Aylık ortalama güneş ışınımı hesaplamalarında ardışık yerine koyma yöntemi /
Yazar: AHMET DURAN ŞAHİN
Danışman: PROF.DR. ZEKAYİ ŞEN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1996
Konu: Meteoroloji = Meteorology
Dizin: Güneş radyasyonu = Solar radiation

Özet:
ÖZET On sekizinci asrın ortalarında başlayan endüstri devrimi ile büyük değişimler sonucunda insanlar daha fazla enerjiye ihtiyaç duymuşlardır. Bunun sonucunda yenilenemiyen enerji kaynaklan olarak bilinen kömür, petrol ve odun tüketimi artmıştır. Artıştaki bu gidiş sonucunda bu kaynakların tükenir olması, çevreyi kirletmeleri alternatif (yenilenebilir) enerji kaynakları arama ihtiyacı ortaya çıkarmıştır. Özellikle 1970'lerdeki petrol krizi bu arayışı hızlandırmıştır. Yenilenebilir enerji kaynaklarının temelini Güneş oluşturmaktadır. Güneşten dünyamızın dış atmosferine ulaşan ışınım, yeryüzüne ulaşana kadar atmosferde yansıma, saçılma, yutulma gibi fiziksel olaylarla karşılaşmaktadır. Yeryüzüne ulaşan ışınım hesaplamaları önemli bir problem oluşturmuştur. Özellikle mühendislik hesaplamalarında aylık ortalama günlük ışınıma ihtiyaç duyulmuştur. Angstrom (1924)'de yeryüzünda ölçülen ışınımın, açık gün ışınımına oranının, ölçülen gökyüzü kapalılığının, açık gökyüzü gün uzunluğuna oranının doğrusal değiştiğini öne sürmüştür. Daha sonraları bu açık gökyüzü ifadesi yerine atmosferin dış yüzüne gelen ışınım ve gün uzunluğu ele alınmıştır. Angstrom doğru şeklindeki denkleminin iki katsayısının genelde bütün yıl boyunca veya mevsimler boyunca sabit kabul edilegelmiştir. Tezin esas amaçları arasında bu katsayıların sabit olmadığı kabulü ile, ülkemizdeki 28 istasyonda ışınım ve güneşlenme verilerinin istatistiksel analizini yaparak en uygun dağılım fonksiyonlarını bulmaya çalışmaktır. Burada geliştirilerek uygulanan ikili yöntemde birbirini izleyen iki ay arasında doğrusallık kabulü yapılarak her bir ay çifti için en uygun katsayılar bulunmuştur. Dolayısıyla herbir istasyon için sabit katsayılar yerine n-1 adet katsayı tahminleri elde edilmiştir. Bu katsayılar dizisinin istatistiksel analizi ile kullanılması gereken en uygun değerin ' en sık değer (mod) ' olduğu sonucuna varılmıştır. Ayrıca en küçük kareler yöntemiyle her bir istasyon için sabit katsayılar kullanılarak haritalar çizilmiştir. İlave olarak herbir istasyon için 'çokgenler' oluşturulmuş ve iki katsayı arasında regresyon analizi yapılmıştır. Katsayıların zamanla değişimi yapılan çalışmalar arasında yer almaktadır. ix

Abstract:
SUMMARY A NEW METHOD FOR ANGSTROM FORMULA WITH PHYSICALLY RANDOM COEFFICENTS AND APLICATION FOR TURKEY A simple substitution method is proposed for dynamic estimation of Angstrom's coefficients which play significant role in relation of the global radiation to the sun shine duration through a linear model. After explaining the physical meaning of the coefficients, their mathematical estimation procedures are presented on the basis of successive global radiation and sun shine duration record substitutions into the model. This new procedure yields a series of parameter estimations, the arithmetic averages of which are closely related to the classical regression method estimates. The series of model parameters estimation provides an ability to assess these parameters statistically. Consequently, such a dynamic parameter estimation procedure evaluates and enables one to make interpretations with their normal and extreme values. The methodology is applied to 28 radiation measurement stations all over Turkey, Angstrom equation parameters' regional variations are obtanied for whole of the country. Additionally, necessary relative frequency distribution functions of these parameters appeared in the form of Beta distribution. The earth has a continuous power input of 1.73xl014 kW from the sun as annual energy 'income' of 1.5xl018 kWh (1.9xl014 ton coal equivalent). This figure so much larger than the magnitudes which we are accustomed. It is difficult to appreciate its significance. It is, in fact, about ten thousand times larger than the current annual world energy consuption. Our first cocern with solar energy is, that it is abudent. We note also that it is free. Unfortunately, it is spread over a large area and the peak power density is only 1 Kw/M2 at the earth's surface at noon in the tropics. Power density also varies considerably with latitude, season and, of course, time of day. Solar power is of particular interest to the developing countries, since most of this lie in lattitudes which recive continous solar energy. In fact, 80% of the world's population lives between the latitudes 35°N and 35°S with 3000 to 4000 hours of sunlight per year. In energy terms this is around 2000 kWh/m2 year (0.25 t.c.e./m2 year) Dunn(1986). Power density is relatively high and in this low latitudes there is little seasonal variation. First of all, we want to show earth-sun relationship and the effect of atmospher to solar radiation. The eccentricity of earth's orbit is such that the distance between the sun and the earth varies by 1.7%. The radiation emitted by the sun and its spatial relationship to the earth result in a nearly fixed intensity of solar radiation outside of the earth's atmosphere. The solar constant Gs, is the energy from the sun, per unit time, received on a unit area of surface perpendicular to the direction of propagation of the radiation, at mean earth-sun distance, outside of the atmosphere. Before rockets and spacecraft, estimates of the solar constant had to be made from ground based measurements of solar radiation after it had been transmitted through the atmosphere and thus in part absorbed and scattered by components of the atmosphere. These studies and later measurements from rockets were summarized byJohnson (1945), Abbot's value of the solar constant of 1322 W/m2 was revised upward by Johnson to 1395 W/m2. Additional spacecraft measurements have been made with Hickey et. al. (1982) reporting 1373 W/ m2 and Wilson et. al. (1981) reporting 1368 W/ m2. Measurements from three rocket fligths reported by Duncan et. al. (1982). The World Radiation Center (WRC) has adopted a value of 1367 W/ m2, with an uncertainty of the order of %1. We will use this constant at calculation of daily extraterresrial radiation to horizontal surface. The source of variation in extraterresrial radiation must be considered. The first is the variation in the radiation emitted by the sun. It has been suggested that there are small variations (less than ±1'.5%) with different periodicities and variation related to sunspot activities. Willson et. al.(l?81) report variances of up to 0.2% correlated with the development of sunspots.,jR, mean earth-sun distance, R, in a time earth-sun distance, Gs solar constant, // latitude angle, S declination angle and H, hour angle using all of these variables we can calculate the extraterresrial radiation as 1440, v ( Cosji ? CosS ? SinH + H ? Strip. Sinö) ( 1 ).71 After that we look at the effect of earth atmosphere to reduce solar radiation. The length of path through the atmosphere will depend on the angle that the sun makes with the vertical at a particular position on the earth's surface. Some of incident radiation is directly reflected by the earth's atmosphere, the remainder is absorbed either by the atmosphere or the earth's surface. Above 150 km, the incident radiation is not affected by the atmosphere: by 88 km the X-rays and some of the ultra-violet has been removed. As the radiation approaches the eart's surface, gas molecules in the air cause scattering, particularly at the shorter wavelength end of the spectrum. This effect gives rise to blue sky, and the red appearance of the sun. The latter is particularly pronounced at sunset and sunrise owing to increasing path length through thr air. Clouds and dust also cause scattering and absorption. About 30% of the incident solar radiation is reflected by the atmosphere, a further 20% is absorbed on passing throuh the atmosphere and the remaining 50% arrives at the earth's surface, where 2% is reflected and the remainder absorbed. An amount equal to 23% of the original solar energy incedent on the outer atmosphere is used in evaporation and the remainder is lost by long wave radiation. Since the atmosphere radiates long wave radiation to the earth's surface, the net long wave loss from the earth's surface will be the difference between these two heat fluxes. About 0.2% is absorbed by the atmosphere in the form of winds and ocean currents. On the other hand, photosnthesis accounts for only 0.05%. The annual mean irradiance on a horizontal plane at the earth's surface is averaged over 24 hours. For the most favoured regions the average flux density is ashigh as 300 W/m2 and the average for the tropics is about 250 W/rn2. In more temperate regions, such as most of Europe, the value is around half of this value. Angström(1924) formula helps to estimate the global daily, monthly and yearly solar radiation amount, H, from the comperatively simple measurements of sun shine duration, S according to 7r = a + ^Tr (2) where' H0 and So are the cloudless daily global irradiation received on a horizontal surface at ground level and sunshine duration, i.e., day length; both a and b are model parameters. This equation has been used most often all over the world in order to calculate the global radiation at locations of sunshine duration measurements and for extending the global radiation estimations from available shorter time interval data. Later, Prescott (1940) has modified this equation by talcing into account some other relevant meteorological variables. Invariably, all over the world the coefficients are estimated from available irradiation and sunshine duration data at a location through the use of statistical least squares regression technique. Routinely recorded daily global radiation and sunshine duration values are used through the regression technique for determining the coefficients in equation (2). This technique separates the scatter diagram of H versus S into two parts. First is the explained part which is included in the coefficient estimations and the remaining is unexplained part which is, in fact, the deviations from the regression line. The use of such determined linear model provides only explained portion of the scatter diagram in the predictions of global radiation from the sunshine duration. In order to include effects of unexplained part, it is necessary to estimate coefficients from the successive data pairs locally rather than globally as in the classical regression approach. Let us first consider the physical meanings of parameters a and b in equation (1). First of all a represents the ratio of actual global radiation, H, to the daily extraterrestrial irradiation, Ho provided that physically the sun is covered by clouds all over the day, so that S = 0, i.e., overcast weather. On the other hand, b corresponds to the slope of the linear relationship which corresponds to the change of global radiation with the sunshine duration, as, h d{HIHo) b-H{srs6)~ (3) This first order ordinary differential equation can be written in terms of backward finite difference method as (H) b!-^J (H) UJ >'-l ^V: [I] i=2,3,4 n (4)Herein, n is the number of records and b'\ is the the rate of global radiation change with the sunshine duration between time instancas i-1 and i. For daily data, these are successive daily rates of change or in the case of monthly records it is the rate of successive monthly change ratios. Arrangement from equation (2) by considering equation (4) leads to the successive timel estimates of or' as fH^ a \HoS '^ V?n J i=2,3,4,...,n (5) The application of these last two equations to actual relevant data yields (n-1) coefficient estimations. Each pair of the coefficient estimate \a.\,b\\ explains the whole information for successive pairs of global radiation and corresponding sunshine duration records. On the other hand, estimations of Angstrom's coefficients by the application of regression technique are obtained as single values as b = and /=! İ-1 J H H *'\ i-\ (6) a H_ \H0 -b- ?=- (7) Comparisons of equations (4) and (6) as well as (5) and (7) indicate that the regression technique estimations do not allow any variability in the coefficients calculation. However, as will be seen in section 4, the range of finite difference method coefficient estimations will subsume the regression technique estimations. This provides flexibility in the parameters estimation. Furthermore, it is possible to obtain the relative frequency distribution, i.e., histogram of Angstrom coefficients, a\ and b\. Additionally, it is also possible to calculate any statistical parameter such as the variance or standard deviation of these parameters. Last but not the least, confidence limits can be stated at a certain significance level as 5% or 10%, in the coefficients estimation. Extreme values of a\ and b\ become observable by the finite difference method solution. Taking the average value of both sides in equation (5) leads to finite difference averages of Angstöm coefficients as (8)Furthermore, the diffrence of this expression from equation (7) results in a'~a = (b~b')\~ ^ (9) This means that the ratio of difference between the regression and substitution method parameters remains constant which is equal to the percentage of sunshine duration over the period considered. Theoretically, equation (9) indicates that only for continuous overcast sky conditions i.e., for S= 0,a' = a. On the contrary, during clear sky conditions equation (9) yields S = S0. Comparison of this expression with equation (7) indicates the invariability of coefficients summation by two different methods as a + b=a' + b'J - I (10) This sum is equivalent to the average ratio of global to extraterrestrial radiation in the case of cloudless sky. Turkey is located between latitudes 36° N and 42° N and longitudes 26° E and 45° E. It has relatively significant solar energy potential especially in the southern parts including the Mediterrenean region. In general, 28 global radiation and sunshine duration measurement stations scattered all over the country are considered for regionalization study in this thesis. Substitution method is applied independently for each station and finally, parameter estimstion series for a' and b' are obtanied but it is neither necessary nor the space of this thesis is suitable for their presentation In any planing, howewer, the use of mode values are recommended. Also the relative error (RE) percentage. Between the classical method arithmetic average and the mode values of the substitution model are considered. These percantages indicate how the arithmetic averages deviate from the mode values. By making use of the longitudes and latitudes the regional variations of the average parameter are shown which are obtained by the Kriging i.e., geostatistical methods in the computers. In this way, it is possible to obtain average a' and b' values for any location within the country. It is also obious from these two maps that both a' and b' do not change significantly in the north-south direction but east-west variations are more often. However, coefficient values have greater values in the eastern part of the country. This is meteorogicaly very plausible because eastern Turkey has many days of the year as overcast sky due to high elavations reaching up to 6500 m above the sea level. Besides, the cool period of the year covers almost 9 months of the year. On the contrary, along the Aegean sea coast in the west towards central Anatolia the days with clear sky are very often and the climate at places has Meditterean sea effects. However, the regional variation of b' coefficient has just the opposite trend to the east-west variation of a' and this is the expected meteorological situation as explained above. In order to support these conclusions in detail are prepared for regional variations of the same parameters but this time with elevation. It is obvious that the highest a' values concentrate on the eastern part of Van city where the Ararat Mountain is located which is the highest peak in the country. In the south which corrosponds to the Mediterraneanregion the values of a' remain almost constant around 0.34. b' values remain constant about 0.24 in the eastern mountainous part of Turkey. Similarly to a', in the south b' values remain almost constant. In short, geographical information to radiation variations over the country. However, maps in Figures 4 and 5 show the change of a' and b' with elevation and lattitude. In northern parts of Turkey, a' increases continuously with elevation but b' has opposite trend. However, in the southern longitudes a' and b' remain almost constant with elevation. The scatter diagram between the Angstrom coefficients is also obtained in the thesis. There appears an inverse relationship between these two parameters. It means that low b' values are coupled with high a' values and vice versa. The general trend relationship between a' and b' is a' = -0.6 W + 0.52 (11) The empirical relative frequency distributions of average a' and b' values on a regional basis can be obtained from data availble in Table 2. It is to be noticed from the same table that a' and b' values are confined between zero and one. This piece of information implies that Beta-type of theoretical frequeny distribution is suitable for the parameters regional estimations.