Ocean Tides I

Model description

The high resolution version of the  MPI-OM (Max-Planck Institute - Ocean Model) model, which has been developed within the framework of the German consortium project STORM, is used and extended by an explicit tidal forcing. The STORMTIDE  model has a  resolution of 5-10 km in the horizontal and 40 z-layers in the vertical. It allows the generation of low mode internal tides [link to video 1] and a realistic simulation of the  meso-scale and large-scale ocean circulation [link to video 2]

Simulated baroclinic M2 tidal energy flux.
ith this high resolution model approach it is possible, e.g. to improve our understanding of non-stationary signals in ocean tides and the conversion of barotropic tidal energy into internal tides. The model is forced with a climatological forcing and an advanced seasonal restoring to climatology, in order to simulate a seasonally stationary ocean circulation and stratification. Ocean tides are forced by a full luni-solar tidal potential, i.e. the position of the sun and the moon are computed for every time-step in the model simulation. 

 (Poster for DKRZ workshop project "High resolution modelling of ocean circulation and tide" [download]))

he seasonal variations of the barotropic and internal tides have been explored in detail. We compared the results of the model simulation with an analysis of 19 years of satellite altimeter data and long-term tide gauge records. In order to compute the seasonal cycle of tides we used two different methods: (1) sub-sampling of the sea level time-series into seasons and (2) computing the annual satellites of the M2 tide. This has been the first global study on this issue and a first paper on the seasonality of internal tides has recently been been published
[ref]. A more detailed paper on the seasonality of barotropic and internal tides, obtained from observations and model simulation is currently under review.
The generation of the low mode M2 internal tide is simulated realistically and the seasonal cycle of the generation and propagation of internal tides show similar characteristics as in the observations (Ray and Zaron, 2011). We explained exemplary the seasonality of the internal tides generated in Luzon Strait, and showed that the variations in stratification change the generation and propagation characteristics of these internal waves. This effect can lead to seasonal changes of 5-15 mm in the surface internal tide signal.


In polar and shallow water regions the barotropic tides vary seasonally by 5-10%. The comparison of the model results with the satellite altimeter data and tide-gauge records reveals that the model is able to capture the seasonal signal of  barotropic tides. In detail we explored the seasonal cycle of the M2 tide in the North Sea, the Yellow and East China Sea, and in the Hudson Bay region. In high latitudes the seasonally ice coverage induces a seasonal tide by frictional processes between the sea-ice and the ocean surface layer. This effect has been parametrized in the model and the simulated seasonal tide compares well with that of observations.
n coastal regions, e.g. in the North Sea and Yellow and East China Sea, the model shows that the seasonality is caused by the impact of seasonal stratification on the vertical eddy viscosity and in turn on the vertical tidal current profile. So far, this effect has been observed in tidal current profiles, but not considered in ocean tide modelling studies and thus gave rise to a theoretical approach to proof the significance of this effect 
[ref]We solved analytically the equations of motion for the one dimensional barotropic transport dependent on eddy viscosity, linear bottom friction, ocean depth and Coriolis parameter. What we found is that the barotropic transport is indeed sensitive to the mean vertical eddy viscosity and that changes in stratification impact the transport by 1-10 %. These results were confirmed by simulations with the General Ocean Turbulence Model (GOTM), which showed that stratification changes in the southern North Sea can be seasonally modified by up to 5 %, and thus are consistent with the results we got from the high-resolution ocean circulation and tide model. Another surprising result is that a change in 10 meter of the mixed layer depth can already modify the barotropic transport by 1-2 %. Thus, it might be that the secular trends of ocean tides might be in some regions related to global warming of the upper ocean .

The barotropic tidal flow over topography generates baroclinic tidal energy. The amount of energy converted from barotropic-to-baroclinic motions is large with about 1.7 TW. This estimate from the STORMTIDE model includes the eight largest semi-diurnal and diurnal tidal constituents and represent the first computations from a 3D tide model with realistic stratification. In general, the spatial distribution and total conversion rates compare well with analytical and numerical model studies and have been published recently. One of the surprising results is that a significant amount of diurnal baroclinic tidal energy is generated poleward of the critical latitudes (about 0.11 TW or 30% of the global diurnal energy conversion). In these latitude internal waves are prohibited to propagate freely and only exist as trapped waves. Thus, these sub inertial internal tides are transferred locally to turbulent mixing processes with a high efficiency. 

Selected variables of the model output and different analysis products are available for download at the World Data Center for Climate at the DKRZ in Hamburg, Germany. The direct link for downloading these files is here

The following files are available:
  • 2D tidal patterns of sea level 
  • 3D horizontal and vertical tidal velocity field
  • barotropic-to-baroclinic tidal energy conversion rates 
  • 3D tidal density perturbations
  • seasonal sub-sampling of M2 tidal sea level and velocities
  • daily values of the last year of (u,v,w, T, S) in 100 and 2000 meter depth
  • monthly mean values of eight years of several ocean variables