If the day maximum screen temperature is denoted by (Tx) and the air-mass dew point temperature (Td), and the latter is assumed not to change appreciably overnight, then
T(min)=1/2 (Tx + Td) - K
where K varies according to the expected surface wind speed and average cloud amountovernight.
McKenzie originally did his work for Dyce (Aberdeen) and it was presented (though not published) in 1944 in an internal memorandum within the Meteorological Office. Since that time, constants for many Met Office site have been calculated (Claude Kensett), but as a rough guide:-
Wind / cloud overnight
|Dead calm / clear skies throughout night||~ 8 or 9 (an extreme case)|
|Light wind / small amounts cloud||~ 6 to 8|
|Light wind / cloud coming and going||~ 4 to 7|
|Light wind / generally cloudy||~ 2 or 3|
|Moderate wind / small amounts cloud||~ 3 to 5|
|Moderate wind / cloud coming and going||~ 2 to 4|
|Moderate wind / generally cloudy||~1 or 2|
|Brisk winds (most cloud classes)||~ 1 or 2|
There are other corrections you can apply given the time of year etc. The beauty of the method, is that it is easy to apply .. add together a couple of commonly known variables, divide by 2, and then fudge the 'correction' K.
The initial figure (i.e. before applying 'K' above), gives an approximation to the dusk temperature, following (empirical) work performed by Boyden & Saunders. However, when there is an inversion of temperature in the lowest few hundred metres of the atmosphere, then take off 2degC from this value.
If the midday (12 GMT) screen temperature is denoted by (T) and the midday (12 GMT) dew point temperature (Td), then
T(min)=0.316T + 0.548Td - 1.24 + K
where K varies between -2.2 for near calm, clear skies or near clear overnight to + 2 or 3 for windy, mostly cloudy situations. This method is only applicable for inland stations, and was developed over Eastern England.
Methods for forecasting day maximum temperatures are listed elsewhere on this site:-
- Based upon the 850 hPa actual temperature
- Based upon the 850 - 1000 hPa partial thickness
- Based upon the 850 hPa Theta E (or Theta W) method
- Based upon the 500 - 1000 hPa total thickness (or Relative Topography)
General notes: solar (short-wave) radiation [ or insolation ] absorbed at the earth's surface is converted into heat and warms the ground (raises the temperature) - the warm ground in turn radiates a good deal of heat back to space at long wavelengths (relative to the shorter solar radiation) - much of this is absorbed in various ways by the atmosphere - water vapour - water droplets in clouds - and CO2 - subsequently returned to earth as LW radiation (back, or counter-radiation). A very shallow zone on / near the surface is warmed directly (by conduction) - but the bulk of the heat gained is directly re-distributed by convection or through turbulent mixing of air in contact with the surface or through radiation, and indirectly through latent heat processes.
The standard model of how the temperature varies throughout the 24 hours is neatly illustrated in the diagram (below), which is here reproduced from T. R. Oke ( 1978: 'Boundary Layer Climates', Methuen, London, pp. 31-34. The times are for illustrative purposes only. )
During the daylight hours (except at either end), when the sun is appreciably high in the sky, solar energy is received faster at the surface than it can be distributed upwards as net outgoing terrestrial (long-wave) radiation. This is indicated on the diagram between the points 'A' and 'B'. This leads to a rise in temperature (T) from the point of minimum (Tmin) to the time of day maximum (Tmax). Note carefully how Tmax occurs after the insolation peak - in summer this can be many hours later. During the periods when the sun is very low in the sky (early morning & late afternoon or evening, depending upon season), and also overnight, the rate of energy loss from the surface dominates and therefore the ground and air immediately above it undergo cooling - i.e. between 'B' and 'C', and between 'D' and 'A'. The difference between the daily maximum and minimum surface air temperature is known as the daily range of temperature and the profile described above is an approximation to the theoretical diurnal temperature range.
Once the 'standard' model is set, there are a number of conditions producing modification to the profile.
Wind speed (turbulence): The stronger the wind within the first few 10's of metres of the ground, the 'flatter' will be the profile of temperature depicted above. This is because wind-generated turbulence will mix the air (in much the same way as bath water is mixed by agitation), and so day-time heating is mixed through a deeper layer (rather than concentrated in the first few metres), and night-time cooling offset by warmer air being dragged down from above.
Humidity content: One of the most important controls on the night-time temperature is the absolute humidity content of the over-lying air. This is usually represented in the various algorithms by the dew-point (or perhaps wet-bulb) temperature. Water vapour is a very efficient absorber of outgoing long-wave radiation, which it then re-radiates - some of which comes back to the surface and offsets the fall of temperature. Even under clear skies, if the air is humid then the nocturnal fall of temperature is not as great as with low-humidity air. Also, if other factors are favourable then fog and / or low cloud will result, further arresting the fall of temperature.
Cloud cover (or fog): cloud cover (and fog) will reduce the amount of incoming solar radiation during the day, with maxima reduced from the theoretical potential as a result. At night, the cloud / fog will absorb, reflect and re-emit radiation back to the surface, acting like a 'blanket' and subsequent minima will be higher than if there was no cloud. Even irregular / fitful cloud banks will have an effect, and although layer low cloud types (stratocumulus, stratus etc.) are the most effective, even relatively thin & well-broken altocumulus will have a marked impact upon the final minimum.
State of ground: Day and night-time temperatures are lower over snow surfaces than than those without snow-cover. There are three reasons for this . . .
- Snow, particularly fresh snow, is a good reflector of incoming solar radiation, thus reducing the effectiveness of daytime sunshine.
- Snow (again, fresh cover in particular) is a good insulator due to the potentially large amount of air trapped within the snow. This prevents heat reaching the snow surface from the underlying ground.
- Snow surfaces radiates strongly, and at night this produces a strong radiative cooling effect.
[ The combined effect of (2) & (3) above is that night-time minima under clear skies and with light winds are likely to be some 2 to 4 degC lower than predicted by the equations above, and the time of minimum is much earlier in the night than for surfaces clear of snow. With cloud cover, then roughly 1 degC lower. ]
Temperatures tend to be higher by day and lower by night over dry, bare soil (or sandy) surfaces, away from urban influences.
- By day, little or no radiant energy is required to evaporate moisture - all energy is therefore available to heat the ground (and therefore the overlying air).
- With loose soil or sand in particular, the air trapped between the particles, prevents deep distribution of the heat energy, and it is most effective at the surface - again allowing a strong influence on daytime maxima.
- Overnight, dry, bare surfaces radiate strongly - and have little or no moisture available to raise the overlying humidity, which would offset any heat loss.
- Loosely bound surfaces (light soils, fine desert sand etc.), act like fresh snow - little or no heat can be conducted upwards from deeper down, and thus strong radiational cooling from the very top of the surface layers takes place. [This is something often forgotten by people visiting desert areas in winter - just how cold it can get.]