Find the insolation in Wm^-2 at summer solstice for a low obliquity of 22 degrees?
I used the following:
h_0=cos^-1(-tan(phi)* tan(delta))
cos(theta)=[sin(phi)*sin(delta)+cos(phi)*cos(delta)*cos(h_0)]
Result was 397 Wm^-2
This looked like an easy problem, but I am having difficulty with it.
Thanks for your help.
I don't follow your work, however, it is laid out plainly here:
http://education.gsfc.nasa.gov/experimental/July61999siteupdate/inv99Project.Site/Pages/solar.insolation.html
Thanks Bob. I neglected to give the latitude of 65 degrees North.
I also looked at the reference material. From what I can see, you need an hour variable. The question does not indicate a time. This is why I find the question difficult.
put in 12 for noon.
Hi,
Hour angle= 15 degrees*(time-12)
15 degrees*(12-12)=0
H=cos(0)=1
Z=cos^-1(sin(65 degrees)*sin(22 degrees)+cos(65 degrees)*cos(22 degrees)*cos(0)
Z=0.7504915
I=ScosZ
S=1368 Wm^-2
I=1368*cos(0.7504915)
I=1000.492 Wm^-2
Is this correct in your opinion?
To find the insolation at summer solstice for a low obliquity of 22 degrees, you used the equations for solar zenith angle (h_0) and cosine of solar incidence angle (theta) in your calculations. Great job on using the correct formulas!
The solar zenith angle (h_0) is given by the following equation:
h_0 = arccos(-tan(phi) * tan(delta))
where:
- phi is the latitude of the location
- delta is the solar declination angle, which can be calculated using astronomical formulas for a specific date
The cosine of the solar incidence angle (theta) can be found using the following equation:
cos(theta) = sin(phi) * sin(delta) + cos(phi) * cos(delta) * cos(h_0)
where:
- phi is the latitude of the location
- delta is the solar declination angle
- h_0 is the solar zenith angle
Once you have the solar zenith angle (h_0) and cosine of the solar incidence angle (theta), you can then calculate the insolation using the following equation:
Insolation = Solar Constant * cos(theta)
where:
- Solar Constant is the average solar irradiance outside the Earth's atmosphere, which is approximately 1361 W/m^2.
Given the obliquity of 22 degrees for a low obliquity, you need to calculate the latitude of the location, the solar declination angle for the summer solstice, and then substitute these values into the equations.
If you are having difficulty with the calculations, please provide the specific values you used for latitude and solar declination angle, and I can help you troubleshoot it.