Paper No. CSBE17057 Evaluation of Cloud Cover Based Model ... · The model uses cloud amount in...
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Paper No. CSBE17057
Evaluation of Cloud Cover Based Model for Simulation of Hourly Global Solar Radiation in Western Canada
Md Shamim Ahamed Ph.D. student, Environmental Engineering, University of Saskatchewan, Canada email:[email protected]
Huiqing Guo Professor, Mechanical Engineering, University of Saskatchewan, Canada
email: [email protected]
Karen Tanino Professor, Plant Science, University of Saskatchewan, Canada
email: [email protected]
Written for presentation at the CSBE/SCGAB 2017 Annual Conference
Canad Inns Polo Park, Winnipeg, MB 6-10 August 2017
ABSTRACT: The solar radiation data are very important for building thermal performance and solar application analysis. However, the continuous time series solar radiation data are not available for the most part of the world and the measured data available from a solar station become less accurate for a given location beyond 50 km from the measuring station. Cloud cover based solar radiation models (CRM) are very simple and convenient as the models require only cloud cover data which are mostly available from the meteorological stations. In this study, the performance of a cloud cover based solar radiation model (Kasten-Czeplak model) with original and locally fitted coefficient were evaluated for estimating the hourly global solar radiation for four different locations of Western Canada. The average R2, MBE, and RMSE are 0.82, -28.1 W m-2, and 109 W m-2, respectively, for the model with original coefficients, and 0.89, 1.2 W m-2, 76 W m-2 with locally fitted coefficients. Results show that Kasten-Czeplak model quit successfully estimate the hourly solar radiation of four different locations in Western Canada, but the use of local coefficients significantly improves the
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model accuracy. Also, the analysis of model performance indicates that the model with original coefficients has limited accuracy under intermediate cloud cover condition.
Keywords: global solar radiation, Kasten-Czeplak model, cloud cover, local coefficient.
1.0 INTRODUCTION
Continuous time series data of solar radiation are very important for solar energy application.
However, the time series solar radiation data are mainly available in the developed countries,
whereas very limited resources in the developing countries. Also, the measured data available from
a solar station become less accurate for a given location beyond 50 km from the measuring station
(Younes & Muneer, 2007). The surface weather stations which recording the solar radiation data is
very small compared to the number of meteorological stations that record meteorological data
including temperature, precipitation, relative humidity, sunshine duration, and cloud cover. In
addition, the observational records for solar radiation are usually short and often have missing data
because of equipment malfunction (Cutforth & Judiesch, 2007). Therefore, many empirical models
were developed for simulation of solar radiation by using more commonly available data such as
sunshine duration, temperature, precipitation, relative humidity, and cloud cover. Solar radiation
models (Bakirci, 2008; Trnka et al., 2005) based on sunshine duration data are considered to be
more reliable because the sunshine data are precisely recorded by a sunshine recorder whereas
cloud cover data based on a visual estimation and satellite image. The variation of solar insolation
explained by sunshine duration is 70-85% whereas 50% quoted against the cloud amount (Bennett,
1969). However, sunshine data are not easily available from the weather stations. The temperature-
based models (Spokas & Forcella, 2006; Supit & van Kappel, 1998) are a convenient tool for
estimating solar radiation because of the wide availability of air temperature data, but accuracy cloud
be limited for hourly simulation as these models estimate the solar radiation based on the daily
maximum and minimum temperature. Previous studies (El-Metwally, 2004; Younes & Muneer, 2007)
shows that the performance of the solar radiation models varies significantly depending on the
location of the study area. Hence, it is very important to evaluate the performance of these models
against the local data set, and also need to estimate the local coefficients for solar radiation
estimation. De Jong & Stewart (1993) estimated the daily solar radiation of Western Canada by using
temperature and precipitation data. Similarly, Barr et al. (1996) evaluated the solar radiation model
by using sunshine duration and temperature. Kahimba et al. (2009) evaluated the SolarCalc model
developed by Spokas & Forcella (2006) for estimating the hourly incoming solar radiation by daily
total precipitation (mm), and daily maximum and minimum air temperatures. Jeong et al. (2016) used
several empirical models to simulate daily solar radiation in Quebec using two meteorological input
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such as daily temperature and relative humidity. To the best of our knowledge, no previous studies
are found related to the prediction of solar radiation from cloud cover data in Canada. Therefore, the
objective of this study is to evaluate the selected cloud cover based solar radiation models for
different locations in Western Canada.
2.0 CLOUD COVER SOLAR RADIATION (CRM) MODELS Several empirical models have been developed for estimating the daily/hourly solar radiation using
cloud cover information. Most of these models (Badescu, 1999; Bennett, 1969; Black, 1956; Sarkar,
2016) are used for estimating the daily average total solar radiation using cover cloud data. Kasten
& Czeplak (1980) developed a cloud cover solar radiation model by using 10 years (1964–1973) of
continuous hourly data from Hamburg, Germany. The model uses cloud amount in Octas which
ranging from 0-8, and Zero Octas indicate a completely clear sky and 8 Octas designates a
completely overcast sky. Younes & Muneer (2007) evaluated the performance of several cloud cover
based models for estimation of hourly global solar radiation for different location over the world.
Results show that the Kasten and Czeplak model performed relatively better than the other models.
Kasten-Czeplak model has been tested against the dataset for different locations over the world, but
the model not been evaluated against the data set from high northern latitudes. Therefore, the Kasten
and Czeplak model with the original coefficient and the locally fitted coefficient were considered for
evaluating their performance against the dataset of four different location in Western Canada. For
this analysis, the original Kasten and Czeplak model is referred to as M1. According to the Kasten
& Czeplak (1980), the global solar radiation (Ig) on the horizontal surface under cloud cover condition
can be given as follows:
I" = I"$(1 − 0.75,-
../) (1)
Where Igc clear sky global solar radiation (W m-2); N is the cloud cover (Octas), ⍺ is the solar altitude
angle (degrees).
The Kasten and Czeplak model with locally fitted coefficients can be written as follows:
I" = I"$(1 − A,-
3) (2)
Where A and B are the locally fitted coefficient. This model is referred to as M2 for this analysis.
The Katen-Czeplak model estimates the clear sky solar radiation based on empirical equations
related to the solar altitude angle which is apparently very simple as the model avoids the
atmospheric attenuation of solar radiation (Orsini et al., 2002). The clear sky solar radiation depends
on the solar altitude angle and the atmospheric turbidity. By considering the atmospheric turbidity,
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the clear sky global solar radiation on the horizontal surfaces, and the direct normal irradiance on
any terrestrial region can be calculated as follows (Tiwari, 2003):
I"$ = I, cos θ8 +:.(I<= − I,) cos θ8 (4)
I, = I<= expABC
D.EFE./GHI⍺, ⍺ = 90 − θ8 (5)
According to Spencer (1971), the extraterrestrial heat from the sun on a surface normal to the sun’s
ray on the nth day of the year is given by:
I<= = IG$ 1 + 0.033× cos 360× IA..OP
(6)
3.0 METEOROLOGICAL DATA FOR THE STUDY Figure-1 shows the selected location of the study area in Western Canada including Saskatoon,
Winnipeg, Fort McMurray, and Vancouver. The metrological data including solar radiation and cloud
cover data for the study was collected from the National Solar Radiation Data Base (NSRDB). Three
years of data from 2013-2015 were considered for estimating the local coefficients. The local
coefficients were fitted against the local data set for all selected locations. The details of geographical
information of the selected locations and the estimated local coefficients are listed in Table-1.
Figure 1. Map of the study area with the location of the satiations.
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Table 1. Description of sample location in Western Canada and local coefficients of the Kasten-
Czeplak model.
Locations Latitude
(˚N)
Longitude
(˚W)
Altitude
(m)
Coefficient,
A
Coefficient,
B
Data period
Saskatoon, SK 52.13 106.74 477 0.63 0.62 2013-2015
Winnipeg, MB 49.85 96.98 231 0.59 0.62 2013-2015
Fort McMurray, AB 56.73 111.38 261 0.62 0.56 2013-2015
Vancouver, BC 49.29 123.14 15 0.71 0.55 2013-2015
4.0 STATISTICAL PARAMETER FOR MODEL EVALUATIONS
The statistical indices including the coefficient of determination (R2), mean bias error (MBE), root
mean square error (RMSE), and t-statistics (t-stat) were considered to evaluate the adequacy of the
cloud cover based solar radiation model. The MBE can be used to figure out the tendency of
overestimation or underestimation of the model, and the RMSE can be used to figure out the degree
of dispersion of the estimated radiation against the measured radiation (Kim et al., 2014). The
negative value of MBE show the overestimation while the positive indicates underestimation, and low
values of RMSE and t-stat are desirable. The MBE, RMSE, and t-stat can be estimated by the
following equations:
MBE = TUATVI
(7)
RMSE = (TUATV)Y
Z (8)
t − stat = ]3^Y(IA:)_]`^YA]3^Y
(9)
where Io is the measured solar radiation (W m-2); and Ie is the estimated solar radiation (W m-2); n is
the number of data points.
5.0 STATISTICAL PARAMETER FOR MODEL EVALUATIONS
5.1 Cloud cover
Three years of hourly cloud cover data downloaded from the NSRDB for four cities of Western
Canada were analyzed and the frequency of occurrence is shown in Figure-2. The peak frequency
of occurrence is observed at the value of 0 and 4 Octas. The maximum occurrence about 29.6% is
observed at the value of 0 Octa in Vancouver, and the minimum 21.5% in Fort McMurray. The peak
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frequency of 4 Octa accounting 30% is observed in Fort McMurray and the minimum value of 24% in
Winnipeg. The second most frequent cloud cover is 7 Octa, accounting for 26.75%, 24.05%, 29.95%,
and 26.25%, respectively, for Saskatoon, Winnipeg, Fort McMurray, and Vancouver. The least
frequency of occurrence of cloud cover about 1.0% is observed for the value of 2 and 5 Octas.
Figure 2. The frequency of occurrence of cloud cover.
5.1 Global solar radiation The estimated global solar radiation from the Kasten-Czeplak model was compared with the solar
radiation data of 2015 from the NSRDB. Figure 4-7 shows the comparative performance of the Kasten
and Czeplak model with original and locally fitted coefficients for the four different cities of Western
Canada. The scatter plots indicate that the cloud cover model with locally fitted coefficients performs
well as compared the model with the original coefficient. Also, the figures show that the model with
0
5
10
15
20
25
30
0 1 2 3 4 5 6 7 8
Freq
uenc
y of
occ
uran
c (%
)
Octas
Saskatoon Winnipeg Fort McMurray Vancouver
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the original coefficient has relatively higher tendency to overestimation as compared the model with
the locally fitted coefficient.
Figure 3. Comparison scatterplots between the measured solar radiation and the estimated global
solar radiations by the Kasten-Czeplak models, (a) without original coefficient (b) locally fitted
coefficients for Saskatoon.
Figure 4. Comparison scatterplots between the measured solar radiation and the estimated global
solar radiations by radiations by the Kasten-Czeplak models, (a) without original coefficient (b)
locally fitted coefficients for Winnipeg.
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Figure 5. Comparison scatterplots between the measured solar radiation and the estimated global
solar radiations by radiations by the Kasten-Czeplak models, (a) without original coefficient (b) locally
fitted coefficients for Fort McMurray.
Figure 6. Comparison scatterplots between the measured solar radiation and the estimated global
solar radiations by radiations by the Kasten-Czeplak models, (a) without original coefficient (b) locally
fitted coefficients for Vancouver.
Tables-2 shows the statistical indicators obtained for four different locations for the model with the
original coefficient and locally fitted coefficient. The coefficient of determination (R2) values ranging
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from 0.88 to 0.91 for the model with the local coefficients, and from 0.81 to 0.83 with the original
coefficient. The negative value of MBE with the original coefficients indicates that the model has a
tendency to overestimate the solar radiation for all the selected locations. In contrast, the model with
locally fitted coefficient underestimated the solar radiation except for the data set from Vancouver.
The RMSE and t-stat value are noticeably lower for the Kasten-Czeplak model with the locally fitted
coefficient. The RMSE value with local coefficients ranging from 69 to 82 W m-2, with an average
RMSE of 76 W m-2, whereas from 99 to 117 W m-2, with an average value of 109 W m-2 for original
coefficients. Based on the result from statistical indicators, it shows that the estimation of hourly solar
radiation from the model with local coefficients has more consistent with the measured data.
However, the estimation accuracy of the model with original coefficients also quite satisfactorily
because the value of the statistical indicators with original coefficients are close the results from
others models (Lam and Li, 1998; Spokas and Forcella, 2006; Younes and Muneer, 2007) with their
site specific coefficients.
Table 2. Comparison of statistical parameters for estimating the hourly solar radiation for four
different cities in Western Canada.
Location Model R2 MBE
(W m-2)
RMSE
(W m-2) t-stat
Saskatoon, SK M1 0.82 -27.16 110.01 23.85
M2 0.89 1.91 77.91 2.23
Winnipeg, MB M1 0.81 -18.71 110.41 16.09
M2 0.88 2.69 81.44 3.09
Fort McMurray, AB M1 0.83 -26.51 99.41 25.91
M2 0.89 2.39 69.01 3.24
Vancouver, BC M1 0.83 -38.89 116.38 33.18
M2 0.91 -2.24 73.65 2.85
As the cloud cover is the only parameter for the model, so accurate measurement of cloud cover is
very important to get a relatively good result from the model. The cloud cover observer has general
tendency to underestimate cloud cover under low overcast condition but overestimates under high
overcast condition (Brinsfield et al., 1984). Therefore, the evaluation of the models performance
under different cloud conduction would be helpful for analyzing their performance. The cloud cover
data were grouped into three groups such as clear skies (N ≤ 1), intermediate skies (1< N <7), and
overcast skies (N ≥ 7). The performance evaluation indicators value for selected the model under
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different sky condition is given in the Table-3. Sometimes, it becomes difficult to decide from the
statistical indicators. Therefore, a scoring system introduced by Muneer & Gul (2000) was used to
give a better understanding of each model's performance. The score was estimated by adding the
absolute values of the MBEs and RMSEs for different skies conditions, and the lowest score would
indicate the best. The results indicate that the model performance is very consistent under clear skies
both with original and local coefficients. However, the model with original coefficients performs poorly
under intermediate skies conditions because original coefficients do not consider the local
atmospheric effect on solar radiation. The average scores with original coefficients under
intermediate skies conditions is 232.0 W m-2, whereas about 101.0 W m-2 with the locally fitted
coefficients. The performance of the model with locally fitted coefficients is relatively bad by a small
margin under overcast conditions. Because, the cloud cover observation usually overestimate the
cloud amount for the overcast condition, so the model has a relatively higher tendency to
overestimation of solar radiation.
Table 3. Evaluation of cloud cover model based on different set of cloud cover data.
Location Model Cloud cover
(Octas) R2 MBE
(W/m2)
RMSE
(W/m2)
Scores
(W/m2)
Saskatoon
M1
N ≤ 1 0.97 4.67 45.45 50.11
1< N <7 0.75 -74.63 152.89 227.52
N ≥ 7 0.74 9.96 85.25 95.21
M2
N ≤ 1 0.97 9.1 49.50 58.63
1< N <7 0.76 -14.17 89.69 103.86
N ≥ 7 0.77 20.23 90.67 110.91
Winnipeg
M1
N ≤ 1 0.97 0.66 46.02 46.68
1< N <7 0.78 -81.32 156.55 237.88
N ≥ 7 0.76 27.67 106.61 134.28
M2
N ≤ 1 0.97 6.56 50.65 57.21
1< N <7 0.79 -22.76 90.46 113.22
N ≥ 7 0.82 26.85 101.18 128.03
Fort McMurray
M1
N ≤ 1 0.98 2.51 39.83 42.34
1< N <7 0.76 -70.61 142.08 212.68
N ≥ 7 0.83 7.89 62.64 70.52
M2 N ≤ 1 0.97 10.12 44.79 54.91
1< N <7 0.76 -12.18 82.32 94.49
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N ≥ 7 0.83 16.31 71.83 88.14
Vancouver
N ≤ 1 0.98 -5.36 47.40 52.76
M1 1< N <7 0.73 -85.67 166.63 252.30
N ≥ 7 0.7 -8.52 82.32 90.84
N ≤ 1 0.97 -0.89 51.82 52.71
M2 1< N <7 0.73 -13.92 81.83 95.75
N ≥ 7 0.70 20.06 92.16 112.23
CONCLUSION
In this study, the cloud cover model based Kasten-Czeplak model were evaluated for estimating the
hourly global solar radiation of different locations in Western Canada. The hourly global solar
radiation data from NSRDB are more consistent with the estimated solar radiation from the model
with a locally fitted coefficient, but the model without local coefficients also perform satisfactorily. The
results also indicate that the model without local coefficients perform poorly under intermediate skies
condition, but with local coefficients the performance is better than the overcast condition.
Acknowledgements
The authors are highly thankful to the College of Graduate Studies and Research (CGSR) in
University of Saskatchewan, Innovation Saskatchewan for their financial support to this research.
REFERENCES Badescu, V. (1999). Correlations to estimate monthly mean daily solar global irradiation: Application
to Romania. Energy, 24(10), 883–893. https://doi.org/10.1016/S0360-5442 (99)00027-4
Bakirci, K. (2008). Correlations for Estimation of Solar Radiation on Horizontal Surfaces, 134(4), 130–
134.
Barr, A. G., McGinn, S. M., & Cheng, S. B. (1996). A comparison of methods to estimate daily global
solar irradiation from other climatic variables on the Canadian prairies. Solar Energy, 56(3), 213–
224. https://doi.org/10.1016/0038-092X(95)00100-6
Bennett, I. (1969). Correlation of daily insolation with daily total sky cover, opaque sky cover and
percentage of possible sunshine. Solar Energy, 12, 391–393.
Black, J. N. (1956). The distribution of solar radiation over the Earth’s surface. Archiv Für
Meteorologie, Geophysik Und Bioklimatologie, 7(2), 165–189.
https://doi.org/10.1007/BF02243320
Brinsfield, R., Yaramanoglu, M., & Wheaton, F. (1984). Ground level solar radiation prediction model
12
including cloud cover effects. Solar Energy, 33, 493–499.
Cutforth, H. W., & Judiesch, D. (2007). Long-term changes to incoming solar energy on the Canadian
Prairie. Agricultural and Forest Meteorology, 145(3–4), 167–175.
https://doi.org/10.1016/j.agrformet.2007.04.011
De Jong, R., & Stewart, D. W. (1993). Estimating global solar radiation from common meteorological
observations in western Canada. Can. J. Plant Sci., 73, 509–518. https://doi.org/10.4141/cjps93-
068
El-Metwally, M. (2004). Simple new methods to estimate global solar radiation based on
meteorological data in Egypt. Atmospheric Research, 69(3–4), 217–239.
https://doi.org/10.1016/j.atmosres.2003.09.002
Jeong, D. I., St-Hilaire, A., Gratton, Y., Bélanger, C., & Saad, C. (2016). Simulation and
Regionalization of Daily Global Solar Radiation: A Case Study in Quebec, Canada. Atmosphere-
Ocean, 54(2), 117–130. https://doi.org/10.1080/07055900.2016.1151766
Kahimba, F. C., Bullock, P. R., Sri Ranjan, R., & Cutforth, H. W. (2009). Evaluation of the SolarCalc
model for simulating hourly and daily incoming solar radiation in the Northern Great Plains of
Canada. Canadian Biosystems Engineering / Le Genie Des Biosystems Au Canada, 51.
Kasten, F., & Czeplak, G. (1980). Solar and terrestrial radiation dependent on the amount and type
of cloud. Solar Energy, 24(2), 177–189. https://doi.org/10.1016/0038-092X(80)90391-6
Kim, K. H., Baltazar, J. C., & Haberl, J. S. (2014). Evaluation of meteorological base models for
estimating hourly global solar radiation in Texas. Energy Procedia, 57, 1189–1198.
https://doi.org/10.1016/j.egypro.2014.10.106
Lam, J. C., & Li, D. H. W. (1998). Correlation analysis of solar radiation and cloud cover. International
Journal of Ambient Energy, 19(4), 187–198. https://doi.org/10.1080/01430750.1998.9675305
Muneer, T., & Gul, M. S. (2000). Evaluation of sunshine and cloud cover based models for generating
solar radiation data. Energy Conversion and Management, 41(5), 461–482.
https://doi.org/10.1016/S0196-8904(99)00108-9
Orsini, A., Tomasi, C., Calzolari, F., Nardino, M., Cacciari, A., & Georgiadis, T. (2002). Cloud cover
classification through simultaneous ground-based measurements of solar and infrared radiation.
Atmospheric Research, 61, 251–275.
Sarkar, M. N. I. (2016). Estimation of solar radiation from cloud cover data of Bangladesh.
Renewables: Wind, Water, and Solar, 3(1), 11. https://doi.org/10.1186/s40807-016-0031-7
Spencer, J. W. (1971). Fourier series representation of the position of the sun. Search, 2(5), 172.
Spokas, K., & Forcella, F. (2006). Estimating hourly incoming solar radiation from limited
meteorological data. Weed Science, 54(February), 182–189. https://doi.org/10.1614/WS-05-
13
098R.1
Supit, I., & van Kappel, R. R. (1998). A simple method to estimate global radiation. Solar Energy,
63(3), 147–160. https://doi.org/10.1016/S0038-092X(98)00068-1
Tiwari, G. N. (2003). Greenhouse Technology for Controlled Environment. Pangbourne, England:
Alpha Science International Ltd.
Trnka, M., Žalud, Z., Eitzinger, J., & Dubrovský, M. (2005). Global solar radiation in Central European
lowlands estimated by various empirical formulae. Agricultural and Forest Meteorology, 131(1–2),
54–76. https://doi.org/10.1016/j.agrformet.2005.05.002
Younes, S., & Muneer, T. (2007). Comparison between solar radiation models based on cloud
information. International Journal of Sustainable Energy, 26(3), 121–147.
https://doi.org/10.1080/14786450701549824