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**Modele maree Oceanique**

Finite Element System FES 2004 FES 2012 Rmsdiff semi-annual as large as 3cm open ocean: importance of luni solar K1 aliasing

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**a: Equilibrium semi-diurnal tides**

amplitude phase 17cm, M2 8cm, S2 b: Equilibrium diurnal tides amplitude phase 10cm, K1 c: M2 and K1 dynamic estimates amplitude amplitude 60cm,M2 24cm,K1 SI- data 1

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**a: Equilibrium long period tides**

amplitude phase 3.02 cm, Mf; cm, Mm; 1.35 cm, Ssa; 2.07 cm, Sa b: amplitude Mf dynamic estimate 2.8cm c: total tidal transport (kg m2/s) SI- data 2

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**c: dynamic M2 and K1 tidal amplitudes**

60cm,M2 24cm,K1 b: equilibrium long period tides amplitude phase 3 cm, Mf 1.5 cm, Mm c: dynamic Mf tidal amplitude 2.8cm, Mf SI- Data 2

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**K1 LuniSolar tidal elevation (cm) in Arctic**

Hemispheric averages of K1 meridional transport current N S S (cm/s) N (m2/s) hour hour maxNorth maxNorth SI-persp3

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**Tidal Energy Flux Vector M2 K1**

Ray et al., 2005 Fig 5 and Fig6 from Ray et al (2005) fluxes smaller than 20kW/m are not drawn 3.5 TW is the tidal power dissipated by the oceans, 3.4 TW is the average total (gas, electricity, etc.) power consumption of the U.S. in 2005 1.1 TW is the tidal power used by oceans to mix and maintain stratification 0.7 TW to 1.5 TW is the power induced by OVW stresses in the oceans (90% are dissipated in the upper 100m) Semi-diurnal (12h25mn) Diurnal (23h56mn) Lunar Luni-Solar Min (1997)/ Max (2006) Lunar Inclinaison nodal factors: with inclination, K1 increases 3 times more than M2 decreases Role K1 increase (18.6yrs) on decadal climate at high lat where K1 big (Ray, 2007), AND in tropics because of Yanai increase

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**SSS SST a: mean differences: daily TAO (winds) – QSCAT (OVW)**

Courtesy of Dr. Kelly (OVWST, 2007) b: mean Ocean currents from drifters at 15m NECC SEC SSS SST c: Zonal components d: Meridional components North Trade winds diff=NECC QSCAT 180ºW…………..longitudes……..90ºW tide diff QSCAT Equator …..……….…. Latitudes …………….. …….. winds 180ºW………… Longitudes ……..90ºW Trade winds QSCAT diff=SEC South

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**SI- data4 Solar climatology of OST (cm) +20 --20 +12 --12 +12 --12**

October – April ECCO +20 --20 +12 --12 October – April ECCO – (QSCAT) ECCO July-Jan +12 --12 NORTH average (cm) SOUTH average (cm) TPJ O(QSCAT) TPJ O(QSCAT) month month SI- data4

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**Total tidal transports (kg m2/s) 3 hours apart**

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**On average between 25º and 60º latitude:**

66% area is ocean in South, 43% area is ocean in South On average between 60º latitudes, North Pac is 22% deeper than South

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**= annual cycle for K1 detected by QSCAT or ASCAT**

V transport K1 (m2/s) maxNorth and is bigger than maxSouth horizontal axis duration = 24h ~ K1 tidal cycle (period=23h56mn) = annual cycle for K1 detected by QSCAT or ASCAT Significant phase difference (4hours) between currents and transport North budgets because averaged North Pacific deeper than South. Tidal current values are provided by TPXO7.2 on 1 Nov 2007 from 00h:30 to 23h:30.

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**SI- data 5 a: LOD-moon time series b: LOD_moon wavelet**

c: LOD_sun wavelet 0.50 0.05 days days SI- data 5

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**b: New and Full moon during June and December solstices**

a: Last and First Quarter around September equinoxes ~2 weeks apart * ecliptic plane * b: New and Full moon during June and December solstices ~6 months apart The Earth Moon Mass Center (EMMC) remains in the ecliptic plane. The Earth mass center is 4670 km away from the EMMC.

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**Fig 11 Energy of the horizontal and vertical acceleration speeds**

days a: zonal 0.6 1.4 1.2 b: meridional c: vertical Fig 11

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**3.5 TW is the tidal power dissipated by the oceans**

3.4 TW is the average total (gas, electricity, etc.) power consumption in US in 2005 1.1 TW is the tidal power used by oceans to mix and maintain stratification 0.7 <-> 1.5 TW is the power induced by OVW stresses in the oceans (90% are dissipated in the upper 100m)

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**2D Vectors (instant) u , v , w =sqrt(u2+v2) speed**

Units? Ocean Wind Stress (TX,TY)… Pascal (kg m/s2) Ocean Vectors of Work done by the (air-sea) Wind Stress on the ocean circulation: (OVWWx,OVWWy) =Sum_surf*time {(TX*u+TY*v) dx.dy.dt } OVWW: the biggest unknown: between 0.4TW and 1.7TW Ocean Tidal Energy (EX,EY)… (kg m2/s) = Sv/m (Ex, Ey) = r g Sum_period{ (u,v)H(h+hs) dt } / period M2:period=12h25mn K1: period=23h56mn S2: period=12h hs=hbody+hload

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**Tidal astronomic forcing M2 K1**

Fig 5 and Fig6 from Ray et al (2005) fluxes smaller than 20kW/m are not drawn 3.5 TW is the tidal power dissipated by the oceans, 3.4 TW is the average total (gas, electricity, etc.) power consumption of the U.S. in 2005 1.1 TW is the tidal power used by oceans to mix and maintain stratification 0.7 TW to 1.5 TW is the power induced by OVW stresses in the oceans (90% are dissipated in the upper 100m) semi-diurnal (12h25mn) diurnal (23h56mn semi-diurnal symmetric, diurnal antisymmetric the ocean responses loose symmetry because waters are squeezed to flow between the ocean bottom, its surface and the continents.

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**Indian and Pacific warm pools**

QSCAT OVW stress TPJ wave/swell +2.0 3 2 -1.4 1 Tropical Swell pools 100% 72% Indian and Pacific warm pools 32º 24º 13º

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*** * mean Sea Level simulated by OGCM forced by QuikSCAT vectors**

relative to observed MSL model forced by QuikSCAT vectors (CORE2): courtesy of Dr. Large (NCAR), OVWST, 2008 cm The difference between model and observed MSL is too big to be real. It corresponds to a change in Earth’s oblateness which is incompatible with the observed range of LOD variations. New Moon in North around June solstice * * Full Moon In South in June-July 14.7 days apart

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**What energy vector are detectable by scatterometers for climate?**

(U,V) winds in (m/s)… Stress (TX, TY) in (kg/m/s2) = r (u’w’, v’w’) (vertical transfer of turbulent momentum) = r CD Wa (Ua, Va) (CD: drag coefficient) = r CD Wshear (Ushear, Vshear) where (Ushear, Vshear) = (atmosphere – ocean) horizontal flows (Ua-Uo-0.8Uorb) = u*/k ln[….z/z0…] TX (Va-Vo-0.8Vorb) = v*/k ln[….z/z0…] TY where (Uorb, Vorb) =Vector of orbital wave velocities Energy in (kg*m2/s2): (OVWEx, OVWEy) and (TideOVEx, TideOVEy) (Sum_surf*time {(TX*Uo, TY*Vo) dx.dy.dt } ) (r g Sum_period{(Udx,Vdy) *H*(hT+hTs) ) dt }) 2D- vectors: OVW work rates (per dt, per length) in (kg*m/s3= Watt/m) 1) over which dt do we choose to compute the OVW work rates? 2) over which thickness dz do we choose (u, v) ocean surface? 3) we need the (Uo, Vo) due to p_atmos, tides and fast (TX,TY) as well? 4) we need the work rate via wave/swell too. s0,H1/3 altimeter? Issues so far unresolved due to ocean-air curl/mass discontinuities at interface between 2 thin shells at the surface of the Earth. Emerging solution: 3D- vectors (OA)Momentum in (kg*m2/s)

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**SI- data 3 +30 -30 a: mean meridional OVW difference: ECMWF - QSCAT**

b: OVWy stress along 6ºN +0.6 +2 QSCAT62 QSCAT65 QSCAT66 ERS61 FSU10 NCEP15 dyn/cm2 longitude -2 -0.2 m/s c: zonal averages of meridional winds, QSCAT, differences and tides +1 V QSCAT (200 kg m2/s) VECMWF-VQSCAT (m/s) winds QSCAT diff tide m/s -1 latitude S Equatpr N 60S EQ N d: 2000:2004 mean OST: model forced by QSCAT– observations +30 cm -30 SI- data 3

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