Random Temperature Variation

2.2 Random Temperature Variation

In addition to the more or less predictable diurnal and annual temperature variations shown in Figs. 2.2 and 2.3, and the strong, predictable spatial variation in the vertical seen in Fig. 2.1, there are random variations, the details of which cannot be predicted. We can describe them using statis- tical measures (mean, variance, correlation etc.), but can not interpolate or extrapolate as we can with the annual, diurnal, and vertical variations.

Figure 2.3 shows an example of these random variations. The long-term monthly mean temperature shows a consistent pattern, but the daily av- erage temperature varies around this monthly mean in an unpredictable way. Figure 2.4 shows air temperature variation over an even shorter time.

It covers a period of about a minute. Temperature was measured with a

25 diameter thermocouple thermometer. The physical phenomena associated with the random variations seen in Figs. 2.3 and 2.4 make interesting subjects for study. For example, the daily variations seen in Fig. 2.3 are closely linked to weather patterns, cloud cover, and input of solar energy. The fluctuations in Fig. 2.4 are par- ticularly interesting because they reflect the mechanism for heat transport in the lower atmosphere, and are responsible for some interesting optical phenomena in the atmosphere.

Since heat transfer in air is mainly by convection, or transport ofparcels of hot or cold air, we might expect the air temperature at any instant to

Random Temperature Variation

Time (s)

F IG URE 2.4. Air temperature 2 m above a desert surface at White Sands Missile Range, NM. Measurements were made near midday using a 25 diameter thermocouple.

differ substantially from the mean air temperature that one might measure with a large thermometer. The relatively smooth baseline in Fig. 2.4, with jagged interruptions, indicates a suspension of hot ascending parcels in a matrix of cooler, descending air. Well mixed air is subsiding, being heated at the soil surface, and breaking away from the surface as convective bubbles when local heating is sufficient.

Warm air is less dense than cold air, and therefore has a lower index of refraction. As light shines though the atmosphere, the hot and cold parcels of air act as natural lenses, causing the light to constructively

and destructively interfere, giving rise to a diffraction pattern. Twinkling of stars and the scintillation of terrestrial light sources at night are the result of this phenomenon. The diffraction pattern is swept along with the wind, so you can look at the lights of a city on a clear night from some distance and estimate the wind speed and direction from the drift of the scintillation pattern.

So-called "heat waves" often seen on clear days also result from re-

fractive index fluctuations (Lawrence et al., 1970). The drift

waves can be seen, and wind direction and speed can sometimes be estimated from the drift velocity. This phenomenon has been used to measure wind speed (Lawrence et al., 1972). More extreme heating at the surface can result in a mirage, where the heated, low-density air near the surface of the earth refracts the light from the sky to the observers eye, making land

Temperature

look like water. This is the result of the systematic vertical variation in temperature above the heated surface, rather than the result of the random

variations that we were just discussing. Air temperatures are often specified with a precision of

to 0. C. From Fig. 2.4 it should be clear that many instantaneous temperature

measurements would need to be averaged, over a relatively long time period, to make this level of precision meaningful. Averages of many readings, taken over 15 to 30 minutes, are generally used. Figures 2.1 and 2.2 show the behavior of such long-term temperature averages. Large thermometers can provide some of this averaging due to the thermal mass of the sensing element.

Random temperature variations are, of course, not limited to the time scales just mentioned. Apparently random variations in temperature can

be shown from the geologic record, and were responsible, for example, for the ice ages. There is considerable concern, at present, about global warming and climate change, and debate about whether or not the climate has changed. Clearly, there is, always has been, and always will be climate change. The more important question for us is whether human activity has or will measurably alter the random variation of temperature that has

existed for as long as the earth has been here.