# CORRELATIONS FOR A MEDITERRANEAN CLOUD COVER MODEL

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3 Figure 1. Comparison between both models to evaluate the best behavior for Rome latitude, during a completely cloudless day. The G(N)/G(0) ratio was calculated for each hour where N was estimated and all this values were analyzed in monthly, seasonal and globally range. In the same way the D(N)/G(N) ratio was carried out. For both ratios power and polynomial fitting were achieved, to make a comparison with the previous described models. 2.1 Global radiation data analysis As shown in Figure 2, total mean data set trough power and polynomial functions were investigated and their both correlation coefficients were compared. Standard deviation of the recorded data was also shown for each value of N. Therefore, could be evident the higher value of the correlation coefficient related to power function than the polynomial one, but it does not take in account the high value of G(N)/G(0) between 1 otka and 3 okta. This behavior is interesting because give additional information about the bond between global and scattered radiation, successively discussed. The comparison with Kasten and Czeplak power function for the ratio G(N)/G(0) was proposed in Figure 2 with polynomial trend and power trend that best approximates Tor Vergata s data. Polynomial trend has a maximum value (1.13) for N 3 (partially overcast) and decrease till 0,44 for N=8 (overcast condition). Power fit starts from 1.1 at N=0 and decrease till 0.34 for N=8. Figure 2. Data trend of global radiation are presented with their standard deviation. Polynomial and power function related to mean data plot are presented. In addition Kasten and Czeplak fit is shown.

4 Otherwise the function s trend of Kasten and Czeplak has a maximum value (1) for N=0 (clear sky condition) and decrease till 0,25 for N=8 (overcast condition). The equations produced through a Mathcad 14.0 regression estimate using the data collected in Rome are shown below: G(N) G(0) *N *N 2 (4) G(N) G(0) 1.1 0,757*( N 8 )6 (5) G(N) G(0) 1 0,75*( N 8 ) (6) Equation (4) is the second order polynomial function proposed by the author; equation (5) is a function in which coefficient were generated by power regression of all the data collected in Rome, as proposed by Kasten and Czeplack (6) but in which coefficient has been calculated in Hamburg. The high value of the exponential coefficient give a wider flat trend and a low decrease that starts at 4 okta instead of 2 okta as Kasten s trend. This behavior is known in literature, but often not so extensively with respect to N values: when compared with the classical curves from Kasten and Czeplak [2], the results obtained for Rome show as a matter of evidence a wider platform of high values of G(N)/G(0). For a complete comparison between different climates we propose also another Italian work carried out in Bologna (44 29 N E, norther taly) by Nardino and Georgiadis [8]. Table 1. Coefficients of the power function proposed by Kasten and Czeplak, for G(N)/G(0) ratio calculated in three different sites. G(N)/G(0) Hamburg Rome Bologna a -0,75-0,757-0,99±0,06 b 3,4 6 1,3±0,1 2.2 Diffuse radiation data analysis The diffuse radiation rate was also investigated. In this case are represented polynomial and power fit in order to make a complete comparison with Kasten and Czeplak work. Correlation coefficient shows that the fit that best approximate Tor Vergata s data is polynomial. The comparison with Kasten and Czeplak trend shows, moreover, the overestimation that their formula performs in Mediterranean climate. The equation of the D(N)/G(N) ratio for Hamburg and Rome are proposed below: - (7) (8) (9)

5 Figure 3. Data trend of diffuse radiation are presented with their standard deviation. Polynomial and power function related to mean data plot are presented. In addition Kasten and Czeplak fit is shown. Again the best approximation is given for polynomial fit. Two consideration were necessaries: during summer time D(N)/G(N) decreases for 1 N 3 because direct component is strongest than the scattered one. During coldest season the decrease for 1 N 3 is lower because the scattered is strongest than the direct component. The comparison with Kasten and Czeplak trend shows, moreover, the overestimation that their formula performs in Mediterranean climate. Is important to put in evidence that this correlation does not include any model, as happen for global radiation: both D(N) and G(N) are measured value, so their trend is not affected by model s errors. 2.3 Applications An useful application of this graphs is that the knowledge of one parameter (as example D(N)/G(N) ratio Figure 3) could be used to find the corresponding N value and then find the provisional G(N)/G(0) ratio using the other graph (Figure 2), as shown in Figure 4. Figure 4. Example of correlation s application.

6 The same procedure could be done by inverting the parameter s choice to evaluate the scattered rate. For a complete comparison between different climates, the work carried out in Bologna by Nardino and Georgiadis [8] is again considered: Table 2. Coefficients of the power function proposed by Kasten and Czeplak, for D(N)/G(N) ratio calculated in two different sites. D(N)/G(N) Hamburg Rome a 0,3 0,15 b 0,7 0,65 A possible explanation of this fact is attempted in the paper, by means of the role played by the simultaneous effects of either water vapor content of the air (high), and wind speed (low), both at the ground level. 2.4 Seasonal data trends Seasonal data were investigated to give additional information about the influence of clime variability during the year. Little differences in seasonal data trends help to understand why the authors chose the polynomial function as the best approximation for Rome s latitude. Figure 5. Data trend of global radiation from April 15 th 2009 to May 31 th 2010 are presented with their standard deviation. Polynomial and power function related to mean data plot are presented. In addition Kasten and Czeplak fit is shown.

7 Figure 6. Data trend of diffuse radiation from April 15 th 2009 to May 31 th 2010 are presented with their standard deviation. Polynomial and power function related to mean data plot are presented. In addition Kasten and Czeplak fit is shown. As shown in Figure 5 spring time gives a pronounced polynomial fitting, while winter time is more close to power fitting. It probably depends on the different kind of cloud that are prevailing in every seasons. In fact is more presumable that during spring cumulus clouds occurs, while during winter stratus clouds are more frequent. Usually cumulus clouds does not cover the whole sky and scatter radiation in all directions. Otherwise stratus often cover uniformly the whole sky, reducing reflection and scattering phenomenon. Equation for every season of polynomial fit are presented in Table 3 and in Table 4: Table 3. Seasonal coefficient of polynomial fit of G(N)/G(0) ratio. Season Coefficient A Coefficient B Coefficient C Autumn Winter Spring Summer

9 5. REFERENCES [1] Kimura K., Stephenson D.G., 1969, Solar radiation on cloudy days, ASHRAE Transaction, Vol. 75, [2] Kasten F., Czeplak G., 1980, Solar and Terrestrial Radiation dependent on the Amount and Type of Cloud, Solar Energy, Vol. 24, [3] Duffie, J. A., Beckman W. A., 1980, Solar Engineering of Thermal Processes, John Wiley, New York, pp [4] Duchon C.E., O Malley M.S., 1998, Estimating Cloud Type from Pyranometer Observations, Journal of Applied Meteorology, Vol. 38, [5] Spena A., 1996, Fondamenti di Energetica, Cedam, Vol. I, Padova, pp [6] A. Spena, C. Cornaro, G. Intreccialagli, D. Chianese, Data Validation and Uncertainty Evaluation of the ESTeR Outdoor Facility for Testing of Photovoltaic Modules, 12 th EU PV SEC, Hamburg, September [7] A. Spena, S. Bartocci, C. Cornaro, G. D Angiolini, C. Di Tivoli, C. Strati, Advanced results of modelling, experiments, and innovative solar energy components conception at FTA laboratories, ASME-ATI-UIT 2010 Conference on Thermal and Environmental Issues in Energy Systems, May, 2010, Sorrento, Italy. [8] Nardino M., 2003: Effetti della copertura nuvolosa nella ripartizione dell energia solare: studio del microclima locale per scopi Agrometeorologici, PhD Thesis, Facoltà di Agraria, Università di Sassari.

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