Chapter 5
The ground surface solar radiation is an amalgamation of several layers that emit and absorb radiation of various wavelengths, and goes through different processes of assimilation and dispersion. Water droplets, dust and air molecules are the main cause of the dispersion while the absorption is due to ozone, oxygen, carbon dioxide, carbon monoxide, water vapors and nitrogen (Tiwari, 2002).
Accurate prediction of incident solar radiation at a given location is of great importance for any solar radiation based application or sizing models in PV power systems and building design applications. There are also other uses for such information in quantitative eco-physiological studies as the source of energy used in photosynthesis and evapotranspiration. It is important for tropical developing countries such as Sri
Lanka, where the annual average solar irradiation is in the range of 5.5 KWhm
-2 d
-1
and available throughout the year with low seasonal variations, to actively pursue the production of renewable energy through PV technology in the light of massive expenditure on imported fossil fuel. In Sri Lanka, less than 30% of the total energy demand is met by the fast depleting hydro power sources as at December 2008 (source:
Central Bank of Sri Lanka). Considering the growing popularity of small scale domestic stand alone photo voltaic (SAPV) systems used in rural Sri Lanka, where grid based power supply is not available and the continued interest shown by the agriculture sector for PV pumping systems, it is important and relevant to predict the amount of solar irradiation at a given location for optimum sizing to minimize the total cost due to high capital cost involved with the PV technology.
However, since solar radiation reaching the earth’s surface depends on the factors such as cloud cover and turbidity, which are not global in nature, on-site radiation data are essential. However, available solar radiation records in Sri Lanka are meager because of cost and complexity of standard apparatus, cost of maintenance and the difficulties involved in calibration of the instruments. Although attempts had been made to collect
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daily solar radiation data in several locations of the country using Actinographs, the method lasted only 3-4 years in many cases due to the above mentioned factors
(Punyawardena et al., 1996). In addition, accuracy of those data are questionable because Actinograph is less accurate than Angtrom type formula for estimating solar radiation from other weather parameters such as sunshine duration, temperature and humidity (Stanhill, 1965). It is therefore necessary to supplement solar radiation records by use of related information and approximate formulae.
In Sri Lanka, several radiation correlations have been employed but a general radiation model which can be reliable for estimation of solar energy for the three climatic zones
(wet, dry and intermediate) does not exist. As the incident terrestrial solar irradiation at a given location varying with geometrical parameters (such as latitude and altitude) and meteorological parameters (sunshine duration, relative humidity, ambient temperature and cloud cover amount), an approximate generalized model has to be selected from models developed for similar climatic conditions and validated for Sri Lanka identifying the parameters which most impact the outcome. It is also important to identify a model which will rely on easily obtainable data without using complex instrumentation and the resultant inaccuracies that can arise in measurements.
The Meteorological Department of Sri Lanka measures global solar radiation only at the
Colombo (6
0
54’N, 79
0
51E, H=10m) weather station while sunshine data are recorded using Campbell-Stokes sunshine recorders at four stations, namely, Colombo (Western
Province), Nuwara Eliya (6
0
50’N, 80
0
50’E, H=1500m) (Central Province),
Anuradhapura (8
0
20’N, 80
0
25’E. H=25m)(North-Central Province) and Hambantota
(6
0
10’N, 81
0
15’E, H=8m)(Southern Province). They are located in very different climatic regions where western province (WP) is humid and at low altitude, Central
Province (CP) is humid and at high altitude and North Central Province (NCP) and
Southern Provinces (SP) are dry and are at low altitudes. Even though Sri Lanka is a tropical island of latitudinal extent less than 4
0
and a land mass area of approximately
65000 km
2
, it is having a wide variation in geographical features so that estimating incident solar radiation using spatial interpolation techniques cannot be recommended for locations at distances greater than 50 km from weather stations.
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Spatial interpolation techniques allow estimation of solar radiation at any given point from nearby stations records (Suckling 1979, WMO 1981). The accuracy of this method depends on the mean grid size of the radiation measurement network and on the mean variability of weather conditions over the studied region. Weather variability may depend on many factors, especially the topography. Suckling (1985) studied the relationship between the extrapolation distance and the error in radiation estimates due to extrapolation for a large number of climatic regions. It is noted that in central
Europe, mean absolute errors due to extrapolation are a linear function of the extrapolation distance and are normally greater than 2 MJm
-2 d
-1
(Bindi, 1991)
The solar radiation that arrives at ground depends mainly on the day of the year, the latitude of the location and on the atmospheric transmittance, also termed as the clearness index K
T,
though ground albedo and elevation also having a smaller contribution. Predicting the variation of K
T, depending on the atmospheric conditions such as the cloudiness and turbidity, is the basis of the development of correlations for the calculation of incident solar radiation. Angstrom’s (1924) linear correlation to predict solar radiation from sunshine hours is one of the earliest correlations which attempted to estimate cloudiness in a given period by measuring sunshine duration at a given location. Many developments have been carried out on this model using long term data simulations and quadruple equations based on relative sunshine duration, which are not so location dependent, have been developed (Equations 2.29 and 2.30)..
Measuring cloud cover using satellite technology and ground based visual measurements has led to development of a set of correlations where calculations are based on cloud fraction (CF) in which cloudiness is measured in Octas. On reaching the earth’s surface, the incoming radiation is partly reflected and partly absorbed. Net radiation, corresponding to the overall balance of absorbed solar radiation and longwave exchange, is converted to the sum of sensible heat, latent heat and ground heat fluxes. During day time the earth’s surface receives radiative energy and both air and soil temperatures are expected to increase. At night, the surface loses energy by emitting radiation, especially during clear sky conditions. Hence, a clear day is expected to be generally characterized by an increased difference between night and day
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temperatures. On overcast days, the cloudiness reduces the incoming radiation during day time and also reduces the outgoing radiation at night. The difference between night and day temperatures is therefore expected to be reduced. Accordingly, the difference between the thermal ranges of two consecutive days is expected to be related to the difference in the mean sky transmittance (mean value for K
T
) of the same two days
(Bindi, 1984).
Of the many correlations that are used to predict incident solar radiation using weather parameters such as sunshine duration and temperature difference related to cloud cover, the high cost and low accuracy of measurement has limited the practice to a few weather stations. However, due to the high atmospheric humidity levels, the possibility of rain events when overcast conditions prevail is high in tropical countries. This is more so in tropical islands, where formation of convective low and middle clouds over the surrounding ocean cause frequent rain events, occurring through-out the year culminating in monsoons and inter-monsoons depending on the wind patterns and directions. As such, it is worthwhile to explore the possibility of calculating a value for
K
T
based on the number of rainy days and use it to predict the incident solar radiation which could be used as a low cost technique.
Daily sunshine duration data, daily maximum and minimum temperatures and daily rainfall data are obtained from the Meteorological Department of Sri Lanka for four locations, Colombo, Nuwara Eliya, Anuradhapura and Hambantota representing the
Wet zone, Central Hills, Intermediate and the Dry zones respectively. The zones are differentiated by the amount of rainfall each receives annually with the wet zone receiving over 2000 mm per year, intermediate zone receiving 1000mm to 2000 mm per year while the dry zone receiving less than 1000 mm per year (Meteorological
Department of Sri Lanka). The Central Hills can be grouped together with the wet zone where the precipitation levels are high at altitudes over 750 m.
It is also observed that once a correlation is selected to predict the solar radiation incident on a horizontal surface, an estimation of radiation incident on any surface of the building envelope is essential in calculating the radiation heat gain for power
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generating PV system designing and for solar thermal applications in engineering and architectural design process. Global horizontal irradiation data can be obtained from the meteorological department of Sri Lanka for major cities, which can be used for calculations within the respective region, but the users must get tilted plane irradiation using slope irradiation models. The models help analyzing the numerical relationship between global solar irradiation on horizontal surface and those on the tilted surface.
However, if presented in graphical form, a set of curves (each curve representing a calendar month) developed for the solar irradiation on tilted surface when the solar irradiation on horizontal surface is given, for tilt angles
β
, 0
0 ≤ β ≤
0
0 will be a useful design tool to determine the solar radiation levels on tilted surfaces at any time of the year for a given location.
•
To identify a generalized model for daily global radiation predictions in Sri
Lanka highlighting the most impacting parameters on the outcome.
•
To derive an inter-relationship between cloud fraction (CF) and the number of rainy days to arrive at a generalized value for Clearness Index (K
T
) in three main climatic zones of Sri Lanka.
•
To derive the climatology of the monthly mean global radiation with a higher degree of accuracy.
•
To develop a simplified method presented in graphical form based on the predictive model for the ratio of monthly mean solar radiation on a tilted surface
G m-
β to that of horizontal surface G m-h using correlation factors presented by
Liu–Jordan (1964).
The tilt ratio R m
= G m-
β
G m-h
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is plotted against the tilt angle
β
, for
β
= 0
0 to 90
0
for each calendar month for south facing surfaces in a region having a common clearness index, K
T that can be used as a design tool in solar radiation applications.
Global solar radiation values incident at a given location are measured using a variety of equipment such as pyronometers (Solarimeters) in many weather stations. In Sri Lanka, the National Meteorological Department obtains solar radiation measurements at its weather station located in Colombo, in the wet region of Sri Lanka. However, it should be noted that incident solar radiation is influenced by many geographical and meteorological factors and hence the accuracy of measured data are subject to wide variations depending on the level of sophistication and the length of measurement.
In developing CA vs Cs charts (chapter 4) and for calculating the power output in PV modules local measurement of Global Solar Radiation (GSR) is useful. For this purpose, to obtain approximate GSR values incident at a particular location, simplified measuring equipment such as Solarimeter which operates on PV technology can be used. If sufficient precautions are taken to prevent reflective radiation affecting the measured GSR values, these equipment would give fairly accurate figures. Nonavailability of measured GSR data from the National Meteorological Department for sites other than Colombo also necessitates the use of equipment such as Solarimeters.
In this research, a Solarimeter is used to measure incident GSR at sites located in
Colombo in the wet region and in Anuradhapura in the dry region of Sri Lanka.
Incident GSR values are recorded on hourly basis from 6.00 am to 6.00 pm for the full year of 2009 (Given in the annexure to the thesis) and integrated to obtain the daily
GSR (Given in Appendix 4.1). Validity of measured data are checked comparing to the corresponding data obtained from the National Meteorological Department of Sri Lanka for Colombo in 2009 and is given in Chart 5.3
164

165

Chart 5.2
: Monthly average daily GSR (measured) for Colombo, 2009
Monthly average daily global solar radiation figures for Sri Lanka have been predicted using geo-stationary satellite images and ground data from the Solar and Wind Energy
Resources Assessment (SWERA) project funded by the United Nations (UN) environment program. The images give an approximate global radiation values in monsoon and inter-monsoon periods which can be used for initial gross calculations in photo voltaic (PV) system design. However it is clear that some of the important meteorological parameters such as the minimum and maximum ambient temperature, which varies with geographical parameters such as altitude and presence of water bodies in the location is not accounted for. As Sri Lanka is a tropical island with a vast number of inland water bodies and rich vegetation, the impact of micro-climate should also be considered in predicting incident radiation.
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Figure 5.1
: Weather stations in Sri Lanka under the SWERA program
Figure 5.1 – 5.2 show the location of weather stations and the annual mean solar irradiation on a south facing flat plate collector tilted at latitude obtained from satellite technology (National Renewable Energy Laboratory, United States Department of
Energy).
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Figure 5.2
: Annual average solar radiation on a tilted plate at tilt angle equal to latitude
Monthly average daily GSR obtained from site measurement are compared to that of corresponding SWERA TMY data and is given in Chart 5.3
The variations and the non-availability of measuring equipment requires predicting of solar radiation values using correlations developed based on meteorological parameters.
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Chart 5.3
: Measured SR values (2009) against SWERA TMY data for Colombo, SL
Using equation 2.22 and 2.23, daily extra-terrestrial radiation, G o
can be calculated for a given location and equation 2.24 gives the maximum possible sunshine duration on a given day. Applying the calculated daily extraterrestrial radiation H
0 and maximum daily sunshine duration S
0
in the three correlations, for given daily sunshine duration values and temperature difference values, the daily average global solar radiation can be found. Daily average global radiation, daily average sunshine duration and daily values of maximum and minimum air temperature are obtained from four weather stations of the meteorological department of Sri Lanka located at Colombo (WP), Nuwara Eliya
(CP), Anuradhapura (NCP) and Hambantota (SP) representing the four major climatic regions of Sri Lanka, for a duration of one year (from 1 January 2008 to 31 December
2008). Plotting monthly average daily incident solar radiation for Colombo, Nuwara
Eliya, Anuradhapura and Hambantota, clearly shows that data obtained from
Angstrom’s linear correlation is closely compatible with SWERA TMY data and hence can be generally accepted to predict solar radiation levels in different climates of Sri
Lanka (Chart 5.4-5.7) Further, data obtained from the three correlations are compared with SWERA (Solar and Wind Energy Resource Assessment) TMY data along with statistical error parameters RMSE and MBE for compatibility (Table 5.1)
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Chart 5.4
: Global SR in Colombo Chart 5.5
: Global SR in N’Eliya
Chart 5.6
: Global SR in A’pura Chart 5.7
: Global SR in H’tota
Appendix 4.1 gives the measured data and calculations in obtaining global solar radiation values from empirical correlations. In the Charts 5.4 to 5.7, G m-h
TMY, G mh an, G m-h md and G m-h
TD denotes monthly average daily global radiation on a horizontal plane derived from SWERA Typical Meteorological Year data, from Angstrom
170

correlation, from modified Angstrom correlation and from Temperature Difference
(TD) correlation.
Table 5.1
: Statistical error parameters for the correlations compared with SWERA data
Station RMSE
Angstrom
Colombo 51.97
N’eliya 32.22
A’pura
H’tota
36.88
56.59
RMSE
Modified
54.75
52.36
43.78
61.35
RMSE
TD
34.21
39.92
68.14
68.50
MBE
Angstrom
0.115
0.83
1.18
0.85
MBE
Modified
1.25
2.76
2.24
1.67
MBE
TD
1.56
-0.81
1.74
2.81
SWERA project funded by the United Nations Environment Program, is developing high quality information on solar and wind energy resources in 14 developing countries including Sri Lanka. SWERA project provide typical year data for solar radiation and can be taken as highly accurate for validations and comparisons against locally collected data.
Table 5.1 demonstrates that Angstrom’s linear correlation with the lowest error parameters is the most suitable correlation, among the studied correlations, to be used to predict solar radiation in Sri Lanka.
It can be seen from the Charts 5.4 to 5.7 that the curve representing Angstroms equation with parameters developed for Visakhapatnam in South India generally follows the
SWERA solar radiation data curve for all four climatic regions in Sri Lanka. However, the percentage variation of incident radiation from SWERA data (Table 5.2) indicate that in all four locations, predictive figures over-estimate the SWERA data figures in the range of 5% to 30% from March to August while under-estimating by 1% to 40% from October to February. The minimum percentage variations in March-April and
September-October, when the sun path crosses the equator, indicate that the variations are more likely due to meteorological factors rather than geographical factors.
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Table 5.2
: % variation of predicted radiation from Angstrom model to SWERA data
Region Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Colombo 22.7 17.4 -9.9 -13 -18.1 -30.5 -26.6 -16.9 3.2 6.9 22.4 35
N'Eliya 9.8 5.4 -21.7 -12.6 -12.7 -28.9 -28.9 -16.3 4.6 0.2 14.6 31.8
A'pura
H'tota
23.4 19.1 -10.7
39.6 16.4
-7.9 -5.7 -27.1 -25.9 -18.9
-4.8 -18.1 -17.1 -29.7 -26.4 -22.6
3.7 -
2.4
- -
2.8 20.8 36.7
As for a given location meteorological parameters vary temporally and it is important to simulate data over a considerable period of time (over 50 years or so) to identify seasonal patterns which could then be used to calculate climatic parameters such as the clearness index K
T
. From Table 5.2 the percentage variations indicate a relationship to cloud cover over the regions considered over-estimating or under-estimating K
T
when the declination angle is greater. However, due to temporal variability of the meteorological parameters, accurate predictions of incident solar radiation can only be obtained by simulating long term weather data as demonstrated by Chart 5.2. Measured monthly average daily global radiation data for Colombo for the year 2009 are plotted against corresponding SWERA data in Chart 5.3. The clear deviation of the measured data from the SWERA data reiterates the necessity of long term data and as such
Angstrom’s linear equation could produce better results if at least 25 years of longer time series data are used.
In addition, if accurate long term weather data are available, empirical coefficients a and b for Angstrom’s correlation can be calculated specifically for Sri Lankan climatic regions using data fitting techniques. It should be noted that, though empirical coefficients developed for Visakhapatnam is selected primarily due to geographical proxiness, climatic conditions of the two regions show clear disparity due to topography and the unique monsoon patterns experienced by tropical islands to that of subcontinent regions. As such, equation 2.28 can be considered as a gross approximation of a correlation to predict solar radiation for Sri Lanka in the absence of developed empirical coefficients due to lack of long term weather data. Therefore, it is important to adopt equation 2.28, generalized for Sri Lanka, with a knowledge of percentage variation of data calculated from the correlation, to that of measured data.
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Chart 5.8
: Radiation from SWERA TY data Chart 5.9
: Radiation from Angstrom
model
The Charts 5.8 and 5.9 depict the monthly average daily incident global radiation on a horizontal surface obtained using data from SWERA data set and from Angstrom’s correlation. From the Charts, it can be clearly identified that the locations Colombo and Nuwara Eliya, which are in the wet region of the country (annual rainfall over 2000 mm) with frequent cloud cover, depressing the incident radiation more than that in the dry region (annual rainfall less than 2000 mm). As such mean radiation values are established in both SWERA data and Angtrom scenarios as shown in the Charts 5.10 and 5.11. Figure 5.3 shows the wet dry regions of Sri Lanka (source: Meteorological department of Sri Lanka)
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Figure 5.3
: Climatic zones of Sri Lanka (annual average rainfall)
174

Chart 5.10
: Mean SR for wet and dry regions Chart 5.11: Mean SR for wet and dry
(SWERA data) regions (Angstrom correlation)
Comparing measured data for the wet and dry regions with the corresponding data from
Angstrom model gives a clearer parallels as shown in Charts 5.12 and 5.13
Chart 5.12
: SWERA (wet) against Angtrom Chart 5.13
: SWERA (dry) against
(Wet) Angtrom (dry)
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Chart 5.10 is obtained by plotting the monthly average daily incident GSR for Colombo and Nuwara Eliya representing the wet region of Sri Lanka and Anuradhapura and
Hambantota representing the dry region. The GSR values are from SWERA TMY data base for Sri Lanka. Similarly, Chart 5.11 is obtained by using the Angstrom correlation with clearness index K
T
calculated using regression coefficients corresponding to that of
Visakhapatnam in South India to calculate the monthly average daily GSR for the two main climatic regions.
The calculations are given in Appendix 4.3
Table 5.3 depicts the percentage variation of incident solar radiation for the two regions compared with the corresponding mean measured data.
Wet
Dry
Table 5.3
: Percentage variation of mean radiation from Angstrom model to mean
SWERA data
Region Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
16.4 11.3 -15.9 -12.7 -15.3 -29.9 -27.8 -16.5 3.8
31.7 17.9 -8.5 -13.2 -11.4 -28.3 -26.3 -20.7 2.9
3.7 18.4 33.2
3.4 24 45.2
The two curves obtained from Angstrom correlation show consistency in variation with respect to SWERA data. The near 30% under-estimated radiation values reflect the low
K
T
values calculated from Angstrom’s correlation from March to August as the first inter-monsoonal rains (March to May) and south-west monsoons (June to September) set in and fast moving low and middle clouds interfering in the accuracy of recorded sunshine durations. Further, this period coincides with the summer time in the northern hemisphere and as such the day lengths are longer than that of during November to
February. The over-estimation of radiation values from November to February could be attributed to a less cloudy period in an otherwise wet season in the dry region in 2009 emphasizing the need to simulate data over a longer period of time. Shorter day lengths in the period could also increase the clearness index values marginally. The formation of high clouds, particularly in the mornings, due to lower humidity levels and cooler
176

night time temperatures during December to February also contribute to the decreased intensity of solar radiation impacting the accuracy of calculated radiation values using sunshine duration. This study therefore strengthens the argument that outcome from the
Angstrom’s correlation is location dependent and as such the need to define equation parameters developed through long term simulation of sunshine data particularly for regions of dissimilar climatic conditions.
It is shown that Angstrom’s linear correlation can be generally accepted for predicting incident global solar radiation levels in Sri Lanka. However, since the sunshine duration is related to cloud cover, it is worthwhile to explore the relationship between rainfall and K
T as cloud cover in the tropics is closely related to rain events due to high perceptible water content in the atmosphere. Besides, although Angstrom type models have been based on the clear sky conditions, there is ample evidence that sufficient number of dust, haze and other types of non-Rayleigh particles exist even in clearest cases of the natural atmosphere to produce significant scattering and absorption of incoming solar radiation (Coulson, 1975). It has also been shown that tropical atmosphere is rich in turbid particles, especially during hot and dry periods (Mani et al.,
1973).
Therefore, determining clearness index values for clear and overcast days based on the amount of water vapor and turbidity in the atmosphere as modeled by Bindi (1991) can be considered as appropriate. From equations 2.33 to 2.35 and taking w = 5 representing the tropical hum id conditions and β = 0.1 to represent the urban nature of the weather station location, clearness index for a clear day (K
T
)
C is calculated to be 0.68.
(Appendix 4.4) Taking cc=1 for low and middle clouds which are the most prevalent and rain causing in Sri Lanka, clearness index for an overcast day (K
T
)
O is calculated to be 0.28. The clearness index, K
T
was calculated using equations 2.33, 2.34 and 2.35 for all locations using rainfall data where a rainy day is considered when rainfall in 24 hours is greater than 0.3 mm.
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Angtrom’s (1924) correlation, which is the most commonly used correlation to predict solar radiation in Sri Lanka, is used for comparison of results with correlation constants developed for Visakhapatnam (Latitude 10
0
Longitude 74
0
E) in South India mainly due to geographical similarities in the absence of correlation constants developed for Sri
Lanka.
Charts 5.14 to 5.17 show monthly average daily incident solar radiation from SWERA for the four stations compared with the corresponding values from Angstrom’s and
Rainfall (RF) models. In this case G m-h
TMY, G m-h
an and G m-h
r denote the monthly average daily global radiation on a horizontal surface obtained from SWERA data base,
Angstrom and Rainfall (RF) correlations respectively.
Chart 5.14
: Comparison of GSR for
Colombo
Chart 5.15
: Comparison of GSR for
N’Eliya
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Chart 5.16
: Comparison of GSR for Chart 5.17
: Comparison of GSR for H’tota
A’pura
Calculations pertaining to K
T
on clear and overcast days are given in Appendix 4.3
From the charts and statistical parameters it can be inferred that Rainfall (RF) model is more closely compatible with Angstrom’s model in the intermediate and dry zones where the rainfall is seasonal and the distinction between clear and overcast days are more pronounced. Since the wet and the high altitude regions experience cloudy but non rainy days in between clear and overcast days, a longer time series of data is required to accommodate the K
T
values between the two extremes. The importance of such is depicted in Charts 5.18 to 5.21 where 10 day moving average values for daily clearness index, K
T
developed from the two models are plotted for all four stations. The moving average method uses a technique where the average value of a number of consecutive data are averaged and developing a progression of average values so that a vastly higher number of data can be obtained from a limited number of data.
179

Chart 5.18
: Angstrom vs ARF model (Col) Chart 5.19
: Angstrom vs ARF model (NE)
Chart 5.20
: Angstrom vs ARF model (A) Chart 5.21
: Angstrom vs ARF model (H)
Therefore, it can be concluded that RF model can be employed for any location in Sri
Lanka where monthly average daily solar radiation for a particular month can be obtained by calculating K
T
by simply averaging corresponding clearness index values for rainy and non rainy days for the respective month. However, it can be seen that much accurate predictions can be made if the data on the number of rainy days per
180

month can be calculated over a period of minimum 5 years. Chart 5.22 to 5.25 show monthly averaged daily values of incident solar radiation calculated with monthly average K
T
values (RF model) averaged over 5 years against monthly average daily solar radiation values from SWERA data for the four stations.
Chart 5.22
: Comparison of GSR(RF), Col. Chart 5.23
: Comparison of GSR(RF),NE
Chart 5.24: Comparison of GSR(RF), Chart 5.25
: Comparison of GSR(RF),
A’pura H’tota
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Charts 5.22 to 5.25 clearly demonstrate that when a longer time span is used to calculate the average number of rainy days, the increase in compatibility with corresponding
SWERA data. Table 5.4 shows that global radiation values obtained from the Average
Rainfall Model (ARF) displaying close compatibility with the corresponding values obtained from the Angstroms model. The statistical parameters Root Mean Square
Error (RMSE) and Mean Biased Error (MBE) between the values obtained from the two correlations clearly show that the values from ARF model can be used in place of
Angstrom model.
Table 5.4
: Statistical error parameters for the two correlations
Region Correlation RMSE MBE
Colombo Angstr 52.03 0.12
ARF
N'Eliya Angstr
ARF
A'pura Angstr
ARF
H'tota Angstr
ARF
76.59
32.26
31.69
31.97
39.52
69.31
63.33
2.01
0.83
0.92
0.89
-0.09
0.33
1.39
The percentage variation of global radiation calculated from the average rainfall (ARF) model from the corresponding SWERA data are shown in Table 5.5. It is clear that a distinctive pattern exists for individual locations but generalization of the pattern into a broader region is not possible.
Table 5.5
: Percentage deviation of Gm-h (ARF) from corresponding SWERA data
Station Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Colomb o
-26.1 -21.3 5.9 21.8 38.6 36.5 30.8 20.7 16.7 27.9 -1.4 -20.7
N'Eliya -15.9 -19.4 5.0 20.2 20.9 24.5 30.9 10.7 2.6 11.2 3.6 -24.1
A'pura -25.2 -24.3 3.14 17.9 15.8 17.7 22.2 12.2 0.18 22.1 0.92 -8.2
H'tota -8.3 1.48 15.1 20.5 27.0 30.0 32.3 29.2 18.4 17.8 -1.4 -10.4
Charts 5.26 and 5.27 show the monthly average daily global radiation for the four locations obtained from SWERA data and ARF model indicating that in both cases sites
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located in the wet region displaying lower radiation levels after the end of the North-
East monsoon period, i.e. from March to October.
Chart 5.26
: Gm-h SWERA for all locations Chart 5.27
: Gm-h ARF for all locations
This phenomenon is due to the distinctive nature of the North-East monsoon where rainfall is primarily from low and middle cloud formations due to low pressure systems in the Bay of Bengal. The winds also blow from the North across the Indian subcontinent land mass causing very little or no rain. As a result, historically there are more clear days in the N-E monsoon compared to the South-West (S-W) monsoon where the rain causing clouds are moving in from the south-Western direction across vast expanse of ocean and the days are cloudier with frequent rainy and overcast days.
As such, the sites located in the dry region which depend primarily on the N-E monsoon for rain receives more solar radiation than the sites in the wet region. It is also observed that the solar radiation values for sites in the wet region, except the locations in the central hills, are higher than that of sites in the dry region during the N-E monsoon.
This is due to the rain clouds losing their potential for rain when moving across the semi-arid North-Central plains in to the wet region. The behavior of the curves with regard to rainfall can be further explained as follows: During September to November, due to convectional activity, North-East monsoonal winds and formation of depressions in Bay of Bengal thick and dense clouds (Cumulus and Cumulonimbus) are common
183

particularly in the dry region. Therefore, absorbance and transmittance by clouds during this period of the year may be much higher than what is expected. Although first half of the year consists of a minor rainy season during March and April, development of thick and dense clouds is rare because of the weak convectional nature of the first inter-monsoonal rains (Suppaiah, 1989). Thus, influence of clouds for downward solar radiation is minimal during the first half of the year.
The highest radiation values of around 20 MJ m
-2
day
-1
have been obtained throughout the period of February to April, followed by a peculiar depression in July. Despite being a rainy month, January solar radiation values are observed to be higher than that of the values in November and December (Punyawardena et al., 1996). The high insolation during February to April is invariably due to increased number of bright sunshine hours per day. Naturally, solar radiation in March and April must have lower values compared to February value because these two months have been categorized as a convectional rainy season.
Higher insolation in March and April could also be due to the fact that the relative position of the earth with respect to sun. As the sun is directly overhead of the equator on March 21 (Vernal Equinox), during the period of March-April sun rays are nearly perpendicular to the earth surface of the equatorial regions. Since vertical incidence of sunrays always bring more insolation intensity than inclined incidence, solar radiation that reaches earth’s surface during these two months are comparatively higher than in
February (Punyawardena et al., 1996). During May to September during the South-
West monsoons the dry region shows a marked increase in solar radiation over the wet region. This can be explained as the effect of the central highland acting as an orographic barrier to South-West monsoonal blowing making it a dry desiccating wind when reaching the dry region. In general, the effect of the two inter-monsoonal rains on the incident solar radiation can be taken as low, as these convectional rains mostly occur as late afternoon, short duration, high intensity thunder storms.
The peculiar depression of solar radiation values during the June-July months can be explained astronomically. Since the orbit of the earth is elliptical, the sun-earth distance
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varies throughout the year and causes a variation of the amount of solar energy reaching the earth surface. The sun-earth distance reaches its maximum on July 3 (Alphelion), its minimum on January 3 (Perihelion). Although the eccentricity of the orbit is small
(only 0.01673), there is about 7% difference in the solar energy flux at the top of the atmosphere between Perihelion and Aphelion (Coulson, 1975). Therefore, the flux is highest in early January and lowest in early July. Hence, reduced solar radiation interception during the period of June-July could be due to the earth’s position with respect to the sun. Despite being a rainy month, higher solar radiation during January could be due to relatively high extraterrestrial flux compared to other months.
Therefore, it is justified to demarcate the landmass of Sri Lanka broadly into two regions where the area encompassing the South-West and the Central hills receiving over 2000 mm of rain annually as the wet region and the combination of the intermediate zone and the dry zone receiving less than 2000 mm of rain per year defined as the dry region.
Charts 5.28 and 5.29 depicts the mean monthly average daily global radiation values for the wet and dry regions obtained using SWERA and ARF model data.
Chart 5.28
: Gm-h mean SWERA for all Chart 5.29
: Gm-h mean ARF for all locations locations
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Table 5.6 shows the percentage variation of mean monthly average daily global radiation values for the wet and dry regions obtained from ARF model with the corresponding values of SWERA data which clearly show that a distinctive genralized pattern can be established.
Table 5.6
: Percentage deviation of mean wet & dry values of Gm-h from mean wet & dry values of SWERA data
Region Jan Feb Mar Apr Jun Jul Aug Sep Oct Nov Dec
Wet
Dry
-21.2 -20.4 5.5 21.0 30.1 31.1 30.8 16.1 10.2 20.1 0.9 -22.3
-26.2 19.9 6.1 18.7 20.1 24.7 26.4 18.4 5.4 15.2 -5.4 -20.4
The model can be further improved by closely examining the cloud formation patterns, wind directions and seasonal variations of weather in Sri Lanka. Though Sri Lanka is located close to the equator, as a country located in the northern- hemisphere, it still experiences summer and wintry conditions albeit mildly. As such, from December to
February the day length is 3% shorter than the average of 12 hours and humidity is relatively low leading to higher percentage of high clouds formation in the cooler upper atmosphere. These high clouds, though mostly producing no rain or insignificant rainfall as trace precipitations or rain events less than 1 mm, still prevent significant amount of solar radiation penetration particularly during morning hours. Therefore when calculating the number of days in which rainfall events occur for the RF model, trace precipitation events as well as the rainfall events less than 1mm should also be taken into account during December – February period. The summer period from June to August on the other hand is 3% longer in day length from the average and the southwesterly wind with high humidity forms a higher percentage of isolated low and middle clouds, though causing minor rain events not blocking solar penetration for a prolonged period of time. Therefore, when the rain event is less than 1 mm per day, such days can be generally considered as clear days with considerable accuracy. As such, during the period from June to August only the days that produce more than 1mm of rain per day can be counted as rainy days for the RF model. For the in-between seasons precipitations more than 0.3 mm per day can be considered as rain events.
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Further, as Sri Lanka is an island in the tropics, it is observed that more than 50% of the rain events during March to October occuring in the night time due to increased ground temperatures and the resultant wind direction from ocean to the inland, causing more rain events in the night and early morning. Therefore, a considerable improvement in the RF model can be envisaged if only the day time rain events are considered as shown in Chart 5.30. Chart 5.30 shows the monthly average daily global radiation obtained from RF model with 24 hour rain events and non-adjusted for seasonal climate factors,
ARF model with 5 year average rainy days with 24 hour rain events and non-adjusted for seasonal climate factors and the seasonally adjusted RF model with only the day time rain events counted compared with SWERA data for Colombo. It can be seen that the adjusted RF model displays the best compatibility with SWERA data. A further improvement can be envisaged if the adjusted RF model can be provided with data from a longer historical time series of 5 or 10 years of day time rain events.
Chart 5.30
: Comparison of RF model outcomes with SWERA data for C’bo
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In order to ascertain the usability of the Rain Fall (RF) model in predicting GSR values for a given location, it is important to compare such with values obtained from direct measurement of GSR at site. In this case, hourly measured GSR data obtained at site using a Solarimeter in the year 2009 are used to obtain monthly average daily values for the site in Colombo in the wet region of Sri Lanka. The values obtained from direct measurement, rainfall (RF) model (using rainfall data obtained for a single year – in this case the year 2009) and the monthly average daily GSR values obtained from SWERA
TMY data base are plotted to compare the variations and is given by Chart 5.31
Chart 5.31
: Comparison of RF model outcomes with site measured data for C’bo
It is apparent from the Chart 5.31 that the data obtained using Rain Fall (RF) correlation model is showing wide variations from that of site measured GSR values. In fact, for the month of July the variation is almost 53% indicating that the RF model cannot be successfully used in its simpler form. Therefore, as indicated in Chart 5.30, the adjusted average RF model should be used in the absence of suitable equipment to measure solar radiation at a given site. It can also be discerned that if the rainfall figures can be obtained for more than 5 years, the radiation values obtained from the RF correlation could come closer to that of measured values.
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Solar energy has been identified as the most viable source of renewable energy to replace carbon emitting fossil fuels, especially for tropical and sub tropical countries.
However, solar radiation incident at any given site is a variable influenced by the geometrical parameters such as the latitude and altitude, and the meteorological parameters such as the cloud cover, relative humidity and ambient temperature.
Further, the sun azimuth and elevation angles, change in accordance with the change of time.
From equations 2.37, 2.38 and 2.39 tilt factors for beam, diffuse and reflective radiation
R b
, R d, and R r are calculated for tilt angle
β
= 0
0 to 90
0
in 15
0
intervals. Using equation
2.42, K
T
is calculated for each month from Typical Meteorological Year (TMY) data from Solar and Wind Energy Resources Assessment (SWERA) project funded by the
United Nations (UN) environment program. Monthly average daily global radiation on horizontal surface, G m-h, at four different sites in the three main climatic zones and the central hills of Sri Lanka and applied to equation 2.41 to obtain the ratio between monthly average daily diffuse radiation to monthly average daily global radiation on a horizontal surface. Using equation 2.36 the tilt factor R m
is calculated for the four sites and plotted as shown in Charts 5.32 to 5.35. The measured values of G m-h
and D m-h
are also obtained from SWERA data for greater accuracy and reliability.
Calculations pertaining to tilt factor are given in Appendix 4.5
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Chart 5.32
: Tilt factor, Rm for Colombo, Wet zone
Chart 5.33
: Tilt factor, Rm for Nuwara Eliya, Wet zone-Central Hills
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Chart 5.34
: Tilt factor, Rm for Anuradhapura, Intermediate zone
Chart 5.35
: Tilt factor, Rm for Hambantota, Dry zone
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Considering the fluctuations of the monthly ratio all year around, the Charts 5.32 to
5.35 illustrate the monthly ratios of south slope irradiation for surfaces with inclinations from 0
0
(the horizontal) to 90
0
(vertical) and azimuth orientations 0
0
(south) for the four locations representing the different climatic zones of Sri Lanka and each of the curve represents monthly irradiation ratio respectively. The monthly slope irradiation ratio values decrease according to the increasing inclination for south orientation. The upper most curve comprises ratio for December while the lowest curve represents June. The ratio for December with lower inclination of sun path in winter time are larger than the ratio for July with higher inclination of sun path in summer time in response to inclinations from 0
0
to 90
0
. It can be seen that R m
is greater than 1.0 in October to
February when the tilt angle is below 90
0
, indicating that the tilted surface receives more incident global radiation than the corresponding horizontal surface from sunlight with lower inclination of sun path in winter time.. It is also observed from the charts that R m
is the maximum in December when tilt angle is 45
0
and minimum in June when the tilt angle is 90
0
for all four locations. Table 5.7
Table 5.7
: Percentage variation of tilt factor R m
from 1.0 for the four stations
Station
β
=30
0 β
=30
0 β
=45
0 β
=45
0 β
=90
0
(December) (June)
Colombo 17.45
N’eliya 15.62
A’pura
H’tota
17.13
16.39
-21.18
-21.18
-24.49
-24.04
(December)
19.09
16.76
18.72
17.45
((June)
-35.26
-35.26
-40.59
-39.53
(June)
-80.77
-79.96
-91.08
-87.82
Chart 5.36 displays the monthly average daily global radiation incident on a south facing tilted surface G m-
β, with a tilt angle equal to the latitude of the location, for the four locations representing the different climatic zones of Sri Lanka. The values obtained are compared with the corresponding G m-
β values developed by the (National
Renewable Energy Laboratory (NREL) of the United States Department of Energy for
Sri Lanka simulating historical time series geographical and meteorological parameters using satellite technology and ground based measurements of meteorological
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parameters (Figures 5.4 to 5.6). During the North-East (NE) monsoon period from
December to February, for all four locations incident solar radiation on a south oriented surface at a tilt angle equal to the latitude of the corresponding location falls within the
NREL estimated range of 4.5 to 5.5 KWhm
-2 d
-1
(Figure 5.4). From May to September the corresponding solar radiation figures drop to 4 to 5 KWhm
-2 d
-1
as the South-West monsoon sets in (Figure 5.5). Figure 5.5 and 5.6 display the range of solar radiation in
KWhm
-2 d
-1
on a south facing surface with a tilt angle equal to the latitude during the two inter-monsoon periods showing compatibility with solar radiation values in Chart
5.36. These values reveal that the results of experimental verification are acceptable and the estimated method is practical for solar applications in building design. Chart 5.37 shows the incident solar radiation in MJm
-2 d
-1
on a south facing tilted surface at a tilt angle equal to 30
0
representing the majority of roof slopes in Sri Lanka.
Chart 5.36
: GSR on a south facing surface tilted at an angle equal to latitude
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Chart 5.37
: GSR on a south facing surface tilted at an angle equal to 30
0
5.6.1 Comparison of data from Collarez correlation with SWERA TMY values
Charts 5.38 – 5.41 show the monthly average daily ratio of diffuse to global radiation on a horizontal surface comparing values calculated by Collarez correlation with that of corresponding SWERA TMY data for Colombo, Nuwara Eliya, Anuradhapura and
Hambantota. Though the statistical error parameters RMSE and MBE between the two curves do not show much disparity (Table 5.8), clear deviations from the SWERA TMY data can be seen from April to October.
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Chart 5.38
: Colombo Chart 5.39
: Nuwara Eliya
Chart 5.40
: Anuradhapura Chart 5.41
: Hambantota
Table 5.8
: Statistical error parameters for D m-h
/G m-h,
Collarez vs SWERA
Station
Colombo
N’Eliya
A’pura
H’tota
RMSE
.002
.002
.008
.0002
MBE
.006
.0012
.004
.0005
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This is due to the unique weather pattern prevailing in Sri Lanka, particularly during the first inter-monsoonal and south-west monsoons, when frequent fast moving convective low clouds form interspersed with bright sunshine in between increasing K
T
. Therefore, though it is not significantly impacting the tilt factor R m
, a correction factor to the correlation developed by Collarez is recommended to obtain more accurate figures for
D m-h
/G m-h
ratio.
Figure 5.4: SR on tilted plate in NE monsoon
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Figure 5.5
: SR on tilted plate in 1 st
Inter-monsoon
197

Figure 5.6
: SR on tilted plate in SW monsoon
198

Figure 5.7
: SR on tilted plate in 2 nd
Inter-monsoon
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In the absense of a suitable correlation to predict incident global radiation at a given location, SWERA data developed through sattelite technology and certain ground measured data are used in PV and other solar related technological calculations.
However, SWERA data are available only for a limited number of locations and the fact that radiation data cannot be accurately interpolated over a distance more than 50 Km requires numerical predictive models to ascertain solar radiation values. While
Angtrom’s correlation can be generally used with correlation constants developed for similar Indian locations, the unique geographical and weather pattern particular to a tropical island nation like Sri Lanka need a more localised correlation with clearly quantified variations from SWERA data. It is also necessary to be able to predict solar radiation levels using widely available and short term data so that calculations can be cost effectively carried out and quick decisions can be made in designing.
From Table 5.6 very distinctive and similarly distributed percentage variation pattern can be identified for both wet and dry regions. The ARF model under-estimates
SWERA data from April to October reaching maximum levels in June/July while overestimating from November to February reaching minimum values in December-
January. The under-estimation occurs due to considering all rainy days as overcast days where from April to October rain events occur more in isolation interspersed with sun.
This is a direct result of convective low cloud formation in the southern indian ocean blown across at a higher speed from the South-West direction. The over-estimation during November to December occurs during the winter time for the northern hemisphere where non-rain forming high clouds prevail giving low values for K
T
in
SWERA data whereas in the ARF model such days are taken as clear sky days. As such an interpolative method to define K
T
values for days in between clear and overcast days can be employed to minimize the variations.
Charts show that the variation of the tilt factor, R m
is approximately the same for all four locations reflecting the fact that the latitude angle vary only by 3
0
for the length of the country. It also shows that the maximum increase in incident radiation occurs in
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December when the tilt angle is 45
0
and the minimum incident solar radiation occurs in
June on a vertical surface at all locations (Table 5.7). The marginal change in incident solar radiation in Nuwara Eliya can be attributed to the lower clearness index values increasing the diffuse component in global radiation due to frequent cloud cover. In fact the entire wet region (annual rainfall more than 2000 mm) displays a higher K
T values compared to the dry region and hence lower radiation levels.
201