<p>I think you cannot, might be wrong on that though.</p>

<p>In a single-fluid atmosphere without condensibles, the pressure is essentially proportional to <span class="math-container">$P \sim \rho \, T$</span> and potential temperature is essentially <span class="math-container">$\theta \sim T 
P^{1-1/\gamma}$</span>, with the temperature <span class="math-container">$T$</span>, and the adiabatic index of the gas <span class="math-container">$\gamma$</span>.<br>
So in this situation you could reconstruct density and temperature from <span class="math-container">$P$</span> and <span class="math-container">$\theta$</span>, but if you add another fluid into the mix (which is your condensible), then I don't see how that should be possible.</p>

CC BY-SA 4.0
2018-10-29T04:23:48.460Z
In other words, you can get to the same $θ_e$ on a skew-T starting at different temperatures... it could be dry air, where $θ = θ_e$... or it could be very moist air, such that $θ << θ_e$. So you can't use $θ_e$ to get either $θ$ or $r$ (moisture content), because it may be any contribution mix between them.
JeopardyTempest
CC BY-SA 4.0
2018-10-29T04:26:27.063Z
Is this from the same question as [your other one](https://earthscience.stackexchange.com/questions/15452/given-a-3-box-model-of-the-atmosphere-determine-fraction-of-mass-transport-from)? If so, I think you're probably on the wrong track here... see comment there, maybe you can get moving the right direction :) :)
JeopardyTempest
CC BY-SA 4.0
2018-10-28T23:01:17.613Z
2018-10-28T23:01:17.613Z
AtmosphericPrisonEscape
<p>I am given a 3 box model of atmosphere where each layer is 300 mbar thick, and the potential equivalent temperature of each is given (from bottom to top - 350K, 325K, 375K).  Am I able to determine the specific humidity of each layer with just this information?  I am racking by brain, trying to make this work, but I feel I need more information. </p>

<atmosphere><temperature>
Given only pressure and potential equivalent temperature, can I determine other variables?
PattyWatty27
# Given only pressure and potential equivalent temperature, can I determine other variables?

(Asked by: username_0 on 2018-10-28)

I am given a 3 box model of atmosphere where each layer is 300 mbar thick, and the potential equivalent temperature of each is given (from bottom to top - 350K, 325K, 375K). Am I able to determine the specific humidity of each layer with just this information? I am racking by brain, trying to make this work, but I feel I need more information.

**Tags:** atmosphere, temperature


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## 1 answers

### Answer by username_1 on 2018-10-28. Score: 1 | Accepted answer

I think you cannot, might be wrong on that though.

In a single-fluid atmosphere without condensibles, the pressure is essentially proportional to $P \sim \rho \, T$ and potential temperature is essentially $\theta \sim T
P^{1-1/\gamma}$, with the temperature $T$, and the adiabatic index of the gas $\gamma$.  
So in this situation you could reconstruct density and temperature from $P$ and $\theta$, but if you add another fluid into the mix (which is your condensible), then I don't see how that should be possible.

> **Comments:**
> **username_2**: In other words, you can get to the same $θ_e$ on a skew-T starting at different temperatures... it could be dry air, where $θ = θ_e$... or it could be very moist air, such that $θ << θ_e$. So you can't use $θ_e$ to get either $θ$ or $r$ (moisture content), because it may be any contribution mix between them.  
> **username_2**: Is this from the same question as [your other one](https://earthscience.stackexchange.com/questions/15452/given-a-3-box-model-of-the-atmosphere-determine-fraction-of-mass-transport-from)? If so, I think you're probably on the wrong track here... see comment there, maybe you can get moving the right direction :) :)  

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