Estimation of the Global Horizontal Solar Radiation in Iraq

Transcription

1 Estimation of the Global Horizontal Solar Radiation in Iraq M. T. Y. Tadros 1, M. A. M. Mustafa 2, M. Abdel-Wahab 3 1 Department of physics, Faculty of sciences, Mansuora University, Egypt. 2 Department of Physics, Educational College, Ministry of Education, Kirkuk, Iraq 3 Department of Astronomy & Meteorology, Faculty of sciences, Cairo University, Egypt. Abstract The aim of this work is to obtain an empirical simple equation to estimate the global horizontal solar radiation (GHSR) as a function of the latitude only. Therefore three empirical models proposed to estimate the GHSR using 17 different locations across Iraq. The models formulated as: Quadratic, 2nd Fourier and 2nd Gaussian expression. The simply input feature beside a fine predictive ability for modeling and a good agreement showed by comparison with observed values for 21 years with accuracy15%. The quadratic model is considered as more suitable and simple than either Fourier or Gaussian model. It shows that the annual mean predicted error for Amarah is between 3.99%-13.35%, for Rutbah between 2.22%-8.44% and for Biaji between 3.94%-12.11%. The forecasting for the period shows that values of AMPE% for Amarah is between 4.10%-6.95%, for Rutbah is between 7.64%-10.42% and for Biaji is between 5.39%-7.35%.The climatic mean percentage error (CMPE) is 9.37%, 5.21% and 7.38% for Amarah, Rutbah and Biaji respectively. Keywords empirical models, global horizontal solar radiation, Iraq, latitude dependence. I. INTRODUCTION. Incident sunlight at the Earth's surface, or surface solar radiation, is the fundamental source of energy in the climate system, and consequently a key component for life on our planet, due to its central role in the Global Energy Balance (Trenberth et al., 2009) [1]. The modern tendency is to use various utilizations of solar energy technologies in many developing countries [2]. Renewable energy resources like solar energy, wind energy, tidal and biomass are the second option to generate energy and its utilization. Regarding non conventional energy sources sun plays an important role for human beings. The sun's heat and light provide an abundant source of energy that can be used in many ways [3-5]. Solar radiation received at the surface is of primary importance for the purpose of building solar energy devices, estimating crop productivity etc. However, direct measuring is not available in many cases, so numerical technique becomes an effective alternative to estimate the global solar radiation through observed data of meteorological variables [6]. The quantity of solar radiation reaching the earth's surface varies dramatically as function of changing atmosphere conditions as well as the changing position of the sun through the day [7]. The Solar power will become rapidly more common as an alternate method for producing electricity by photovoltaic cells. [8] 587 The global horizontal solar radiation (GHSR) at the location of interest is the most critical input parameter employed in the design and prediction of the performance of solar energy device. The records of global solar radiation measurements are relatively scarce, due to the cost and maintenance and calibration requirements of the measuring equipment; as a result the most frequently used models has been based on empirical methods that require the development of a set of empirical equations to estimate global radiation from variables normally available at a majority of weather stations [9]. The parameters used as inputs in the relationships also include astronomical factors (solar constant, world-sun distance, solar declination and hour angle); geographical factors (latitude, longitude and altitude). To receive maximum solar energy, solar panels are often installed on an unobstructed roof. A prerequisite to the design of solar collector systems is the availability of solar irradiance data at the required location. The best way of knowing the amount of GHSR at a site is to install many pyranometers at many locations in a given region and recording the data. With this situation, most researchers within Iraq use the available theoretical values of meteorological data to compute average irradiance of solar radiation for different locations. The lacks of standard measured data obtained from reliable measuring instrument suitable for their local environment and therefore resort to theoretical prediction using different models for the GHSR [10-14]. In Iraq, only few stations have been measuring GHSR consistently. Therefore various methods have been explored by many Iraqi researchers to estimate, with reasonable accuracy, the components of the solar radiation from other available meteorological data [15-24]. Due to high and reliable monthly means of solar irradiance of about (18.4 MJ m -2 day -1 ) available for global solar energy in Iraq over, it is possible to employ in this work three formulas: Quadratic, 2 nd Fourier and 2 nd Gaussian as latitude dependence function to estimate the temporal and spatial distribution of GHSR using monthly means of daily timeseries from ( ) on horizontal surface at (17) sites over Iraq. to authors: 1magdytadros@yahoo.com 2gamabio2011@gmail.com 3magdywahab1949@gmail.com

2 II. DATA & METHODOLOGY. In the present work the data were collected for 17 sites spread across Iraq. The data includes averaged monthly data of daily GHSR in (MJ m -2 day -1 ) for 21 years (1 st Jan Dec 2004) retrieved from [25] as presented with geographical location of each site in table (1). The suggested method in this work consists of different steps: The first step is to obtain the typical annual time function (TATF) [26, 27] by Applying the Fourier analysis for the mean daily GHSR for one year and for one site (e.g. Mosul 2004) as in figure 1 (a). 1. The second step is to determine the (TATF) for the 21 years and determine the monthly mean values for that station as in figure 1 (b). 2. Third step is to repeat the above two steps for the 17 sites for Iraq to determine the monthly average TATF of the GHSR as in figure Fourth step is to correlate the monthly average GHSR values with the latitudes φ in radians to generate three empirical models, in order to estimate the GHSR for any latitude in the range (29.98 ϕ N) in the following forms: Where (φ) converted into radian scale, a o, a 1, a 2 are the coefficients of the quadratic model as in equation (1), b o, b 1, b 2, b 3, b 4 and (ω) are the coefficients of the Fourier model as in equation (2) and c 1, c 2, c 3, c 4, c 5 and c 6 are the coefficients of Gaussian model given in equation (3). The homogeneity of the monthly GHSR series was checked by means of the Chi-square test to determine whether observed sample frequencies differ significantly from expected frequencies specified in the null hypothesis. The test was applied with the deductive assumption of non-presence of homogenous reference series and consists of testing each of the series against other series which can be due to local properties, e.g. in cloud cover or atmospheric aerosol impacts but no inhomogeneities were detected in these series to all sites [28]. The measured global solar radiation data are checked for errors and inconsistencies. The purpose of data quality control is to eliminate spurious data and inaccurate measurements [29, 30]. The maximum value of χ² appears in June (1.529) but in (Jan, Apr, May, Aug, Oct, Nov) it was (0.882) while the minimum was (0) in Feb, Mar and Jul. The degrees of freedom occurred in the range (14-16) to all these series and asymptotic significance of the Pearson Chi-Square (P-value) in every month was (1) approximately. GHSR = a o +a 1 φ+a 2 φ 2 (1) GHSR = b o +b 1 cos(ωφ)+b 2 sin(ωφ)+ b 3 cos(ωφ)+b 4 sin(ωφ) (2) GHSR = c 1 exp[-((φ-c 2 )/c 3 ) 2 ] + c 4 exp[-((φ-c 5 )/c 6 ) 2 ] (3) TABLE 1 General monthly means (1 st Jan Dec 2004) of daily GHSR (MJm -2 day -1 ), annual means and geographical location of 17 stations Station lat(d) long(d) J F M A M J J A S O N D Ann Fao Alsulman Basrah Nassiryah Smawah Najaf Nukhaib Kut Al-hia Toraybeel Baghdad Kanaqeen Tickreet Kirkuk Sulaymania Musol Arbil Zakho Mean

3 (a) (b) FIGURE 1 (a) Daily GHSR (MJm -2 day -1 ) and Fourier fit for Mosul station-2004 (b) Fourier fit for Mosul station of 21 years Daily GHSR (MJm -2 day -1 ) and the orresponding TATF FIGURE 2 TATF of GHSR (M J m -2 day -1 ) for 17 stations in Iraq The Root Mean Square Error (RMSE) and the relative Mean Bias Error (MBE) are used to evaluate the accuracy of the divergence between the monthly mean daily radiation values predicted by the used models and the measured values. They are defined as in the following equations: 1 MBE = ( H i p H n n i= 1, i, m) (4) Where H i, p is the i th predicted and H i,m is the i th measured monthly mean daily GHSR, n is the number of observations. The negative values give underestimation in the average. The RMSE is defined in the following formula: RMSE = n 1 ( H i p H n i= 1 2, i, m) (5) 589

4 The annual mean percentage error AMPE is defined as the absolute percentage ε% of deviation between the estimated and measured GHSR values for one year given by: AMPE=100* 1 n n i= 1 ( Hi, P Hi, m) / H i, m The climatological mean percentage error CMPE is also given by equation (6) but for (n) is equal to 20 years (239 months). The correlation coefficient (r) is used to determine the relation between predicted and observed values, (r) formulated as: n ( H H )( H H i, p i, p i, m i, m i= 1 r = (7) n n 2 2 ( Hi, p Hi, p ) ( Hi, m Hi, m) i= 1 i= 1 The correlation is (+1) in the case of a perfect increasing linear relationship and (-1) in case of a decreasing linear relationship, and the values in between indicates the degree of linear relationship between for example model and observations. A correlation coefficient of (0) means the there is no linear relationship between the variables [30]. III. RESULTS & DISCUSSIONS. The coefficients used to determine the estimated GHSR for the quadratic model according to equation (1) were given in table 2. The Fourier and Gaussian model coefficients are given in table (3) while table (4) gives the estimated values of the GHSR ( ) for three independent sites with different H i, P latitudes and different climatological characteristics according to the above three empirical models. These estimated values were used to verify the different models by comparing with the measured monthly mean GHSR (H i,m ) [31]. The absolute monthly percentage error [32] ( PE ) between the predicted values for the three H i, P and the measured values H i, m sites [and for 20 years ( )], calculated using the quadratic model, were given in tables (5-7). The monthly absolute percentage error and the AMPE for the Fourier model were given in tables (8-10) and for the Gaussian model were given in tables (11-13). To test the validity of the models, the monthly accuracy had been splitted into two categories. The first category was PE1 ±15% and the second was PE2>±15%. Tables (14), (15) and (16) gave the number of months with the specific accuracy for the quadratic, Fourier and Gaussian models respectively. The quadratic model gave that the percentage of months for Amarah and Biaji stations were and 88.70% which are higher than that for Fourier and Gaussian models. Although table 15 shows that Fourier model gives higher number of months in estimating the GHSR for Rutbah site where the percentage of months % which is slightly higher than that of the Gaussian model 94.56% and of the quadratic model 94.14%, the deviation between the quadratic model and Fourier model is 0.88% therefore it is possible to use the simple quadratic model for estimating the GHSR for all sites in Iraq. ) (6) The minimum and maximum values of AMPE% are given in table 17 for the three models and for the three sites with the exception values of the year Table 17 shows that the quadratic model has the lowest annual mean percentage error AMPE% than the other models for the three sites. Therefore it is possible to use the quadratic model only for estimating the GHSR for any location in Iraq. Table 18 shows that the MBE, RMSE and the correlation coefficient (r) are nearly the same for the three models. The mean values of MBE are (0.6578, , and ) for the quadratic, Fourier and Gaussian models respectively, which are nearly equal but the quadratic has the lowest value. The mean values of RMSE for the three models are (0.9346, and ) which showed also slightly differences. The mean of correlation coefficients (r) are (0.9957, and ) which are nearly equal. The results showed that the quadratic model (as a simple model) is more suitable for prediction of GHSR for all regions in Iraq. The measured values of solar radiation affected accordingly to clouds coverage especially Mediterranean origin over Iraq in Winter or thunder strong weather and dusty conditions which start from April to early June and again from late September through November [33].For the previous given reasons the measured values appeared to be highly affected by the daily weather variations [19] The modeled GHSR compared favorably with observed means, no anomalies found of the three independent sites through the months except for year 2000 that considered of an extreme occurrences in most sites. Therefore the CMPE for the three sites, as in table (19) shows that Rutbah site in western desert zone (Al-Anbar province) had lowest percentage error which indicates that this site has lower pollution, clouds and aerosol optical depth where CMPE was 5.21, 5.36 and 5.40% for the quadratic, Fourier and Gaussian models respectively. Amarah city located on a low ridge next to the Tigris River waterway south of Baghdad about 50 km from the border with Iran. It lies at the northern tip of the marshlands between the Tigris and Euphrates, therefore the climatic percentage error was 9.37, 9.87 and 9.93% for the quadratic, Fourier and Gaussian models respectively. Although Biaji site lies in mid of desert zone to the north of Bagdad, it is considered as an industrial city contains industrial plants deals with oil refineries therefore the CMPE increases to 7.38, 7.43, 7.48 % for quadratic, Fourier and Gaussian models respectively The CMPE% shows that the quadratic model can be used for estimating the GHSR for any location in Iraq with lowest CMPE% using the latitude only. Appling new analysis to investigate the model predictive ability via current weather conditions in same locations over the coverage area and reanalysis their error gives a general evaluation with high-level of confidence about the model performance nowadays, the proposed quadratic model were applied in different latitudes using the available data of global solar radiation in the period at [34] for Amarah, Rutbah and Biaji sites.table (20) shows that the quadratic model is able to predict the GHSR for the three sites under investigation in the period with percentage error about 10%. This indicates that the quadratic model can be used for predicting the GHSR for any location in Iraq. Figure (3) shows the application of the quadratic model for estimating the above period with percentage error lower than 10%. 590

5 TABLE 2 Monthly coefficients of the Quadratic empirical models. Mon Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec a o a a TABLE 3 Monthly coefficients of the Fourier and Gaussian empirical models. Mon Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fourier coefficients. b o b b b b ω Gaussian coefficients. c c c c c c TABLE 4 Estimated monthly mean of GHSR (MJ m -2 day -1 ) for 3 stations using empirical models. Site latitude Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Quadratic Amarah N Rutbah N Biaji N Fourier Amarah N Rutbah N Biaji N Gaussian Amarah N Rutbah N Biaji N

6 TABLE (5) Percentage error between estimated from Quadratic model and observed values for Amarah station φ= N. 592

7 TABLE (6) Percentage error between estimated from Quadratic model and observed values for Rutbah station φ= N. 593

8 TABLE (7) Percentage error between estimated from Quadratic model and observed values for Biaji station φ= N. 594

9 TABLE (8) Percentage error between estimated from Fourier model and observed values for Amarah station φ= N. 595

10 TABLE (9) Percentage error between estimated from Fourier model and observed values for Rutbah station φ= N. 596

11 TABLE (10) Percentage error between estimated from Fourier model and observed values for Biaji station φ= N. 597

12 TABLE (11) Percentage error between estimated from Gaussian model and observed values for Amarah station φ= N. 598

13 TABLE (12) Percentage error between estimated from Gaussian model and observed values for Rutbah station φ= N. 599

14 TABLE (13) Percentage error between estimated from Gaussian model and observed values for Biaji station φ= N. 600

15 TABLE 14 Number of months with percentage error (PE) between the estimated and measured values for the independent sites used to test the validity of Quadratic model (PE1 ±15% and PE2> ±15%). Station Amarah Rutbah Biaji Model Yr PE1 PE2 PE1 PE2 PE1 PE * sum % Quadratic TABLE 15 Number of months with percentage error (PE) between the estimated and measured values for the independent sites used to test the validity of Fourier model Station Amarah Rutbah Biaji Model Yr PE1 PE2 PE1 PE2 PE1 PE * sum % Fourier 601

16 TABLE 16 Number of months with percentage error (PE) between the estimated and measured values for the independent sites used to test the validity of Gaussian model. Station Amarah Rutbah Biaji Model Yr PE1 PE2 PE1 PE2 PE1 PE * sum % Gaussian *July 1986 is missing TABLE 17 Minimum and Maximum values of AMPE% for the three models and for the three sites in the period ( ) with the value of the exception year Site Amarah Rutbah Biaji min max Year min max Year min max Year Model Quadratic Fourier Gaussian TABLE 18 MBE, RMSE and (r) between estimated and observed monthly mean of GHSR (MJ m -2 day -1 ) for the three sites. Model Quadratic Fourier Gaussian Station MBE RMSE r % MBE RMSE r % MBE RMSE r % Amarah Rutbah Biaji Max Min Mean

17 TABLE 19 Climatic mean percentage error for independent three sites of monthly mean of GHSR ( ) Station Latitude Quadratic Fourier Gaussian Amarah N Rutbah N Biaji N TABLE 20 Annual mean percentage error for independent three sites of monthly mean of GHSR ( ) Station Latitude Amarah N Rutbah N Biaji N IV. CONCLUSIONS. The results of this study show that the determination of the GHSR employing the latitude definition. Three proposed models have fine ability, with accuracy 15% can be used to estimate the monthly mean of GHSR at an arbitrary-selected location in Iraq. The quadratic model gave that the percentage of months for Amarah and Biaji is 81.17% and 88.70% respectively which are higher than that for Fourier and Gaussian. Although Fourier model gives higher number of months in estimating the GHSR for Rutbah site where the percentage of months % which is slightly higher than that of the gaussian model 94.56% and of the quadratic model 94.14%, the deviation between the quadratic model and Fourier model is 1.34 % therefore it is possible to use the simple quadratic model for estimating the GHSR for all sites in Iraq. Accordingly the quadratic model was deduced as the best one in the spatial temporal predicting in all independent stations in Iraq. The AMPE% using the quadratic model were between 3.99%-13.35% for Amarah, between 2.22% % for Rutbah and between 3.94%-12.11% for Biaji, with exception values for the year 2000 which reaches about 17.75%, 11.84% and 13.62% for Amarah, Rutbah and Biaji. The CMPE% is 9.37%, 5.21% and 7.38% for Amarah, Rutbah and Biaji stations respectively. GHSR ( MJ m -2 day -1 ) GHSR ( MJ m -2 day -1 ) GHSR ( MJ m -2 day -1 ) Amarah station Quadratic J F M A M J J A S O N D Rutbah station Fourier J F M A M J J A S O N D Biaji station Gaussian J F M A M J J A S O N D 603 FIGURE 3 Verification for prediction of the GHSR for Amarah, Rutbah and Biaji in the period with percentage error 10% using quadratic model.

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