Massentransporte und Massenverteilungen im System Erde  
    Looking into the inside of the ocean - A Moon story by DYNTIDELooking into the inside of the ocean - A Moon story by DYNTIDE  


Looking into the inside of the ocean - A Moon story by DYNTIDE

Prologue: Tides play an important role in the evaluation of satellite missions; they influence the altimetry and change the gravity fields due to short-term variations in the sea level and the associated loading effect on the sea floor. This effect causes aliasing in determining the geoid and in observing ice thickness, for example, on the Antarctica and on the Greenland.


Tides are excited by the gravitational attraction from the Sun and the Moon. The work done by the celestial bodies on the ocean is nowadays computed quite accurately by surface tides obtained by the altimetry[1][2][3]. As shown in Fig.1 (M2 tide as an example), the tidal energy is received by the ocean mainly in lower latitudes and must be completely dissipated anywhere in the ocean. It has long been believed that this occurs in shallow water regions (SW) like the North-West European Shelf (NWES). This is partially true, as can be seen in Fig.3: The energy supplied by the Moon is directed toward the well-known SW. One of the great achievements by the satellite missions is the finding of extended internal tide generation areas5) and connected barotropic[3] and baroclinic[6] dissipation in the deep ocean.


Fig.1: M2-tide energy input from the Moon (HAMTIDE)
Fig.2: M2-tide transport ellipses (HAMTIDE)

Tides are showing not only by the sea surface moving up and down, but also by currents. The magnitude of the tidal currents amounts to less than a few cm/s in the open ocean but often exceeds 1 m/s in shelf areas. The strong currents on the shelves cause mixing due to the vertical shear near the bottom (due to bottom drag), and even currents of small magnitude in the abyssal ocean (depth > 1000m) promote water mass- and heat-exchange by mixing which internal-tide breaking brings about. This occurs because the currents induced by barotropic (surface) tides (Fig.2) emerge in the entire water columns and interact with topographic features generating internal tides in the stratified ocean[3][4]. The existence of such internal tides was first found by means of altimetery data processing[5].


Fig.3: M2-tide energy flux (HAMTIDE)
Fig.4: M2-tide positive dynamical residual power in > 1000 m(HAMTIDE)

Thus, energy produced by the gravitational attraction from the Moon is dissipated mainly by turbulent mixing, which occurs on the one hand via the bottom drag[2][3] and the eddy viscosity[2] on shelves, and on the other hand via the form drag[6] and the internal-tide breaking in deeper ocean[2][3]. The dissipation due to the form drag is termed (barotropic-to-) baroclinic conversion[7] and can be detected using data assimilative models by computing dynamical error work[8] or dynamical residual power[2] appearing in the deeper ocean > 1000 m (Fig.4). Highly accurate satellite altimetry thus allows us to look into the inside of the ocean via determining tidal currents and surface tides.


Exciting story: In the last decade, one has come to regard tidally induced mixing as an important driving force for the abyssal circulation[9] and hence to affect climate[10]. The investigation of this mixing requires good knowledge of tidal dissipation. Especially the baroclinic conversion rate[2] describing energy transfer from surface to internal tides, is hard to estimate, since the parameterization of the conversion is still not sufficiently established. This rate has been assumed to be about 1 TW, which is obtained from simple advective-diffusive balance[9], and from data assimilative models3). The estimation from the latter method is sensitive to the choice of bottom drag and eddy viscosity[2]. We obtained a new conversion rate that is by ~40% larger than previous investigatios[3], where dissipation parameters were estimated a priori within a reasonable range by sensitivity analysis. We found that MAR is the most effective energy conversion site due to its huge area (Fig. 4). The strong energy fluxes along MAR (Fig.3) may support our suggestion. The Weddell Sea and the NWES are coming to appear as significant conversion sites, which other models[3][4] did not detect so far as such.


Pathways of internal tides and their dissipation sites are nearly completely unknown. We suggest that adequately evaluating the dynamical residual power[2] distribution may help to determine a realistic vertical diffusivity.


Epilogue: ‘When asked which is more important, the Moon or the Sun? . The Moon, of course, because the Sun shines only in the daytime when it is bright anywhere[10]…‘.


PS: Tides and Current data of 9 constituents[11][12] are given free to download (



[1] Bosch, B., R. Savcenko, F. Flechtner, C. Dahle, T. Mayer-Gürr, D. Stammer, E. Taguchi, and K-H. Ilk (2009), Residual ocean tide signals from satellite altimetry, GRACE gravity fields, and hydrodynamic modeling, GJI, 178(3), 1185-1192. doi :10.1111/j.1365-246X.2009.04281.x :

[2] Taguchi, E., D. Stammer and W. Zahel (2011), Inferring deep ocean tidal energy dissipation from the global high-resolution data-assimilative HAMTIDE model (submitted to J. Geophys. Res.).

[11] Taguchi,E. and D. Stammer (2011), Ocean tides obtained by the data assimilative HAMTIDE model: 1. Harmonic constants of 9 major tides. ICDC.

[12] Taguchi, E. and D. Stammer (2011), Ocean tides obtained by the data assimilative HAMTIDE model: 2. Harmonic constants of 9 major tidal currents. ICDC.


[3] Egbert & Ray (2001), JGR, 106: [4] Simmons et al. (2004), Dee-Sea R., 51: [5] Ray & Mitchum (1996), GRL, 23: [6] Zaron & Egbert (2006), JPO, 36: [7] Simmons et al. (2004), Dee-Sea R., 51: [8] Egbert (1997), PO, 40: [9] Wunsch & Ferrari (2004), A.R.F.M., 36: [10] S. R. Jayne (2009), JPO,39: [10] Munk & Wunsch (1997), Oceanogr. 10.