<p>Direct measurements of three-dimensional ocean currents are carried out with acoustic Doppler current profilers (<a href="http://www.whoi.edu/instruments/viewInstrument.do?id=819" rel="noreferrer">ADCPs</a>). The ADCPs are usually moored and bottom mounted instead of being ship-based or attached to a floating mooring to minimize the vertical displacement associated with the vertical motions of the ocean surface caused by waves.</p>

<p>The ADCP does not measure horizontal or vertical velocities at a point but determines Doppler shifts along three to five acoustic beams that are typically slanted (most commonly 60°) from the horizontal plane and spaced around the horizontal compass. The most typical configuration (Janus) includes four orthogonal beans. The Doppler shifts measure slant velocities of suspended acoustic backscattering particles moving with the water relative to the instrument. Pairs of slant velocities are combined to produce vertical and horizontal velocities. The underlying assumption is that velocities are horizontally uniform over the beam separation. Other instruments (e.g., <a href="http://www.rdinstruments.com/followV.aspx" rel="noreferrer">Teledyne Sentinel V ADCP</a>) have an integrated fifth beam to provide a third vertical velocity measurement.</p>

<p><a href="https://i.sstatic.net/IV4GU.jpg" rel="noreferrer"><img src="https://i.sstatic.net/IV4GU.jpg" alt="ADCP"></a></p>

<p>Indirect estimates of vertical velocities can be obtain in several ways. The most common approach is to take advantage of the principle of conservation of mass (<a href="http://oceanworld.tamu.edu/resources/ocng_textbook/chapter07/chapter07_07.htm" rel="noreferrer">continuity equation</a>, as described in the answer by Neo).
$$
\dfrac{\partial w}{\partial z} = -\dfrac{\partial u}{\partial x}-\dfrac{\partial v}{\partial y}
$$
where $w$ is the vertical velocity. Assuming $w=0$ at the bottom, then measuring the horizontal velocities throughout the water column will give you an estimate of the vertical velocity. This method, while useful, tend to produce really noisy results as the vertical velocities in the ocean tend to be quite small and are masked by the noise in the horizontal measurements. </p>

<p>A completely different approach was recently introduced by <a href="http://dx.doi.org/10.1029/2009GL038359" rel="noreferrer">Klein et al. (2009)</a>. It uses the surface Quasi-Geostrophic approximation to estimate low-frequency vertical velocities in scales between 20 km and 400 km from the surface down to 500 m. The needed data is some high-resolution Sea Surface Height (SSH, usually from satellites) and an approximation of the large-scale vertical stratification. Vertical velocities are estimated from the buoyancy equations at the surface and at depth in a modified version of the <a href="https://en.wikipedia.org/wiki/Omega_equation" rel="noreferrer">Omega equation</a> (<a href="http://academiccommons.columbia.edu/download/fedora_content/download/ac:151885/CONTENT/qj.49711147002.pdf" rel="noreferrer">Hoskins et al., 1985</a>).</p>

CC BY-SA 3.0
2015-10-02T05:06:23.783Z
+1 but maybe a bit too soon?
Isopycnal Oscillation
CC BY-SA 3.0
2015-10-02T14:05:59.690Z
I know. I thought about waiting, but didn't want to forget about the question. It happens when my mind is in too many places...
arkaia
CC BY-SA 3.0
2015-10-02T19:17:26.653Z
+1 Nice answer. If you don't mind, I will add a section to your answer about measuring w with floats in the next few days when I get a chance
milancurcic
CC BY-SA 3.0
2015-10-01T17:39:07.533Z
2015-10-01T17:39:07.533Z
arkaia
<p>As a non-oceanographer, I might approach this from a continuity standpoint. The sum of the fluxes in each direction must equal 0 (conservation of mass, basically). So you might have some measurements in the x and y directions, which could then give you at least an estimate of the vertical velocities in a given water column, assuming uniform lateral and vertical compositions. There are more assumptions you'd have to make, such as what is a reasonable water column size, that I am not privy too. </p>

<p>While I wouldn't use this in a scientific paper, I'd bet it would be a good enough initial calculation to see if some question is worth doing a more accurate method. </p>

<p>Just an idea... definitely not a definitive answer. </p>

CC BY-SA 3.0
2015-09-29T13:38:50.883Z
I was taught this method in physical oceanography courses, and have seen it used in scientific papers. Not sure why someone objected and marked it down.
Mark Rovetta
CC BY-SA 3.0
2015-09-29T16:44:20.080Z
@MarkRovetta This is certainly an indirect method that can be used to derive vertical velocity in the ocean. I downvoted because of colloquialism and lack of scientific approach. Also, second sentence is false - conservation of mass, not momentum.
milancurcic
CC BY-SA 3.0
2015-09-29T18:57:31.790Z
ie conservation of momentum: my mistake, it cannot be conserved because as the volume changes (through a pipe for example) the velocity increases but the mass does not.
Neo
CC BY-SA 3.0
2015-09-28T17:35:32.617Z
2015-09-29T18:57:48.143Z
2015-09-29T18:57:48.143Z
Neo
<p>While horizontal velocities in the ocean are relatively easy to measure, what methods are available to measure vertical velocities? Is there some indirect way to estimate vertical velocities from observations?</p>

CC BY-SA 3.0
2015-09-28T18:17:57.680Z
[Neutral-buoyancy floats](http://www-argo.ucsd.edu/Gould_Float_history.pdf) are the most direct method that I know of.
Pont
<ocean><oceanography><ocean-currents>
How to measure ocean vertical velocity?
arkaia
# How to measure ocean vertical velocity?

(Asked by: username_0 on 2015-09-28)

While horizontal velocities in the ocean are relatively easy to measure, what methods are available to measure vertical velocities? Is there some indirect way to estimate vertical velocities from observations?

**Tags:** ocean, oceanography, ocean-currents

> **Comments:**
> **username_1**: [Neutral-buoyancy floats](http://www-argo.ucsd.edu/Gould_Float_history.pdf) are the most direct method that I know of.  

---

## 2 answers

### Answer by username_0 on 2015-10-01. Score: 7

Direct measurements of three-dimensional ocean currents are carried out with acoustic Doppler current profilers ([ADCPs](http://www.whoi.edu/instruments/viewInstrument.do?id=819)). The ADCPs are usually moored and bottom mounted instead of being ship-based or attached to a floating mooring to minimize the vertical displacement associated with the vertical motions of the ocean surface caused by waves.

The ADCP does not measure horizontal or vertical velocities at a point but determines Doppler shifts along three to five acoustic beams that are typically slanted (most commonly 60°) from the horizontal plane and spaced around the horizontal compass. The most typical configuration (Janus) includes four orthogonal beans. The Doppler shifts measure slant velocities of suspended acoustic backscattering particles moving with the water relative to the instrument. Pairs of slant velocities are combined to produce vertical and horizontal velocities. The underlying assumption is that velocities are horizontally uniform over the beam separation. Other instruments (e.g., [Teledyne Sentinel V ADCP](http://www.rdinstruments.com/followV.aspx)) have an integrated fifth beam to provide a third vertical velocity measurement.

[![ADCP](https://i.sstatic.net/IV4GU.jpg)](https://i.sstatic.net/IV4GU.jpg)

Indirect estimates of vertical velocities can be obtain in several ways. The most common approach is to take advantage of the principle of conservation of mass ([continuity equation](http://oceanworld.tamu.edu/resources/ocng_textbook/chapter07/chapter07_07.htm), as described in the answer by Neo).
$$
\dfrac{\partial w}{\partial z} = -\dfrac{\partial u}{\partial x}-\dfrac{\partial v}{\partial y}
$$
where $w$ is the vertical velocity. Assuming $w=0$ at the bottom, then measuring the horizontal velocities throughout the water column will give you an estimate of the vertical velocity. This method, while useful, tend to produce really noisy results as the vertical velocities in the ocean tend to be quite small and are masked by the noise in the horizontal measurements.

A completely different approach was recently introduced by [Klein et al. (2009)](http://dx.doi.org/10.1029/2009GL038359). It uses the surface Quasi-Geostrophic approximation to estimate low-frequency vertical velocities in scales between 20 km and 400 km from the surface down to 500 m. The needed data is some high-resolution Sea Surface Height (SSH, usually from satellites) and an approximation of the large-scale vertical stratification. Vertical velocities are estimated from the buoyancy equations at the surface and at depth in a modified version of the [Omega equation](https://en.wikipedia.org/wiki/Omega_equation) ([Hoskins et al., 1985](http://academiccommons.columbia.edu/download/fedora_content/download/ac:151885/CONTENT/qj.49711147002.pdf)).

> **Comments:**
> **username_2**: +1 but maybe a bit too soon?  
> **username_0**: I know. I thought about waiting, but didn't want to forget about the question. It happens when my mind is in too many places...  
> **username_3**: +1 Nice answer. If you don't mind, I will add a section to your answer about measuring w with floats in the next few days when I get a chance  

---

### Answer by username_4 on 2015-09-28. Score: 0

As a non-oceanographer, I might approach this from a continuity standpoint. The sum of the fluxes in each direction must equal 0 (conservation of mass, basically). So you might have some measurements in the x and y directions, which could then give you at least an estimate of the vertical velocities in a given water column, assuming uniform lateral and vertical compositions. There are more assumptions you'd have to make, such as what is a reasonable water column size, that I am not privy too.

While I wouldn't use this in a scientific paper, I'd bet it would be a good enough initial calculation to see if some question is worth doing a more accurate method.

Just an idea... definitely not a definitive answer.

> **Comments:**
> **username_5**: I was taught this method in physical oceanography courses, and have seen it used in scientific papers. Not sure why someone objected and marked it down.  
> **username_3**: @username_5 This is certainly an indirect method that can be used to derive vertical velocity in the ocean. I downvoted because of colloquialism and lack of scientific approach. Also, second sentence is false - conservation of mass, not momentum.  
> **username_4**: ie conservation of momentum: my mistake, it cannot be conserved because as the volume changes (through a pipe for example) the velocity increases but the mass does not.  

---

