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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:mda469@mail.usask.ca

Huiqing Guo Professor, Mechanical Engineering, University of Saskatchewan, Canada

email: huiqing.guo@usask.ca

Karen Tanino Professor, Plant Science, University of Saskatchewan, Canada

email: karen.tanino@usask.ca

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.

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