Is it an actual increase in temperature, with altitude, or can it be just a relatively constant temperature but obviously well above the ISA lapse rate?
The former is quite rare, although I have seen it enough times.
IMHO: inversion = rise of temperature with altitude, isothermal layer = constant temperature
An isothermal layer exists in the lower part of the stratosphere. Don't know how likely it is in the troposphere.
The former is quite rare
It depends on where you live, but north but close to the alps it's the norm rather than the exception in autumn (i.e. now).
Today it's quite extreme, forecast for 11 LT:
Temperature @2000ft: 7 degC
Temperature @5000ft: 17 degC
One month ago I spent some days in Tenerife. Two days I went up to Teide National Park. A sea level both days we were about 26ºC. At 7000' the temperature had risen up to 36-37 ºC both days.
Definition of an inversion = anti cyclonic gloom
Peter,
The ISA lapse rate has no physical significance; it is just an average across the entire atmosphere. That doesn't mean that if you use the ISA lapse rate of 2 degrees C to predict temperatures above the surface that it won't be right, but then even a blind squirrel gets an acorn now and again. Another example is one can reduce the fraction 16/64 by crossing out the sixes and in this case it produces the correct answer, but it is not a reliable method of reducing fractions.
The actual atmosphere has two lapse rates, the dry adiabatic lapse rate and the saturated adiabatic lapse rate. The dry adiabatic lapse rate is simple, it is 3 degrees C per 1000 feet. The saturated adiabatic lapse rate is more complex and is not a straight line and it varies with temperature and pressure. These two lapse rates along with the surface temperature and dew point can be used to determine where the bases of clouds will form and whether or not the actual temperature verses altitude will be stable or unstable.
If you are looking for a temperature inversion, most of the time fog or smog forms or low visibility prevails from the surface, the situation is caused by a temperature inversion. Of course UK never experiences fog. :)