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Contour maps for sunshine ratio for Oman using radial basis function generated data
Renewable Energy 28 (2003) 487–497 www.elsevier.com/locate/renene
Data bank
Contour maps for sunshine ratio for Oman using radial basis function generated data J.A. Jervase a, A. Al-Lawati a, A.S.S. Dorvlo b,∗ a
b
Information Engineering Department, College of Engineering, Sultan Qaboos University, PO Box 33, Al-Khod 123, Muscat, Oman Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, PO Box 36, Al-Khod 123, Muscat, Oman Received 8 October 2001; accepted 26 February 2002
Abstract Contour maps for sunshine hours and sunshine ratios for Oman have been generated. The data to generate these maps were obtained using an RBF neural network model. This model estimates sunshine hours and ratios for a given point based on its latitude, longitude, altitude and month of the year. Data from 25 locations were used to plot the contour maps. These maps provide a needed reference for the spatial distribution of sunshine hours and sunshine ratios on a monthly basis for the whole of Oman from which estimates can be made for any location. 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction A number of applications require the knowledge of sunshine hours and sunshine ratio. These include among others, photovoltaic system sizing, modeling and design of solar crop dryers and estimation of solar radiation and clearness index. The number of sunshine hours per day is usually one of the parameters collected by meteorological stations. These stations are limited in number due to the cost involved in establishing and maintaining them. This limits the availability of data to a few locations. Thus, alternative means have to be developed to generate these data for locations with no meteorological stations. In this work, a Radial Basis Function (RBF) neural ∗
Corresponding author. Tel.: +968-515-400; fax: +968-513-415. E-mail address: [email protected] (A.S.S. Dorvlo).
0960-1481/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 0 - 1 4 8 1 ( 0 2 ) 0 0 0 3 5 - 6
488
J.A. Jervase et al. / Renewable Energy 28 (2003) 487–497
network model is developed for estimating sunshine hours, S, and sunshine ratio, S/So, where So is the optimum sunshine hours at a given location. Using the computed values, contour maps were plotted for Oman. These maps provide a means to estimate sunshine hours and ratios for locations without expensive measuring devices. The Sultanate of Oman lies between latitude 16°40⬘N and 26°20⬘N and longitudes 51°50⬘E and 59°40⬘E, which is in the solar belt. The climatic conditions are mainly desert in the north and subtropical in the far south. Oman has a great potential for solar energy harnessing due to the long daily duration of sunshine hours [1]. There are at the moment only 25 weather stations in Oman that routinely measure climatic parameters like sunshine hours, solar radiation, temperature, rainfall, atmospheric pressure and humidity [2]. However, not all the meteorological stations record all of these parameters. Furthermore, there are large areas of Oman with no meteorological stations. The objective of this work is to plot contours maps for sunshine hours and sunshine ratios by means of an RBF network at any given location in Oman based on its latitude, longitude, altitude and month of the year. These maps will provide a distribution of sunshine hours and sunshine ratios and enable their estimation at locations without the use of RBF, which is a computer intensive method. The estimation of sunshine hours and ratios may be treated as a multivariable interpolation problem for which Artificial Neural Networks (ANN) have been successfully used [3–9]. A description of the data used is given in Section 2. Section 3 embodies the development of the RBF model. The results obtained are discussed in Section 4 followed by conclusions in Section 5. 2. Data The data used in this study were obtained from the Directorate General of Civil Aviation and Meteorology [2]. Table 1 shows the geographical details of the meteorological stations in Oman. Out of the 25 stations, only the first eight (Buraimi, Fahud, Marmul, Masirah, Salalah, Seeb, Sohar and Sur) had long-term data of 10 years or more for sunshine hours for the period from 1986 to 1998. Data from these eight stations are used in developing the RBF models. The long-term average sunshine hours, S, for these are given in Table 2. Table 3 shows the corresponding values for the sunshine ratios, S/So. The number of optimum sunshine hours, So, for a given location is computed using the relationship [10] So ⫽ where
2 cos⫺1(⫺tanftand) 15
冉
(1)
冊
284 ⫹ n (in degrees), d ⫽ 23.45sin 360 365 f is the latitude of the location and n is the day number; for example, n is one for the first of January.
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489
Table 1 Meteorological stations in Oman considered in the study Location 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur Khasab Saiq Nizwa Yalooni Thumrait Qairoon Hairiti Mina Raysut Diba Rustaq Samail Rusayl Mina Sultan Qaboos Bahla Adam Ibra Umm Zamaim Mina Sultan Qaboos Buoy
Latitude (°N) 24.24 22.35 18.14 20.67 17.03 23.58 24.47 22.54 26.21 23.07 22.86 19.95 17.67 17.25 16.90 25.62 23.41 23.31 23.56 23.63 22.99 22.39 22.74 20.82 23.68
Longitude (°E)
Elevation (m)
55.79 56.49 55.17 58.91 54.09 58.29 56.64 59.47 56.24 57.64 57.54 57.12 54.02 54.09 53.92 56.26 57.42 57.94 58.21 58.57 57.31 57.52 58.51 57.12 58.54
298.9 170.0 269.0 18.8 20.0 8.4 3.6 13.8 3.1 1754.9 459.5 153.6 466.9 878.3 3.0 19.8 322.0 414.0 66.5 4.1 589.2 285.1 469.2 131.0 0.0
3. RBF models for S and S/So estimation The multivariable interpolation problem of estimating sunshine hours and sunshine ratio at any given location based on its latitude, longitude, altitude and month of the year may be tackled using an RBF neural network. The algorithm developed follows. Step 1: Select six stations out of the eight as the training set. (There are 28 possible combinations to achieve this.) Step 2: Use the geographical details, namely, latitude, longitude and altitude of these stations, month of the year and the corresponding number of sunshine hours for training the RBF network. Step 3: Use the data for the remaining two stations for model validation. Compute the overall root mean square error, (RMSE), between the actual and estimated sunshine hours. Record this value for that particular combination. Step 4: Repeat Steps 1–3 for all the other remaining combinations. Step 5: Select the model with the least RMSE between the actual and estimated sunshine hours.
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Table 2 Measured and estimated average daily sunshine hours using developed RBF neural network model by month for eight meteorological stations (All numbers multiplied by 10) Location January
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur
a b
March
April
May
June
Ma
Eb
M
E
M
E
M
E
M
E
M
E
86 86 93 94 96 84 82 85
86 86 93 94 96 84 84 85
86 87 96 96 93 88 86 92
87 87 96 96 93 89 85 92
93 94 102 94 94 85 81 86
93 93 102 93 94 85 85 86
106 104 106 100 102 97 94 101
106 104 106 100 102 95 88 100
118 115 112 114 111 114 111 112
118 115 112 113 111 105 91 113
123 118 105 100 66 112 108 110
123 117 105 101 66 102 91 108
Location July
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur
February
August
September
October
November
December
M
E
M
E
M
E
M
E
M
E
M
E
121 112 99 79 19 98 89 88
12 113 99 77 19 91 88 90
116 108 103 82 13 100 89 94
116 109 103 83 14 92 88 93
110 106 106 91 56 103 95 99
110 105 106 90 57 97 89 100
104 102 103 101 102 102 98 101
104 102 103 101 102 96 88 101
98 96 96 99 100 97 96 98
98 96 96 99 100 94 87 98
90 79 93 92 95 88 85 88
90 79 93 92 96 86 84 88
Measured. Estimated.
Step 6: Use the developed model to generate sunshine hours and sunshine ratios data for all the meteorological stations in Oman with no record of daily sunshine hours. Step 7: Use Eq. 1 to compute the corresponding sunshine ratios. Step 8: Use data in Steps 6 and 7 to generate contour maps to show the spatial variation of the average daily S and S/So on a monthly basis for Oman. 4. Implementation and results The Matlab Neural Network Toolbox function ‘newrb’ was used for the implementation of the radial basis function network [11]. Based on a given width (spread), this function iteratively adds one neuron at a time to the network until the sumsquared error falls below a specified error goal or a maximum number of neurons is attained. The best model was found when the spread used was 0.75 and the goal set as 0.008. The input parameters were latitude, longitude, altitude and month of year whereas the output parameter was the sunshine hours, S. The data used to train
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Table 3 Measured and estimated average daily sunshine ratios by month for eight meteorological stations in Oman (All numbers multiplied by 1000) Location January
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur
a b
March
April
May
June
Ma
Eb
M
E
M
E
M
E
M
E
M
E
808 793 840 860 861 781 770 791
808 793 840 860 861 781 785 791
773 773 845 845 811 787 770 817
774 774 845 845 811 792 762 816
784 785 855 788 786 718 683 723
784 785 855 786 786 715 714 725
839 826 854 800 826 775 749 802
839 830 853 804 826 760 700 796
898 878 868 876 863 870 838 853
896 879 868 869 864 798 691 864
910 886 801 752 508 837 797 821
913 880 801 762 508 763 673 808
Location July
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur
February
August
September
October
November
December
M
E
M
E
M
E
M
E
M
E
M
E
906 849 762 598 145 739 667 664
903 854 762 588 145 683 656 678
901 850 821 649 107 781 692 739
902 852 820 657 107 721 683 728
910 873 876 749 468 848 784 821
911 867 876 745 468 802 730 829
915 890 890 877 881 897 862 883
915 894 890 879 881 841 773 880
906 878 861 903 89 898 887 901
910 877 861 902 890 866 806 902
852 742 850 854 868 834 813 828
852 742 850 854 868 810 795 827
Measured. Estimated.
and validate are provided in Table 2. Data from six stations were used to train the network and the data from the remaining two stations were used for the validation of the models. To arrive at the best possible model, all possible combinations of six out of eight stations data, a total of 28 combinations, were used in training the network and the remaining two for validation. The criterion for selecting the model was based on the least RMSE between the measured and estimated values. Of the 28 possible combinations, the combination that gave the least RMSE value used data from Buraimi, Fahud, Marmul, Masirah, Salalah and Sur for training and Seeb and Sohar for validation. This RMSE value was 0.75 h. Tables 2 and 3 show both the measured and estimated sunshine hours and sunshine ratios, respectively for the eight stations used to train and validate the model. From these tables, it can be seen that the difference between the measured and estimated values is almost zero for the training stations, which is expected. For the stations used for validation (Seeb and Sohar), the deviation varies from 0 to 1 h for S and from 0 to 0.107 for S/So. The RBF model developed for the estimation of sunshine hours and sunshine ratios was used to generate data for the other meteorological stations. The results obtained
a
8.6 8.6 9.3 9.4 9.6 8.4 8.4 8.5 8.4 8.4 8.4 8.8 8.4 8.4 9.5 8.4 8.5 8.4 8.4 8.3 8.4 8.5 8.4 8.8 8.3
Jan
Mina Sultan Qaboos.
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur Khasab Saiq Nizwa Yalooni Thumrait Qairoon Hairiti Mina Raysut Diba Rustaq Samail Rusayl MSQa Bahla Adam Ibra Umm Zamaim MSQ Buoy
Location
8.7 8.7 9.6 9.6 9.3 8.9 8.5 9.2 8.4 8.4 8.4 8.9 8.5 8.4 9.2 8.4 8.6 8.4 8.8 8.9 8.4 8.6 8.4 8.9 8.9
Feb 9.3 9.3 10.2 9.3 9.4 8.5 8.5 8.6 8.4 8.4 8.5 9.2 8.5 8.4 9.3 8.4 9.0 8.5 8.6 8.4 8.4 9.0 8.4 9.3 8.4
Mar 10.6 10.4 10.6 10.0 10.2 9.5 8.8 10.0 8.5 8.4 8.6 9.8 8.5 8.4 10.2 8.6 9.7 8.8 9.6 9.6 8.4 9.8 8.5 9.9 9.5
Apr 11.8 11.5 11.2 11.3 11.1 10.5 9.1 11.3 8.6 8.4 8.7 10.5 8.6 8.4 11.0 8.8 10.5 9.0 10.6 10.6 8.4 10.6 8.5 10.8 10.5
May 12.3 11.7 10.5 10.1 6.6 10.2 9.1 10.8 8.6 8.4 8.7 10.1 8.5 8.4 6.6 8.8 10.8 9.1 10.4 10.3 8.4 10.8 8.5 10.5 10.3
Jun 12.0 11.3 9.9 7.7 1.9 9.1 8.8 9.0 8.5 8.4 8.7 9.4 8.5 8.4 2.0 8.7 10.6 9.0 9.4 9.1 8.4 10.6 8.5 9.6 9.1
Jul 11.6 10.9 10.3 8.3 1.4 9.2 8.8 9.3 8.5 8.4 8.7 9.4 8.5 8.4 1.5 8.6 10.3 8.9 9.4 9.3 8.4 10.3 8.5 9.5 9.3
Aug 11.0 10.5 10.6 9.0 5.7 9.7 8.9 10.0 8.5 8.4 8.6 9.4 8.5 8.4 5.7 8.7 10.0 8.8 9.8 9.8 8.4 10.0 8.5 9.6 9.8
Sep 10.4 10.2 10.3 10.1 10.2 9.6 8.8 10.1 8.5 8.4 8.6 9.7 8.5 8.4 10.1 8.6 9.6 8.7 9.7 9.6 8.4 9.7 8.5 9.8 9.6
Oct
Table 4 Estimated average daily sunshine hours by month using developed RBF neural network model for all the meteorological stations
9.8 9.6 9.6 9.9 10.0 9.4 8.7 9.8 8.5 8.4 8.5 9.3 8.5 8.4 9.9 8.5 9.3 8.6 9.4 9.4 8.4 9.3 8.4 9.4 9.4
Nov 9.0 7.9 9.3 9.2 9.6 8.6 8.4 8.8 8.4 8.4 8.5 8.4 8.4 8.4 9.5 8.3 8.7 8.5 8.4 8.6 8.4 8.5 8.4 8.2 8.6
Dec
492 J.A. Jervase et al. / Renewable Energy 28 (2003) 487–497
a
Mina Sultan Qaboos.
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur Khasab Saiq Nizwa Yalooni Thumrait Qairoon Hairiti Mina Raysut Diba Rustaq Samail Rusayl MSQa Bahla Adam Ibra Umm Zamaim MSQ Buoy
Location
0.808 0.793 0.840 0.860 0.861 0.781 0.785 0.791 0.792 0.779 0.781 0.805 0.762 0.755 0.857 0.789 0.795 0.784 0.784 0.777 0.779 0.791 0.778 0.808 0.776
Jan
0.774 0.774 0.845 0.845 0.811 0.792 0.762 0.816 0.756 0.746 0.748 0.784 0.741 0.732 0.808 0.757 0.763 0.751 0.788 0.792 0.746 0.764 0.746 0.786 0.791
Feb 0.784 0.785 0.855 0.786 0.786 0.715 0.714 0.725 0.708 0.706 0.713 0.778 0.715 0.704 0.783 0.711 0.755 0.719 0.726 0.711 0.706 0.761 0.709 0.779 0.710
Mar 0.839 0.830 0.853 0.804 0.826 0.760 0.700 0.796 0.673 0.668 0.684 0.785 0.687 0.676 0.821 0.682 0.775 0.697 0.767 0.762 0.668 0.782 0.674 0.796 0.758
Apr 0.896 0.879 0.868 0.869 0.864 0.798 0.691 0.864 0.646 0.639 0.664 0.808 0.667 0.654 0.857 0.660 0.799 0.683 0.804 0.803 0.640 0.808 0.649 0.831 0.797
May 0.913 0.880 0.801 0.762 0.508 0.763 0.673 0.808 0.631 0.625 0.653 0.769 0.653 0.644 0.510 0.646 0.804 0.675 0.775 0.770 0.626 0.810 0.637 0.794 0.765
Jun 0.903 0.854 0.762 0.588 0.145 0.683 0.656 0.678 0.634 0.632 0.658 0.720 0.655 0.648 0.156 0.645 0.800 0.678 0.704 0.687 0.633 0.803 0.642 0.733 0.686
Jul 0.902 0.852 0.820 0.657 0.107 0.721 0.683 0.728 0.661 0.656 0.680 0.740 0.677 0.667 0.119 0.671 0.807 0.699 0.735 0.725 0.657 0.810 0.665 0.751 0.723
Aug 0.911 0.867 0.876 0.745 0.468 0.802 0.730 0.829 0.703 0.691 0.712 0.780 0.706 0.693 0.471 0.713 0.826 0.730 0.805 0.810 0.692 0.828 0.700 0.790 0.807
Sep 0.915 0.894 0.890 0.879 0.881 0.841 0.773 0.880 0.749 0.733 0.749 0.840 0.735 0.723 0.875 0.757 0.844 0.764 0.845 0.844 0.733 0.846 0.738 0.856 0.840
Oct
Table 5 Estimated average daily sunshine ratio by month using developed RBF neural network model for all the meteorological stations
0.910 0.877 0.861 0.902 0.890 0.866 0.806 0.902 0.791 0.770 0.783 0.838 0.758 0.749 0.885 0.795 0.854 0.795 0.865 0.869 0.771 0.849 0.774 0.854 0.866
Nov 0.852 0.742 0.850 0.854 0.868 0.810 0.795 0.827 0.804 0.790 0.796 0.772 0.771 0.762 0.864 0.798 0.821 0.804 0.795 0.811 0.790 0.796 0.791 0.765 0.811
Dec
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Fig. 1.
Contour maps for average daily sunshine ratios for Oman (January–April).
are given in Tables 4 and 5. These data served as the input for generating contour plots for sunshine hours and sunshine ratios. Figs. 1–3 show these for sunshine ratios. The closeness of the contour lines around Salalah throughout the year indicates a wide variability of sunshine hours in this area. A similar pattern can also be observed in the north of Oman, around Saiq, for most of the year. The sunshine ratios also show similar spatial distribution as the sunshine hours. However, the contours in the middle and western belts of Oman show very small changes in sunshine hours and sunshine ratios.
J.A. Jervase et al. / Renewable Energy 28 (2003) 487–497
Fig. 2.
495
Contour maps for average daily sunshine ratios for Oman (May–August).
5. Conclusions The use of radial basis function neural network for modeling sunshine hours was demonstrated. The model developed can be used to estimate both the sunshine hours and sunshine ratios for any given location in Oman based on its latitude, longitude, altitude and month of the year. The estimates from 25 stations were used to plot contour maps for Oman. These maps provide a reference for the spatial distribution
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J.A. Jervase et al. / Renewable Energy 28 (2003) 487–497
Fig. 3.
Contour maps for average daily sunshine ratios for Oman (September–December).
of sunshine hours and sunshine ratios on a monthly basis for the whole of Oman from which estimates can be made for other locations.
References [1] Dorvlo ASS, Ampratwum DB. Summary climatic data for solar technology development in Oman. Renewable Energy 1998;14:255–62.
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[2] Oman Ministry of Communications. Annual Climatic Summaries. Directorate General of Civil Aviation and Meteorology, Department of Meteorology, Sultanate of Oman; 1986–1998. [3] Fausett L. Fundamentals of neural networks. Englewood Cliffs, NJ: Prentice-Hall, 1994. [4] Haykin S. Neural networks. New York, USA: McMillan/IEEE Press, 1994. [5] Kung SY. Digital neural networks. Englewood Cliffs, NJ: PTR Prentice-Hall, 1993. [6] Klerfors D. Artificial Neural Networks. Project MISB-420-0, Saint Louis University; 1998. [7] Mohandes M, Balghonaim A, Kassa M, Rehman S, Halawani TO. Use of radial basis functions for estimating monthly mean daily solar radiation. Solar Energy 2000;68(2):161–8. [8] Sfetsos A, Coonick AH. Univariate and multivariate forecasting of hourly solar radiation with artificial intelligence techniques. Solar Energy 2000;68(2):169–78. [9] Tarassenko L. A guide to neural computing applications. New York: Wiley, 1998. [10] Duffie JA, Beckman WA. Solar engineering of thermal processes. New York: Wiley, 1991. [11] Demuth H, Beale M. Neural network toolbox, user’s guide Version 3.0. The MathWorks, Inc.; 1998.
Data bank
Contour maps for sunshine ratio for Oman using radial basis function generated data J.A. Jervase a, A. Al-Lawati a, A.S.S. Dorvlo b,∗ a
b
Information Engineering Department, College of Engineering, Sultan Qaboos University, PO Box 33, Al-Khod 123, Muscat, Oman Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, PO Box 36, Al-Khod 123, Muscat, Oman Received 8 October 2001; accepted 26 February 2002
Abstract Contour maps for sunshine hours and sunshine ratios for Oman have been generated. The data to generate these maps were obtained using an RBF neural network model. This model estimates sunshine hours and ratios for a given point based on its latitude, longitude, altitude and month of the year. Data from 25 locations were used to plot the contour maps. These maps provide a needed reference for the spatial distribution of sunshine hours and sunshine ratios on a monthly basis for the whole of Oman from which estimates can be made for any location. 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction A number of applications require the knowledge of sunshine hours and sunshine ratio. These include among others, photovoltaic system sizing, modeling and design of solar crop dryers and estimation of solar radiation and clearness index. The number of sunshine hours per day is usually one of the parameters collected by meteorological stations. These stations are limited in number due to the cost involved in establishing and maintaining them. This limits the availability of data to a few locations. Thus, alternative means have to be developed to generate these data for locations with no meteorological stations. In this work, a Radial Basis Function (RBF) neural ∗
Corresponding author. Tel.: +968-515-400; fax: +968-513-415. E-mail address: [email protected] (A.S.S. Dorvlo).
0960-1481/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 0 - 1 4 8 1 ( 0 2 ) 0 0 0 3 5 - 6
488
J.A. Jervase et al. / Renewable Energy 28 (2003) 487–497
network model is developed for estimating sunshine hours, S, and sunshine ratio, S/So, where So is the optimum sunshine hours at a given location. Using the computed values, contour maps were plotted for Oman. These maps provide a means to estimate sunshine hours and ratios for locations without expensive measuring devices. The Sultanate of Oman lies between latitude 16°40⬘N and 26°20⬘N and longitudes 51°50⬘E and 59°40⬘E, which is in the solar belt. The climatic conditions are mainly desert in the north and subtropical in the far south. Oman has a great potential for solar energy harnessing due to the long daily duration of sunshine hours [1]. There are at the moment only 25 weather stations in Oman that routinely measure climatic parameters like sunshine hours, solar radiation, temperature, rainfall, atmospheric pressure and humidity [2]. However, not all the meteorological stations record all of these parameters. Furthermore, there are large areas of Oman with no meteorological stations. The objective of this work is to plot contours maps for sunshine hours and sunshine ratios by means of an RBF network at any given location in Oman based on its latitude, longitude, altitude and month of the year. These maps will provide a distribution of sunshine hours and sunshine ratios and enable their estimation at locations without the use of RBF, which is a computer intensive method. The estimation of sunshine hours and ratios may be treated as a multivariable interpolation problem for which Artificial Neural Networks (ANN) have been successfully used [3–9]. A description of the data used is given in Section 2. Section 3 embodies the development of the RBF model. The results obtained are discussed in Section 4 followed by conclusions in Section 5. 2. Data The data used in this study were obtained from the Directorate General of Civil Aviation and Meteorology [2]. Table 1 shows the geographical details of the meteorological stations in Oman. Out of the 25 stations, only the first eight (Buraimi, Fahud, Marmul, Masirah, Salalah, Seeb, Sohar and Sur) had long-term data of 10 years or more for sunshine hours for the period from 1986 to 1998. Data from these eight stations are used in developing the RBF models. The long-term average sunshine hours, S, for these are given in Table 2. Table 3 shows the corresponding values for the sunshine ratios, S/So. The number of optimum sunshine hours, So, for a given location is computed using the relationship [10] So ⫽ where
2 cos⫺1(⫺tanftand) 15
冉
(1)
冊
284 ⫹ n (in degrees), d ⫽ 23.45sin 360 365 f is the latitude of the location and n is the day number; for example, n is one for the first of January.
J.A. Jervase et al. / Renewable Energy 28 (2003) 487–497
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Table 1 Meteorological stations in Oman considered in the study Location 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur Khasab Saiq Nizwa Yalooni Thumrait Qairoon Hairiti Mina Raysut Diba Rustaq Samail Rusayl Mina Sultan Qaboos Bahla Adam Ibra Umm Zamaim Mina Sultan Qaboos Buoy
Latitude (°N) 24.24 22.35 18.14 20.67 17.03 23.58 24.47 22.54 26.21 23.07 22.86 19.95 17.67 17.25 16.90 25.62 23.41 23.31 23.56 23.63 22.99 22.39 22.74 20.82 23.68
Longitude (°E)
Elevation (m)
55.79 56.49 55.17 58.91 54.09 58.29 56.64 59.47 56.24 57.64 57.54 57.12 54.02 54.09 53.92 56.26 57.42 57.94 58.21 58.57 57.31 57.52 58.51 57.12 58.54
298.9 170.0 269.0 18.8 20.0 8.4 3.6 13.8 3.1 1754.9 459.5 153.6 466.9 878.3 3.0 19.8 322.0 414.0 66.5 4.1 589.2 285.1 469.2 131.0 0.0
3. RBF models for S and S/So estimation The multivariable interpolation problem of estimating sunshine hours and sunshine ratio at any given location based on its latitude, longitude, altitude and month of the year may be tackled using an RBF neural network. The algorithm developed follows. Step 1: Select six stations out of the eight as the training set. (There are 28 possible combinations to achieve this.) Step 2: Use the geographical details, namely, latitude, longitude and altitude of these stations, month of the year and the corresponding number of sunshine hours for training the RBF network. Step 3: Use the data for the remaining two stations for model validation. Compute the overall root mean square error, (RMSE), between the actual and estimated sunshine hours. Record this value for that particular combination. Step 4: Repeat Steps 1–3 for all the other remaining combinations. Step 5: Select the model with the least RMSE between the actual and estimated sunshine hours.
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Table 2 Measured and estimated average daily sunshine hours using developed RBF neural network model by month for eight meteorological stations (All numbers multiplied by 10) Location January
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur
a b
March
April
May
June
Ma
Eb
M
E
M
E
M
E
M
E
M
E
86 86 93 94 96 84 82 85
86 86 93 94 96 84 84 85
86 87 96 96 93 88 86 92
87 87 96 96 93 89 85 92
93 94 102 94 94 85 81 86
93 93 102 93 94 85 85 86
106 104 106 100 102 97 94 101
106 104 106 100 102 95 88 100
118 115 112 114 111 114 111 112
118 115 112 113 111 105 91 113
123 118 105 100 66 112 108 110
123 117 105 101 66 102 91 108
Location July
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur
February
August
September
October
November
December
M
E
M
E
M
E
M
E
M
E
M
E
121 112 99 79 19 98 89 88
12 113 99 77 19 91 88 90
116 108 103 82 13 100 89 94
116 109 103 83 14 92 88 93
110 106 106 91 56 103 95 99
110 105 106 90 57 97 89 100
104 102 103 101 102 102 98 101
104 102 103 101 102 96 88 101
98 96 96 99 100 97 96 98
98 96 96 99 100 94 87 98
90 79 93 92 95 88 85 88
90 79 93 92 96 86 84 88
Measured. Estimated.
Step 6: Use the developed model to generate sunshine hours and sunshine ratios data for all the meteorological stations in Oman with no record of daily sunshine hours. Step 7: Use Eq. 1 to compute the corresponding sunshine ratios. Step 8: Use data in Steps 6 and 7 to generate contour maps to show the spatial variation of the average daily S and S/So on a monthly basis for Oman. 4. Implementation and results The Matlab Neural Network Toolbox function ‘newrb’ was used for the implementation of the radial basis function network [11]. Based on a given width (spread), this function iteratively adds one neuron at a time to the network until the sumsquared error falls below a specified error goal or a maximum number of neurons is attained. The best model was found when the spread used was 0.75 and the goal set as 0.008. The input parameters were latitude, longitude, altitude and month of year whereas the output parameter was the sunshine hours, S. The data used to train
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491
Table 3 Measured and estimated average daily sunshine ratios by month for eight meteorological stations in Oman (All numbers multiplied by 1000) Location January
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur
a b
March
April
May
June
Ma
Eb
M
E
M
E
M
E
M
E
M
E
808 793 840 860 861 781 770 791
808 793 840 860 861 781 785 791
773 773 845 845 811 787 770 817
774 774 845 845 811 792 762 816
784 785 855 788 786 718 683 723
784 785 855 786 786 715 714 725
839 826 854 800 826 775 749 802
839 830 853 804 826 760 700 796
898 878 868 876 863 870 838 853
896 879 868 869 864 798 691 864
910 886 801 752 508 837 797 821
913 880 801 762 508 763 673 808
Location July
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur
February
August
September
October
November
December
M
E
M
E
M
E
M
E
M
E
M
E
906 849 762 598 145 739 667 664
903 854 762 588 145 683 656 678
901 850 821 649 107 781 692 739
902 852 820 657 107 721 683 728
910 873 876 749 468 848 784 821
911 867 876 745 468 802 730 829
915 890 890 877 881 897 862 883
915 894 890 879 881 841 773 880
906 878 861 903 89 898 887 901
910 877 861 902 890 866 806 902
852 742 850 854 868 834 813 828
852 742 850 854 868 810 795 827
Measured. Estimated.
and validate are provided in Table 2. Data from six stations were used to train the network and the data from the remaining two stations were used for the validation of the models. To arrive at the best possible model, all possible combinations of six out of eight stations data, a total of 28 combinations, were used in training the network and the remaining two for validation. The criterion for selecting the model was based on the least RMSE between the measured and estimated values. Of the 28 possible combinations, the combination that gave the least RMSE value used data from Buraimi, Fahud, Marmul, Masirah, Salalah and Sur for training and Seeb and Sohar for validation. This RMSE value was 0.75 h. Tables 2 and 3 show both the measured and estimated sunshine hours and sunshine ratios, respectively for the eight stations used to train and validate the model. From these tables, it can be seen that the difference between the measured and estimated values is almost zero for the training stations, which is expected. For the stations used for validation (Seeb and Sohar), the deviation varies from 0 to 1 h for S and from 0 to 0.107 for S/So. The RBF model developed for the estimation of sunshine hours and sunshine ratios was used to generate data for the other meteorological stations. The results obtained
a
8.6 8.6 9.3 9.4 9.6 8.4 8.4 8.5 8.4 8.4 8.4 8.8 8.4 8.4 9.5 8.4 8.5 8.4 8.4 8.3 8.4 8.5 8.4 8.8 8.3
Jan
Mina Sultan Qaboos.
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur Khasab Saiq Nizwa Yalooni Thumrait Qairoon Hairiti Mina Raysut Diba Rustaq Samail Rusayl MSQa Bahla Adam Ibra Umm Zamaim MSQ Buoy
Location
8.7 8.7 9.6 9.6 9.3 8.9 8.5 9.2 8.4 8.4 8.4 8.9 8.5 8.4 9.2 8.4 8.6 8.4 8.8 8.9 8.4 8.6 8.4 8.9 8.9
Feb 9.3 9.3 10.2 9.3 9.4 8.5 8.5 8.6 8.4 8.4 8.5 9.2 8.5 8.4 9.3 8.4 9.0 8.5 8.6 8.4 8.4 9.0 8.4 9.3 8.4
Mar 10.6 10.4 10.6 10.0 10.2 9.5 8.8 10.0 8.5 8.4 8.6 9.8 8.5 8.4 10.2 8.6 9.7 8.8 9.6 9.6 8.4 9.8 8.5 9.9 9.5
Apr 11.8 11.5 11.2 11.3 11.1 10.5 9.1 11.3 8.6 8.4 8.7 10.5 8.6 8.4 11.0 8.8 10.5 9.0 10.6 10.6 8.4 10.6 8.5 10.8 10.5
May 12.3 11.7 10.5 10.1 6.6 10.2 9.1 10.8 8.6 8.4 8.7 10.1 8.5 8.4 6.6 8.8 10.8 9.1 10.4 10.3 8.4 10.8 8.5 10.5 10.3
Jun 12.0 11.3 9.9 7.7 1.9 9.1 8.8 9.0 8.5 8.4 8.7 9.4 8.5 8.4 2.0 8.7 10.6 9.0 9.4 9.1 8.4 10.6 8.5 9.6 9.1
Jul 11.6 10.9 10.3 8.3 1.4 9.2 8.8 9.3 8.5 8.4 8.7 9.4 8.5 8.4 1.5 8.6 10.3 8.9 9.4 9.3 8.4 10.3 8.5 9.5 9.3
Aug 11.0 10.5 10.6 9.0 5.7 9.7 8.9 10.0 8.5 8.4 8.6 9.4 8.5 8.4 5.7 8.7 10.0 8.8 9.8 9.8 8.4 10.0 8.5 9.6 9.8
Sep 10.4 10.2 10.3 10.1 10.2 9.6 8.8 10.1 8.5 8.4 8.6 9.7 8.5 8.4 10.1 8.6 9.6 8.7 9.7 9.6 8.4 9.7 8.5 9.8 9.6
Oct
Table 4 Estimated average daily sunshine hours by month using developed RBF neural network model for all the meteorological stations
9.8 9.6 9.6 9.9 10.0 9.4 8.7 9.8 8.5 8.4 8.5 9.3 8.5 8.4 9.9 8.5 9.3 8.6 9.4 9.4 8.4 9.3 8.4 9.4 9.4
Nov 9.0 7.9 9.3 9.2 9.6 8.6 8.4 8.8 8.4 8.4 8.5 8.4 8.4 8.4 9.5 8.3 8.7 8.5 8.4 8.6 8.4 8.5 8.4 8.2 8.6
Dec
492 J.A. Jervase et al. / Renewable Energy 28 (2003) 487–497
a
Mina Sultan Qaboos.
Buraimi Fahud Marmul Masirah Salalah Seeb Sohar Sur Khasab Saiq Nizwa Yalooni Thumrait Qairoon Hairiti Mina Raysut Diba Rustaq Samail Rusayl MSQa Bahla Adam Ibra Umm Zamaim MSQ Buoy
Location
0.808 0.793 0.840 0.860 0.861 0.781 0.785 0.791 0.792 0.779 0.781 0.805 0.762 0.755 0.857 0.789 0.795 0.784 0.784 0.777 0.779 0.791 0.778 0.808 0.776
Jan
0.774 0.774 0.845 0.845 0.811 0.792 0.762 0.816 0.756 0.746 0.748 0.784 0.741 0.732 0.808 0.757 0.763 0.751 0.788 0.792 0.746 0.764 0.746 0.786 0.791
Feb 0.784 0.785 0.855 0.786 0.786 0.715 0.714 0.725 0.708 0.706 0.713 0.778 0.715 0.704 0.783 0.711 0.755 0.719 0.726 0.711 0.706 0.761 0.709 0.779 0.710
Mar 0.839 0.830 0.853 0.804 0.826 0.760 0.700 0.796 0.673 0.668 0.684 0.785 0.687 0.676 0.821 0.682 0.775 0.697 0.767 0.762 0.668 0.782 0.674 0.796 0.758
Apr 0.896 0.879 0.868 0.869 0.864 0.798 0.691 0.864 0.646 0.639 0.664 0.808 0.667 0.654 0.857 0.660 0.799 0.683 0.804 0.803 0.640 0.808 0.649 0.831 0.797
May 0.913 0.880 0.801 0.762 0.508 0.763 0.673 0.808 0.631 0.625 0.653 0.769 0.653 0.644 0.510 0.646 0.804 0.675 0.775 0.770 0.626 0.810 0.637 0.794 0.765
Jun 0.903 0.854 0.762 0.588 0.145 0.683 0.656 0.678 0.634 0.632 0.658 0.720 0.655 0.648 0.156 0.645 0.800 0.678 0.704 0.687 0.633 0.803 0.642 0.733 0.686
Jul 0.902 0.852 0.820 0.657 0.107 0.721 0.683 0.728 0.661 0.656 0.680 0.740 0.677 0.667 0.119 0.671 0.807 0.699 0.735 0.725 0.657 0.810 0.665 0.751 0.723
Aug 0.911 0.867 0.876 0.745 0.468 0.802 0.730 0.829 0.703 0.691 0.712 0.780 0.706 0.693 0.471 0.713 0.826 0.730 0.805 0.810 0.692 0.828 0.700 0.790 0.807
Sep 0.915 0.894 0.890 0.879 0.881 0.841 0.773 0.880 0.749 0.733 0.749 0.840 0.735 0.723 0.875 0.757 0.844 0.764 0.845 0.844 0.733 0.846 0.738 0.856 0.840
Oct
Table 5 Estimated average daily sunshine ratio by month using developed RBF neural network model for all the meteorological stations
0.910 0.877 0.861 0.902 0.890 0.866 0.806 0.902 0.791 0.770 0.783 0.838 0.758 0.749 0.885 0.795 0.854 0.795 0.865 0.869 0.771 0.849 0.774 0.854 0.866
Nov 0.852 0.742 0.850 0.854 0.868 0.810 0.795 0.827 0.804 0.790 0.796 0.772 0.771 0.762 0.864 0.798 0.821 0.804 0.795 0.811 0.790 0.796 0.791 0.765 0.811
Dec
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Fig. 1.
Contour maps for average daily sunshine ratios for Oman (January–April).
are given in Tables 4 and 5. These data served as the input for generating contour plots for sunshine hours and sunshine ratios. Figs. 1–3 show these for sunshine ratios. The closeness of the contour lines around Salalah throughout the year indicates a wide variability of sunshine hours in this area. A similar pattern can also be observed in the north of Oman, around Saiq, for most of the year. The sunshine ratios also show similar spatial distribution as the sunshine hours. However, the contours in the middle and western belts of Oman show very small changes in sunshine hours and sunshine ratios.
J.A. Jervase et al. / Renewable Energy 28 (2003) 487–497
Fig. 2.
495
Contour maps for average daily sunshine ratios for Oman (May–August).
5. Conclusions The use of radial basis function neural network for modeling sunshine hours was demonstrated. The model developed can be used to estimate both the sunshine hours and sunshine ratios for any given location in Oman based on its latitude, longitude, altitude and month of the year. The estimates from 25 stations were used to plot contour maps for Oman. These maps provide a reference for the spatial distribution
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Fig. 3.
Contour maps for average daily sunshine ratios for Oman (September–December).
of sunshine hours and sunshine ratios on a monthly basis for the whole of Oman from which estimates can be made for other locations.
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