Analysis of Diurnal Solar Intensity Variation: Lab Report, University

This lab report investigates the diurnal variation of solar intensity, focusing on its cosinusoidal pattern and the influence of latitude and longitude. The study involved setting up an orb for equinoctial settings and measuring the solar cell output voltage at various longitudes and latitudes at hourly intervals. The report presents the experimental results in tabulated form and plots the normalized solar intensity against time for different longitudes. Analysis of the data reveals that the incoming solar radiation begins at sunrise, peaks at noon, and shuts off at sunset. A correlation analysis comparing experimental and calculated values demonstrates that the cosinusoidal expression accurately determines solar intensity at any point in time on the earth's surface, with slight deviations attributed to factors such as sky clearance and equipment inefficiencies. The report concludes that equation 1 can be used to describe the intensity of light at different times of the day and that the experimental results align closely with the theoretical results. The study confirms that the diurnal variation in solar intensity is the same pattern that is experienced in the seasonal cycle.

Diurnal of Solar Intensity 1
Diurnal of Solar Intensity Lab Report
By
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(Professor’s Name)
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Diurnal of Solar Intensity 2
Introduction
Information of the periodic development of global, diffuse and uninterrupted solar radiation
at the surface is vital for climate researches, solar collector efficacy approximation, water use
assessments of greenhouses and other agricultural structures, as well as for plant growth
simulation researches and a number of meteorological uses (University of Oklahoma, & United
States, 2005). In addition, these diurnal weather array data are not readily accessible for most
places round the world. To some extent more accessible are mean monthly values of total daily
solar radiation, of maximum and minimum air temperature, and of vapour pressure (Kitchen,
2016, Pg. 5).
In this assignment we will consider a daily co-sinusoidal diurnal variation in solar intensity.
Every day is like a small periodic cycle – Sun emissions most powerful around noon – As is the
circumstance with the seasons, the highest temperatures hold-up the peak arriving solar
radioactivity. An accepting of the daytime cycle in temperature necessitates comprehending
diverse approaches of atmospheric heating and cooling: Radiation, Conduction and Convection
(Park, 2009, Pg. 17).
Theory
The day time variation in the standardized solar intensity, can be defined as
It
I12
=cos ( 2 πt
24 )… … … … … … … … … .. equation 1
Between dawn and dusk and zero at altogether other times where:
It Intensity of Solar at time t hrs
I12 Solar intensity at noon (Mooney & Zavaleta, 2016).

Diurnal of Solar Intensity 3
Figure 1: Plot of It/I12 against time
Objectives
 To test the co-sinusoidal day time variation in the intensity of solar.
In this assignment the main objective is study the effects of longitude and latitude on the light
intensity received on the earth surface.
Methodology /Procedure
1. The orb was set up for equinoctial settings (Sun above the Equator) with the Greenwich
Meridian in the direction of the light source.
2. The noon solar cell output voltage, I12, was dignified (in mV on the 200 mV scale) with the
cell parallel to the surface of the earth and the cell on the Greenwich Meridian at the equator.
3. We worked out how to rotate the globe to a new longitude with the solar cell on the Meridian
and the Equator, to determine It at hourly intermissions from 0600 to 1800.
4. We repeated the experimentation at 15o intermissions from the Equator to 75o north.
5. The results were tabulated as shown in the table below.

Diurnal of Solar Intensity 4
Results
The measurements were taken as stated on the procedure. The values of It/I12 were then
calculated in order to complete the table.
Latitude 0 15 30
Time Longitudeo cos(Long) It It/I12 It It/I12 It It/I12
0600 90oW 0.0000 013 0.0565 012 0.0561 013 0.0714
0700 75oW 0.2588 024 0.1043 021 0.0981 034 0.1868
0800 60oW 0.5000 096 0.4174 073 0.3411 094 0.5165
0900 45oW 0.7071 185 0.8043 167 0.7804 157 0.8626
1000 30oW 0.8660 221 0.9609 211 0.9860 185 1.0165
1100 15oW 0.9659 223 0.9696 215 1.0047 180 0.9890
1200
& I12
0oW 1.0000 230 1.0000 214 1.0000 182 1.0000
1300 15oE 0.9659 204 0.8870 191 0.8925 161 0.8846
1400 30oE 0.8660 157 0.6826 146 0.6822 124 0.6813
1500 45oE 0.7071 106 0.4609 105 0.4907 080 0.4396
1600 60oE 0.5000 051 0.2217 054 0.2523 055 0.3022
1700 75oE 0.2588 020 0.0870 023 0.1075 019 0.1044
1800 90oE 0.0000 011 0.0478 011 0.0514 011 0.0604
Latitude 45 60 75
Time Longitudeo cos(Long) It It/I12 It It/I12 It It/I12
0600 90oW 0.0000 014 0.1007 014 0.1818 011 0.4783
0700 75oW 0.2588 034 0.2446 028 0.3636 014 0.6086
0800 60oW 0.5000 074 0.5324 046 0.5974 017 0.7391
0900 45oW 0.7071 115 0.8273 069 0.8961 021 0.9130
1000 30oW 0.8660 135 0.9712 078 1.0130 023 1.0000
1100 15oW 0.9659 137 0.9856 078 1.0130 024 1.0435

Diurnal of Solar Intensity 5
1200
& I12
0oW 1.0000 139 1.0000 077 1.000 023 1.000
1300 15oE 0.9659 126 0.9065 066 0.8571 020 0.8696
1400 30oE 0.8660 098 0.7050 052 0.6753 016 0.6957
1500 45oE 0.7071 079 0.5683 035 0.4545 012 0.5217
1600 60oE 0.5000 044 0.3165 021 0.2727 011 0.4783
1700 75oE 0.2588 019 0.1367 013 0.1688 009 0.3913
1800 90oE 0.0000 011 0.0791 010 0.1299 008 0.3478
Analysis
We plotted the normalised solar intensity for different longitudes as shown below:
600 800 1000 1200 1400 1600 1800
Time
0
0.2
0.4
0.6
0.8
1
1.2
Normalised solar intensity
Plot Normalised solar intensity against time
0 degrees
15 degrees
30 degrees
45 degrees
60 degrees
75 degrees
Figure 2: Plot of normalised solar intensity against time for different longitudes.

Diurnal of Solar Intensity 6
Relationship investigation to more thoroughly test the equation using the equatorial data.
Time It/I12 from the experiment −cos ( 2 πt
24 )
0600 0.1007 0.000
0700 0.2446 0.2588
0800 0.5324 0.5000
0900 0.8273 0.7071
1000 0.9712 0.8660
1100 0.9856 0.9659
1200 1.0000 1.0000
1300 0.9065 0.9659
1400 0.7050 0.8660
1500 0.5683 0.7071
1600 0.3165 0.5000
Time It/I12 from the experiment −cos ( 2 πt
24 )
1700 0.1367 0.2588
1800 0.0791 0.0000

Diurnal of Solar Intensity 7
600 800 1000 1200 1400 1600 1800
Time
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalised solar intensity
Plot Normalised solar intensity against time
experimental
calculated
Figure 3: Plot of normalised solar intensity against time for different longitudes.
DISCUSSION
From the plots of the diurnal variation we can see that the incoming solar radiation begins at
sunrise from 0600Hr. The solar radiation is maximum at the noon 1200Hr and shuts off at sunset
1800Hr for both experimental and calculated values.
For a specified set of atmospheric settings, the irradiance at any point on the Ground's
surface is determined by the solar elevation. This intensifies in the course of the day from zero (or
its least value in the Arctic or Antarctic for the period of the summer) at beginning to its highest
value at noon, and then reduces in a specifically proportioned manner to zero (or the least value) at
dusk. The exact manner of the disparity with time of day is subject to the latitude, and on the solar
declination, at the time. The declination is the angle through which a given hemisphere (north or
south) is sloping towards the Sun. In summer it has a positive value, in winter a negative one; at

Diurnal of Solar Intensity 8
the spring and autumn equinoxes its value is zero. Its maximum value, positive or negative, is 23
°27'.
CORRELATION ANALYSIS
From the plot as shown in figure 3 for equatorial data using calculated values and
experimental values depicts that the two curves almost fit on top of each other. Therefore
cosinusoidal expression can be used to determine the amount of solar intensity at any point in time
on the earth surface. The slight deviation is as a result of the influence of other factors affecting
solar intensity on the earth surface i.e the sky clearance. Also the in-efficiencies of the equipment
used in the experiment contributed to the deviation.
CONCLUSION
From the experimental and theoretical results we can conclude equation 1 can be used to
describe the intensity of light at different times of the day. Since the experimental results were
exactly or close to the theoretical results. The deviation was a results of fault in the equipment
used to measure the light intensity.
From our experiment we can ascertain that daily co-sinusoidal diurnal variation in solar
intensity is the same pattern that is experienced in the seasonal cycle Every day is like a small
periodic cycle – Sun emissions most powerful around noon – As is the circumstance with the
seasons, the highest temperatures hold-up the peak arriving solar radioactivity. An accepting of the
daytime cycle in temperature necessitates comprehending diverse approaches of atmospheric
heating and cooling: Radiation, Conduction and Convection

Diurnal of Solar Intensity 9
Reference
IP, W.-H. (2006). Advances in geosciences. Volume 2, Volume 2. Singapore, World Scientific.
Available from: http://site.ebrary.com/id/10698784.ngapore,World Scientific Pub. Co. (Date of
Access; 11th May 2018)
Kitchen, D. E. (2016). Global Climate Change: Turning Knowledge Into Action. Old Tappan,
Taylor and Francis. Available from: http://public.eblib.com/choice/publicfullrecord.aspx?
p=4692497 . (Date of Access; 11th May 2018)
Mooney, H. A., & Zavaleta, E. (2016). Ecosystems of California. Boca Raton, FL, CRC Press.
Park, N., & Ip, W.-H. (2009). Advances in geosciences Vol. 11: Hydrological science (HS). Old
Tappan, Taylor and Francis.
University of Oklahoma, & United States. (2005). Toward a Diurnal Climatology of Cold-
Season Turbulence Statistics in Continental Stratocumulus as Observed by the Atmospheric
Radiation Millimeter- Wavelength Cloud Radars. Washington, D.C, United States. Dept. of
Energy. Available from: http://www.osti.gov/servlets/purl/841470-bulsav/native/. (Date of
Access; 11th May 2018)