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I recently compiled ten years of NOAA local climatological data. I noticed that the maximum relative humidity dropped linearly from 100% at about 80°F to 20% at about 110°F. Nothing obvious comes to mind that explained this observation.

Here is my scatterplot:

Dry Bulb Temperature Vs. Relative Humidity

Here is graph showing the edge of interest:

enter image description here

I would have expected to see relative humidity values at or near 100%, even for temperatures near 100°F. Obviously, that's not what I see. Maybe this has something to do with a limit of absolute humidity or density?

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  • $\begingroup$ Your plot shows that it drops to about 20%, not 0%. $\endgroup$
    – Sandejo
    Mar 21 at 2:27
  • $\begingroup$ Fixed in the body of the text. $\endgroup$ Mar 23 at 13:44

1 Answer 1

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Nothing obvious comes to mind that explained this observation.

Consider a simple model with the following aspects/assumptions:

  • The coastal regions of large bodies of water on Earth are at most as hot as about 80°F.
    (Some exceptions exist, such as the Persian Gulf. If the data are taken from weather stations near areas of human occupancy, such as airports, note also that regions with a wet-bulb temperature much greater than about 80°F are generally hazardous to humans.)

  • Water enters the atmosphere predominantly through evaporation from these large bodies of water, up to the maximum relative humidity at that maximum temperature. That fixes one point of the line you observed: 100% relative humidity at 80°F (300 K).

  • The vapor pressure $P_\text{vapor}$ of water increases with increasing temperature $T$; a simple model of this exponential relation is the August equation $P_\text{vapor}\approx\exp\left(20- \frac{5100}{T}\right)$, with $T$ measured in kelvins.

  • The relative humidity corresponds to the actual partial pressure of water vapor relative to the saturation vapor pressure at that temperature. We characterize this behavior in part through psychrometric charts.

  • Therefore, we should expect a downward-sloping maximum relative humidity with increasing temperature as the saturated vapor is transported inland to regions over land that may be hotter. The maximum mass of water vapor remains the same, as does the maximum absolute humidity, but the maximum relative humidity drops with increasing temperature.

  • What's the slope of that relationship? The maximum relative humidity according to this model is $$\text{RH}=\frac{\exp\left(20- \frac{5100}{300}\right)}{\exp\left(20- \frac{5100}{T}\right)},$$ or $\text{RH}=\exp\left[5100\left(\frac{1}{T}-\frac{1}{300}\right)\right],$ which for small changes around 300 K is approximately $\text{RH}= 1-\frac{17(T-300)}{300}$.

What maximum relative humidity do we therefore expect at 100°F, 311 K, for example? We expect 38%, pretty much exactly what your data tell us.

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  • $\begingroup$ The actual slope is a little steeper than the one you predicted. Thoughts about reasons? $\endgroup$ Mar 23 at 13:54
  • $\begingroup$ What slope and error do you estimate from the data? $\endgroup$ Mar 23 at 15:02
  • $\begingroup$ I take it back. I see no discrepancy between your slope and the observed slope. Your linear equation simplifies to RH= -1700%/300K*T +1800%. Multiplying the slope of that equation by 5/9 to convert it to °F gives a slope of -3.15%/°F. The maximum slope I observe between 80°F and any of the relative humidities above 80°F is exactly -3.15%/°F. Thank you for the great answer. $\endgroup$ Mar 29 at 15:56

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