydrodynamic model parameters

Data :n Tide gauges, current-meter/ADCPsn Altimeter data: homogenous, widely available, practicable accuracy (T/P, Jason1,

Jason2, …) -> approach mainly relies on these data

Toolsn T-UGOm modeling (ensemble generation)n X-TRACK (i.e. coastal) altimeter data processing and error estimaten SpEnOI assimilation

Spectral, ensemble optimal interpolation, based on the representer approach (Lyard, 1999), Letellier (2004)

xa = xf + r.bb = [H Pf Ht + R]-1 (y0 – H xf) xf prior model state vector y0 observation vector xa analysis state vectorH observation operator matrix r representer matrix: r = Pf Ht

Pf model errors covariance matrix R observation errors covariance matrix

Pf model errors covariance matrix computed from ensemble members' harmonic analysis

Data error estimatesObjectives: establish "automated" procedures to estimate accuracy of

altimeter-derived tidal constants

Provide data assimilation errors bars and covariancesn Emphasis on shelf and coastal seasn Reduce data editing burden before data assimilation

Qualifify altimeter-derived tidal constants(product distribution purposes)

Assess existing altimeter-derived atlases accuracyn Estimate data accuracy at atlases production timen Estimate atlas accuracy against most recent data analysis

( ) ( ) ( )obsobs CNJ hhhhh

e--= -1*

21

Data error estimates processing

3 criteria used to estimate harmonic constants accuracy:

n X-over (ascending versus descending) harmonic analysis incoherence: aliasing contamination from non-tidal ocean signaltidal drying…

n Along-track constant smoothnessInternal tides signatureSevere data loss (near-shore regions)Instrument noise

n Harmonic analysis internal diagnostic (posterior diagonal variances)Record lengthFrequency separation

Hydrodynamic model

Geometry:n NOAA shorelines + Space imagery

(Landsat, …)n SHOM bathymetryn O(1) km resolution along the shorelines

Forcing :n FES2004 OBCsn Astronomic forcingn FES2004 loading/self-attraction

Dissipation :n Homogeneous bottom rugosity lengthn Internal wave dragn Smagorinsky horizontal diffusion

Genesis mesh/data editor

Use GoogleEarth image to valide shorelines

bathymetry

Ensemble generationBathymetryn Collect various bathymetry databasen Create/select a "most trusted" bathymetryn Generate randomly perturbed bathymetry:

with

Open boundary conditionsn Collect various tidal atlasesn Create/select a "most trusted" atlasn Generate randomly perturbed OBCs:

with

Bottom rugosityn Identify significant bottom friction regions from

prior tidal energy mappingn Create a partition (using polygons)n Generate perturbed rugosity by varying

rugosity value in each region (following a normal law)

Internal tidal wave dragn Identify significant internal drag regionsn Create a partition (using polygons)n Generate perturbed rugosityby varying wave

drag value in each region (following a normal law)

Bathymetry set dispersion(%)

Rugositypartition

å+=i

ikiok hhh ,a 0, =åi

kia

å+=i

ikiok hbhh ,~ 0, =å

ikib

Optimal atlas M2 tide K1 tide

Altimeter data assimilation only20

2

5

M2FES2004GOT4.7Optimal

754331

M4FES2004GOT4.7Optimal

141410

K1FES2004GOT4.7Optimal

403921

Atlas accuracy, mm (/tide gauges)

Prior solutions

Optimal solutions

Data error estimates (cm)

Is there a life after data assimilation?Can we learn anything about model parameters from the data assimilation ?

Bathymetry, friction, …

How?n Parameters inversion

Use b vector and multivariate ensemble covariancesn Energy considerations

Inferring optimal rugosity :Assumes no significant depth errors (or ignore them)Compute bottom friction RoW from energy balanceInfer corresponding Cd

n Propagation considerationsInferring optimal bathymetry :

Compute phase difference prior/optimal solutionCompute wave celirity deltaInfer optimal h

What independant check could done to validate parameters inversion ?n In situ measurementsn Energy budget examinationn Wave-to-wave consistency

Hydrodynamic OptimalM2

energy budget

Energy fluxes (w/m)

Bottom friction RoW (w/m2)

4.5 gW4.25 gW

o objective: retrieve hydrodynamic parameters from assimilation solution

o Approach: closure of energy bufget

Diagnostic:

bottom friction to be re-worked

correct energy input (=OBC's accurate enough)

Remedy:

new friction coefficient distribution

Budget

Hydrodynamic OptimalK1

energy budget

2 gW1 gW

Energy fluxes (w/m)

o objective: retrieve hydrodynamic parameters from assimilation solution

o Approach: closure of energy bufget

Diagnostic:

bottom friction distribution incorrect

deficient energy input (=OBC's not accurate enough)

Remedy:

new friction coefficient distribution

improvement of OBCs

Bottom friction RoW (w/m2)

Budget

Obidos

Amandes tidal model

River/estuary/shelf systemCollaborations franco-brésilienne LMTG/LEGOS/CEREGE/CNPq

Le Bars et al., Ocean Modelling, 2010; Lyard et al., J. Marine Systems, submitted

Obidos: limit oftidal influenceAmazon plume Tidal dissipation

•Presently purely hydrodynamic•Most accurate atlas (2010)•Assimilation planned for 2011

Harmonic analysis error budget

Loss of data (coastal effects)

Internal tides signature

X-over incoherence

X-over analysis incoherence special case: aliased neap/spring tides data acquisition rate anomaly (3 years

cycle) in very shallow depths

M2 HF along-track residuals

tidal prediction

acquisition anomalies

cross-over 037-202

spring tidesneap tides

3 years

Reduction of variance in altimetry SLAblue=improved performances

ASSIM/FES2004 ASSIM/GOT4.7ASSIM/REF

COMAPI regional atlases

Optimal versus prior Optimal versus GOT 4.7Optimal versus FES2004

ConclusionsHave a robust, generic tool for shelf and coastal seas tidesstill hard work to treat a sole regionn Very efficient for the main tidal constituentsn More difficult for non-linear and minor astronomic constituents

Further improvements neededn Multi-wave (poly-chromatic) assimilation

Better discrimination for model parameter identificationImprove non-linear constituents assimilation

n Iteration on tidal loading (for consistent ocean and loading tides)Model parameters improvements still need more work around…n Explore parameters inversionn Extend energy budget control investigations

Need for financial support/collaboration to extend CSS coverage