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The Relationship Between Global Solar Radiation and Sunshine Durations in Cameroon

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The Relationship Between Global Solar Radiation and Sunshine Durations in Cameroon Open Journal of Air Pollution, 2018, 7, 107-119 http://www.scirp.org/journal/ojap ISSN Online: 2169-2661 ISSN Print: 2169-2653 The Relationship between Global Solar Radiation and Sunshine Durations in Cameroon R. Mbiaké1, A. Beya Wakata2, E. Mfoumou3, E. Ndjeuna4, L. Fotso1, E. Tiekwe1, J. R. Kaze Djamen5, C. Bobda6 1University of Douala, Faculty of Sciences, Douala, Cameroon 2University of Yaoundé, Faculty of Sciences, Yaoundé, Cameroon 3Nova Scotia Community College, Division of Applied Research, Springhill, Canada 4Ecole Normale Supérieure d’Enseignement Technique (ENSET), Douala, Cameroon 5Centre de Physique Atomique, Moléculaire Optique et Quantique (CEPAMOQ), Douala, Cameroon 6Public Health of the San Diego University, San Diego, USA How to cite this paper: Mbiaké, R., Beya Abstract Wakata, A., Mfoumou, E., Ndjeuna, E., Fotso, L., Tiekwe, E., Kaze Djamen, J.R. and Based on the well-known modified Angstrom formula on the relationship Bobda, C. (2018) The Relationship between between the sunshine duration and the global solar radiation, this paper Global Solar Radiation and Sunshine Dura- aimed to estimate the value of the constant a and b in Cameroon. Only five ci- tions in Cameroon. Open Journal of Air ties (Maroua, Garoua, NGaoundéré, Yaoundé and Douala) had the both Pollution, 7, 107-119. available in-situ data recorded during the period of eleven years (1996-2006) https://doi.org/10.4236/ojap.2018.72006 beside which four others cities (Dschang, Koundja, Yoko and Manfé) had on- Received: January 10, 2018 ly the in-situ sunshine duration available data recorded during the period of Accepted: June 11, 2018 twenty years (1986-2006). The 9 cities were grouped in 3 different climate re- Published: June 14, 2018 gions. Based on the data of the 5 first cities belonging the 3 regions, the follow Copyright © 2018 by authors and constant values a1 = −0.05, a2 = −0.02, a3 = −0.14 and b1 = 0.94, b2 = 0.74, b3 = Scientific Research Publishing Inc. 1.12 were obtained. The Root Mean Square Error (RMSE) Mean Bias Error This work is licensed under the Creative (MBE) and correlation coefficient (r) were also determined. Then we used Commons Attribution International these values to estimate the global solar radiation for the other four remain ci- License (CC BY 4.0). ties. The constants a and b obtained values are in accordance with those of the http://creativecommons.org/licenses/by/4.0/ West Africa region which Cameroon belongs to. So they can be employed in Open Access estimating global solar radiation of location in Cameroon paying attention only to the geographical location information. Keywords Solar Radiation, Sunshine Duration, Angstrom Constants, Climatic Region 1. Introduction Energy is the motive force behind the sustained technology development, espe- cially for developing countries, where the renewable energy is capable of sup- DOI: 10.4236/ojap.2018.72006 Jun. 14, 2018 107 Open Journal of Air Pollution R. Mbiaké et al. plying the necessary energy for their rapid development. The awareness of the limited availability of non-renewable resources and their associated environ- mental problems is making it imperative that the world shift emphasizes the re- newable energy resources. The environment consequences of harnessing these non-renewable energy sources are assuming alarming proportions. So, the knowledge of global solar radiation and the sunshine duration received during the average day of each month are prerequisite in any solar energy ex- ploitation for the optimal design and the prediction of the system performance. Obviously the best way of knowing the amount of global solar radiation at a given site is to install Pyrhéliomètre as possible at many locations in the region and look after them day to day. A global study of the world distribution of the solar radiation has been carried out by Lof et al. [1] and Gueymard et al. [2], while there have been many at- tempts to find common models applicable anywhere in the world [3]. Beside these studies, the Angstrom-Prescott relationship has been examined in many countries throughout the world, e.g. Australia [4], Canada [5], Caribbean coun- tries as Guatemala [6], the West Indies [7], South Asian countries such as Sri Lanka [8], Pakistan [9] in Africa continent Nigeria [10], Sudan [11], and South East Asia as Hong Kong [12]. Nevertheless, one can notice that comparing to Northern countries, where there is a several hundreds of ground meteorological stations directly and indi- rectly measuring solar radiation, and continuous irradiance values deriving di- rectly from the meteorological geostationary satellites (e.g.; METEOSAT), the countries in development face with the insufficient of these meteorology sta- tions. Definitively in these regions, modeling is the better tool for estimating in- coming global solar radiation from the sunshine duration, in a day of location where the measurements are not available [13]. To reduce this gap in the African continent, this work aims to improve the global solar radiation in Cameroon by it estimation for the four cities (Manfé, Koundja, Yoko and Dschang) where only daily sunshine records are available. 2. Methodology 2.1. Theoretical Aspect Theoretically, the global solar radiation that reaches at the earth’s surface is a result of complex interactions between the solar radiations at the top of the 2 earth’s atmosphere evaluated by the solar constant Gsc = 1369 ± 6 W/m and the climatic conditions of the location. This evaluation does take also into account the rotation of the earth about its own axis and by its elliptical orbit about the sun and the solar declination (δ). Excluding the meteorological and climatic conditions, the daily extraterrestrial solar radiation H0 on a horizontal surface for a day in a month is well approximated by the given expression [14]: 2 R0 24× 3600 HG0 =××sc ×cos(L) cos(δω) cos( ) + sin(L) sin ( δ) (1) R π DOI: 10.4236/ojap.2018.72006 108 Open Journal of Air Pollution R. Mbiaké et al. L is the latitude and ω is the solar hour angle. The solar declination (δ ) is expressed by: δ =23.45sin 0.986×+( J 284) (2) Equation (1) overestimates the global irradiation as it does not take into ac- count the interaction with atmosphere’s components. Indeed, the intensity of solar radiation through the atmosphere is attenuated by various atmospheric constituents, namely gases (air, molecules, ozone, CO2, OH, etc.), liquid and solid particles (aerosols PM2.5, PM10 and clouds). This attenuation is mainly due to clouds, and the path length through atmosphere is also critical. Facing with the insufficiency and the quality of the in-situ measurement glob- al solar radiation data, and the overestimation of the global irradiation by Equa- tion (1), let us used in this paper the general empirical approach formula pio- neered by angstrom in 1942 [15], and later completed by Prescott 1940 [16]. This formula relates average daily global radiation with average daily sunshine hours: d H= H0 ab + (3) d0 where a, b are the constants to be determined. d is the monthly mean daily bright sunshine duration obtained by the Campbell-Stokes recorder, and d0 is the highest monthly mean daily sunshine duration that can be calculated using the followed expression: 2 − dL= cos1 ( tanδ × tan ) (4) 0 15 2.2. Solar Radiation Data in Cameroon Despite the lowest availability of the radiation in-situ instruments at meteoro- logical stations in Cameroon, we used in this paper, the sunshine duration of nine (9) stations and five (5) global solar radiations of them. These data were furnished by the Cameroon National Meteorological Office (DNM). Based on the Trewarth’s climatic classification [17], the 9 stations were grouped by region. Owing to its geographical position stretching from latitude 4˚N to 14˚N, Cameroon belongs to three following types of climate. Douala, Yaoundé, Manfé and Dschang cities belonging to latitude 3˚50'N and 5˚45'N make up the first region with a humid subtropical climate. The second region stretching from latitude 5˚50'N to 7˚30'N with a tropical wet climates contains the cities of Yoko, Koundja and N’Gaoundéré, while a warm and dry climate make up the third region with Garoua and Maroua. The 9 stations shared out in the 3 regions are presented in Table 1. Among the 9 meteorological stations where these data were recorded, only 5 had the both types of data: the hour’s solar length in a day (d) and the global so- lar radiation (H) (Table 2). DOI: 10.4236/ojap.2018.72006 109 Open Journal of Air Pollution R. Mbiaké et al. Table 1. Geographical location of cities and records length. Location Solar Location Latitude Longitude Height (m) Sunshine duration radiation Region 1 Yaoundé 03˚50'N 11˚31'E 760 1996-2005 1986-2006 Douala 04˚01'N 09˚44'E 005 1996-2006 1986-2006 Manfé 05˚40'N 09˚20'E 126 - 1980-1996 Dschang 05˚45'N 10˚04'E 1399 - 1981-1999 Region 2 Yoko 05˚54'N 12˚20'E 1031 - 1981-1996 Koundja 05˚63'N 10˚50'E 1217 - 1981-1999 N’Gaoundéré 07˚21'N 13˚33'E 933 1996-2006 1976-2006 Region 3 Garoua 09˚20'N 13˚23'E 242 1996-2006 1986-2006 Maroua 10˚27'N 14˚15'E 394 1996-2004 1986-2006 Table 2. Stations with global solar radiation and sunshine duration availables. Location Solar Sunshine Location Latitude Longitude Height (m) Radiation Duration Region 1 Yaoundé 03˚50'N 11˚31'E 760 1996-2005 1986-2006 Douala 04˚01'N 09˚44'E 005 1996-2006 1986-2006 Region 2 N’Gaoundéré 07˚21'N 13˚33'E 933 1996-2006 1986-2006 Region 3 Garoua 09˚20'N 13˚23'E 242 1996-2006 1986-2006 Maroua 10˚27'N 14˚15'E 394 1996-2004 1986-2006 For the 9 stations, the monthly average daily values over 10 to 20 years of measured data for the sunshine length hours were computed.
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