Evaluation of cloudiness/haziness factor for composite climate

Transcription

1 Evaluation of cloudiness/haziness factor for composite climate H.N. Singh, G.N. Tiwari * Centre for Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi , India Abstract In this communication, an attempt has been made to evaluate the cloudiness/haziness factor for the composite climate of New Delhi (latitude: 28.58v N; longitude: 77.02v E; elevation: 216 m above msl). To estimate the hourly variation of beam and diffuse radiation on a horizontal surface for any day, atmospheric transmittances for beam and diffuse radiation have been introduced to take into account the uncertain behaviour of atmospheric conditions. For the present study, the hourly data of global and diffuse solar radiation on a horizontal surface for a period of 10 years ( ) have been used and analyzed using linear regression analysis. The data have been obtained from the Indian Meteorological Department, Pune, India. It has been observed that there is about 15% maximum deviation between predicted and observed values of hourly varying beam and diffuse radiation for clear (blue sky) weather condition. Keywords: Solar radiation; Cloudiness/haziness factor and atmospheric transmittance 1. Introduction Solar energy has diurnal and seasonal variability. Based on climatic parameters and atmospheric transmission, a large number of radiation models have been proposed and tested. In order to determine direct normal irradiance (DNI) in terrestrial regions, the concept of turbidity coefficients was introduced by various scientists. These refer to: the Linke turbidity factor, T L (broad band) [1-6]; Angstrom turbidity parameters a and b (spectral band) [7-9]; the Shuepp coefficient, B (broad band); the Unsowrth-Monteith turbidity factor, T U (broad-band), etc. [10].

2 H.N. Singh, G.N. Tiwari / Energy XX (2004) XXX-XXX Nomenclature IHB terrestrial beam solar radiation on a horizontal surface at ground level (W/m 2 ) IHD diffuse solar radiation on a horizontal surface at ground level (W/m 2 ) ION normal extraterrestrial solar radiation (W/m 2 ) I N normal terrestrial solar radiation at the ground level (W/m 2 ) I Sc solar constant (W/m 2 ) K1 perturbation factor (dimensionless) K 2 background diffuse radiation (W/m 2 ) m air mass (dimensionless) n day of the year, starting from 1 st January T R cloudiness/haziness factor (dimensionless) e root mean square of percentage deviation r regression coefficient Greek letters i atmospheric transmittance for beam radiation (dimensionless) 8 integrated Rayleigh scattering optical thickness h z solar zenith angle The above models are applicable only to clear (cloudless) sky condition. Nayak [11] has reviewed the developed models to estimate the monthly average of daily total and diffuse radiation on a horizontal surface. Kasten [12,13] has studied in detail the attenuation of solar radiation in terms of air mass, optical thickness of clear and dry atmosphere and Linke turbidity factor. Ineichen and Perez [14] have attempted the formulation of air mass independent turbidity coefficients to evaluate beam radiation. Skartveit et al. [15] and Perez et al. [16] have developed direct conversion models to estimate direct radiation from global radiation. It has been observed that the selection of a model for estimating the hourly beam and diffuse radiation at ground level on a horizontal surface is difficult and such a model is rarely available [17,18], particularly for composite climate (one of the Indian climatic conditions). Both the hourly beam and diffuse radiation depend on a number of factors, such as (i) accuracy of estimation, (ii) average climatic conditions, (iii) latitude, (iv) seasonal variations and (v) the earthsun angles. The hourly beam and diffuse radiation on a horizontal surface are the basic need for any solar energy system for optimization of parameters before fabrication. In this communication, an attempt has been made to develop a simple model to evaluate the hourly varying beam and diffuse radiation from measured hourly global and diffuse radiation data for the following weather conditions: (a) clear day (blue sky); (b) hazy day (fully);

3 H.N. Singh, G.N. Tiwari / Energy XX (2004) XXX-XXX (c) (d) hazy and cloudy (partially); and cloudy day (fully). The above four weather conditions constitute the composite climate of New Delhi. 2. Present approach In terms of air mass m, integrated Rayleigh scattering optical thickness of atmosphere e and Linke turbidity factor T R, the terrestrial beam radiation received on a horizontal surface is expressed in classical equation form as: I HB = I N cosh z = ION exp( m e 7R) cosh z where I O N (W/m 2 ) is the normal extraterrestrial solar radiation and is expressed by I ON = 7 sc [1.0 þ 0 : 033 cos(360«/365)] I H B is the hourly beam radiation on the horizontal surface derived from hourly global and diffuse radiation (Table 1); h z is the solar zenith angle at a given time (Eq. (1.13) of [19]). The parameters m and e [12,13] are expressed as: and m = [cos6 z þ 0 : 15 x ( Z )- L253 }- 1 e = 4 : 529 x 10" 4 m 2-9 : x 10" 3 m þ 0 : The Linke turbidity factor T R for clear blue sky condition (type 'a') has been calculated by linear regression analysis using Eq. (1a). The results for hourly variation of beam radiation on horizontal surface (Eq. (1a)) by using the obtained Linke turbidity factor T R are shown in Fig. 1. The raw data of hourly variation of beam radiation on a horizontal surface from Table 1 are also shown in the same figure for comparison. These figures indicate that there is a significant deviation between predicted (by using calculated T R ) and given data (Table 1). The Linke turbidity factor T R, which is a measure of the vertically integrated amounts of aerosol and other suspended particulate matter in the atmosphere, is different at different times on even the same day. Since m and e are computed from theoretical assumptions, Eq. (1a) does not accommodate the level of cloudiness/haziness (condition types 'a-d'), and transient and unpredictable changes in the atmospheric conditions. To accommodate the additional depletion in DNI in terrestrial regions due to cloudiness/haziness, and transient and unpredictable changes, atmospheric transmittance for beam radiation, a, has been introduced in Eq. (1a) as IHB = ION exp[-(m e TR þ a)] cosh z (4) This additional depletion in DNI can be considered to be due to the following main reasons: 1. transient change of aerosol level (dust) in terms of content as well as size; 2. unpredictable movements and disturbances in the upper atmosphere due to temperature difference between the layers. (1a) (1b) (2) (3)

4 4 H.N. Singh, G.N. Tiwari / Energy XX (2004) XXX-XXX Table 1 Average hourly global and diffuse radiation (W/m 2 ) in (a) January (b) June for all weather types Time (a) January Weather type a Total Diffuse b Total Diffuse c Total Diffuse d Total Diffuse (b) June Since Eq. (4) accommodates the precipitable water level in the lumped atmosphere, henceforth, T R will be defined as cloudiness/haziness factor for the lumped atmosphere Regression analysis for cloudiness / haziness factor (T R ) and atmospheric transmittance for beam radiation (a) Eq. (4) can be rewritten after normalization as or ION cosh z = exp[ (m ETR þ a ln ION IHB = -T R -(m (5)

5 H.N. Singh, G.N. Tiwari / Energy XX (2004) XXX-XXX e = 15.66% r = 1.00 Seam (obs) Beam (pre) Diffuse (pre) Diffuse (obs) Beam {obs) Beam {pre) Diffuse (obs) Diffue (pre) Time (hours) Fig. 1. Hourly variation in beam and diffuse radiation with time for the months of (a) January and (b) June (type 'a' weather condition) using Linke turbidity coefficient. Comparing Eq. (5) with the standard straight line equation Y1 = M 0 X 1 þ C (6) we can write 7, =ln X = m e

6 6 H.N. Singh, G.N. Tiwari / Energy XX (2004) XXX-XXX M' = T R and C = -a. By linear regression analysis of Y1 on X1, regression coefficients M and C0, and hence the cloudiness/haziness factor T R and atmospheric transmittance for beam radiation a, can be evaluated Regression analysis for perturbation factor and background diffuse radiation for lumped atmosphere In order to evaluate hourly diffuse radiation on the horizontal surface, a well known expression is given [19] by IHD = -T- (/ON - cosh z (7a) The above equation can be used to determine hourly diffuse radiation with the help of Eq. (1a,b). Its variation for the clear sky (type 'a') condition for typical winter and summer months have been shown in Fig. 1. It is evident that there is a significant difference between calculated hourly values of diffuse radiation and the given data of Table 1. Hence, there is a strong need to modify Eq. (7a). Eq. (7a) can be rewritten in terms of constants K 1 (dimensionless) and K 2 (W/m 2 ) as IHD = K1 ÐION - /N) cosh z þ K 2 where IN (W/m 2 ) is the normal terrestrial solar radiation at ground level. The constants K1 and K 2 can be defined as atmospheric transmittances for diffuse radiation and can be evaluated using linear regression analysis for given data of hourly variation in diffuse radiation (Table 1) and known hourly values ofion (Eq. (1b)), IN and cos h z (Eq. (1a)). Further, the constant K 1 can be interpreted as the 'perturbation factor' for describing scattering out of a beam traversing the lumped atmosphere, and K 2 can be referred to as 'background diffuse radiation'. After obtaining the hourly beam (Eq. (4)) and diffuse (Eq. (7a,b)) radiation and the horizontal surface, the total radiation for a solar thermal device of any inclination and orientation can be evaluated using the Liu and Jorden formula [20]. (7b) 2.3. Root mean square of percentage deviation (e) and coefficient of correlation (r) The closeness of hourly predicted values of solar radiation, using the evaluated parameters T R, a, K1 and K 2, to the experimental averaged data has been presented in terms of root mean square of percentage deviation and coefficient of correlation using the expression: e = (8)

7 H.N. Singh, G.N. Tiwari / Energy XX (2004) XXX-XXX where -<*pre(z) ^pre(z) -<*exp(z) x 100 and r = Xpre fe N- fe^re) " i pre The values of e and r for the reproduced data are shown in respective figures. 3. Experimental data For the present study, the hourly global and diffuse solar radiation (W/m 2 ) on a horizontal surface for a period of 10 years ( ) have been used. The data have been obtained from the India Meteorological Department, Pune, India. The data for the composite climate of New Delhi have been obtained using a thermoelectric pyranometer with (diffuse) and without (global) a shade ring. The shade ring factor (SRF) has been used to make corrections for shaded sky assuming that sky radiation is isotropic. The pyranometers used are calibrated once a year with reference to the World Radiometric Reference (WRR). The estimated uncertainty in the measured data is about ±5%. For the computation of TR, a, K1 and K 2, the beam radiation data have been derived from the measured hourly global and diffuse radiation data. For every month over the period of 10 years, the number of days falling under different weather conditions has been given in Table 2. The average number of days falling under different weather conditions in each month has been obtained on the basis of recorded weather observations, given total sunshine hours and daily global radiation. Table 1 gives the average hourly measured data for total and diffuse radiation for the typical Table 2 Total number of days under different weather types in different months during Climate type a b c d Month Jan 28 (9%) 72 (23%) 111 (36%) 99 (32%) Feb 34 (12%) 45 (16%) 117 (42%) 85 (30%) Mar 45 (15%) 63 (20%) 123 (40%) 79 (25%) Apr 41 (14%) 67 (22%) 139 (46%) 53 (18%) May 39 (13%) 90 (29%) 117 (38%) 64 (20%) June 32 (11%) 38 (13%) 137 (46%) 93 (30%) July 13 (4%) 24 (8%) 91 (29%) 182 (59%) Aug 14 (5%) 27 (9%) 65 (21%) 204 (65%) Sept 65 (22%) 27 (9%) 106 (35%) 102 (34%) Oct 52 (17%) 94 (30%) 133 (43%) 31 (10%) Nov 66 (22%) 96 (32%) 119 (40%) 19 (6%) Dec 29 (9%) 72 (23%) 133 (43%) 76 (25%)

8 Table 3 Evaluated cloudiness/haziness factor and atmospheric transmittances (TR, a, K1, K 2 ) for (a) weather type 'a', (b) weather type 'b', (c) weather type 'c' and (d) weather type 'd' Parameter Month Jan (10) Feb (10) Mar (10) Apr May June July Aug Sept Oct Nov (9) Dec (9) (a) Weather TR a K1 K 2 type 'a' Otq (b) Weather TR a K1 K 2 type 'b' c; (c) Weather TR a K1 K 2 type 'c' ^ (d) Weather TR a K 1 K 2 type 'd'

9 H.N. Singh, G.N. Tiwari / Energy XX (2004) XXX-XXX (c) Ma) Ki(b) Me) K,(d Ki(avg) Jan Feb Mar Apr May June July Aug Sept Oct NDV Dec Month Jan Feb War Apr May June July Aug Sept Oct Nov Dec Month a (a) «(b) a(c) ci(d) o(avg) Ma) Mb) Me) Md> K;(avg) Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Month Month Fig. 2. Variation of (a) cloudiness/haziness factor (TR), (b) atmospheric transmittance for beam radiation (a), (c) perturbation factor (K1) for diffuse radiation and (d) background diffuse radiation (K 2 ) for diffuse radiation in different months for all weather types. months of January (winter conditions) and June (summer conditions), respectively. The data of Table 1 have been used in evaluating T R, a, K 1 and K 2. Similar data for other months have also been obtained and used. The numbers in brackets represent the monthly average daily total sunshine hours in different months. 4. Results and discussion In order to evaluate TR and a of Eq. (4), for the month of January and June, Eq. (6) has been used for linear regression analysis. For regression analysis, the data of Table 1 have been used. Similarly, T R and a for other months have also been obtained. The results for each month and all weather conditions (types 'a-d') are given in Table 3 and shown in Fig. 2, which can be used to generate the hourly beam and diffuse radiation data for New Delhi. Table 4 Evaluated cloudiness/haziness factor and atmospheric transmittances (T R, a, K 1, K 2 ) for average weather condition (types a-d) Month Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Parameter (10) (10) (10) (12) (12) (13) (12) (12) (9) (9) K

10 10 H.N. Singh, G.N. Tiwari / Energy XX (2004) XXX-XXX 700 -i 600 e = 2.36% r= ' Beam (obs) - - Beam (pre) -*- Diffuse (obs) -*- Diffuse (pre) i e = 11.00% r = Beam (obs) - - Beam (pre) -*- Diffuse (obs) -»- Diffuse (pre) Fig. 3. Hourly variation in beam and diffuse radiation with time for the month of January: (a) type 'a' and (b) type 'd', using cloudiness/haziness factor and atmospheric transmittances. The atmospheric transmittances K 1 and K 2 for diffuse radiation in Eq. (7b) have again been obtained by regression analysis from the data of Table 1 and other months. The results for K 1 and K 2 for each month and all weather conditions (types 'a-d') are given in the same table (Table 3). From Fig. 2a, it can be seen that the cloudiness/haziness factor T R is maximum for cloudy days (type 'd') due to attenuation of radiation in the atmosphere, unlike for clear days (type 'a'). The values of T R for other weather conditions (types 'b' and 'c') lie between these two extreme values, as expected (Fig. 2a).

11 H.N. Singh, G.N. Tiwari / Energy XX (2004) XXX-XXX 11 e = 9.59 % r = Beam (obs) - Beam (pre) - Diffuse (obs) - Diffuse (pre) Time (hours) -Beam (obs) - Beam (pre) -Diffuse (obs) - Diffuse (pre) Time (hours) Fig. 4. Hourly variation in beam and diffuse radiation with time for the month of June: (a) type 'a' and (b) type 'd' using cloudiness/haziness factor and atmospheric transmittances. The values of atmospheric transmittance for beam radiation a are higher for cloudy conditions (type 'd', Table 3), as expected (Fig. 2b). The values of K 1 and K 2 for each month vary according to the weather conditions and instability in them (Fig. 2c and d). Table 4 provides the values of T R, a, K1 and K 2 for average data (types 'a-d') of each month over a period of 10 years. It indicates that the value of TR is minimum for an average clear month and maximum for an average cloudy/hazy month. The other constants (a, K 1 and K 2 ) behave according to the average weather conditions.

12 12 H.N. Singh, G.N. Tiwari / Energy XX (2004) XXX-XXX Figs. 3 and 4 give the hourly variation in observed and predicted beam and diffuse radiation for the typical months of January (winter) and June (summer), respectively. It is inferred that there is a 2-5% deviation between observed and predicted values for clear days (type 'a'), as shown in Fig. 3. This percentage deviation increases up to 10-15% for the month of June due to unstable weather conditions, as shown in Fig. 4. This percentage deviation is more dominant for the type 'd' weather condition, as expected. 5. Conclusions and recommendation From the present studies, it is evident that by defining T R as the cloudiness/haziness factor and introducing atmospheric transmittance for beam radiation a, the perturbation factor K1 and background diffuse radiation K 2 for diffuse radiation provide a simple model for the prediction of hourly beam and diffuse radiation on a horizontal surface for the composite climate of New Delhi. The present studies should be extended to the other climatic conditions of India. Acknowledgements The authors are grateful to the Indian Meteorological Department, Pune, India for providing the hourly global and diffuse radiation data for the period of 10 years from 1989 to References [1] Linke F. Transmission koeffiezient and turbidity factor. Beitr Phys Fr Atom 1922;10: [2] Gueymard C. Critical analysis and performance assessment of clear sky solar irradiance models using theoretical and measured data. Solar Energy 1993;51: [3] Gueymard C. Direct solar transmittance and irradiance predictions with broadband models. Part-I: detailed theoretical performance assessment. Solar Energy 2003;74: [4] Gueymard C. Direct solar transmittance and irradiance predictions with broadband models. Part-II: validation with high-quality measurements. Solar Energy 2003;74: [5] Kasten F. A simple parameterization of two pyrheliometric formulae for determining the Linke turbidity factor. Meter Rdsch 1980;33: [6] Grenier JC, Casiniere ADL, Cabot T. A spectral model of Linke's turbidity factor and its experimental implications. Solar Energy 1994;52(4): [7] Pinazo JM, Canada J, Bosca JV. A new method to determine Angstrom's turbidity coefficient: its application for Valencia. Solar Energy 1995;54(4): [8] Tadros MTY, El-Metwally M, Hamed AB. Determination of Angstrom coefficients from spectral aerosol optical depth at two sites in Egypt. Renew Energy 2002;27: [9] Gueymard C. Importance of atmospheric turbidity and associated uncertainties in solar radiation and luminous efficacy modelling, Edinburgh; [10] Unsowrth MH, Monteith JL. Aerosol and solar radiation in Britain. QJR Meteorol Soc 1972;98: [11] Kamal R, Maheshwari KP, Sahney RL. Solar energy and energy conservation. New Delhi: Wiley Eastern Limited; [12] Kasten F. A new table and approximate formula for relative optical air mass. Arch Meteorol Geophys Bioklimatel Ser B 1965;14: [13] Kasten F, Young AT. Revised optical air mass tables and approximation formula. Appl Opt 1989;28:

13 H.N. Singh, G.N. Tiwari / Energy XX (2004) XXX-XXX 13 [14] Ineichen P, Perez R. A new air mass independent formulation for the Linke turbidity coefficient. Solar Energy 2002;73(3): [15] Skartveit A, Olseth JA, Tuft ME. An hourly diffuse fraction model with correction for variability and surface albedo. Solar Energy 1998;63(3): [16] Perez R, Ineichen P, Maxwell E, Seals R, Zelenka A. Dynamic global to direct conversion models. ASHRAE Trans 1990;98: [17] Hawas MM, Muneer T. Study of diffuse and global radiation characteristics in India. Energy Covers Mgmt 1984;24(2): [18] Muneer T, Gul M, Kambezedis H. Evaluation of an all-sky meteorological radiation model against long-term measured hourly data. Energy Covers Mgmt 1998;39(3/4): [19] Tiwari GN. Solar energy fundamentals, design, modeling and applications. USA: CRC Press; [20] Liu BYH, Jordan RC. The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 1960;4(3):1-19.