CMNSEM 1107 13 Estimating Global Diffuse Solar Radiation Sunshine Duration

7/28/2019 CMNSEM 1107 13 Estimating Global Diffuse Solar Radiation Sunshine Duration

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Canadian Journal on Computing in Mathematics, Natural Sciences, Engineering and Medicine Vol. 2 No.9, December 2011

237

Estimating Global and Diffuse Solar Radiation from Sunshine Duration at Qena/

Egypt

S.M. El Shazly , A. A. Hassan, Kh. O. Kassem*, M. E. Adam and Z.M. Ahmed

Physics Dept., Faculty of Science at Qena, South Valley University, Qena, Egypt

Abstract

The clearness index (Kt) and diffuse fraction (KD) at Qena / Upper Egypt have

been expressed in terms of the sunshine fraction (n/N) with the aim of using them to

estimate the values of global (G) and diffuse (D) solar radiation in the study region. A

variety of regression forms, namely linear, exponential, power, second and third orderpolynomial has been applied in this process. The significance and performance of these

regression forms have been evaluated with the aid of several procedures of statistical

analysis. In view of this analysis it has been found that all of them can reasonably be used

to represent the effect of (n/N) on both (Kt) and (KD). In this paper the simple linear

forms are applied to estimate both (G) and (D), since the other forms of the regressions

do not improve the accuracy of the estimation. Comparison between measured and

estimated values of (G) and (D) are performed. The accuracy of estimation of these

components is tested by calculating the mean bias error (MBE), absolute bias errors

(MAE), root mean square errors (RMSE), model efficiency (ME), modeling index (d)

and t-statistic test. The obtained values of these parameters indicate the performance and

validity of the suggested empirical models in estimating (G) and (D). Few estimates is

found to fall beyond 10% accuracy level.

Key words: Global solar radiation - Diffuse solar radiation - Sunshine fraction Daily

values Monthly averages statistical analysis

____________________________________________________________

* Corresponding author:

E-mail: [email protected]

Introduction


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The interest in the applications of solar energy has increased largely in the last

years owing to the expected demands in energy resulting from the increase in the world

population. This demand can not be met from traditional sources of energy, which will be

depleted by the year 2050 (El sayigh, 1992). Renewable energy must and can meet this

challenge. Solar energy is one of the most promising renewable sources. It is

environmentally kindly, plentiful and easy to utilize. For optimal exploitation of the solar

energy, a detailed and accurate knowledge of the solar radiation data at a location is

necessary for engineering design of collectors and storage systems and evaluation of its

efficiency. In the other hand, at any location on the earth's surface, the solar radiation is

also a function of various atmospheric variables such as: the nature and extent of cloud

cover, the aerosol and water vapor contents of the atmosphere --- etc. Therefore solar

radiation data can also enable the scientist to study the atmospheric and environmental

properties that attenuate them and affect its amount received at the ground. Review

through a lot numbers of references (e.g. Benghanem and Joraid, 2007; Zekai, 2007;

Almorox and Hontoria, 2004; Tarhan and Sari, 2005; Ahmed and Ulfat, 2004) has shown

that the "best" measurements to be used in the above utilities of solar energy are those

measured at the location of interest. However, these in-situ measurements, including

global solar radiation and its direct and diffuse components, are not always available in

all locations. Accordingly, development of calculation procedures has been prompted to

provide estimates for places where measurements are not made and places where there

are gaps in the measurement record. This paper aims mainly to calculate the global (G)

and diffuse (D) solar radiation components at Qena, Upper Egypt, a city of abundant

solar radiation, at which data are not always available. These calculations were made for

the first time at Qena, since the solar radiation observations were not feasible at this city

before the establishment of the meteorological station at the south valley university in 1 /

4 / 2000 . The calculation process has carried out using different correlations between

the sunshine fraction (n/N) with each of the clearness index kt (G/G 0) and the diffuse

fraction kd (D/G), where G0 is the daily extraterrestrial solar radiation. Daily values as

well as monthly averages of these components have been calculated. These types of

results are needed to satisfy the requirements of the solar energy utilities in the study

region either for engineers or for scientists. Some of these utilities, at least in this time,


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are using this energy as a source of thermal energy, that can be used in homes and water

heating projects as well studying the atmospheric contaminants in view of the attenuation

caused by it in the incoming solar radiation before it reaches the earth's surface. These

data may be used to some extend in the adjoining locations of similar atmospheric

characteristics.

2. Data and methodology

Daily data of global (G) and diffuse (D) solar radiation components as well as the

sunshine duration (n) were obtained from Egypt meteorological department in south

valley university station at Qena /upper Egypt ( 26 17N, 32 43E, Height 78 asl) in the

period from 2001 to 2004. Global solar radiation is measured by "first class' precise

spectral pyranometer, Eppley No. 163171S (WMO 1996) with errors around 3-4%.

Diffuse solar radiation is measured by shading the direct beam from similar pyranometer

using anodized aluminum shadow band. The sunshine duration is measured using

Campbellstokes sunshine recorder (burn method) with uncertainty 0.1 h and a

resolution of 0.1 h. The extraterrestrial possible solar radiation G0 and the day length N

are calculated using standard procedure (Duffi and Beckman, 1991, 1994; El-shazly,

1994; and Aljamal, 1987).The following essentials regression forms are used in fitting the

measured data:

Y = a + bx (1)

Y = a +bx + cx2 (2)

Y = a +bx + cx2 + dx3 (3)

Y = ax b (4)

Y = a e bX (5),

where a, b, c and d are regression coefficients. They were determined by regression

analysis using the well known least mean square method and they depend on the location.

In the above equations the terms Y represent Kt andkd; while the x terms are the sunshine

fraction (n/N).The obtained correlations are then used to estimate the three solar radiation

components G and D in the study region. Different performance measures are used to

ensure the accuracy of estimation of these components such as the mean bias error

(MBE), absolute bias errors (MAE), root mean square errors (RMSE), model efficiency


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(ME), modeling index (d) and t-statistic test. The following formulae are used to

calculate these errors

= mc YYn

MBE1

(6)

( ) = mc YYn

MAE1

(7)

( )5.0

21

= mc YY

nRMSE (8)

( )

( )

=

2

2

1

mm

cm

YY

YYME (9)

( )

( )

+

=

2

2

1

mcmm

cm

YYYY

YYd (10)

( ) 5.022

21

=

MBERMSE

MBEnt (11)

In all the above statistical tests of accuracy, except ME and d, the smaller value,

the better is the model performance, while values of ME and d closer to 1 indicate the

superior model performance (Willmott, 1982; Mayer and Butler, 1993; Stone, 1993;

Torul et al, 2000; Torul, 1998). For any equation estimates to be significant, the t-

values produced by eq. (11) must be smaller than the values for that confidence level in

standard statistical tables.

3. Results and discussion

3.1 Correlation between clearness index (Kt) and sunshine fraction (n/N)

Figs. 1 and 2 show the percentage of the frequency distribution of daily K t and(n/N) through the study period (2001-2004). It is clear that more than 98 % of Kt values

are > 0.5 and more than 89 % of (n/N) lies in the range > 0.7. This reflects the abundance

of solar energy and semi cloudless weather characterizing the study region through the

year months and consequently the importance of using it in solar energy projects.

Relation between the daily values of K t and (n/N) is presented in Fig. 3. This relation has


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been described and analyzed quantitatively using the above given equations 1-5. The

obtained values of the regression constants a, b, c and d as well as the results of the

statistical analysis of these equations are summarized in Table 1. According to this table,

the high values of the correlation coefficients and F- value (compared to its critical value

given in this table) illustrate that all these formulae can compute the daily global solar

radiation (Gd) with a good accuracy. Also the T-ratio for each coefficient has values

greater than zero, reflecting the significance of their great contribution and high certainty

to the fitting process.

In view of the above statistical analysis, the following simple linear correlation:

Kt = 0.33 + 038 (n/N) (12),

is used in our calculation process to calculate the daily and monthly averages of global

solar radiation at Qena in the study period (2001 -2004).

3.1.1 Daily global solar radiation (Gd)

3.1.1.1 Model performance

Fig. 4 represents a regression form for the variation of both the daily measured (Gdm)

and calculated (Gdc) values of global solar radiation in this period. All data are used in

this figure. In spite of the apparent small deviations between the measured and calculated

values of Gd

in some months in spring and summer seasons, the suggested model (eq.12)

can estimate Gd with a very good accuracy. The high effect of atmospheric constituents in

these months such as aerosols, clouds etc. may be the reason for these deviations(El-

Shazly, 1989). Fig.5a, b represents the percentages of the relative deviation and its

frequency distribution of calculated global solar radiation (Gdc) from measured ones

(Gdm) atQena through the study period. From this fig., about 68% and 94% of the relative

deviation percentage of the results lie in the ranges < 5% and < 10%, respectively.

To confirm the performance of eq. (12) in estimating the daily global solar

radiation Gd, some statistical analysis has been done. The result is summarized in Table

2. It is evident in this table that, the percentages of MBE, RMSE, and MAE are in the

acceptable range with respect to the mean value of Gd, while the values of ME and d are

closed to unity. Also t- value is less than its critical one (2.57). Accordingly, one can

conclude that this equation can estimate the daily global solar radiation with a high


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accuracy and indicates the model performance.

3.1.1.2 Model validation

To test the validity of the proposed equation, it was used to calculate Gd for new

measurements of sunshine fraction at Qena during the period from May 2005 to April2006. Fig. 6 shows the relation between their calculated and measured values in this

period. A very good correlation between both of them (r = 0.99) is clear in this figure.

The statistical analysis of the results is shown in Fig.7a, b and Table 2. The figure and the

table give an evidence for using the proposed equation in calculating Gd, where 73% of

the results have relative deviation percentage < 5% and 96% of them lie in the range


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3.2 Correlation between the diffuse fraction (KD) and sunshine fraction (n/N)

In this section the same techniques as in sec 3.1 was applied to study the correlation

between KD and n/N. Fig. 10 shows the percentage of the frequency distribution of KD

through the study period. The figure indicates that 95.67% of the results have the values

0.7.These results support the above

mentioned conclusion in sec. 3.1 related to the semi cloudless weather in the study region

(Adam and El-Shazly, 2007; EL- Nouby 2006, and EL-Shazly et al., 1997).

Fig. 11 represents the relation between the daily values of the diffuse fraction

(KD) and sunshine fraction (n/N) in the study area through the study period (2001-2004).

This figure clearly indicates that the values of KD decrease with increasing (n/N). Least

mean square method is used to analyze this relation in view of the above suggested

formulae 1-5. The resultant values of the different regression and statistical parameters

are summarized in Table (3). Similar to what done in section 3.1.1, all of these formulae

may estimate the diffuse solar radiation with a high accuracy. In this work the following

linear one is used to calculate the daily values and monthly averages of diffuse solar

radiation at Qena.

( ) ( )13............................................079.1/945.0 += NnKD

3.2.1 Daily diffuse solar radiation (Dd)

3.2.1.1 Model performance

The relation between the calculated (Ddc)and the measured (Ddm)values of daily

diffuse solar radiation using this equation are represented in Fig. 12 for all daily data (D d)

through the study period. This figure indicates the high correlation between the two

parameters.

To verify whether the obtained relationship (eq.13) allows a reliable estimate of

daily diffuse solar radiation Dd, the percentage of the frequency distribution of the

relative deviation (RD) of its calculated values (Ddc) from the measured ones (Ddm)

through the study period is computed as shown in Fig. 13. According to this figure one

can conclude that 40.29% of the results lie in the range < 10%; 74.11% lie in the range

< 20% and 25.9% only have relative deviation > 20%. These results demonstrate an

acceptable accuracy of the calculation.


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Statistical analysis of the calculated daily diffuse solar radiation (Ddc) during the whole

period (2001-2004) is summarized in Table 4. According to the values of the different

parameters given in this table one can conclude that this equation can estimate the daily

diffuse solar radiation with a good accuracy.

3.2.1.2 Model validation

Measured data of available sunshine fraction during new periods at Qena (Jan.

2006 Apr. 2006; May 2000Aug. 2000 and Sep. 2005Dec. 2005) which are not used

in the fitting process, are introduced in equation 13 to calculate the corresponding values

of daily diffuse solar radiation. The calculated values (Ddc) were compared with the

corresponding measured ones (Ddm) during the mentioned periods as shown in Fig. 14. It

can be observed from this figure that there is a strong correlation between the calculated

and measured values of Dd (0.87). The percentage of the frequency distribution of

relative deviation of its calculated values from the measured ones is also computed as

indicated in Fig. 15. It is clear that the used equation provide best estimates for Dd where

27.40% of the results lie in the range < 5%; 44.18% lie in the range < 10%; 37.67% lie

in the range (10%) (20%) and only 18.15% of the results have relative deviation >

20%.

Statistical analysis has been done with the aim of supporting the validity of the used

model in calculating daily diffuse solar radiation Dd in the new period (Jan. 2006 Apr.

2006; May 2000Aug. 2000 and Sep. 2005Dec. 2005). The results are summarized in

Table 4. These results indicate that equation 13 is eligible to calculate the diffuse solar

radiation in the study region with high accuracy.

3.2.2 Monthly averages of diffuse solar radiation (m

D )

The relation between the calculated (mc

D ), using equation 13, and the measured

(mm

D ) values of monthly averages of diffuse solar radiation through the study period is

shown in Fig. 16 . It is clear from this figure that both parameters change in a similar

pattern through the months of the year with a high degree of correlation (corr. = 0.97). As

shown in Fig. 17, the percentage of the frequency distribution of the relative deviation of

calculated monthly averages of diffuse solar radiation from the experimental ones in the


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study period indicates that 50% of the results lie in the range < 5%; 91.67% lie in the

range < 10%; while 8.33% only lie in the range > 10%. Also Table 4 summarizes the

statistical study of the calculation process. In view of the above discussions in the

previous sections, equation (13) proofs its validity in calculating (m

D ) with a high

accuracy.

4. Comparison of the constants of the linear regression forms at different locations

in Egypt

Comparison of the linear regression constants of equations (12) and (13) with that

estimated at different locations in Egypt (El-sebaii and Trabea, 2003, 2005) is given in

Table (5). It is obvious from this table that both the constants (a) and (b) change from

location to another, especially with respect to KD correlations. This is due to the different

geographic and climatic conditions as well as the nature and the concentration of the

atmospheric constituents (e.g. aerosols and water vapor) characterizing these locations.

Near values of (a) and (b) are found at Qena and Aswan (288 Km south of Qena) owing

to their quasi similar climatic conditions.

5. Conclusions

On the light of the preceding results, the following conclusions can be deducted:

1. The necessity of using solar radiation as an alternative source of energy at

Qena/Egypt to help in solving the problem of energy demand, since this region is

characterized with abundant solar radiation and semi cloudless weather. On the

average more than 98% of the values of K t > 0.5 and more than 89% of the

sunshine periods can extend to > 70% of the maximum possible bright hours.

2. Several equations of different types (1-5) have been developed and performed for

use in estimating (G) and (D) at the study region. All of them can be used with a

good accuracy in the estimation process. The simple first order relations (12) and

(13) are proposed for estimating both of them in this work.

3. The proposed equations are found to be valid to estimate (G) and (D) in the study

region with high accuracy. Few estimates are found to fall beyond accuracy level

10%. They can also be used to some extend in the adjoining locations of


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similar atmospheric characteristics. This conclusion is somewhat different with

respect to (D), because it depends largely on the impact of atmospheric

constituents (e.g. aerosols and water vapor) on the solar radiation incident on the

Earth's surface, which varies from region to region according to their nature of

man- and industrial activities.

References

Adam M.El-Nouby and El Shazly S. M., 2007. Attenuation of UV-B radiation in the

atmosphere: Cloud effect, at Qena (Egypt). Atmospheric Environment 41, 4856

4864.

Almorox J. and Hontoria C., 2004. Global solar radiation estimation using sunshine

duration in Spain. Energy Conversion and Management. 45(9-10):1529-1535.

Benghanem M. and Joraid A.A., 2007. A multiple correlation between different solar

parameters in Medina, Saudi Arabia. Renewable Energy; 32(14): 2424-2435.

Duffie J.A. and Beckman W.A., 1994. Solar Engineering of thermal processes, 2nd

Edn.John Wiley, New York.

Duffie J.A., Beckman W.A., 1991. Solar engineering of thermal processes. John

Wiley, New York.

E. El Nobi, 2006. Surface Ultraviolet Radiation Measurements in Qena Upper

Egypt. M. Sc. thesis South Valley University, Qena/ Egypt.

El-sayigh, A.A.M., 1992. Renewable energy is an option to reduce emission of co2

in the atmosphere. International conference on application of solar renewable energy

(ASRE92), Cairo / Egypt No. 1, pp.1-25.


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El-Shazly S. M., 1994. Solar radiation component at Qena-Egypt, DOJARAS Quart J.

Hungarian Meteorol. Service, 101, 215-231.

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characteristics at Qena / Egypt. IDOJARAS, Quarterly Journal of Hungarian

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El-Shazly, S.M., 1989. Studies of the number concentration and size distribution of

the suspended dust particles in the atmosphere of Qena/ Egypt. Water, Air and Soil

pollution 45,121-133.

EL-sebaii, A.A. and Trabea,A.A., 2005. Estimating of Global Solar radiation on

horizontal surfaces over Egypt, Egypt. J. Solids, 28, No. (1), 163- 175.

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radiation in Egypt, Energy Conservation and Management, 44, 2471-2482.

Firoz Ahmed, Intikhab Ulfat, 2004. Empirical models for the correlation of monthly

average daily global solar radiation with hours of sunshine on a horizontal surface at

Karachi, Pakistan. Turk J. Phys 28, 301 - 307.

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Stone R. J., 1993. Improved statistical procedure for the evaluation of solar radiation

estimation models. Solar Energy, 51:289.

Torul,IT and Emin Onat, 2000. A comparison of estimated and measured values of

solar radiation in Elazi , Turkey. Renewable Energy 20, 243-252.


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Torul,IT, Hasan Torul, Dugyu Evin, 2000a. Estimation of global solar radiation

under clear sky radiation in Turkey. Renewable Energy 21 (2000) 271-287.

Torul,IT, Hasan Torul, Dugyu Evin, 2000b. Estimation of monthly global solar

radiation from sunshine duration measurement in Elazi. Renewable Energy 19, 587-

595.

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Zekai Sen., (2007). Simple nonlinear solar irradiation estimation model. Renewable

Energy; 32(2): 342350.

Table 1 Calculated regression constants of equations 1-5 and its statistical analysis, with

respect to Kt, in the period (2001-2004) in the study region

Statistical parameters

Models

LinearSec.order

Thirdorder

Power Exponential

Correlation 0.75 0.75 0.76 0.76 0.79

F- statistics 1054.4 532.31 364.27 1133.6 1323.1

F critical 254.31 19.496 8.526 254.31 254.31

parameters

a 0.33 0.29 0.37 0.7 0.36b 0.38 0.513 -0.09 0.34 0.69

c - -0.1 1.03 - -

d - - -0.61 - -

St.Deviation

a 0.011 0.02 0.03 0.002 0.006

b 0.012 0.059 0.178 0.01 0.019

c - 0.042 0.318 - -


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d - - 0.171 - -

T- ratio

a 31.1 14.52 12.55 376.9 58.83

b 32.47 8.698 0.51 33.67 36.37

c - 2.25 3.25 - -

d - - 3.58 - -

Table 2 Statistical analysis of calculated global solar radiation (Gc) during different

periods

Statistical parametersDaily values(2001-2004)

Daily values ( May2005 Apr 2006)

Monthly averages(2001-2004)

MBE% -0.476 2.39 -0.0749

RMSE% 5.809 4.794 2.799

MAE% 4.687 3.83 2.407ME

0.963 0.966 0.986

D 0.985 0.992 0.996

t- test (critical value) 2.358 (2.57) 9.824 (12.706) 0.088 (2.57)

Table 3Calculated regression constants of equations 1-5 and its statistical analysis, with

respect to KD, in the period (2001-2004) in the study region

Statistical parameters

Models

Linear Quadratic Cubic Power Exponential

Correlation 0.92 0.67 0.71 0.68 0.82

F- statistics 4464.12 2550.45 1699 638.96 1598.03

F critical 254.31 19.496 8.526 254.31 254.31

parameters

a 1.08 0.19 0.11 0.18 2.46

b - 0.95 1.62 3.86 - 1.12 - 2.74

c - - 1.73 - 6.99 - -

d - - 3.16 - -

St.Deviation

a 0.013 0.022 0.033 0.002 0.153

b 0.014 0.067 0.202 0.044 0.069

c - 0.049 0.363 - -d - - 0.196 - -

T- ratio

a 84.14 8.74 3.37 84.52 16.08

b 66.81 24.30 19.11 25.23 39.97

c - 35.52 19.26 - -

d - - 16.14 - -


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Table 4 Statistical analysis of calculated daily diffuse solar radiation (Dc) during different

periods

Statisticalparameters

Daily values(2001-2004)

Daily values (Jan. 2006 Apr.2006, May 2000Aug. 2000 and

Sep. 2005Dec. 2005)

Monthly averages(2001-2004)

MBE% 1.04 0.68 -2.03

RMSE% 18.85 16.53 6.94

MAE% 14.52 12.57 5.59

ME 0.88 0.84 0.93

d 0.94 0.93 0.98

t- statistics(criticalvalue) 1.53(1.65) 0.705(1.65) 1.02(1.79)

Table 5 Comparison of constants of the linear regression equations (12&13) at

different locations in Egypt

Locations Type of

correlation

Correlation

coefficients

Regression constants

a b

Rafah (3113

N, 34

12E, 73 m)

Kt & (n/N) 0.965 0.367 0.342

KD & (n/N) 0.67 0.730 -0.433

AL Arish (31 07N,

3345

E, 32 m)

Kt & (n/N) 0.970 0.295 0.423

KD & (n/N) 0.78 0.941 -0.683

Matruh (31 21N, Kt & (n/N) 0.973 0.508 0.186


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2713

E, 38 m) KD & (n/N) 0.85 0.618 -0.335

Tanta (30 47N, 31

E, 8 m)

Kt & (n/N) 0.960 0.247 0.489

KD & (n/N) - - -

Aswan (23 58N,

32 47E, 191.7 m)

Kt & (n/N) 0.950 0.334 0.389

KD & (n/N) 0.78 0.886 -0.618

Qena (26 10N, 32

43E,78 m)

Kt & (n/N) 0.99 0.330 0381

KD & (n/N) 0.97 1.08 -0.95

Fig. 1 Percentage of the frequency distribution of daily clearness index KtatQena through the study period (2001-2004).

1.18%

95.04%

3.78%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

percentageofclearnessindex(%)

< 0.5 0.5 ? 0.7 > 0.7

clearness index (Kt)


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Fig. 2 Percentage of the frequency distribution ofdailysunshine fraction(n/N) at Qena through the study period (2001-2004).

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

sunshine fraction (n/N)

clearnessindex(Kt)

Fig. 3 Relationship between the daily values of clearness index

(Kt) and sunshine fraction (n/N) at Qena through the

study period (2001-2004).

1.72%

8.33%

89.94%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

percentageofsunshin

efraction(%)

< 0.5 0.5 ? 0.7 > 0.7

sunshine fraction (n/N)


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Figure 4 Variation of the daily measured (Gdm) and calculated (Gdc) global solarradiation values through the study period at Qena /Egypt

Julian day

Dailyglobalsolarradia

tion(Gd)in

Wh/m2

0

2000

4000

6000

8000

10000

1 31 61 91 121 151 181 211 241 271 301 331 361

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

winter spring summerAutumn

(Gdc) (Gd m)


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-40

-30

-20

-10

0

10

20

30

40

1 31 61 91 121 151 181 211 241 271 301 331 361

Julian day

Relativedeviation

(R.D.)

%

68.17%

26.25%

5.35%

0.24%

0%

10%

20%

30%

40%

50%

60%

70%

Fr e

quencydist ribut ioni n

Per c

ent age

( %)

0 (5) (5) (10) (10) (20) > 20

Relative deviation (R.D.) (%)

N= 561

N= 216

N= 44N= 2

Figure 5: Percentages of the relative deviation (a) and its frequency distribution(b) of calculated daily global solar radiation (Gdc)from measured ones(Gdm) atQena through the study period

( b )

( a )


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0

2000

4000

6000

8000

10000

0 2000 4000 6000 8000 10000

measured daily global solar radiation (Gdm) in Wh/m2.day

Ca

lcu

latedda

ilyg

loba

lso

larra

diatio

n(G

dc

)inWh/m

2.d

ay

Figure 6 Relation between the daily values of the measured (Gdm) and the calculated

(Gdc) global solar radiation values through the period (May 2005 April 2006)

at Qena /Egypt.


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Figure 7 Percentages of the relative deviation (a) and its frequency distribution(b) of calculated daily global solar radiation (Gdc)from measured ones(Gdm) atQena through the period (May 2005 Apr 2006)

73.04%

22.87%

3.41%0.68%

0%

10%

20%

30%

40%

50%

60%

70%

80%

FrequencydistributioninPercentage(%)

0 ? (5) (5) ? (10) (10) ? (15) (15) ? (20)

Relative deviation (R.D.) (%)

N= 214

N= 67

N= 10N 2

-40

-30

-20

-10

0

10

20

30

40

1 31 61 91 121 151 181 211 241 271 301 331 361

Julian day

Relativedeviation(R.D.)

%


21/25


257

0

2000

4000

6000

8000

10000

Jan. Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

monthlyaverageglobalsolarradiation(G

m)inWh/m

2

Gmc Gmm --------

Fig. 8 Relation between the measured (Gmm) and calculated (Gmc) values ofmonthly average of global solar radiation through the study period (2001-

2004) at Qena /Egypt.

-25

-20

-15

-10

-5

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 11 12

months

Re

lative

devia

tion

%

Figure 9 Percentage of the relative deviation of calculated monthly average of

global solar radiation from experimental ones through the study period

at Qena / Egypt..


22/25


258

95.67%

2.77%

1.56%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

per c

entageofdif fus ef rac ti o

n( %

)

< 0.5 0.5

0.7 > 0.7Diffuse fraction (KD)

N= 1106

N= 32N= 18

Figure 10: Percentage of the frequency distribution of the diffuse fraction (KD) at

Qena through the study period (2001- 2004).

Figure 11: Relation between the daily values of diffuse fraction (K D ) andsunshine fraction (n/N) at Qena through the study period (2001-2004).

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Sunshine fraction (n/N)

Diffusefraction(K

D)


23/25


259

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000

Measured daily diffuse solar radiation Ddm in Wh/m2.day

Ca

lcu

latedda

ilydiffuseso

larrad

iation

Ddc

inWh/m

2.d

ay

Figure 12 Relation between daily values of the measured (Ddm) and calculated (Ddc)

diffuse solar radiation through the study period (2001-2004) at Qena / Egypt.

40.29%

33.82%

17.97%

6.74%

1.19%

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Frequencydist ri b

ut ioni nP

er c

ent age( %

)

0 (10) (10)(20) (20) (30) (30) (40) > 40

Relative deviation (R.D.)%

N= 305

N= 136

N= 51

N= 9

N= 256

Figure 13 Percentage of the frequency distribution of relative deviation of daily

calculated values (Ddc ) of diffuse solar radiation from measured ones

(Ddm) at Qena through the study period (2001-2004).


24/25


260

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000

measured diffuse solar radiation (Ddm) in Wh/m2.day

calculateddiffusesolarradia

tion(D

dc)

inWh/m

2.day

Figure 14: Relation between daily values of the measured (Ddm) and calculated

(Ddc) diffuse olar radiation through the periods (Jan. 2006 Apr.

2006, May 2000Aug 2000 and Sep 2005Dec. 2005) at Qena /Egypt.

27.40%

44.18%

37.67%

18.15%

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Fre q ue ncy d i s t ri butio n

inp e r ce nta g e ( %

)

0(5) < (10) (10) (20) > 20

Relative deviation (RD) %

N= 129

N=53

N= 110

N= 80

Figure 15 Percentage of the frequency distribution of relative deviation of daily

calculated values (Ddc ) of diffuse solar radiation from measured ones

(Ddm) at Qena through the periods (Jan. 2006 Apr. 2006, May 2000

Aug. 2000 and Sep. 2005Dec. 2005) at Qena /Egypt.


25/25


0

500

1000

1500

2000

2500

Jan. Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Months

Monthlyaveragediffusesolarradiation(Dm

)inWh/m2

Figure 16 Relation between the values of the measured (Dmm) and calculated

(Dmc) monthly average of the diffuse solar radiation through the

study period (2001- 2004) at Qena /Egypt.

50.00%

91.67%

8.33%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Frequenc y di s t ribution

inperc entag

e( %)

0 (5) < (10) >(10)

Relative deviation (R.D.)%

N= 6

N= 11

N= 1

Figure 17 Percentage of frequency distribution of relative deviation of calculated

(Dmc) monthly average diffuse solar radiation from measured ones at

Qena through the study period (2001- 2004).

Documents

CMNSEM 1107 13 Estimating Global Diffuse Solar Radiation Sunshine Duration