Interciencia ISSN: 0378-1844 [email protected] Asociación Interciencia

Almorox, Javier; Benito, Marta; Hontoria, Chiquinquirá ESTIMATIO N OF GLOBAL SOLAR RADIATION IN VENEZUELA Interciencia, vol. 33, núm. 4, abril, 2008, pp. 280-283 Asociación Interciencia , Venezuela

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SUMMARY

A new relationship between sunshine duration and solar ra- percentage error. It is recommended that the t-statistic be used diation was investigated through the analysis of data on monthly in conjunction with a set of error statistical parameters to more global solar radiation and hours of bright sunshine for eleven reliably assess a model’s performance. All the models fitted the meteorological stations in Venezuela during the period 1964- data adequately and can be used to estimate monthly mean 1993. Linear regression was used to fit the Angström-Prescott solar global radiation from sunshine hours. The Angström- equation. Estimated values were compared with measured val- Prescott’s correlation obtained for the eleven cities can be used ues in terms of root mean square error, mean bias error, mean for estimating global solar radiation in Venezuela where only absolute bias error, mean percentage error, and mean absolute sunshine hours data were available.

Introduction of a solar energy device the evapotranspiration from The empirical models (Hussain et al., 1999). Offi- Penman´s method would be can be roughly classified Knowledge of the local cial studies (Contreras et al., approximately the same as into three categories: a) global solar radiation is re- 2006) indicate that there is for the estimate of radiation. sunshine-based models, b) quired by most of the models great potential for alternative In spite of the importance cloud-based models, and c) that simulate crop growth. It energies in Venezuela, where of solar radiation measure- meteorological data-based is also essential for many solar energy could solve part ments, these data are not models (Almorox and Hon- applications, including ar- of energy demand problem. available due to the opera- toria, 2004; Menges et al., chitectural and solar energy Furthermore, as the energy tional difficulty in taking 2006; Yang et al., 2006). systems design, and evapo- source for photosynthesis direct measurements and, The Angström-Prescott mod- transpiration estimates. The and evapotranspiration, so- hence, must be estimated. els are sunshine-based and global solar radiation on lar radiation is an important Venezuela has a variety of have been widely applied horizontal surface at the lo- input to crop growth models climates and is located in a to estimate global solar ra- cation of interest is the most (Allen et al., 1998). Boisvert region where the potential diation. A well calibrated critical input parameter em- (1990) reported that the error of global solar radiation in Angström-Prescott model ployed in the design and pre- introduced by the estimate applications and agriculture is usually more accurate diction of the performance of global radiation used in are considerably high. than a temperature based

KEYWORDS / Angström-Prescott Equation / Correlation Models / Global Solar Radiation / Sunshine Duration / Received: 03/29/2007. Modified: 02/14/2008. Accepted: 02/20/2008.

Javier Almorox Alonso. Doctor tamento de Edafología, Escuela Marta Benito Capa. Doctor Chiquinquirá Hontoria Fernán­ in Agronomical Engineering, Técnica Superior de Ingenieros in Agronomical Engineering, dez. Doctor in Agronomical Universidad Politécnica de Ma- Agrónomos, Avd. Complutense s/ UPM, Spain. Professor, UPM, Engineering, UPM, Spain. Pro- drid (UPM), Spain. Professor, n 28040. Madrid. Spain. e-mail: Spain. e-mail: marta.benito@ fessor, UPM, Spain. e-mail: UPM, Spain. Address: Depar- [email protected] upm.es [email protected]

280 0378-1844/08/04/280-04 $ 3.00/0 APR 2008, VOL. 33 Nº 4 ESTIMACIÓN DE LA RADIACIÓN SOLAR GLOBAL EN VENEZUELA Javier Almorox, Marta Benito y Chiquinquirá Hontoria RESUMEN

Una nueva relación entre la duración de la insolación y centual absoluto medio MAPE. Se recomienda también el la radiación solar global se estudia a través del análisis uso del estadístico t en conjunción con todos esos errores de datos de radiación solar global y horas de sol de once estadísticos para una mejor validación del modelo. Todos estaciones meteorológicas de Venezuela en el período 1964- los modelos analizados estiman los datos de forma adecua- 1993. Se usó el método de la regresión lineal para estimar da y pueden ser empleados en la estimación de la radiación la ecuación de Angström-Prescott. Los valores estimados global solar a partir de los datos de insolación. El método fueron comparados con las mediciones usando los estadís- de Angström-Prescott puede ser usado para estimar la ra- ticos error cuadrático medio RMSE, los errores de sesgo diación solar en Venezuela cuando se dispone de los datos MBE y MABE; los errores porcentual medio MPE, y por- de insolación únicamente.

ESTIMAÇÃO DA RADIAÇÃO SOLAR GLOBAL EM VENEZUELA Javier Almorox, Marta Benito e Chiquinquirá Hontoria RESUMO

Uma nova relação entre a duração da insolação e a radia- meio MPE, e percentual absoluto meio MAPE. Se recomen- ção solar global estuadia-se por meio do análise dos dados dou também o uso do estatístico t em conjunção com todos de radiação solar global e horas de sol de onze estações esses erros estatísticos para uma melhor validação do mode- meteorológicas da Venezuela usando a série 1964-1993. Se lo. Todos os modelos analisados estimam os dados de uma usou o método da regressão linear para estimar a equação forma adequada e podem ser usados na estimativa da radia- de Angström-Prescott. Os valores estimados se compararam ção global solar a partir dos dados de insolação. O método com os medidos usando os estatísticos erro quadrático meio de Angström-Prescott pode usarse para estimar a radiação RMSE, os erros de sesgo MBE e MABE; os erros percentual solar com dados de insolação na Venezuela.

model and a cloud based for estimating global solar surface (MJ·m-2·day-1), and tion in various locations in model (Iziomon and Mayer, radiation is sunshine du- a and b: empirically deter- Venezuela. 2001; Trnka et al., 2005). ration; can be easily and mined regression constants. The model has gained much reliably measured, and data These constants can assume Models and data popularity over the years. A are widely available. The a wide range of values de- number of studies have fo- first author who employed a pending on the location con- In order to obtain sets of cused on tuning the empiri- linear relationship between sidered, and can be inferred regression constants with cal constants, and show that global radiation and sun- from correlations established data available in Venezuela, the parameters can be quite shine duration was Ang- at neighboring locations. For measured data of monthly distinct in different regions. ström (1924): example, when using the mean of global solar radia- The applicability of these FAO 56 Penman estimation tion and sunshine duration H/H = k + (1- k) (n/N) methods remains geographi- c method (Allen ., 1998), use corresponding to the period cally limited and thus the where H: amount of global of Angström values calibra- between 1964 and 1993 was model parameters have to radiation; Hc: global radia- tion is recommended. In a employed. The data were be calibrated locally (Mar- tion under a real atmosphere general sense it may be said obtained from the World Ra- tínez-Lozano et al., 1984; in completely clear days; k: that the factors influencing diation Data Centre (WRDC, Gueymard et al., 1995). empirical constant, deter- a and b are (Almorox et al., http://wrdc-mgo.nrel.gov/) Several empirical models mined by Angström as k= 2005): latitude, height of from eleven meteorological have been developed to cal- 0,25 from Stockholm data; the station, reflection coef- stations across Venezuela, culate global solar radiation n: number of hours measured ficient of the surface, mean given in Table I. using various parameters. by a sunshine recorder; and solar altitude, water vapor Daily extraterrestrial ra- The parameters used as N: maximum possible num- concentration, natural or diation on a horizontal sur- inputs in the calculations ber of hours of sunshine. artificial pollution concen- face H 0 can be calculated include sunshine duration, The modified version of the tration. as a function of the solar mean temperature, maxi- Angstrom’s correlation has The object of the pres- constant (Isc), the latitude of mum temperature, soil tem- been the most convenient ent paper is to develop an the site (λ), the eccentric- perature, relative humidity, and widely used correlation improved Angström-Prescott ity correction factor of the number of rainy days, alti- for estimating the global ra- estimation for the prediction Earth’s orbit (E0), the solar tude, latitude, total precipi- diation (Prescott, 1940): of monthly average global declination (δ) and the mean table water, albedo, atmos­ radiation on a horizontal sunrise hour angle (w ); us- H/H = a + b (n/N) (1) s pheric pressure, cloudiness 0 surface from sunshine dura- ing the equation and evaporation. The most where H0: extraterrestrial so- commonly used parameter lar radiation on a horizontal

APR 2008, VOL. 33 Nº 4 281 Table I et al., 2000; Sabziparvar et summed and averaged. The Geographical location of the al., 2007). MBE and MPE offer informa- meteorological stations used in this study tion regarding overestima- tion or underestimation of Station name Longitude (W) Latitude (N) Altitude (m) estimated data; low values Coro 69.68º 11.42º 16 of these mean errors are 71.73º 10.57º 66 desirable, though it should be noted that overesti- 69.32º 10.07º 613 mation of an individual 67.65º 10.25º 436 data element will cancel Caracas (La Carlota) 66.88º 10.50º 835 where di: difference between underestimation in a separate Barcelona 64.68º 10.12º 7 the measured and calculated observation.

Merida 71.18º 8.60º 1479 ratios H m /H 0 -H c /H 0, Nobs: However, these estimated er- Ciudad Bolivar 63.55º 8.15º 43 number of data pairs, H im: rors provide reasonable criteria S. Fernando de 67.42º 7.90º 47 measured solar radiation, to compare models but do not Tumeremo 61.45º 7.30º 180 Hic: calculated solar radia- objectively indicate whether a Puerto Ayacucho 67.5º 5.60º 73 tion, and Hio: extraterrestrial model’s estimates are statisti- solar radiation. cally significant. The t-statistic Source: WRDC The RMSE provides infor- allows models to be compared mation on the short-term per- and at the same time it indi- formance of the correlations cates whether or not a model’s I sc is the amount of en- Methods of analysis by allowing a term-by-term estimate is statistically signifi- ergy received at the top comparison of the deviation cant at a particular confidence of the Earth’s atmosphere Coefficient values were between the calculated and level (Stone, 1993; Jacovides measured at an average calculated from regression measured values. The smaller and Kontoyiannis, 1995; Toğrul distance between the Earth analysis between H/Ho and the value, the better the model et al., 2000). The t-statistic is and the Sun on a surface n/N for a long period and performs, but a few large er- defined as oriented perpendicular to for each month. This meth- rors in the sum can produce the Sun. The generally ac- od is considered by Tadros a significant increase in the cepted solar constant of (2000) as the best for pre- indicator. The values of the 118.108MJ·m -2 · day -1 is a dicting global solar radia- MBE represent the system- Results and Discussion satellite-measured yearly tion. Yorukoglu and Celik atic error or bias, while the average. The solar decli- (2006) concluded that the RMSE is a non-systematic er- According to the statistical nation in degrees can be statistical analysis should ror. A positive value of MBE test results, it can be seen computed from the Spencer be based on the ratio of shows an over-estimate while that all the regression equa- formula (Spencer, 1971): solar radiation to extrater- a negative value represents an tions gave good results. Table under-estimate by the model. II shows the values of the The MABE gives the absolute Angström model parameters, value of bias error and is a the statistical parameters cal- measure of the goodness of culated using the models are where the day angle Γ (ra- restrial solar radiation vs the correlation. The MPE is presented in Table III. dians) is given by the ratio of sunshine dura- an overall measure of fore- It is evident from Table II tion to day length. cast bias, computed from the that the values of a and b are Γ = 2π(nday-1)/365 The performance of the actual differences between subjected to a very large vari- models was evaluated on a series of forecasts and ac- ability. In the developed mod- where nday is the number of the basis of the statistical tual data points observed; els, the values of the constant the Julian day of the year, measures like root mean each difference starting from the first of Janu- square error (RMSE), being expressed Table II ary. The eccentricity correc- mean bias error (MBE), as a percentage Regression coefficients of Eq. (1) tion factor is calculated by the mean absolute bias error of each observed for each station expression (Spencer, 1971) (MABE), mean percent- data point, then summed and Station name a b averaged. The Coro 0.338 0.350 MAPE is an Maracaibo 0.253 0.263 and the geometric mean sun- age error (MPE), and mean overall measure of rise hour angle on a horizontal absolute percentage error forecast accuracy, Barquisimeto 0.260 0.376 surface, or theoretical sunrise/ (MAPE). These tests are computed from Maracay 0.297 0.291 Caracas (La Carlota) 0.315 0.226 sunset ws, can be calculated in the ones that are most the absolute dif- degrees from commonly applied in com- ferences between a Barcelona 0.283 0.296 paring the models of series of forecasts Merida 0.300 0.343 solar radiation esti- and actual data Ciudad Bolivar 0.302 0.256 mations (Ampratwum observed; each ab- S. Fernando de Apure 0.308 0.279 For a given month, the and Dorvlo, 1990; Hus- solute difference Tumeremo 0.269 0.352 maximum possible sunshine sain et al., 1999; Rehman, is expressed as a Puerto Ayacucho 0.289 0.215 duration can be calculated as 1999; Ertekin and Yaldiz, percentage of each All stations 0.263 0.344 N= ws /7.5 2000; Tadros, 2000; Toğrul actual data, then

282 APR 2008, VOL. 33 Nº 4 Table III Jacovides CP, Kontoyiannis H Results for t-statistic and explored errors (1995) Statistical procedures for the evaluation of evapo- Station name t-statistic * RMSE MBE MABE MPE MAPE transpiration computing mod- els. Agric. Water Manag. 27: Coro 0.000205 0.0321 0.000000 0.0244 -0.3166 4.2741 365-371. Maracaibo 0.000248 0.0313 0.000000 0.0238 -0.6243 5.9553 Martínez-Lozano JA, Tena F, Barquisimeto 0.000091 0.0502 0.000000 0.0424 -1.0325 8.6737 Onrubia JE, de la Rubia J Maracay 0.000358 0.0341 0.000001 0.0263 -0.4992 5.4417 (1984) The historical evolu- tion of the Angström for- Caracas (La Carlota) 0.000117 0.0317 0.000000 0.0256 -0.5400 5.9140 mula and its modifications: Barcelona 0.000223 0.0269 0.000000 0.0199 -0.3056 4.1159 review and bibliography. Merida 0.000265 0.0257 0.000000 0.0196 -0.2616 3.9600 Agric. For. Meteorol. 33: Ciudad Bolivar 0.000028 0.0273 0.000000 0.0212 -0.3391 4.5405 109-128. S. Fernando de Apure 0.000030 0.0539 0.000000 0.0468 -1.2903 9.8638 Menges HO, Ertekin C, Sonmete MH (2006) Evaluation of Tumeremo 0.000037 0.0377 0.000000 0.0287 -0.6759 6.3727 global solar radiation models Puerto Ayacucho 0.000246 0.0344 -0.000001 0.0291 -0.7259 7.2791 for Konya, Turkey. Energy All stations 0.000597 0.0517 0.000001 0.0410 -1.1738 8.7260 Conv. Manag. 47: 3149-3173. Prescott JA (1940) Evapora- * t at 5%=1.96. critical tion from water surface in RMSE: root mean-square error, MBE: mean bias error, MABE: mean absolute bias error, MPE: mean percentage relation to solar radiation. error, and MAPE: mean absolute percentage error. Trans. R. Soc. Sci. Austr. 64: 114-118. a varies from 0.253 to 0.338, of global solar radiation to the Almorox J, Benito M, Hontoria C Rehman S (1999) Empirical while the Angström-Prescott point where it has applications (2005) Estimation of monthly model of development and Angström-Prescott equation comparison with existing cor- coefficient b varies from 0.215 in the estimation of evapo- coefficients from measured relations. Appl. Energy 64: to 0.376. The overall mean and transpiration and crop growth daily data in Toledo, Spain. 369-378. deviation of the eleven values models. Renew. Energy. 30: 931-936. Sabziparvar AA, Shetaee H of a, b, and a+b were, respec- Ampratwum DB, Dorvlo ASS (2007) Estimation of global tively, 0.292 ±0.045; 0.295 Conclusion (1990) Estimation of solar solar radiation in arid and ±0.080; and 0.587 ±0.100. radiation from the number of semi-arid climates of East For the estimation of month- Solar radiation data is es- sunshine hours. Appl. Energy and West Iran. Energy 32: 62: 161-167. ly mean daily global solar ra- sential to the work of energy 649-655. Angström A (1924) Solar and diation, the best performance planners, engineers and agri- Spencer JW (1971) Fourier series terrestrial radiation. Quart. J. representation of the position based on RMSE, MABE, MPE cultural scientists. Based on Roy. Met. Soc. 50: 121-125. and MAPE was achieved for data at eleven stations in Ven- of the Sun. Search 2: 172. Boisvert JB, Hayhoe HN, Dubé the stations of Merida, Bar- ezuela, the Angström-Prescott PA (1990) Improving the es- Stone RJ (1993) Improved statis- celona and Coro. The results equation was obtained and timation of global solar ra- tical procedure for the evalu- were worse for S. Fernando, the corresponding empirical diation across Canada. Agric. ation of solar- radiation esti- For. Meteorol. 52: 275-286. mation models. Solar Energy Barquisimeto, Puerto Ayacucho coefficients are given for each 51: 289-291. and Tumeremo. The compari- station (Table II). The results Contreras A, Fausto Posso F, T son between the different mod- show that these Angström- Nejat Veziroglu (2006) Mod- Tadros MTY (2000) Uses of sun- eling and simulation of the shine duration to estimate the els according to the t value Prescott coefficients are site- production of hydrogen using global solar radiation over shows that for all the stations, dependent, and showed good hydroelectricity in Venezuela. eight meteorological stations the calculated t values were agreement. As the global solar Int. J. Hydrogen Energy. 32: in Egypt. Renew. Energy 21: less than the critical t value. radiation data are not available 1219-1224. 231-246. These results show that the for most areas in Venezuela, a Ertekin C, Yaldiz O (2000) Toğrul IT, Toğrul H, Evin D equations have statistical sig- countrywide general equation Comparison of some existing (2000) Estimation of global nificance for all the stations was developed on the basis of models for estimating global solar radiation under clear solar radiation for Antalya (Table III). the information at eleven sta- sky radiation in Turkey. Re- (Turkey). Energy Conv. Man- new. Energy 21: 271-287. Utilizing a combination of tions. This equation (2) can be ag. 41: 311-330. 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Guidelines MM (1999) Techniques to solar radiation by importing monthly average daily global for computing crop water obtain improved predictions global data sets. Agric. For. solar radiation in areas where requirements. FAO Irriga- of global radiation from sun- Meteorol. 137: 43-55. the radiation data is missing or tion and Drainage 56. Rome, shine duration. Renew. En- ergy 18: 263-275. unavailable. Its form is Italy. 290 pp. Yorukoglu M, Celik AN (2006) Almorox J, Hontoria C (2004) Iziomon MG, Mayer H (2001) A critical review on the es- H/Ho= 0.26+0.34(n/N) (2) Global solar radiation esti- Performance of solar radia- timation of daily global solar mation using sunshine dura- tion models - a case study radiation from sunshine dura- The present work will help tion in Spain. Energy Conv. Agric. For. Meteorol. 110 : tion. Energy Conv. Manag. advance the state of knowledge Manag. 45: 1529-1535. 1-11. 47: 2441-2450.

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