Bradbury Rulecloudbase in feet = 400 times (temperature / dewpoint split)
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Many pilots will be familiar with this rule of thumb, named after glider pilot / professional meteorologist Tom Bradbury.
The rule links temperature, dewpoint and cloudbase with a very simple formula.  (the rule can easily be verified from a soundings diagram)
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The difference between surface temperature and surface dewpoint multiplied by 400 (Tdry-Tdew) *400
gives an excellent estimation of cloud base in feet above ground level

This method is better for predicting cumulus cloud base than Tafs 
Tafs usually give the lowest base during the forecast period
Note: this works out depth of convection ONLY if cumulus actually forms. 
On blue days, the height of thermals has to be determined by other methods
Example:  measurements or from metars during morning
Tdew during morning = 12C
No change in basic airmass is anticipated, so when Tdry reaches around 19C, (ie Tdry / Tdew split = 7), a cloud base of around 2,800 feet can be anticipated,
Forecast afternoon Tdry maximum is 23C, so eventual split = 11 giving best cloud base of 4,400 feet
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Temperature profile (lapse rate) below cloud or in blue thermals
Air temperature (below cloud), either rising in thermal or having been previously affected by convection,  decreases by 3.0C for every 1,000 feet increase in height. 
This is called the "Dry Adiabatic Lapse Rate". 
 
In practice, there is usually an excess of around 1 near the ground. 
This is called a super-adiabatic
Example:
Assume: Tdry = 23C 
At 4,000 feet it is therefore 4 * 3C lower, ie = 11C
However, adding that super-adiabatic in the lowest 1,000 ft the temperature at 1,000 agl is more like 23 - 4 = 19C and thus at 4,000 feet, probably around 10C.
These figures have been verified by actual in-flight temperature measurements. 
Note.  Above cloud base or tops of blue thermals, different parameters apply. 
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Bradbury in practice - an example

Assume dewpoint remains unchanged at 11 C during day (a not unreasonable assumption unless  change of airmass)
When Tdry  rises to 18C during the morning with that Tdew = 11C , cloudbase = 2,800 feet
(remember, Tdry -  Tdew = 7 equating to a cloudbase  of 7 x 400 feet  = 2,800 feet)

However, that was during the morning.  The  surface temperatures is forecast to reach 21C
Assuming Tdew remains unchanged at 11C,  then cloud base should eventually rise to 4,000 feet
It can be seen that each degree rise in temperature means a 400 foot rise in cloudbase
A very good guide to Tdew can be found from various internet reports such as Metars and can form the basis for predictions.
There are also specialized instruments for calculating dewpoint.
But it is not  always necessary to know Tdew.  Many modern cars have thermometers.  Note the temperature, get a cloudbase from eg a glider already soaring during the morning, and you can easily infer the dewpoint at present and thus infer expected best cloudbase at maximum Tdry.
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Reminder - The forecast Max Tdry minus present Tdry times 400 = expected cloudbase at best time of day.
This rule of thumb of course goes wrong if cloud base rises so much as to overtake cloud tops, ie the day turns blue. 
There are lots of ifs and buts, but while bearing these limitations in mind, this method gives a very useful guide.
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Spreadout
This is a term to describe what happens sometimes after cumulus has been forming for some while.  The developing clouds run up against a lid (maybe an inversion) and can rise no further,  They spread sideways and cut off the sun thus affecting the amount of heat reaching the ground.  An extensive sheet of strato cumulus develops at say 4 to 6,000 feet.  Surface temperatures cease to rise and can even fall by a degree or two.  Convection is now very poor.  This of course not only is of major significance to glider pilots, but the general public get irritated when a beautifully sunny start turns to extensive cloud during the late morning.
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Spreadout is notoriously difficult to predict and may indeed affect only some areas (but why?).  A clue, but no more than that, is provided by the time when the first puffs of cumulus appear.  If this happens early, then spreadout is POSSIBLE.  On the other hand, if the first cumulus do not occur until late (and by implication, quite at high base and at a surface temperature only just short of the expected maximum) then spreadout is LESS likely
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Bradbury is very useful for convective situations.  But do bear in mind its limitations.  Temperatures are often known only to the nearest degree. 
Thus if Tdry is in fact 0.5C lower than reported (metars) and Tdew 0.5C higher, then cloudbase using the quoted temperatures would be 400 feet in error.
But of course, with 'rounding', things tend to average out