Soil Temperature Changes with Depth and Time
2.4 Modeling Temporal Variation in Air
Temperature
Historical weather data typically consist of measurements of daily maximum and minimum temperature measured at a height of approximately
1.5 m. There are a number of applications which require estimates of
hourly temperature throughout a day. Of course, there is no way of knowing what the hourly temperatures were, but a best guess can be made by
assuming that minimum temperatures normally occur just before sunrise
and maximum temperatures normally occur about two hours after solar
noon. The smooth curve in Fig. 2.2 shows this pattern. The smooth curve
was derived by fitting two terms of a Fourier series to the average of
many days of hourly temperature data which had been normalized so that
the minimum was 0 and the maximum was 1. The dimensionless diurnal
temperature function which we obtained in this way is:
where w = n/12, and t is the time of day in hours (t = 12 at solar noon).
Using this function, the temperature for any time of the day is given by
T(t) = Tx,i-~r(t> + Tn,i[l - r(t>I
O < t 1 5
T(t) = Tx,ir(t) + Tn,i[l - r(t>I
5 < t 5 14
(2.3)
T(t) = Tx,ilr(t) + Tn,i+l[l - r(t)I
14 < t < 24.
Here, Tx is the daily maximum temperature and Tn is the minimum temperature. The subscript i represents the present day; i - 1 is the previous
day, and i + 1 is the next day. The curve in Fig. 2.2 was drawn using
Eqs. (2.2) and (2.3). Note that t is solar time. The local clock time usually
differs from solar time, so adjustments must be made. These are discussed
in detail in a later chapter.
Example 2.3. Estimate the temperature at 10 AM on a day when the
minimum was 5" C and the maximum was 23" C.
Solution. At t = 10 hrs, (note that angles are in radians)
+ 0.11 sin (
2 x 3.14 x 10
12
Since 10 is between 5 and 14, the middle form of Eq. (2.3) is used, so
2.5 Soil Temperature Changes with Depth and
Time
The temperature of the soil environment is also important to many living organisms. Figure 2.1 shows a typical range for diurnal temperature
2.4 Modeling Temporal Variation in Air
Temperature
Historical weather data typically consist of measurements of daily maximum and minimum temperature measured at a height of approximately
1.5 m. There are a number of applications which require estimates of
hourly temperature throughout a day. Of course, there is no way of knowing what the hourly temperatures were, but a best guess can be made by
assuming that minimum temperatures normally occur just before sunrise
and maximum temperatures normally occur about two hours after solar
noon. The smooth curve in Fig. 2.2 shows this pattern. The smooth curve
was derived by fitting two terms of a Fourier series to the average of
many days of hourly temperature data which had been normalized so that
the minimum was 0 and the maximum was 1. The dimensionless diurnal
temperature function which we obtained in this way is:
where w = n/12, and t is the time of day in hours (t = 12 at solar noon).
Using this function, the temperature for any time of the day is given by
T(t) = Tx,i-~r(t> + Tn,i[l - r(t>I
O < t 1 5
T(t) = Tx,ir(t) + Tn,i[l - r(t>I
5 < t 5 14
(2.3)
T(t) = Tx,ilr(t) + Tn,i+l[l - r(t)I
14 < t < 24.
Here, Tx is the daily maximum temperature and Tn is the minimum temperature. The subscript i represents the present day; i - 1 is the previous
day, and i + 1 is the next day. The curve in Fig. 2.2 was drawn using
Eqs. (2.2) and (2.3). Note that t is solar time. The local clock time usually
differs from solar time, so adjustments must be made. These are discussed
in detail in a later chapter.
Example 2.3. Estimate the temperature at 10 AM on a day when the
minimum was 5" C and the maximum was 23" C.
Solution. At t = 10 hrs, (note that angles are in radians)
+ 0.11 sin (
2 x 3.14 x 10
12
Since 10 is between 5 and 14, the middle form of Eq. (2.3) is used, so
2.5 Soil Temperature Changes with Depth and
Time
The temperature of the soil environment is also important to many living organisms. Figure 2.1 shows a typical range for diurnal temperature