Analysis of Statistical Methods for Estimating Solar Radiation

Transcription

1 ISSN (hard copy) ISSN (olie) Aalysis of Statistical Methods Jaković Aleksadar A *, Lalić Braislava B Received: February 18, 014 Revised: March 11, 014 Accepted: April, 014 Abstract Daily global radiatio is ot oly required for a large umber of ecological, physiological ad agro-meteorological models but also is required for the desig ad evaluatio of solar eergy systems. Global radiatio data is quite frequetly ot available for all locatios. For such locatios daily global radiatio ca be estimated statistically usig cotiuous series of other measurable meteorological parameters. This paper cosiders four statistical methods for estimatig the daily global radiatio: Agstrom- Prescott, Coulse, Hargreaves ad Supit va Kapel method. The empirical coefficiets that characterize these methods were determied usig the least squares method for the two locatios ear Belgrade i Serbia. The results showed that calculated empirical coefficiets are similar to values that were previously determied i similar researches for eighborig coutries. Further aalysis verified accuracy ad applicability of four empirical relatios, where Ǻgstrom-Prescott ad Supit-Va Kappel methods proved to be by far the most reliable i the assessmet of daily global radiatio. Key words: Solar radiatio, meteorology, Agstrom-Prescott method, empirical coefficiets, Serbia, Belgrade Itroductio For statios where the global radiatio is ot measured or is partly missig there are several techiques for estimatig ad modelig global radiatio. All these models ca be divided ito two groups. The first group is based o the astrophysical properties of the Earth, atmospheric physics ad geometry of locatio for which global radiatio eeds to be estimated (Paulescu, et al., 013). Such modelig is called progostic or physical modelig, where it is commo to model seperately shortwave ad logwave solar radiatio. The secod group icludes those models which are based o statistical data or data obtaied from satellite observatios. This approach is called statistical modelig, where the most commoly used method is based o empirical relatios ad requires the developmet of equatios for estimatig solar radiatio accordig to the commoly measured meteorological variables. This type of modelig is kow as statistical modelig of global radiatio. The most accessible ad measured data are used as iput data for estimatig such as sushie duratio, air temperature, air temperature combied with cloudiess ad air temperature combied with total daily raifall (Trka, et al., 005). Researches o the assessmet of daily global radiatio i this regio were carried out i the previous period, but oe of these studies icluded all four referred methods for the area of Belgrade. The best kow are studies that Supit ad va Kappel (1998) performed for the eighborig coutries of Croatia ad Sloveia, Katic et al. (1979) for Vojvodia ad Paltieau ad Mihailescu (00) for eighborig Romaia. A Faculty of Architecture ad Civil Egieerig, Uiversity of Baja Luka, Stepe Stepaovića 77, Baja Luka, Bosia ad Herzegovia; ajakovic@agfbl.org B Faculty of Agriculture, Uiversity of Novi Sad, Trg Dositeja Obradovića 8, 1000 Novi Sad, Serbia; braka@polj.us.ac.rs * Correspodig author: Jaković Aleksadar, ajakovic@agfbl.org Geographica Paoica Volume 18, Issue 1, 1-5 (March 014) 1

2 Aalysis of Statistical Methods Methods ad data Methods Ǻgstrom proposed model for assesmet of daily global radiatio that was later altered ad improved by Prescott. Accordig to this method daily global radiatio G d is depedet o daily solar radiatio that reaches the top of the atmosphere G a ad the relative sushie duratio S r : G =G ( a +b S ) d a a a r where a a ad b a are empirical coefficiets for a give locatio (Sabziparvar, et al., 013). Empirical coefficiet a a has physical meaig ad represets the ratio of solar radiatio that reaches the earth s surface o a completely cloudy day ad solar radiatio that reaches the top of the atmosphere. The sum of coefficiets a a + b a represets same ratio of these two variables but durig a completely cloudless days (Tahâş, et al., 011). The values of these coefficiets are depedet o geographical locatio of statio. Ǻgstrom- Prescott method is based o the liear relatioship betwee variables. Atmospheric pheomea that most affect the radiatio that reaches the Earth s surface are clouds. O the basis of previous studies Supit ad Va Kappel (1998) a method i which depedece is preseted i the form of: G = G a ( T T ) + b 1 + c 8 d a s max mi s s where represets daily cloudiess i eights, T max ad T mi the maximum ad miimum daily temperatures ad a s, b s, ad c s the empirical coefficiets (Supit, va Kappel, 1998). Coulso method gives the empirical relatioship betwee the daily global radiatio G d ad daily cloudiess via: [ ] Gd = Gd0 1+ ( 1 ξ ) where itroduced labels have the followig meaigs, G d0 represets daily global radiatio that reaches the earth s surface o cloudless day, while ξ represets costat determied by empirical meas (Mihailović, 1988). Hargreaves et al.(1985) proposed simple method for estimatig daily global radiatio based o daily amplitude of air temperature: G d =Ga a H ( Tmax -Tmi)+ bh where a h ad b h represet empirical costats (Hargreaves, et al., 1985). Descriptio of locatio ad data sets Ǻgstrom- Prescott, Supit-Va Kappel, Coulso ad Hargreaves methods have bee tested for two locatios ear Belgrade, Zeleo Brdo (44 47 N ad 0 5 E, 4 m) ad Pačevo (44 50 N ad 0 40 E, 76 m). Data sets of measured global radiatio ad sushie duratio were required for testig Ǻgstrom-Prescott method. For verificatio of Supit-Va Kappel method data sets of measured global radiatio, maximum ad miimum daily temperatures ad cloud cover were required. I Coulso equatio daily global radiatio that reaches the earth s surface o cloudless day had bee determied by statistical aalysis as product of the mea aual value of trasmitace o cloudless day ad daily solar radiatio that reaches the top of the atmosphere. I additio to measured global radiatio data sets of cloudiess were required for this method. Data sets of measured global radiatio ad daily temperature amplitude were required for aalysis of Hargraves method. Groud measured global radiatio had bee take from two meteorological statios at Zeleo Brdo ad Pačevo, while data sets of daily cloudiess, sushie duratio, maximum ad miimum daily temperatures have bee take from climatological yearbook of RHMS (Republic Hydrometeorological Service of Serbia) ( rs/). Calculatio of empirical coefficiets Empirical coeficiets for Ǻgstrom- Prescott, Supit- Va Kappel, Coulso ad Hargreaves equatios were calculated usig the least squares method. I geeral case expressios for the coefficiets of liear fuctio are obtaied by applyig the least squares method i the form of: a= b= x y- xy ( ) x - x x xy- x y x - x ( ) where x ad y represet the calculated ad measured daily global radiatio, while represets the umber of measuremets (days) (Irwa, et al., 01). Root mea square error () i (kj/cm ) had bee calculated i order to verify obtaied results as well as the relative error i Gd : = ( Gd -Gi) Geographica Paoica Volume 18, Issue 1, 1-5 (March 014)

3 Jaković Aleksadar, Lalić Braislava = Gd Gd -Gi G where G d ad G i represet the observed ad estimated daily global radiatio ad represets umber of days for which daily global radiatio was estimated ad measured (Sabziparvar, 007). Results Mothly values of empirical coefficiets for both statios are show i Table 1. As previously stated these coefficiets are most depedet o the geographic locatio of statio (Rahma, et. al 005). To validate obtaied results we compared values of calculated coefficiets for three methods to values that Supit determied i his research for eighborig coutries. Average values of calculated empirical coefficiets for Ǻgstrom- Prescott method are approximate to the values that Supit obtaied i his research for adjacet lad Croatia (Zagreb, a a = 0. ad o b a = 0.56 ) (Supit, va Kappel, 1998). A similar thig applies to the calculated values of empirical coefficiets for Supit-Va Kappel method. They are approximate to values of empirical coefficiets that Supit determied o the basis of log-time series of measured global radiatio for adjacet lad Croatia (Split, a s = 0.11, b s = 0.36 ad Zagreb, a s = 0.10, b s = 0.3) (Supit, va Kappel, 1998). It must be emphasized that calculated values of empirical coefficiets for Coulso method fit almost perfectly with value that Katic ad associates determied i their research for Novi Sad i 1978 (Novi Sad, ξ = 1.89) (Mihailović, 1988). As with the first two metioed methods average values of calculated empirical coefficiets correspod to values that Supit determied for eighborig coutry Sloveia (Ljubljaa, a h = 0.18 ad Portorož, b h = 0.) (Supit, va Kappel, 1998). Ability of cosidered methods to truly reproduce daily global radiatio i area aroud Belgrade ad the validity of obtaied results ca be see i Figure 1 where is show correlatio betwee the calculated ad observed daily global radiatio. Table 1. Calculated empirical coefficiets for Ǻgstrom- Prescott, Supit-Va Kappel, Coulso ad Hargreaves methods Statio Pačevo Zeleo Brdo Moth Ǻgstrom-Prescott Supit-Va Kappel Coulso Hargreaves a a b a a s b s c s ξ a h b h Jauary February March April May Jue July August September October November December Average Jauary February March April May Jue July August September October November December Average Geographica Paoica Volume 18, Issue 1, 1-5 (March 014) 3

4 Aalysis of Statistical Methods Figure 1. Correlatio betwee observed ad measured daily global radiatio for a) Ǻgstrom- Prescott, b) Supit-Va Kappel, c) Coulso ad d) Hargreaves methods Table. Root mea square errors () ad relative errors () Statio Pačevo Zeleo Brdo Moth Ǻgstrom-Prescott Supit-Va Kappel Coulso Hargreaves (kj/cm ) (kj/cm ) (kj/cm ) (kj/cm ) Jauary February March April May Jue July Avgust September October November December Average Jauary February March April May Jue July Avgust September October November December Average Geographica Paoica Volume 18, Issue 1, 1-5 (March 014)

5 Jaković Aleksadar, Lalić Braislava It was ecessary to determie relative () ad root mea square error () for each moth i order to quatitatively aalyze obtaied results. The results are show i Table. All four methods estimate global radiatio poorer durig the cold period of the year. This applies especially to the moths of November ad December. O the other had all four methods estimate daily global radiatio very well i the moths of Jue ad July. Coclusio Aalysis of statistical modelig of global solar radiatio icluded the verificatio of the accuracy ad applicability of four empirical relatios: Ǻgstrom- Prescott, Supit-Va Kappel, Coulso ad Hargreaves methods for estimatig the daily global radiatio. It was ecessary to determie the coefficiets that characterize this geographic area for each of the empirical relatios. To determie the coefficiets it was ecessary to provide a cotiuous series of measured global radiatio as well as the other measured meteorological variables: sushie duratio, daily cloudiess ad daily temperature amplitude. Ǻgstrom-Prescott method proved to be by far the most reliable i the assessmet of daily global radiatio. Supit-Va Kappel method has also achieved very satisfactory estimate of daily global radiatio. Coulse ad Hargreaves method were chose for testig because of the ease ad availability of data, but o the other had those two methods proved to be far less able to estimate daily global radiatio. Evaluatio of daily gloal radiatio of the first two methods i the period from April to August is very good. Evaluatios for all other moths are to be regarded as satisfactory, except for December ad November whe the relative error is too large. The last two methods estimate daily global radiatio well i warmer part of year, but do ot estimate at satisfactory level i witer moths. The most likely cause of large deviatios of predicted value from measured value is the cloudiess that is most difficult to properly parameterize i these relatios. Refereces Hargreaves, G.L., Hargreaves, G.H., Riley, P Irrigatio water requiremet for the Seegal River Basi. Joural of Irrigatio ad Draiage Egieerig ASCE 111, Irwa, Y.M., Mohamed, I., Hussi, A. G., Safwati, I., Gomesh, N., Irwato, M. 01. Fidig the Best Fit for Solar Radiatio by statistical compariso betwee Liear Regressio (LS) ad Least Trimmed Squares (LTS) Regressio Method. Iteratioal Joural of Egieerig & Computer Sciece IJECS- IJENS Vol: 1 No: 06, Katic, P., Djukaović, D., Djakovic, P Climate of SAP Vojvodia. Faculty of Agriculture. Istitute of Field ad Vegetable Crops, Novi Sad, 37 pp. (i Serbia) Mihailovic, D., Basics of meteorological observatios ad data processig, Faculty of Agriculture. Istitute of Field ad Vegetable Crops, Novi Sad, 17 pp (i Serbia) Paltieau, C.R., Mihailescu, I.R., Torica, V., Albu, A.N. 00. Correlatio betwee sushie duratio ad global solar radiatio i south-easter Romaia. Iteratioal Agrophysics 16, Paulescu, M., Paulescu, E., Gravila, P., Badescu, V Weather Modelig ad Forecastig of PV Systems Operatio, Gree Eergy ad Techology, Spriger-Verlag Lodo, Rahma, M.M., Zakaria, M Modified Agstrom coefficiets for the sushie-irradiatio correlatio. Idia Joural of Radio & Space Physics, Vol. 34, Sabziparvar A. A A simple formula for estimatig global solar radiatio i cetral arid deserts of Ira. Reewable Eergy No: 33, Sabziparvar, A.A., Mousavi, R., Marofi, S., Ebrahimipak, N.A., Heidari M A Improved Estimatio of the Agstrom Prescott Radiatio Coefficiets for the FAO56 Pema Moteith Evapotraspiratio Method. Water Resources Maagemet, Volume 7, Issue 8, Supit, I., va Kappel, R.R A simple method to estimate global radiatio. Solar Eergy, Tahâş, S.V., Ristoiu, D., Cosma, C Treds of the global solar radiatio ad air temperature i Cluj- Napoca, Romaia ( ). Atmosphere ad earth physics, vol. 56, Nod 5-6, Trka, M., Žalud, Z., Eitziger, J., Dubrovsky, M Global solar radiatio i Cetral Europea lowlads estimated by various empirical formulae. Agriculture ad Forest Meteorology 131, Geographica Paoica Volume 18, Issue 1, 1-5 (March 014) 5