Cloud base calculation

[jack.h...@gmail.com]

A well known empirical rule (no doubt someone could prove the science) is that convective cloud base (and to an extent, non-convective) can be determined with remarkable accuracy from temperature and dewpoint. 

The dewpoint depression (Tdry - Tdew) multiplied by 400 gives the cloud base in feet.

For example Tdry = 9C, Tdew = 1C implies around 3,200 feet.

Now dewpoint depression has a good correlation with relative humidity.  So if an instrument (such as the ThermoPro that I have) measures RH rather than Tdew, then that RH can be converted very approximately to dewpoint depression and hence cloud base.

Various online tools such as this:
https://www.kwangu.com/work/psychrometric.htm

are available.

But to cut a long story short, as a guide, this table converts RH to cloud base to a reasonable degree of accuracy

50% ~ 4,000 ft

55% ~ 3,500 ft

60% ~ 3,000 ft

65% ~ 2,600 ft

70% ~ 2,200 ft

75% ~ 1,800 ft

80% ~ 1,400 ft

85% ~ 1,000 ft

90% ~   600 ft

95% ~   300 ft

100% ~ fog!

Jack

[Metman2012]

I don't know about the science, but forecasters use(d) a tephigram to calculate cloud base (normally convective) using the temperature and the dewpoint at the surface and lines from the former along the DALR lines and from the latter along the Humidity Mixing Ratio Lines, and where they cross is the base of convective cloud. I'm not sure it works for other types of cloud. Perhaps a forecaster (Freddie?) could chime in here. I think your empirical rule is based on something like this.

[Freddie]

Yes, it is the same thing - both the tephigram lines and the (dewpoint depression * 400) are based on the same theory.  In a well-mixed atmosphere it works okay.  Note, though, at the end of the afternoon - although the temperature starts to fall, you won't see the cloud base decreasing, you will see the cloud dispersing.  This is true for convective days.  It's not so straightforward for stratus and other layer clouds.

-- 

Freddie

Alcaston

Shropshire

148m AMSL

http://www.hosiene.co.uk/weather/

Stats for the month so far: https://www.hosiene.co.uk/weather/statistics/latest.xlsx

[Graham Easterling]

That's a useful table.

Talking of dewpoints I notice there are some very low ones being reported from eastern England/East Anglia. -8C at Lakenheath, -6C at Wittering for example. Around +3C here.

The sun has stayed out, all the cloud that developed inland is spreading out but dissipating quickly at the same time. In the easterly drift the cloud that is drifting west from the Lizard is dissipating over Mount's Bat before it reaches Penzance. SE facing coasts are the place to be.

 We've just hit 13C for the 1st time since 13.4C on 2nd. 

Graham

Penzance 

On Tuesday, 13 April 2021 at 07:10:56 UTC+1 jack.h...@gmail.com wrote:

[Freddie]

On Tuesday, 13 April 2021 at 07:10:56 UTC+1 jack.h...@gmail.com wrote:

Now dewpoint depression has a good correlation with relative humidity.  So if an instrument (such as the ThermoPro that I have) measures RH rather than Tdew, then that RH can be converted very approximately to dewpoint depression and hence cloud base.

Various online tools such as this:
https://www.kwangu.com/work/psychrometric.htm

are available.

But to cut a long story short, as a guide, this table converts RH to cloud base to a reasonable degree of accuracy

50% ~ 4,000 ft

55% ~ 3,500 ft

60% ~ 3,000 ft

65% ~ 2,600 ft

70% ~ 2,200 ft

75% ~ 1,800 ft

80% ~ 1,400 ft

85% ~ 1,000 ft

90% ~   600 ft

95% ~   300 ft

100% ~ fog!

 One thing that needs to be pointed out with this table is the fact that a particular dewpoint depression at low temperatures has a lower RH when compared to an identical dewpoint depression at higher temperatures.  Also, there is a variation with air pressure.  But, as Jack points out, the table converts with reasonable accuracy.

[jack.h...@gmail.com]

Another trick I use in convective situations is based on the dry adiabatic lapse rate of 3 C / 1000 feet.

In Britain, there is often a super-adiabatic near the surface so as an empirical rule, 4 C for first 1000 feet thereafter 3 C

I use my remote reading thermometer to measure cloud base temperature.  Let's give an example.

Cloud base temperature measurement = 3 C.  Now at the same time, surface temperature = 16 C.

By simple application of that rule of thumb I can work out that at 1,000 ft above ground, it is 12 C and then 3 C less for each subsequent 1,000 feet.  3 C thus occurs at 4,000 feet. 

Hence I have the cloud base height..

This rule of thumb correlates beautifully with the previously mentioned dewpoint depression calculations and confirms cloud base.

When I was gliding, I would often take the temperature (over say Cambridge) at cloud base, the height of which of course I knew.  Doing these sums in reverse, I could work out the temperature and dewpoint on the ground below.  I would then listen to the [radio] weather report and lo and behold, the agreement was usually perfect.

I should mention that although not a scientifically trained meteorologist, I would use tricks like these in my gliding weather forecasts and reports.  I would forecast at competitions and although I would be last to say that I always got it right, I often did:-)

Jack