<p>In addition to other information others have written in comments, gradients measure the rate of change of "a quantity".</p>

<p>For example, take a hill. As you walk up the hill your elevation increases relative to the base of the hill. The steeper the hill the more quickly your elevation changes. The slope of the hill is defined as the gradient of the hill. The steeper the hill the greater the rate of change of elevation, with respect to the horizontal component of distance traveled.</p>

<p>With atmospheric gradients, imagine there are two towns, each with a weather station. The distance between the two is 100 km.</p>

<p>Each weather station measures pressure &amp; temperature at defined times, usually at half hourly intervals.</p>

<p>If the first town measures a pressure of 1011 hPa and temperature of 25 C @ 10 am and the second town, at 10 am, measures a pressure of 1008 hPa and a temperature of 20 C, then between the two towns there is a pressure gradient of 0.03 hPa/km [(1011-1008)/100]. Likewise there is a temperature gradient of 0.05 C/km [(25-20)/100].</p>

<p>Now, if at 11 am the weather station in the first town records a pressure of 1012.5 hPa and a temperature of 28 C, then over time, there has been a pressure gradient over the first town of 1.5 hPa/h [(1012.5-1011)/1] and a temperature gradient of 3 C/h [(28-25)/1].</p>

<p>So when it comes to gradients, it depends what is being measured (pressure, temperature, humidity) and what is it be measured against (distance, time, etc.), and for atmospheric quantities the distance could be lateral distance or vertical distance.</p>

CC BY-SA 3.0
2017-09-19T09:05:12.380Z
2017-09-19T09:36:15.207Z
2017-09-19T09:36:15.207Z
Fred
<p>Did you check <a href="https://en.wikipedia.org/wiki/Gradient" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Gradient</a> ? 
That's the basic definition that everybody can agree upon. 
A Vector $\vec \nabla= \vec e_x \; \partial_x +\vec e_y \; \partial_y +\vec e_z \; \partial_z$ made up of three derivative components and three unit vectors $\vec e$.<br>
It needs to act on a scalar quantity to make sense, so only something like the mentioned Temperature gradient $\vec \nabla T$ makes sense to write down.</p>

<p>Meteorogists often speak only of one component, the horizontal one. This is not rigurously defined, as x and y are both horizontal components. But it usually means $\partial_h T$ which is the derivative of T along the direction h which is at the moment of interest, no matter what the rigid coordinate system says.  </p>

<p>A rate of change $\frac{\partial T}{\partial x}$ is often approximated as it's discrete counterpart of finite differences $\frac{\Delta T}{\Delta x}$ (implying smooth change of T over a distance $\Delta x$).
Thus mathematically sloppy statements like 'The gradient is 2 Pa over 100 km in Northwest direction' come to life.</p>

<p>Gradients in time are not gradients, they are rates of change. Only in General Relativity can you speak of a 4D-gradient, because time and space become the same mathematical field.</p>

CC BY-SA 3.0
2017-09-19T17:36:03.827Z
2017-09-19T17:36:03.827Z
AtmosphericPrisonEscape
<p>If there is a quantity that varies in the atmosphere, there is inherently a gradient.</p>

<p>Since you know there is a pressure and temperature gradient, there must also be a density gradient.</p>

<p>There is also wind speed gradients, buoyancy gradients, wind shear gradients, isentropic gradients, vorticity gradients etc.</p>

<p>let $\chi$ be a scalar quantity with the diagnostic equation: $$\frac{\partial \chi}{\partial t}+\vec{v}\cdot \nabla \chi=F(x,y,z,t)$$, where $\vec{v}$ is the wind vector, and $F$ is the forcing term (source-sink)</p>

<p>Therefore $$\nabla \frac{\partial \chi}{\partial t}=\frac{\partial \nabla\chi}{\partial t}
$$
and $$\frac{\partial \nabla\chi}{\partial t}+\nabla \vec{v}\cdot\nabla\chi+\vec{v}\cdot\nabla(\nabla\chi)=\nabla F(x,y,z,t)$$</p>

<p>Therefore changes in the gradient of a quantity is dependent on the changes of the advection of the quantity and the changes in the forcing of the quantity.</p>

<p>For example, an advancing cold front (effectively a moving thermal gradient) can be strengthened if the cold side is cooled/warm side is warmed, or the spacing decreases.</p>

CC BY-SA 3.0
2017-09-19T17:45:42.027Z
2017-09-19T17:45:42.027Z
BarocliniCplusplus
<p>My question is a two part question. First I currently know of two different gradients.I think there is more; however, I don't completely understand what makes a gradient. So, here is my questions.</p>

<ol>
<li>What properties can make up a gradient in atmospheric science?</li>
<li>What atmospheric gradients are there?</li>
</ol>

<p>Here are the two I knw about.</p>

<ol>
<li>Pressure gradient</li>
<li>Temperature gradient</li>
</ol>

<p>Examples would be nice; however, not necessary.</p>

<p>Thanks</p>

CC BY-SA 3.0
2017-09-18T20:21:57.293Z
Welcome to EarthScience.SE! For me, it is unclear what you are exactly asking. Gradient means that a numerical quantity is increasing/decreasing in space (spatial gradient) or time (temporal gradient). Commonly, atmospheric properties/variables change in space and time. You will have a gradient in air pollution from regions of high anthropogenic activity to regions of low anthropogenic activity. There exists a stable vertical temperature gradient (lapse rate). Do mean that?
daniel.heydebreck
CC BY-SA 3.0
2017-09-18T20:50:19.407Z
Sorry for the confusion. @daniel.neumann I think you answer sounds great. What you are telling me is I can create any gradient along as the variable is in respect to time or space. All of the gradients I have encountered have been in respect to space not time. The mathematic definition I assumed is being followed; however, with possibility of having extra guidelines placed due to atmosphere. For example there are state variables and then there are process variables each have a different meaning. I hope this helps you understand what I meant.
hthornto
CC BY-SA 3.0
2017-09-18T23:15:32.917Z
See also: https://physics.stackexchange.com/questions/314369/what-does-a-gradient-mean-in-physics/314383
JeopardyTempest
CC BY-SA 3.0
2017-09-19T09:55:43.177Z
There are many different conventions for example in atmospheric sciences what a certain gradient by default means: pressure gradient is usually assumed to be the change of pressure in horizontal space. Gradient though is a very general term that is basically the linear change in a limited area of inspection of a quantity with regards to another quantity.
Communisty
<meteorology><atmosphere><mathematics>
What makes up a gradient
hthornto
# What makes up a gradient

(Asked by: username_0 on 2017-09-18)

My question is a two part question. First I currently know of two different gradients.I think there is more; however, I don't completely understand what makes a gradient. So, here is my questions.

1. What properties can make up a gradient in atmospheric science?
2. What atmospheric gradients are there?

Here are the two I knw about.

1. Pressure gradient
2. Temperature gradient

Examples would be nice; however, not necessary.

Thanks

**Tags:** meteorology, atmosphere, mathematics

> **Comments:**
> **username_1**: Welcome to EarthScience.SE! For me, it is unclear what you are exactly asking. Gradient means that a numerical quantity is increasing/decreasing in space (spatial gradient) or time (temporal gradient). Commonly, atmospheric properties/variables change in space and time. You will have a gradient in air pollution from regions of high anthropogenic activity to regions of low anthropogenic activity. There exists a stable vertical temperature gradient (lapse rate). Do mean that?  
> **username_0**: Sorry for the confusion. @daniel.neumann I think you answer sounds great. What you are telling me is I can create any gradient along as the variable is in respect to time or space. All of the gradients I have encountered have been in respect to space not time. The mathematic definition I assumed is being followed; however, with possibility of having extra guidelines placed due to atmosphere. For example there are state variables and then there are process variables each have a different meaning. I hope this helps you understand what I meant.  
> **username_2**: See also: https://physics.stackexchange.com/questions/314369/what-does-a-gradient-mean-in-physics/314383  
> **username_3**: There are many different conventions for example in atmospheric sciences what a certain gradient by default means: pressure gradient is usually assumed to be the change of pressure in horizontal space. Gradient though is a very general term that is basically the linear change in a limited area of inspection of a quantity with regards to another quantity.  

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## 3 answers

### Answer by username_4 on 2017-09-19. Score: 1

In addition to other information others have written in comments, gradients measure the rate of change of "a quantity".

For example, take a hill. As you walk up the hill your elevation increases relative to the base of the hill. The steeper the hill the more quickly your elevation changes. The slope of the hill is defined as the gradient of the hill. The steeper the hill the greater the rate of change of elevation, with respect to the horizontal component of distance traveled.

With atmospheric gradients, imagine there are two towns, each with a weather station. The distance between the two is 100 km.

Each weather station measures pressure & temperature at defined times, usually at half hourly intervals.

If the first town measures a pressure of 1011 hPa and temperature of 25 C @ 10 am and the second town, at 10 am, measures a pressure of 1008 hPa and a temperature of 20 C, then between the two towns there is a pressure gradient of 0.03 hPa/km [(1011-1008)/100]. Likewise there is a temperature gradient of 0.05 C/km [(25-20)/100].

Now, if at 11 am the weather station in the first town records a pressure of 1012.5 hPa and a temperature of 28 C, then over time, there has been a pressure gradient over the first town of 1.5 hPa/h [(1012.5-1011)/1] and a temperature gradient of 3 C/h [(28-25)/1].

So when it comes to gradients, it depends what is being measured (pressure, temperature, humidity) and what is it be measured against (distance, time, etc.), and for atmospheric quantities the distance could be lateral distance or vertical distance.


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### Answer by username_5 on 2017-09-19. Score: 0

Did you check <https://en.wikipedia.org/wiki/Gradient> ?
That's the basic definition that everybody can agree upon.
A Vector $\vec \nabla= \vec e\_x \; \partial\_x +\vec e\_y \; \partial\_y +\vec e\_z \; \partial\_z$ made up of three derivative components and three unit vectors $\vec e$.  
It needs to act on a scalar quantity to make sense, so only something like the mentioned Temperature gradient $\vec \nabla T$ makes sense to write down.

Meteorogists often speak only of one component, the horizontal one. This is not rigurously defined, as x and y are both horizontal components. But it usually means $\partial\_h T$ which is the derivative of T along the direction h which is at the moment of interest, no matter what the rigid coordinate system says.

A rate of change $\frac{\partial T}{\partial x}$ is often approximated as it's discrete counterpart of finite differences $\frac{\Delta T}{\Delta x}$ (implying smooth change of T over a distance $\Delta x$).
Thus mathematically sloppy statements like 'The gradient is 2 Pa over 100 km in Northwest direction' come to life.

Gradients in time are not gradients, they are rates of change. Only in General Relativity can you speak of a 4D-gradient, because time and space become the same mathematical field.


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### Answer by username_6 on 2017-09-19. Score: 0

If there is a quantity that varies in the atmosphere, there is inherently a gradient.

Since you know there is a pressure and temperature gradient, there must also be a density gradient.

There is also wind speed gradients, buoyancy gradients, wind shear gradients, isentropic gradients, vorticity gradients etc.

let $\chi$ be a scalar quantity with the diagnostic equation: $$\frac{\partial \chi}{\partial t}+\vec{v}\cdot \nabla \chi=F(x,y,z,t)$$, where $\vec{v}$ is the wind vector, and $F$ is the forcing term (source-sink)

Therefore $$\nabla \frac{\partial \chi}{\partial t}=\frac{\partial \nabla\chi}{\partial t}
$$
and $$\frac{\partial \nabla\chi}{\partial t}+\nabla \vec{v}\cdot\nabla\chi+\vec{v}\cdot\nabla(\nabla\chi)=\nabla F(x,y,z,t)$$

Therefore changes in the gradient of a quantity is dependent on the changes of the advection of the quantity and the changes in the forcing of the quantity.

For example, an advancing cold front (effectively a moving thermal gradient) can be strengthened if the cold side is cooled/warm side is warmed, or the spacing decreases.


---

