Diurnal temperature variation
The energy received from the sun is the source of heat to the atmosphere and so the balance of heat exchanges by radiation between the earth and its environment, which is reflected in changes of air temperature, must vary according to the position of the sun in the sky. That is to say, there will be a variation of air temperature against time.
The surface of the earth is at its coolest just before dawn, having had, in the absence of cloud cover, an opportunity of losing heat to the black sky during the whole of the night. Accordingly, it is usual to regard the lowest air temperature as occurring about one hour before sunrise. As soon as the sun rises, its radiation starts to warm the surface of the earth, and as the temperature of the ground rises heat is convected from the surface of the earth
to the layers of air immediately above it. There is thus a progressive increase in air temperature as the sun continues to rise, and also for some little time after it has passed its zenith, because of the fact that some of the heat received by the ground from the sun and stored in its upper layers throughout the morning escapes upwards and is lost by convection in the early afternoon. It is, therefore, usual to find the highest air temperatures between
14.0 h and 16.00 h (sun-time). In fact, between about 13.00 h and 17.00 h one would not expect very great changes of temperature.
On an average basis, it is not unreasonable to suppose that there is some sort of rough sinusoidal relationship between sun-time and air dry-bulb temperature. The curve would not be wholly symmetrical since the time between lowest and highest temperatures would not necessarily equal that between highest and lowest.
For the month of June, sunrise is at about 04.00 h and sunset at about 20.00 h. The time of lowest temperature is at about 03.00 h and the time of highest temperature is at
15.0 h. There is, thus, a lapse of 12 hours while the temperature is increasing. Since the night period for unrestricted cooling is only about 7 hours (20.00 h to 03.00 h) the curve will be broader in daytime than at night. The reverse would be the case in December.
If we assume the outside temperature, /e, varies sinusoidally with time, 0, and its maximum value, f15, occurs at 15.00 h sun-time we can write:
, . (071 — 971)
1 — sm———- 12—
T — t V
LQ ~ *15 — 2
Where D is the difference between the mean daily maximum and minimum temperatures, otherwise termed the diurnal range. Records are kept of weather data at hourly intervals for many locations in the UK and overseas. Such information is commonly stored electronically and, typically, includes: dry-bulb, screen wet-bulb, dew point, wind direction and speed, atmospheric pressure, type of cloud and cloud cover in several layers at different altitudes, solar radiation and so on. Some details for 17 July 1967, the hottest day of that year, for Wethersfield, near Braintree in Essex, have been taken from meteorological weather data and values of dry-bulb temperature and dew point temperature are plotted against time in Figure 5.2. The difference between the maximum (27.8°C at 14.00 h sun-time) and minimum (15.6°C at 03.00 h) is 12.2°C and inserting this for the value of D in equation (5.4) yields the sine curve also shown in Figure 5.2. We see that a sinusoidal assumption is not unreasonable for warm summer weather, at least for Wethersfield. Equation (5.4) is useful for estimating outside air temperatures when heat gains must be calculated for some time other than 15.00 h, in summer. If the meteorological records show that the maximum occurs at a time different from 15.00 h, equation (5.4) should be used assuming that the maximum is at 15.00 h and the answers then shifted by the number of hours necessary to give the maximum at the correct time, See example 5.2.
Equation (5.4) is useful for the determination of temperatures in the vicinity of the time of maximum daily temperature, in summertime. If there is a marked difference between the period from the mean daily maximum to the mean daily minimum and that from the mean daily minimum to the mean daily maximum, then the technique proposed by CIBSE (1999) should be used.
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