Converting Relative Humidity with regards to water, to Relative Humidity with regards to ice


New Member
Hi Metabunkers,

In regards to persistent spreading contrails.

I understand that different contrails ie: short, persistent, persistent and spreading contrails require different environmental conditions to exist.

I've been observing planes leaving persistent spreading contrails at altitudes between 12,000 & 16,000 ft (ADS-B) with a RHw of 9% and a temperature of -14 degree celsius (Global Forecast System via - As far as I understand, for a contrail to persist and spread the environment needs to be ice super-saturated. I have been told that a RHw of 60 - 70% is roughly 100% RHi. Is this right (as RH is with regards to water) I would like to convert this to RHi ( so I can substantiate the environmental conditions required for the contrails persistence and spread)

I understand that conditions can change rapidly,( and without having localised instuments available to report data) how far off the mark could the GFS be in regards to using a program like data be?
I live in Victoria, Australia, the planes I speak of are leaving Tullamarine Melbourne, and heading to Launceston, Tasmania. Usually the contrails produced are persist and spreading (4-5+ hrs) leaving tullamarine and reaching crusing altitude, or leaving Launceston and coming in for landing at Tullamarine.



Mick West

Staff member
I've been observing planes leaving persistent spreading contrails at altitudes between 12,000 & 16,000 ft (ADS-B) with a RHw of 9% and a temperature of -14 degree celsius
The most likely explanation for this is that the planes were misidentified. Can you provide your observations?

Regarding RHw vs. RHi, see:
The relationship between RHw and RHi is complicated but at regular contrail altitudes you get 100% RHI at between 60 and 70% RHW (regular RH).

Contrails need RHW temporarily raised over 100% to form, and then RHI ambiently over 100% to persist and grow.

Here's the code I use to convert RHW to RHI based on pressure and temp:
# convert RHw to RHi, as per
# But see
# ta = temperature of atmosphere, in Celsius
# p = pressure in hPa (hectopascals), which are the same as mb (millibars)
# note this is defined as accurate from -0C to -50C, but it's unclear how inaccurate it is
# at temperatures below -50C
def rhw2rhi(rh, ta, p)
e_sat_w_Ta = (1.0007 + 0.00000346 * p)*6.1121*Math.exp((17.966*ta)/(247.15+ta));
e_sat_i_Ta = (1.0003 + 0.00000418 * p)*6.1115*Math.exp((22.452*ta)/(272.55+ta));
return rh * (e_sat_w_Ta/e_sat_i_Ta);


Senior Member.
Please don't think people are being rude suggesting planes have been misidentified. it's very easy to do until you get used to realising just how far away planes can be. (and even when you are!!)
Say you lived in Sunbury or Melton or Ballarat, and you looked south ish and can see the early morning Jetstar flight Airbus A320 from Melbourne to launceston at 16,000ft on FR24. In roughly the same direction, there would ALSO be a Virgin Australia flight (Boeing 737) from Melbourne to Hobart a way ahead and flying at 29,000ft, which would easily be a more normal height to make a contrail.
Admittedly it is 60km further away, but it;s surprising to find how far away things can actually be. In Bristol UK recently I saw a plane that looked not far off being overhead but it was actually 19km away.


Senior Member.
It took me a while to get used to the scale of things down there. It's hard to realise that Tasmania is not far off the size of England :eek:

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