Modeling Vertical Variation in Air Temperature
21
2. Temperature increases with height when H is negative (heat flux toward the surface) and decreases with height when H is positive. During
the day, sensible heat flux is generally away from the surface so T
decreases with height.
3. The temperature gradient at a particular height increases in magnitude
as the magnitude of H increases, and decreases as wind or turbulence
increases.
Example 2.1. The following temperatures were measured above a 10 cm
high alfalfa crop on a clear day. Find the aerodynamic surface temperature,
To -
Height (m)
0.2 0.4 0.8 1.6
Temperature (C)
26 24 23 21
Solution. It can be seen from Eq. (2.1) that T (z) = To when the In term
is zero, which happens when z = d + ZH since ~ ( Z H / Z H )
= ln(1) = 0.
If h[(z - d)/zH] is plotted versus T (normally the independent variable
is plotted on the abscissa or horizontal axis, but when the independent
variable is height, it is plotted on the ordinate or vertical axis) and extrapolate to zero, the intercept will be To. For a 10 cm (0.1 m) high
canopy, zH = 0.002 m, and d = 0.06 m. The following can therefore be
computed:
-
Height (m)
0.2 0.4 0.8
1.6
Temp. (C)
26
24
23
21
(Z - ~ ) / z H
70 170 370 770
I~[(z - ~ ) / z H ]
4.25 5.14 5.91 6.65.
The Figure for Example 2.1 on the following page is plotted using this
data, and also shows a straight line fitted by linear least squares through
the data points that is extrapolated to zero on the log-height scale. The
intercept is at 34.6" C, which is the aerodynamic surface temperature.
Example 2.2. The mean temperature at 5:00 hrs, 2 m above the soil
surface is 3" C. At a height of 1 m, the temperature is 1" C. If the crop
below the point where these temperatures are measured is 50 cm tall, will
the crop experience a temperature below freezing?
21
2. Temperature increases with height when H is negative (heat flux toward the surface) and decreases with height when H is positive. During
the day, sensible heat flux is generally away from the surface so T
decreases with height.
3. The temperature gradient at a particular height increases in magnitude
as the magnitude of H increases, and decreases as wind or turbulence
increases.
Example 2.1. The following temperatures were measured above a 10 cm
high alfalfa crop on a clear day. Find the aerodynamic surface temperature,
To -
Height (m)
0.2 0.4 0.8 1.6
Temperature (C)
26 24 23 21
Solution. It can be seen from Eq. (2.1) that T (z) = To when the In term
is zero, which happens when z = d + ZH since ~ ( Z H / Z H )
= ln(1) = 0.
If h[(z - d)/zH] is plotted versus T (normally the independent variable
is plotted on the abscissa or horizontal axis, but when the independent
variable is height, it is plotted on the ordinate or vertical axis) and extrapolate to zero, the intercept will be To. For a 10 cm (0.1 m) high
canopy, zH = 0.002 m, and d = 0.06 m. The following can therefore be
computed:
-
Height (m)
0.2 0.4 0.8
1.6
Temp. (C)
26
24
23
21
(Z - ~ ) / z H
70 170 370 770
I~[(z - ~ ) / z H ]
4.25 5.14 5.91 6.65.
The Figure for Example 2.1 on the following page is plotted using this
data, and also shows a straight line fitted by linear least squares through
the data points that is extrapolated to zero on the log-height scale. The
intercept is at 34.6" C, which is the aerodynamic surface temperature.
Example 2.2. The mean temperature at 5:00 hrs, 2 m above the soil
surface is 3" C. At a height of 1 m, the temperature is 1" C. If the crop
below the point where these temperatures are measured is 50 cm tall, will
the crop experience a temperature below freezing?