APPLICATION OF TIME-SERIES METHODS FOR THE MODELING OF SUNSHINE DURATION SEQUENCES UDC :551;5]:523.9

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1 FACTA UNIVERSITATIS Seres: Workng and Lvng Envronmental Protecton Vol.11, N o 2, 2014, pp APPLICATION OF TIME-SERIES METHODS FOR THE MODELING OF SUNSHINE DURATION SEQUENCES UDC :551;5]:523.9 Mlan Protć, Momr Raos, Jasmna Radosavljevć, Ljljana Žvkovć, Nenad Žvkovć, Emna Mhajlovć Faculty of Occupatonal Safety of Nš, Unversty of Nš, Serba Abstract. Ths paper presents the applcaton of statstcal methods to determne the length of solar radaton based on the data obtaned from the meteorologcal staton Negotn, and we may presume that these data are also representatve for a wder area of northeastern Serba. Negotn s a town n northeastern Serba, n the Bor Dstrct, wth the populaton of ca , near the border wth Romana and Bulgara. The results of the applcaton of statstcal methods allow us to predct the future trend of the tme seres,.e. to predct the sunshne duraton n the sample area. We performed the measurements usng several models to predct the trend of the tme seres of sunshne duraton, whereby t was essental to use the most sutable model. Selecton and evaluaton of models were appled to a seres of annual sums of sunshne duraton observed between 1991 and 2011 n the meteorologcal staton n Negotn. Usng an ARIMA model and the trends method, we obtaned the predctons of sunshne duraton n Negotn up to The predcton results show the reduced sunshne duraton on annual bass over the observed tme of predcton. Key words: meteorologcal tme seres, ARIMA model, trends method, sunshne duraton 1. INTRODUCTION Generally, energy s one of the three basc elements of survval of the human speces on Earth, together wth materals and food. The largest source of energy on Earth s the Sun, whch s smultaneously crculatng and beng deposted. Solar energy s clean and nexhaustble, and ts use has the best prospects for the future. The reducton of conventonal energy resources and ncrease of energy demand n the modern world only confrm ths vew. Receved May 20, 2014 / Accepted January 14, 2015 Correspondng author: jasmna.radosavljevc@znrfak.n.ac.rs Faculty of Occupatonal Safety n Nš, Čarnojevća 10A, Nš, Serba Phone: E-mal: jasmna.radosavljevc@znrfak.n.ac.rs

2 154 M. PROTIĆ, M. RAOS, J. RADOSAVLJEVIĆ, LJ. ŽIVKOVIĆ, N. ŽIVKOVIĆ, E. MIHAJLOVIĆ It s known that solar energy s very unevenly dstrbuted, wth sgnfcant spatal and temporal (seasonal and non-perodcal) fluctuatons [1-6]. Solar radaton energy that reaches the Earth's surface and a specfc locaton depends prmarly on the duraton of the radaton. WMO defnes the duraton of sunshne (h- hours) as the perod n whch the tensty of drect solar radaton that reaches the Earth's surface s greater than 120 W/m 2. Duraton of solar radance and ntensty of solar radaton n a certan locaton vares daly and annually [7, 8]. Insolaton of a gven locaton on Earth and the amount of heat comng from the Sun n a short perod of tme s drectly dependent on the degree of cloudness. In hs paper, Stamenc [9] states that the most favorable areas n Serba have a large number of sun hours and that the annual rato of actual rradaton to the total possble rradaton s approxmately 50 % [10-14]. There s an ncreasng number of studes and papers whose am s to determne to what extent the clmate s changng and what the predctons for the future are. The statstcal approach s the most mportant n the analyss of tme seres. Varous statstcal procedures can be used for the modelng of tme seres for sunshne duraton, ncludng varous models based on the applcaton of statstcal tme-seres analyss. Modelng of tme seres assumes that a tme seres s a combnaton of a formula and a random error [9, 15, 16]. There are several models for tme seres predcton: autoregressve models [17], movng-average models, lnear regresson models [18], as well as combned models,.e. autoregressve ntegrated models of movng average (ARIMA). These models have become very popular for predctng seres of meteorologcal elements n an observed tme of predcton. The models are smple to use and useful for predctng data n meteorology and hydrology. In ths paper, we used an ARIMA model and the trends method to predct the trend of sunshne duraton. 2. METHODOLOGY To montor trends of annual sunshne duraton n the regon of Negotn, we used a sequence of data for the perods between 1961 and 1990 and between 1981 and 2010, for the man meteorologcal staton Negotn (lattude 44 o 13 N, longtude 22 o 31 E, H = 42m elevaton above mean sea level). In order to analyze the tme seres of sunshne duraton trends, observed n the perod from 1991 to 2011 at the meteorologcal staton Negotn, we used the trends method and an ARIMA model, verson The processng of the results was performed by means of software program Statstcs, Release 8, developed by Stat Soft Inc., Tulsa, OK, USA. 3. RESULTS AND DISCUSSION The sum of annual sunshne duraton for the perod from 1961 to 1990 n northeastern Serba (Negotn meteorologcal staton) was hours on average, whch s about 46% of the possble duraton (Fgure 1) [12]. Solar radaton n the perod from 1981 to 2010 showed consderably hgher values compared to the mult-year average. Fgure 1 shows the average values of the actual sunshne duraton n the sprng, summer, and wnter, or the vegetaton perod. It can be observed from Fgure 1, that the sprng has more sunshne hours (569.9) than autumn (424.2), whch concdes wth the annual course of ar temperature. The wnter

3 Applcaton of Tme-seres Methods for the Modelng of Sunshne Duraton Sequences 155 perod has the fewest hours of sunshne, only 241.2, whle the most hours of sunshne occur n the summer (874.0). In the vegetaton perod the number of sunshne hours s large ( h), whch has a postve mpact on the vegetaton. In the vegetaton perod between 1961 and 1990, the actual nsolaton was h (55.9% of the possble hours), whereas for the perod between 1981 and 2010 t was h (58.0% of the possble number of hours of nsolaton). Fg. 1 Average values of the actual sunshne duraton for dfferent seasons of the year and for the vegetaton perod expressed n hours [h] Fgure 2 presents the average monthly sunshne duraton. For the perod from 1981 to 2010, durng the calendar year, hgher values of the average monthly sunshne duraton occur n the frst 8 months whereas lower values occur durng the fnal 4 months. The hghest percentage of nsolaton occurs n the month of July amountng to ca h, whch s about 66.3% of the possble nsolaton. The lowest percentage of nsolaton occurs n December, about 22.5% of the possble nsolaton, because durng ths month the degree of cloudness s hgher than durng other months. Fg. 2 Average monthly sunshne duraton expressed n hours [h] Fgure 3 shows the annual amount of solar radaton. Durng the observed perod, the hghest values of solar radaton were regstered n hours. The mnmum value of solar radaton recorded at the Negotn staton was only hours n 2005.

4 156 M. PROTIĆ, M. RAOS, J. RADOSAVLJEVIĆ, LJ. ŽIVKOVIĆ, N. ŽIVKOVIĆ, E. MIHAJLOVIĆ Fg. 3 Annual sums of sunshne duraton n Negotn (northeastern Serba), n hours [h] In addton to the total annual number of sunshne hours, the number of sunshne hours durng certan months s also sgnfcant. Insolaton s the lowest n the wnter months, and the hghest when the days are long, the temperature hgh, and relatve humdty low. Sunshne duraton and cloudness are negatvely correlated f cloudness ncreases, sunshne duraton decreases. The hghest nsolaton of about 10 hours per day s n July and the lowest n December, when the sun shnes averagely 2 hours per day, as shown n Fgure 4. Fg. 4 Average daly sunshne duraton n Negotn (northeastern Serba) expressed n hours [h], S real tme, S o astronomcal The value of the data for average annual cloudness, gven n Fgure 5 for the perod from 1981 to 2011, shows that the sky n Negotn durng a sngle year s more clouded than clear. It can be concluded that the mnmum of cloudness was regstered n 2000, and the maxmum n 1996 [24].

5 Applcaton of Tme-seres Methods for the Modelng of Sunshne Duraton Sequences 157 Fg. 5 Average annual cloudness 4. THE TRENDS METHOD Many researchers suggest that the trends method s the most complex of all statstcal methods of dynamc analyss of mass phenomena. It can be sad that ths s the most mportant method for a tme-seres analyss. Based on ths method we estmate and predct future trends and development of phenomena. Sekarc [14] states that the practce shows that the trends method s best suted for the analyss of the dynamc tme seres that are gven n one-year duratons. Trends and development of sunshne duraton on annual bass shows a straght-lne drecton and the value of the trend ( y ) n a general explct expresson can be mathematcally expressed as: y a bx (1) where a and b are parameters that determne the poston and the nclne of the trend lne. Quantty x s the ndependent varable that observes tme. The trend must satsfy the followng condtons: the sum of the dstances of orgnal data from the trend lne must be equal to zero,.e.: ( y y) 0 (2) the sum of the squared devatons of orgnal data from the trend lne must be less than the sum of the squared devatons of orgnal data 2 ( y y) mn Usng expresson 3, we obtan the system of equatons from whch we calculate parameters a and b, whch satsfy the condton of least squares: y na b x (4) 2 x y a x b x (5) By solvng ths system of equatons wth the condtonal method, we obtan the value of parameters a and b, whch wll serve to calculate the trend for each perod. The parameters a and b can be calculated usng the formulas: (3)

6 158 M. PROTIĆ, M. RAOS, J. RADOSAVLJEVIĆ, LJ. ŽIVKOVIĆ, N. ŽIVKOVIĆ, E. MIHAJLOVIĆ b a y (6) n x y x Analytcal determnaton of the trend functon of sunshne duraton and the numercal calculaton of the value of an element of that sunshne duraton s shown n Table 1. Table 1 Analytcal determnaton of the trend functon of sunshne duraton and the numercal calculaton of the value of an element of that sunshne duraton Year 2 Sunshne duraton [h], y x x x y y n = 21 y x Accordng to ths method, the expected sunshne duraton n 2015 wll be hours. 2 (7) 5. ARIMA MODEL Chronologcally ordered numercal sunshne duraton data n northeastern Serba (meteorologcal staton Negotn) represent tme seres. It s possble to apply the tmeseres calculaton by usng the Box-Jenkns' teratve approach [9, 19, 20] and an ARIMA model. Analyss and predcton of sunshne duraton by means of ARIMA model are shown n Fgure 6.

7 Applcaton of Tme-seres Methods for the Modelng of Sunshne Duraton Sequences 159 Fg. 6 Annual sunshne duraton forecasts ( ) The results of the analyss and predcton of sunshne duraton show a decrease of hours per year, from the ntal hours to hours n the last predcted year, as shown n Fgure 6. Table 2 Sunshne duraton forecasts for the perod from 2012 to 2015 usng an ARIMA model 6. CONCLUSION Results and analyses of sunshne duraton predctons n the observed tme ndcate a decrease n the number of sunshne hours, obtaned by applyng the trends method and an ARIMA model. Accordng to the trends method, the expected sunshne duraton s hours and the ARIMA method predcton s hours. The dfference n predcton between these two methods s 51.3 hours. Ths s a practcal ndcator of the senstvty of dfferent models and evdence that they should be appled carefully.

8 160 M. PROTIĆ, M. RAOS, J. RADOSAVLJEVIĆ, LJ. ŽIVKOVIĆ, N. ŽIVKOVIĆ, E. MIHAJLOVIĆ The mult-year sequence of sunshne duraton for the perod from 1991 to 2011 s an ncreasng one, wth a very favorable seasonal schedule. Resources of solar radaton n Serba are above the European average, so t s possble to use ths type of energy effectvely and n a long term. Ths s evdence that any nvestment n the feld of solar energy n ths regon s justfed and cost-effectve. The broader socal sgnfcance of the use of solar energy s reflected n the substtuton of fossl fuels, envronmental protecton, the prospects of usng solar energy n many branches of ndustry, economc and busness development, and ncreased standard of lvng and qualty of lfe. Acknowledgement. Research reported n ths paper was supported by the Mnstry of Educaton, Scence and Technologcal Development of the, Republc of Serba wthn the project No. III and the project No. TR REFERENCES 1. G. Athanassoul, and G. Massouros (1983): The nfluence of solar and long-wave radaton on the thermal gan of a room wth opaque external wall, Sol. Energy, 30(1983), 2, pp K.Bakrc: Correlatons for Estmaton of Solar Radaton on Horzontal Surfaces, (2008), J. Energy Eng., 134 (2008), 4, CEC, European Solar Radaton Atlas, Vol. I Horzontal Surfaces, Commsson of the European Communtes, 1984a. 4. CEC, European Solar Radaton Atlas, Vol. II Inclned Surfaces, Commsson of the European Communtes, 1984b. 5. D. Feurmann, (1990): A Repettve Day Method for Predctng the Long-Term Thermal Performance of Passve Solar Buldngs, ASME J. Sol. Energy Eng, 112, 1, pp P. Gburck, V. Gburck, and M.B. Gavrlov, V. Srdanovc, S. Mastlovc: Complementary Regmes of Solar and Wnd Energy n Serba, Geographca Pannonca, 10 (2006), pp Y. Jang, (2009): Correlaton for Dffuse Radaton from Global Solar Radaton and Sunshne Data at Bejng, Chna, J. Energy Eng., 135 (2009), 4, pp R.W.Katz, and R.H. Skaggs, (1981): On the use of autoregressve-movng average processes to model meteorologcal tme seres,. Mon. Wea. Rev., 109 (1981), pp Lj. Stamenc, (2009): Use of solar photovoltac energy n Serba, Belgrade. 10. M. Lambc, (2000): Solar walls The Passve solar heatng, 2 nd edton, Unversty of Nov Sad, Techncal Faculty Zrenjann, Serba. 11. G.M.Ljung, and G.E.P. Box, (1979): The lkelhood functon of statonary autoregressve-movng average models, Bometrka, 66 (1979), 2, pp T. Mansh, K. Manoj, and S. Rpunja, (2008): Tme seres models for smoothng and forecastng weather parameters nfluencng forest fres, Statstc n transton, 9, (2008), 3, pp M. Santamours, et al., (1999): Modelng the Global Solar Radaton on the Earth s Surface Usng Atmospherc Determnstc and Intellgent Data-Drven Technques, Journal of Clmate, 12 (1999),10, pp M. Sekarc, (2004): Quanttatve methods, Statstcs, Belgrade. 15. J. Radosavljevc, and A. Djordjevc, (2001): Defnng of the Intensty of Solar Radaton on Horzontal and Oblque Surfaces on Earth, Facta Unverstats, Seres: Workng and Lvng Envronmental Protecton, 2 (2001), 1, pp P. Gburck, et al, (2004): Study of potental of Serba for explotaton of wnd and solar energy, MNZŽS, Natonal energy effcency programs, EE A, Belgrade. 17. J. Ledolter, (1977): The analyss of multvarate tme seres appled to problems n hydrology, Journal of Hydrology, 36 (1977), pp Meteorologcal year book 1, Clmatologcal data, for perod , Hydro-meteorologcal Insttute of Serba, Box. G.E.P., and Jenkns. G.M., (1976): Tme seres analyss: Forecastng and control, San Francsco. CA: Holden Day.

9 Applcaton of Tme-seres Methods for the Modelng of Sunshne Duraton Sequences V.Badesceu, (2008): Use of Sunshne Number for Solar Irradance Tme Seres Generaton, Modelng solar radaton at the earth s surface, Sprnger. 21. Z. Chen, B. Yu,and P.A. Shang, (2007): Calculatng Method Of Albedo and Expermental Study of ts Influence on Buldng Heat Envronment n Summer, ASME, J. Sol. Energy Eng., 129 (2007), 2, pp J. De Goojer, and R. Hyndman, (2006): 25 years of tme seres forecastng, Internatonal Journal of Forecastng, 22 (2006), pp J. Wu, C. Chan, J. Loh, F. Choo, and L.H. Chen, (2009): Solar radaton predcton usng statstcal approaches, ICICS, (2009), pp Republc Hydro-meteorologcal Insttute of Serba, Serba Weather Staton n Negotn, Measurements of cloudness n Negotn for perod PRIMENA METODA VREMENSKIH SERIJA ZA MODELIRANJE NIZOVA DUŽINE TRAJANJA SIJANJA SUNCA Rad predstavlja rezultate prmene statstčkh metoda u određvanju dužne trajanja sjanja Sunca na osnovu podataka dobjenh sa meteorološke stance Negotn, pr čemu se može smatrat da ov podac maju karakter reprezentatvnost za šre područje severostočne Srbje. Rezultat prmene statstčkh metoda daju mogućnost predvđanja trenda budućh vremenskh serja, odnosno mogućnost predvđanja dužne trajanja sjanja Sunca na uzorkovanom prostoru. U radu je koršćeno nekolko modela u predvđanju trenda vremenskh serja dužne trajanja sjanja Sunca, pr čemu je najvažnje prment odgovarajuć model. Izbor ocena modela prmenjen su na serju godšnjh suma dužne trajanja sjanja Sunca posmatranh u perodu god. na meteorološkoj stanc u Negotnu. Prmenom ARIMA metoda metode trenda u radu su data predvđanja trajanja sjanja Sunca na području Negotna (severostočna Srbja) do godne. Rezultat predvđanja pokazuju smanjenje dužne trajanja sjanja Sunca na godšnjem nvou u posmatranom vremenu predvđanja. Kljuĉne reĉ: meteorološka vremenska serja; ARIMA model; metod trenda, dužna trajanja sjanja Sunca