# Why do the dry and moist adiabatic lapse rates converge with height?

Near the surface, the slope of the moist adiabats are much steeper than dry adiabats due (as I understand it) to the the latent heat released as water vapour condenses. The difference is amplified at greater surface temperatures because warmer air can hold more moisture.

Why then, are the two lapse rates very similar in the upper atmosphere? My best guess is that condensation stops for some reason, but I'm not sure why this would be the case.

• You may want to put a lower-resolution version of the image in your question - folks are having difficulties opening it. meta.stackexchange.com/questions/258181/… – Deer Hunter Jun 8 '15 at 6:39
• @DeerHunter Thanks for letting me know - I've done that now. – Luke Thorburn Jun 8 '15 at 8:36

If you look closely at the diagram you'll notice height isn't the primary cause for the convergence between the adiabats, though it is the driver.

Note that toward the upper right there is still appreciable difference between the adiabats and as you move to the left the height they converge at decreases.

The reason for this, as your intuition suggests, is that condensation ceases. The reason, simply, is that there is no more water left in the parcel to condense and release latent heat.

Recall the lines of constant water vapor mixing ratio (the lines you use to connect surface dewpoint to the LCL). These lines decrease to toward the left and are sloped steeper than the isotherms. As moist parcels ascend the latent heat release is correlated to decreasing water vapor. At some point we exhaust the water vapor and any further ascent cools at the dry adiabatic lapse rate as there is no more condensation. This is what causes the moist and dry adiabats to become parallel at upper levels (higher for warmer / moist surface conditions and lower for cooler / drier source parcels).

In the comments, concern was expressed that the skew-t isn't capturing the relevant physics, including how a parcel runs out of water vapor. The skew-t does indeed capture this information and one way you can observe this is by calculating equivalent potential temperature, $\theta_e$. This temperature is the temperature of a parcel with all of the water vapor condensed out of it. The more moisture in a parcel, the higher the equivalent temperature will be over its actual temperature. To calculate it on a Skew-T you raise a parcel high enough for the moist and dry adiabats to be parallel, then descend the parcel. On the way up once saturation is reached you'll ascend via moist adiabat and once the water vapor is exhausted you descend via a dry adiabat. You can try this for various source parcels and convince yourself that the Skew-T captures these physics. You should note that the more moist a surface parcel is, the higher it must ascend and the warmer the equivalent temperature will be.

• Okay, thanks. It seems like the point at which a parcel 'runs out' of moisture would depend on a whole lot of factors, particularly the humidity of the parcel at the surface, and I don't think that information is captured in the diagram. Are we making some assumptions about this? – Luke Thorburn Jun 7 '15 at 23:52
• @LukeThorburn no assumption needed. By definition net condensation is a transfer of water vapor to liquid water, so the mass of water vapor must decrease (and if latent heat is being released, condensation is happening). Look at the lines labeled W_s on your plot, ranging from 0.1 to 45. This is the mass mixing ratio of water vapor. As a moist parcel rises it will cross these lines toward smaller W_s and as it does so the slope of the moist adiabat aligns with the dry one. The humidity of the source parcel is captured by this (look at the behavior of w_s for various source parcels to see) – casey Jun 7 '15 at 23:59
• @LukeThorburn also note that the moist adiabat aligning with the dry occurs to the left of the W_s = 0.1 g/kg, which is quite dry. – casey Jun 8 '15 at 0:01
• @LukeThorburn see my edit and see if that helps at all. – casey Jun 9 '15 at 18:24