I
Estimating Direct and Diffise Short-wave Irradiance
171
(t,) is the time of solar noon (to) minus the half daylength divided by 15
(to convert degrees to hours):
and daylength in hours is twice the half daylength in degrees divided by
1 5 " h (2hs/ 15). Therefore, a 12-hour daylength corresponds to h, =
90".
To find the time of actual sunrise, @ in Eq. (1 1.5) is set to 90". Biologically sigmlicant times, especially for flowering and insect activity,
begin in twilight hours just before sunrise and extend to just after sunset.
Beginning and ending times for "civil twilight" are sometimes used to
define these times of activity. Civil twilight is defined as beginning and
ending when the sun is 6" below the horizon, so @ = 96".
Example 11.1. Find the sun zenith angle for Pullman, WA at 1 O:45 PDT
on June 30. Also find the time of first twilight and the daylength.
Solution. Convert the time of observation to standard time by subtracting one hour and convert minutes to decimal hours, so t = 9.75 hrs.
The calendar day for June 30 is J = 181. Pullman latitude is 46.77",
and longitude is 117.2". The standard meridian is 120". The local meridian is therefore 2.8" east of the standard meridian, so LC = 2.8" +
15"/hr = 0.19 hrs. From Eq. (11.4) or Table 11.1, ET = -0.06 hrs.
Equation (1 1.3) then gives to = 12 - 0.19 - (-0.06) = 11.87 hrs.
Declination, from Table 11.1 or Eq. (1 1.2) is 23.18'. Substituting these
values into Eq. (1 1.1) gives
The result is 34.9". The half daylength (including twilight), from
Eq (1 l.6), is
Converting to hours gives 128" x
= 8.56 hrs. The time of first
twilight is 11.87 - 8.56 = 3.31 hrs (solar time). The daylength is 2 x
8.56 = 17.1 hrs.The timeofsunriseinPDTis3.31 hrs+ LC + ET +
1 hr = 4.44hrs (PDT).
11.2 Estimating Direct and Diffuse Short-wave
lrradiance
Computation of the solar or shortwave component of the radiant energy
budget of an organism requires estimates of flux densities for at least
three radiation streams: direct irradiance on a surface perpendicular to
the beam (S,), diffise sky irradiance on a horizontal plane (Sd), and
reflected radiation from the ground (S,). In addition to these, sometimes
the beam irradiance on a horizontal surface Sb and the total (beam plus
Estimating Direct and Diffise Short-wave Irradiance
171
(t,) is the time of solar noon (to) minus the half daylength divided by 15
(to convert degrees to hours):
and daylength in hours is twice the half daylength in degrees divided by
1 5 " h (2hs/ 15). Therefore, a 12-hour daylength corresponds to h, =
90".
To find the time of actual sunrise, @ in Eq. (1 1.5) is set to 90". Biologically sigmlicant times, especially for flowering and insect activity,
begin in twilight hours just before sunrise and extend to just after sunset.
Beginning and ending times for "civil twilight" are sometimes used to
define these times of activity. Civil twilight is defined as beginning and
ending when the sun is 6" below the horizon, so @ = 96".
Example 11.1. Find the sun zenith angle for Pullman, WA at 1 O:45 PDT
on June 30. Also find the time of first twilight and the daylength.
Solution. Convert the time of observation to standard time by subtracting one hour and convert minutes to decimal hours, so t = 9.75 hrs.
The calendar day for June 30 is J = 181. Pullman latitude is 46.77",
and longitude is 117.2". The standard meridian is 120". The local meridian is therefore 2.8" east of the standard meridian, so LC = 2.8" +
15"/hr = 0.19 hrs. From Eq. (11.4) or Table 11.1, ET = -0.06 hrs.
Equation (1 1.3) then gives to = 12 - 0.19 - (-0.06) = 11.87 hrs.
Declination, from Table 11.1 or Eq. (1 1.2) is 23.18'. Substituting these
values into Eq. (1 1.1) gives
The result is 34.9". The half daylength (including twilight), from
Eq (1 l.6), is
Converting to hours gives 128" x
= 8.56 hrs. The time of first
twilight is 11.87 - 8.56 = 3.31 hrs (solar time). The daylength is 2 x
8.56 = 17.1 hrs.The timeofsunriseinPDTis3.31 hrs+ LC + ET +
1 hr = 4.44hrs (PDT).
11.2 Estimating Direct and Diffuse Short-wave
lrradiance
Computation of the solar or shortwave component of the radiant energy
budget of an organism requires estimates of flux densities for at least
three radiation streams: direct irradiance on a surface perpendicular to
the beam (S,), diffise sky irradiance on a horizontal plane (Sd), and
reflected radiation from the ground (S,). In addition to these, sometimes
the beam irradiance on a horizontal surface Sb and the total (beam plus