<p>The geopotential is the work (force x distance) required to bring a 1kg object to a certain height. The units of work are <span class="math-container">$kg \frac {m^2}{s^2}$</span> Dividing by the unit mass gives the work per kilogram which is the geopotential <span class="math-container">$\Phi$</span> and has units of <span class="math-container">$\frac {m^2}{s^2}$</span></p>
<p>The geopotential height Z is:</p>
<p><span class="math-container">$$Z = \frac {\Phi} g$$</span> where <span class="math-container">$g = 9.8 m/s^2$</span></p>
<p>You need the hypsometric equation to convert to pressure:
<span class="math-container">$$Z_2 − Z_1 =\frac {RT}{g} \ln\frac {p_1} {p_2}$$</span></p>
<p>or</p>
<p><span class="math-container">$$\frac{p_1}{p_2}= e^{\frac g {RT}(Z_2-Z_1)}$$</span></p>
<p>Where R is the gas constant and T is temperature. Z is the geopotential height. <span class="math-container">$Z_1 = 0$</span> at mean sea level.</p>
<p>Hope this was helpful.</p>
<p>Note there are integral forms for this that can be used to account for g varying with height.</p>
<p><a href="https://geo.libretexts.org/Bookshelves/Meteorology_and_Climate_Science/Practical_Meteorology_(Stull)/01%3A_Atmospheric_Basics/1.07%3A_Atmospheric_Structure" rel="nofollow noreferrer">https://geo.libretexts.org/Bookshelves/Meteorology_and_Climate_Science/Practical_Meteorology_(Stull)/01%3A_Atmospheric_Basics/1.07%3A_Atmospheric_Structure</a></p>
<p><a href="https://www.chemeurope.com/en/encyclopedia/Hypsometric_equation.html" rel="nofollow noreferrer">https://www.chemeurope.com/en/encyclopedia/Hypsometric_equation.html</a></p>

CC BY-SA 4.0
2024-07-15T22:11:24.257Z
2024-07-16T05:04:14.367Z
2024-07-16T05:04:14.367Z
Stevan V. Saban
<p>Can someone please explain how to convert geopotential height 500 hPa from ERA5, where units while plotting are displayed as m<sup>2</sup> s<sup>-2</sup>?</p>

<atmospheric-circulation><upper-atmosphere>
Convert Geopotential Height's Unit from $m^2 s^{-2}$ to hPa
gklk_bap
# Convert Geopotential Height's Unit from $m^2 s^{-2}$ to hPa

(Asked by: username_0 on 2024-07-15)

Can someone please explain how to convert geopotential height 500 hPa from ERA5, where units while plotting are displayed as m2 s-2?

**Tags:** atmospheric-circulation, upper-atmosphere


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## 1 answers

### Answer by username_1 on 2024-07-15. Score: 3 | Accepted answer

The geopotential is the work (force x distance) required to bring a 1kg object to a certain height. The units of work are $kg \frac {m^2}{s^2}$ Dividing by the unit mass gives the work per kilogram which is the geopotential $\Phi$ and has units of $\frac {m^2}{s^2}$

The geopotential height Z is:

$$Z = \frac {\Phi} g$$ where $g = 9.8 m/s^2$

You need the hypsometric equation to convert to pressure:
$$Z\_2 − Z\_1 =\frac {RT}{g} \ln\frac {p\_1} {p\_2}$$

or

$$\frac{p\_1}{p\_2}= e^{\frac g {RT}(Z\_2-Z\_1)}$$

Where R is the gas constant and T is temperature. Z is the geopotential height. $Z\_1 = 0$ at mean sea level.

Hope this was helpful.

Note there are integral forms for this that can be used to account for g varying with height.

<https://geo.libretexts.org/Bookshelves/Meteorology_and_Climate_Science/Practical_Meteorology_(Stull)/01%3A_Atmospheric_Basics/1.07%3A_Atmospheric_Structure>

<https://www.chemeurope.com/en/encyclopedia/Hypsometric_equation.html>


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