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 0.5" to 0. lo 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.
2.3 Modeling Vertical Variation in Air
Temperature
The theory of turbulent transport, which we study in Ch. 7, specifies the
shape of the temperature profile over a uniform surface with steady-state
conditions. The temperature profile equation is:
where T ( z ) is the mean air temperature at height z, To is the apparent
aerodynamic surface temperature, zH is a roughness parameter for heat
transfer, H is the sensible heat flux from the surface to the air, j k , is the
volumetric specific heat of air (1200 J m-3 C-' at 20" C and sea level),
0.4 is von Karman's constant, and u* is the friction velocity (related to
the friction or drag of the stationary surface on the moving air). The
reference level from which z is measured is always somewhat arbitrary,
and the correction factor d , called the zero-plane displacement, is used
to adjust for this. For a flat, smooth surface, d = 0. For a uniformly
vegetated surface, Z H 1 : 0.02h, and d 1 : 0.6h, where h is canopy height.
We derive Eq. (2.1) in Ch. 7, but use it here to interpret the shape of the
temperature profile and extrapolate temperatures measured at one height
to other heights. The following points can be made.
1. The temperature profile is logarithmic (a plot of h ( z - d ) / z ~
vs. T ( z )
is a straight line).
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 0.5" to 0. lo 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.
2.3 Modeling Vertical Variation in Air
Temperature
The theory of turbulent transport, which we study in Ch. 7, specifies the
shape of the temperature profile over a uniform surface with steady-state
conditions. The temperature profile equation is:
where T ( z ) is the mean air temperature at height z, To is the apparent
aerodynamic surface temperature, zH is a roughness parameter for heat
transfer, H is the sensible heat flux from the surface to the air, j k , is the
volumetric specific heat of air (1200 J m-3 C-' at 20" C and sea level),
0.4 is von Karman's constant, and u* is the friction velocity (related to
the friction or drag of the stationary surface on the moving air). The
reference level from which z is measured is always somewhat arbitrary,
and the correction factor d , called the zero-plane displacement, is used
to adjust for this. For a flat, smooth surface, d = 0. For a uniformly
vegetated surface, Z H 1 : 0.02h, and d 1 : 0.6h, where h is canopy height.
We derive Eq. (2.1) in Ch. 7, but use it here to interpret the shape of the
temperature profile and extrapolate temperatures measured at one height
to other heights. The following points can be made.
1. The temperature profile is logarithmic (a plot of h ( z - d ) / z ~
vs. T ( z )
is a straight line).