<p>Oceanic topography of the sea surface $\zeta$ can be defined as the height of the sea surface relative to a particular level surface, the <a href="http://en.wikipedia.org/wiki/Geoid">geoid</a>. The geoid to be the level surface that coincided with the surface of the ocean at rest (a list of geoids with application to oceanography can be found in <a href="http://scientiamarina.revistas.csic.es/index.php/scientiamarina/article/view/1533/1715">Talone et al., 2014</a>). </p>

<p>Variations in sea surface height (topography) are due to processes that result in ocean motion: ocean currents, tides, and changes in barometric pressure from the inverted barometer effect. As a result, we usually call it "dynamic topography" or "dynamic height". As geoid undulations are of order 100 times larger than the dynamic height, the shape of the sea surface is dominated by local geoid variations caused by gravity with the effect of the currents being much smaller.</p>

<p>In the image you provide what you have is "dynamic height" and thus is a deviation from the geoid and the result of oceanic currents. By knowing the dynamic height, we can get an idea of the surface geostrophic current:
$\mathrm{u_s= − {g\over f} {\delta\zeta\over\delta y}}$; $\mathrm{v_s= − {g\over f} { \delta\zeta\over\delta x}}$ where f is the Coriolis parameter,  g is gravity, and $\zeta$ is the height of the sea surface above the level surface (geoid).</p>

<p>Now, there is a direct effect between currents and bathymetry that sometimes is referred to as <a href="http://en.wikipedia.org/wiki/Taylor_column">Taylor columns</a>. The <a href="http://en.wikipedia.org/wiki/Taylor%E2%80%93Proudman_theorem">Taylor-Proudman theorem</a> enforces that vertical columns of fluid move along contours of constant fluid depth. The basic idea behind this is that in order to conserve vorticity, fluid parcels tend to follow bathymetric contours (isobaths). So to answer your question, bathymetry affects ocean topography indirectly by affecting ocean currents.</p>

CC BY-SA 3.0
2015-03-20T14:45:15.840Z
The effect is nothing but a conservation of vorticity (http://oceanworld.tamu.edu/resources/ocng_textbook/chapter12/chapter12_02.htm). If a water parcel moves deeper, then it has to change its spin. The same is true if a water parcel moves latitudinally. That results in the general circulation of the ocean: http://oceanworld.tamu.edu/resources/ocng_textbook/chapter11/chapter11_01.htm
arkaia
CC BY-SA 3.0
2015-03-20T15:15:13.967Z
The conservation of vorticity is not related to friction. The planetary boundary layer is a frictional effect and thus ageostrophic in nature. Maybe I don't understand your question.
arkaia
CC BY-SA 3.0
2015-03-20T17:54:17.063Z
Thanks @aretxabaleta for answering my question again. Regarding your last point: I thought the most significant causes of ocean currents are wind, Coriolis force, and the location of the continents. So then, while bathymetry affects ocean currents, is its effect relatively minor? Second question: we see this huge rise in the Pacific near the eastern coast of Japan - is that caused by the seamounts?
user4624937
CC BY-SA 3.0
2015-03-20T18:32:07.573Z
The rise of SSH near Japan is caused by the presence of the Kuroshio (http://en.wikipedia.org/wiki/Kuroshio_Current). The wind and thermohaline circulation affect the momentum balance of the ocean as a fluid. The other balance to consider is the vorticity (angular momentum) balance [(f+spin)/h=const] and in that case bathymetric changes and Coriolis (planetary vorticity) affect the rate of rotation of the water parcel.
arkaia
CC BY-SA 3.0
2015-03-20T14:27:27.457Z
2015-03-20T14:27:27.457Z
arkaia
<p>Here is a map of ocean surface height or topography:</p>

<p><img src="https://i.sstatic.net/IziKc.jpg" alt="enter image description here"></p>

<p>Source: <a href="http://www.esa.int/var/esa/storage/images/esa_multimedia/images/2010/12/mean_dynamic_topography_of_global_ocean/9930795-2-eng-GB/Mean_dynamic_topography_of_global_ocean.jpg" rel="nofollow noreferrer">http://www.esa.int/var/esa/storage/images/esa_multimedia/images/2010/12/mean_dynamic_topography_of_global_ocean/9930795-2-eng-GB/Mean_dynamic_topography_of_global_ocean.jpg</a></p>

<p>How significant is the bathymetry or seabed elevation in shaping the surface topography? What are the major causes of variations in the topography?</p>

CC BY-SA 3.0
2015-03-20T08:08:15.263Z
What do you mean by the surface topography? Do you mean the sea surface height?
Isopycnal Oscillation
CC BY-SA 3.0
2015-03-20T10:19:11.117Z
Sea surface height is largely affected by winds "piling up" water and effects due to Earth's rotation, from what I recollect, but I am not completely sure of this. Anyone else know if this is correct?
mtb-za
CC BY-SA 3.0
2015-03-20T11:24:15.680Z
Sounds logic mtb-za.Probably the centrifugal force also plays it's role to push water from the poles towards the equator?
user2821
CC BY-SA 3.0
2015-03-20T17:47:29.073Z
@gansub The source has been added back. It got lost in the series of edits.
user4624937
CC BY-SA 3.0
2015-03-21T12:33:40.517Z
Title and final Q are different. Yes you can detect seabed topography from surface height. However, it is not a big effect compared to the other processes being discussed in the answers.
mankoff
CC BY-SA 3.0
2015-03-25T05:41:12.157Z
@mankoff Agreed! Feel free to edit the title.
user4624937
<ocean><ocean-currents><sea-level><topography><bathymetry>
Does bathymetry affect ocean topography/height?
user4624937
# Does bathymetry affect ocean topography/height?

(Asked by: username_0 on 2015-03-20)

Here is a map of ocean surface height or topography:

![enter image description here](https://i.sstatic.net/IziKc.jpg)

Source: <http://www.esa.int/var/esa/storage/images/esa_multimedia/images/2010/12/mean_dynamic_topography_of_global_ocean/9930795-2-eng-GB/Mean_dynamic_topography_of_global_ocean.jpg>

How significant is the bathymetry or seabed elevation in shaping the surface topography? What are the major causes of variations in the topography?

**Tags:** ocean, ocean-currents, sea-level, topography, bathymetry

> **Comments:**
> **username_1**: What do you mean by the surface topography? Do you mean the sea surface height?  
> **username_2**: Sea surface height is largely affected by winds "piling up" water and effects due to Earth's rotation, from what I recollect, but I am not completely sure of this. Anyone else know if this is correct?  
> **username_3**: Sounds logic username_2.Probably the centrifugal force also plays it's role to push water from the poles towards the equator?  
> **username_0**: @gansub The source has been added back. It got lost in the series of edits.  
> **username_4**: Title and final Q are different. Yes you can detect seabed topography from surface height. However, it is not a big effect compared to the other processes being discussed in the answers.  
> **username_0**: @username_4 Agreed! Feel free to edit the title.  

---

## 1 answers

### Answer by username_5 on 2015-03-20. Score: 10 | Accepted answer

Oceanic topography of the sea surface $\zeta$ can be defined as the height of the sea surface relative to a particular level surface, the [geoid](http://en.wikipedia.org/wiki/Geoid). The geoid to be the level surface that coincided with the surface of the ocean at rest (a list of geoids with application to oceanography can be found in [Talone et al., 2014](http://scientiamarina.revistas.csic.es/index.php/scientiamarina/article/view/1533/1715)).

Variations in sea surface height (topography) are due to processes that result in ocean motion: ocean currents, tides, and changes in barometric pressure from the inverted barometer effect. As a result, we usually call it "dynamic topography" or "dynamic height". As geoid undulations are of order 100 times larger than the dynamic height, the shape of the sea surface is dominated by local geoid variations caused by gravity with the effect of the currents being much smaller.

In the image you provide what you have is "dynamic height" and thus is a deviation from the geoid and the result of oceanic currents. By knowing the dynamic height, we can get an idea of the surface geostrophic current:
$\mathrm{u\_s= − {g\over f} {\delta\zeta\over\delta y}}$; $\mathrm{v\_s= − {g\over f} { \delta\zeta\over\delta x}}$ where f is the Coriolis parameter, g is gravity, and $\zeta$ is the height of the sea surface above the level surface (geoid).

Now, there is a direct effect between currents and bathymetry that sometimes is referred to as [Taylor columns](http://en.wikipedia.org/wiki/Taylor_column). The [Taylor-Proudman theorem](http://en.wikipedia.org/wiki/Taylor%E2%80%93Proudman_theorem) enforces that vertical columns of fluid move along contours of constant fluid depth. The basic idea behind this is that in order to conserve vorticity, fluid parcels tend to follow bathymetric contours (isobaths). So to answer your question, bathymetry affects ocean topography indirectly by affecting ocean currents.

> **Comments:**
> **username_5**: The effect is nothing but a conservation of vorticity (http://oceanworld.tamu.edu/resources/ocng_textbook/chapter12/chapter12_02.htm). If a water parcel moves deeper, then it has to change its spin. The same is true if a water parcel moves latitudinally. That results in the general circulation of the ocean: http://oceanworld.tamu.edu/resources/ocng_textbook/chapter11/chapter11_01.htm  
> **username_5**: The conservation of vorticity is not related to friction. The planetary boundary layer is a frictional effect and thus ageostrophic in nature. Maybe I don't understand your question.  
> **username_0**: Thanks @aretxabaleta for answering my question again. Regarding your last point: I thought the most significant causes of ocean currents are wind, Coriolis force, and the location of the continents. So then, while bathymetry affects ocean currents, is its effect relatively minor? Second question: we see this huge rise in the Pacific near the eastern coast of Japan - is that caused by the seamounts?  
> **username_5**: The rise of SSH near Japan is caused by the presence of the Kuroshio (http://en.wikipedia.org/wiki/Kuroshio_Current). The wind and thermohaline circulation affect the momentum balance of the ocean as a fluid. The other balance to consider is the vorticity (angular momentum) balance [(f+spin)/h=const] and in that case bathymetric changes and Coriolis (planetary vorticity) affect the rate of rotation of the water parcel.  

---

