<p>I have the same question and found a satisfying answer recently.</p>
<p>The reference state, including wind, temperature and pressure, is a dynamically-steady state to the equation of motion of the atmosphere.  It is a steady-state solution only when the flow is adiabatic and inviscid (no external forcings).  More specifically, the reference state is:</p>
<ul>
<li>zonally uniform,</li>
<li>vertically in hydrostatic balance, and</li>
<li>meridionally in gradient-wind balance</li>
</ul>
<p><strong>everywhere in the domain</strong>.</p>
<p>Although scientists knew there exists such state, only <a href="https://journals.ametsoc.org/view/journals/atsc/67/12/2010jas3503.1.xml" rel="nofollow noreferrer">Nakamura and Zhu (2010)</a> and <a href="https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.2518" rel="nofollow noreferrer">Methven and Berrisford (2015)</a> provided numerical methods to calculate such reference state, given any instantaneous atmospheric state.  This is equivalent to a conservative rearrangement, schematically shown below:</p>
<p><a href="https://i.sstatic.net/z0ZC7.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/z0ZC7.png" alt="conservative rearrangement" /></a></p>
<p>This rearrangement conserve mass between any two isentrops and circulation along each PV contour, which can be called conservative zonalization.</p>
<p>Before these numerical algorithms were proposed, most people use Eulerian average of atmospheric state, like long-term time mean or zonal mean, to give a diffuse estimate of this reference state.  As a result, the jet and temperature front in the averaged state are usually weaker than those in the reference state.</p>
<p>Another reference state, motionless and horizontally flat pressure surface in hydrostatic balance, is also a steady-state solution to the (adiabatic and inviscid) equation of motion.  However, it is a trivial resting state that does not have circulation at all.  Therefore, we may not be interested in this resting reference state.</p>

CC BY-SA 4.0
2022-11-13T06:26:24.213Z
You suggest this is what the NMME plots then?  Any insight on why it would be an output (something to do with how things are setup in the model?  Or it has a common use?)  Or maybe there are multiple definitions for the term (yuck) (gansub's comment suggesting it is a historic time average seems reasonable, what I might have guessed)
JeopardyTempest
CC BY-SA 4.0
2022-11-13T12:31:33.453Z
@JeopardyTempest This is not a NMME plots.  Just a schematic plot showing how to get the reference state (right) corresponding to an instantaneous eddying atmospheric state (left).
MiniUFO
CC BY-SA 4.0
2022-11-19T04:53:26.653Z
right, sorry, wasn't suggesting your plot was from NMME... but wondering if the reference temperature in it that Behzad is asking about is different from what you suggest
JeopardyTempest
CC BY-SA 4.0
2022-11-12T11:47:05.307Z
2022-11-12T12:05:34.917Z
2022-11-12T12:05:34.917Z
MiniUFO
<p>Last week when I was dealing with the North American Multi-Model Ensemble (NMME) seasonal forecasting system, a variable named “tref,” or Reference Temperature, caught my attention.<br />
I read some articles that used reference temperature but couldn’t understand this variable.
My main question is, what is the definition of the reference temperature? And what is the difference between it and average air temperature?<br />
Thank you all.</p>

CC BY-SA 4.0
2022-11-10T02:41:12.307Z
Thank you @gansub
Behzad
<meteorology><climate><temperature>
What are the main differences between the reference temperature and the average air temperature?
Behzad
# What are the main differences between the reference temperature and the average air temperature?

(Asked by: username_0 on 2022-11-09)

Last week when I was dealing with the North American Multi-Model Ensemble (NMME) seasonal forecasting system, a variable named “tref,” or Reference Temperature, caught my attention.  
I read some articles that used reference temperature but couldn’t understand this variable.
My main question is, what is the definition of the reference temperature? And what is the difference between it and average air temperature?  
Thank you all.

**Tags:** meteorology, climate, temperature

> **Comments:**
> **username_0**: Thank you @gansub  

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## 1 answers

### Answer by username_1 on 2022-11-12. Score: 2 | Accepted answer

I have the same question and found a satisfying answer recently.

The reference state, including wind, temperature and pressure, is a dynamically-steady state to the equation of motion of the atmosphere. It is a steady-state solution only when the flow is adiabatic and inviscid (no external forcings). More specifically, the reference state is:

* zonally uniform,
* vertically in hydrostatic balance, and
* meridionally in gradient-wind balance

**everywhere in the domain**.

Although scientists knew there exists such state, only [Nakamura and Zhu (2010)](https://journals.ametsoc.org/view/journals/atsc/67/12/2010jas3503.1.xml) and [Methven and Berrisford (2015)](https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.2518) provided numerical methods to calculate such reference state, given any instantaneous atmospheric state. This is equivalent to a conservative rearrangement, schematically shown below:

[![conservative rearrangement](https://i.sstatic.net/z0ZC7.png)](https://i.sstatic.net/z0ZC7.png)

This rearrangement conserve mass between any two isentrops and circulation along each PV contour, which can be called conservative zonalization.

Before these numerical algorithms were proposed, most people use Eulerian average of atmospheric state, like long-term time mean or zonal mean, to give a diffuse estimate of this reference state. As a result, the jet and temperature front in the averaged state are usually weaker than those in the reference state.

Another reference state, motionless and horizontally flat pressure surface in hydrostatic balance, is also a steady-state solution to the (adiabatic and inviscid) equation of motion. However, it is a trivial resting state that does not have circulation at all. Therefore, we may not be interested in this resting reference state.

> **Comments:**
> **username_2**: You suggest this is what the NMME plots then?  Any insight on why it would be an output (something to do with how things are setup in the model?  Or it has a common use?)  Or maybe there are multiple definitions for the term (yuck) (gansub's comment suggesting it is a historic time average seems reasonable, what I might have guessed)  
> **username_1**: @username_2 This is not a NMME plots.  Just a schematic plot showing how to get the reference state (right) corresponding to an instantaneous eddying atmospheric state (left).  
> **username_2**: right, sorry, wasn't suggesting your plot was from NMME... but wondering if the reference temperature in it that username_0 is asking about is different from what you suggest  

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