Study of diffuse and global radiation characteristics in India

Recently, the Indian Meteorological Department has made available, for 13 locations in India, pyranometric data for total and diffuse radiation on an hourly and daily basis. The period of observation is from 1957 to 1975. This data is analysed to reexamine the correlations between monthly-average daily values of diffuse and total insolation and between hourly and daily insolation. The relationship between monthly diffuse/total and total/extraterrestrial ratios is found to be linear. The present correlation implies that the diffuse component is significantly larger than that predicted by other correlations. No noticeable effect of location or seasonal variation was found. Comparison of the present data with earlier studies for India indicates a trend of increasing diffuse radiation with the lapse of time. The ratio of hourly to daily insolation agrees with the Liu and Jordan correlation for total insolation but differs significantly for diffuse radiation. The need for refinement of the Liu and Jordan correlation between hourly and daily diffuse radiation is pointed out.     

The frequency distribution of daily insolation values

Frequency distributions of insolation values are needed in order to derive simple correlations for predicting the performance of solar energy systems. In this paper the frequency distribution of daily total hemispherical solar irradiation values on the horizontal surface is derived from measured data for 90 locations in the U.S. The results can be approximated by generalized distribution curves which depend only on the clearness index, defined as ratio of terrestrial over extraterrestrial insolation. The results agree well with the curves originally derived by Liu and Jordan, except for a correction at high insolation values. The deviation of individual locations from the generalized curves is examined. A breakdown according to time of year reveals some seasonal variation. The theoretical distribution corresponding to random insolation sequences is also derived; it agrees very well with the generalized frequency distribution curves.     

Simple procedure for predicting long term average performance of nonconcentrating and of concentrating solar collectors

The Liu and Jordan method of calculating long term average energy collection of flat plate collectors is simplified (by about a factor of 4), improved, and generalized to all collectors, concentrating and nonconcentrating. The only meteorological input needed are the long term average daily total hemispherical isolation on a horizontal surface and, for thermal collectors the average ambient temperature. The collector is characterized by optical efficiency, heat loss (or U-value), heat extraction efficiency, concentration ratio and tracking mode. An average operating temperature is assumed. If the operating temperature is not known explicitly, the model will give adequate results when combined with the , f-chart of Klein and Beckman.A conversion factor is presented which multiplies the daily total horizontal insolation to yield the long term average useful energy delivered by the collector. This factor depends on a large number of variables such as collector temperature, optical efficiency, tracking mode, concentration, latitude, clearness index, diffuse insolation etc., but it can be broken up into several component factors each of which depends only on two or three variables and can be presented in convenient graphical on analytical form. In general, the seasonal variability of the weather will necessitate a separate calculation for each month of the year; however, one calculation for the central day of each month will be adequate. The method is simple enough for hand calculation.Formulas and examples are presented for five collector types: flat plate, compound parabolic concentrator, concentrator with east-west tracking axis, concentrator with polar tracking axis, and concentrator with 2-axis tracking. The examples show that even for relatively low temperature applications and cloudy climates (50°C in New York in February), concentrating collectors can outperform the flat plate.The method has been validated against hourly weather data (with measurements of hemispherical and beam insolation), and has been found to have an average accuracy better than 3 per cent for the long term average radiation available to solar collectors. For the heat delivery of thermal collectors the average error has been 5 per cent. The excellent suitability of this method for comparison studies is illustrated by comparing in a location independent manner the radiation availability for several collector types or operating conditions: 2-axis tracking versus one axis tracking; polar tracking axis versus east-west tracking axis; fixed versus tracking flat plate; effect of ground reflectance; and acceptance for diffuse radiation as function of concentration ratio.     

Hourly vs daily method of computing insolation on inclined surfaces

Insolation on south-facing inclined planes has been computed using hourly values of total and diffuse radiation, obtained from experimental data. Such a computation procedure is then compared with the widely used method by Liu and Jordan for obtaining daily insolation on surfaces tilted toward the equator. Very small differences are noted between the results obtained by the two methods. These differences are mainly due to three factors; (a) Liu and Jordan's formulation uses a theoretical day-length while the hourly method uses day-length as incicated by the radiation data; (b) hourly method takes into account the asymmetries of total and diffuse radiation around solar noon while the daily method implicitly assumes symmetry of the same; (c) the daily method assumes uniform atmospheric transmissivity to beam radiation throughout the day. On the other hand, the hourly method assumes constant atmospheric transmissivity for one hour only.     

Diffuse solar radiation estimates from sunshine hours and clearness index for Karachi, Pakistan

Correlations for the estimation of monthly average daily diffuse solar radiation as a function of the sunshine hours and clearness index have been obtained from Karachi. Generally, two types of correlations are used: (a) diffuse radiation as a function of relative sunshine hours and extraterrestrial radiation, and (b) diffuse radiation as a function of global and extraterrestrial radiation. These correlations are mostly first- and second-order polynomials in the sunshine hours and clearness index, indicating the presence of the diffuse solar radiation component. The diffuse solar radiation shows a peak value during the monsoon months of July–August. The diffuse to global ratio is found to be 0.32 from the analysis, and the diffuse to extraterrestrial radiation ratio is nearly 0.19 throughout the year. Among the established relations, Iqbal and Stanhill overestimate the radiation value, while Liu and Jordan underestimate it.     

Estimation of daily total and diffuse insolation in India from weather data

Insolation and weather data for a large number of cities in India is analysed and correlated. Correlations based on a citywise regression analysis indicate that daily total insolation correlates best with sunshine duration, all clouds and precipitation. However these relations are not useful for predicting insolation at locations where this data is not measured. Monthwise correlations which are valid over a region are more useful. Hence such correlations have been developed for Indian conditions. In order to increase the accuracy of prediction of these correlations, India is divided into two regions on the basis of the climatic characteristics of the winter monsoon.Finally the Liu and Jordan model for predicting daily diffuse radiation from daily total radiation has been tested and found to be applicable for Indian conditions. However the numerical values obtained are very different from those obtained for conditions in the United States.     

A novel approach for calculating the monthly average daily fraction of diffuse solar radiation

A novel approach for calculating the monthly average daily fraction of diffuse radiation has been developed. It is based upon the use of concurrent total solar radiation measurements for both a tilted surface and a horizontal surface. It divides the data into two categories, clear and cloudy day, on an hourly basis. The clear day data is analyzed by means of both Liu and Jordan's and Page's empirical equations. The cloudy day data is analyzed by Liu and Jordan's equation for determining the insolation ratio on a tilted to a horizontal surface. A monthly average value for the diffuse fraction is then determined by calculating a weighted average of the clear and cloudy day values.The monthly average values, for twelve months of Beer Sheva data, for the fraction of diffuse radiation have been calculated and compared to the empirical relationships derived by Liu and Jordan and Page. The agreement between the calculated values and empiriical relationship is somewhat better in the latter case.     

Empirical relations for the determination of solar radiation in Ibadan, Nigeria

Variations in the average monthly, seasonal and daily patterns of total radiation, relative humidity, temperature and sunshine duration in Ibadan have been presented. Various empirical models relating solar radiation to the basic climatological parameters such as relative humidity, sunshine hours, temperature as well as geographical declination, latitude and altitude factors were investigated from the viewpoint of obtaining appropriate empirical formulae to determine solar radiation from such common parameters. The average monthly total radiation is shown to be predicted with reasonable accuracy by a couple of empirical formulae with the best result obtained from a newly proposed formula. The new formula is shown to give also good agreement when applied to the analysis of annual daily insolation data on a seasonal basis. Finally, the proposed formula predicts a linear relationship between the daily diffuse radiation and the daily total radiation in line with the Liu and Jordan model but with the fiffuse component generally higher in qualitative agreement with observations in the tropics.     

Diffuse solar radiation in Cairo,Egypt

In the present paper, the correlations of Page, Liu and Jordan, and Iqbal were employed to predict the monthly mean daily diffuse solar radiation in Cairo. However, it was found that the coefficients used in these correlations were not applicable in the case of Cairo. New coefficients were obtained and used in the above correlations in order to predict values of the monthly average daily diffuse radiation. The present coefficients were found to be very different from those obtained for conditions in other locations. The estimated diffuse radiations were compared with the measured values. It is concluded that all correlations (i.e. equations which use either the cloudiness index or the relative sunshine) with the present coefficients, may be used to predict the monthly mean daily diffuse radiation in Cairo.     

Monthly average solar radiation in panama—Daily and hourly relations between direct and global insolation

Regressions are developed to estimate daily global and direct radiation and the hourly distribution of direct radiation for Barro Colorado Island, Panama from monthly mean values observed 35 km away at Chiva-Chiva. The ratio model of Liu and Jordan and the logarithmic model of Anderson for estimating direct from global radiation are compared. Both gave satisfactory results after accounting for “seasonal” variation, but the ratio model was preferred in this case for the smaller number of separate regressions required. The ratio model fitted for diffuse radiation at Chiva-Chiva agreed closely with regressions for stations at similar latitude. For a given value of the clearness index, the direct component of solar radiation was relatively (but not absolutely) reduced during the dry season compared with the wet season. A likely explanation for this unexpected result is increased marine and terrestrial aerosol during the dry season when offshore winds are stronger and burning of crop and wasteland occurs. The models of Whillier and of Garnier and Ohmura, which assume constant atmospheric transmittance throughout the day, gave unsatisfactory fits to the hourly distribution of direct radiation. They were also unable to mimic an observed morning/afternoon asymmetry that was strongest in the wet season. Hourly direct radiation was accurately estimated from hourly global radiation by quadratic polynomials fitted separately to the morning and afternoon data. The resulting regressions will enable estimation of radiation in forest understory from measurements of insolation in the open by computerized image analysis of hemispherical canopy photos.     

Solar ponds—Corrections

Variations in the average monthly, seasonal and daily patterns of total radiation, relative humidity, temperature and sunshine duration in Ibadan have been presented. Various empirical models relating solar radiation to the basic climatological parameters such as relative humidity, sunshine hours, temperature as well as geographical declination, latitude and altitude factors were investigated from the viewpoint of obtaining appropriate empirical formulae to determine solar radiation from such common parameters. The average monthly total radiation is shown to be predicted with reasonable accuracy by a couple of empirical formulae with the best result obtained from a newly proposed formula. The new formula is shown to give also good agreement when applied to the analysis of annual daily insolation data on a seasonal basis. Finally, the proposed formula predicts a linear relationship between the daily diffuse radiation and the daily total radiation in line with the Liu and Jordan model but with the fiffuse component generally higher in qualitative agreement with observations in the tropics.     

Diffuse solar irradiation model evaluation in the North Mediterranean Belt area

The performance of daily and hourly diffuse horizontal solar irradiation models and correlations is examined using an assembled data set of multivariate meteorological time series from countries in the North Mediterranean Belt area. The correlations reviewed use only daily global, hourly global or daily diffuse irradiation as input, for the daily or hourly time scale. The best overall performance was presented by the Frutos correlation for the estimation of the daily diffuse radiation by an adapted version of the Liu and Jordan correlation for the mean daily diffuse radiation profile, and by the Hollands and Crha model for estimation of hourly diffuse values from the corresponding global values. The results show that the best correlation for each site varies. Two empirical piecewise correlations were also developed by the authors with the help of the data bank available, yielding models that showed even better fits to the data. The results show some seasonal and location dependence.     

Derivation of method for predicting long term average energy delivery of solar collectors

Based on the utilizability concept of Hottel, Whillier, Liu and Jordan, an analytical model has been developed to predict the long term average energy delivery of almost any solar collector. The presentation has been split into two separate papers: a users guide (without explanation of the origin of the formulas) and the present paper (which derives these formulas and documents the validation). The model is applicable whenever the average operating temperature of the collector (receiver surface, fluid inlet, fluid outlet or mean fluid) is known. If the operating temperature is not known explicitly the model will give adequate results when combined with the , f-chart of Klein and Beckman. By contrast to the alternative of hour-by-hour simulation, prediction methods such as the present model and the f-chart offer the advantages of automatically averaging over year-to-year weather fluctuations and of being sufficiently simple to permit hand calculation of long term performance. In a comparison with hourly summations of insolation data, the present model has been found to have an error of less than 3 per cent for the radiation available to a solar collector and an error of about 5 per cent for the heat delivery of solar thermal collectors.     

Correlation between daily diffuse and global radiation for India

Solar radiation characteristics have been studied in various countries and many correlations developed. In the absence of such studies, the same correlations are applied in other countries. Since radiation records are now available in most developing countries, it is possible to perform similar studies for these regions. The purpose of this study is to use daily global and diffuse radiation data for 13 stations in India to establish a correlation between the daily diffuse ratio and the clearness index. Plotting individual values of the daily diffuse ratio against the clearness index for all Indian Stations showed the existence of a definite relationship between them, confirming the validity of Liu and Jordan approach. It was found that a cubic equation provides a fairly accurate fit for this relationship. Comparison with other studies showed that no single correlation is applicable to all regions, and that each region possesses its own characteristics. Although the stations considered had diverse latitude, climate and geographical variations, the study showed that none had any effect on the correlation.     

Analysis of experimental data on diffuse solar radiation in Athens,Greece, for building applications

Proper design and performance prediction of solar energy systems requires accurate information on the availability of solar radiation. The diffuse-to-total radiation correlation, originally developed by Liu and Jordan, has been extensively used as the technique and provided excellent results, although it was latitude dependent and not universally applicable. Thus, diffuse fraction correlations of this type have been developed by few other authors and for different location. This paper presents an analysis of hourly diffuse radiation on a horizontal surface. Hourly pyranometer data from Athens, Greece, are used to establish relationships between the diffuse fraction and the clearness index k _T for hourly and daily values. The results of the proposed equations are then compared with earlier equations. For the urban conditions of Athens the developed correlation fit to the empirical data.     

Estimation of solar radiation over Jordan—predicted tables

As measured solar radiation data for all parts of Jordan are not available, they have to be estimated using correlation relations and models. This paper presents, for the first time, values of solar radiation over Jordan as estimated from these relations. Measurements of global solar irradiance on a horizontal surface and sunshine duration at nine meteorological stations in Jordan are correlated and used for prediction of the regression coefficients of an Angstrom type correlation relation at these stations and others which only have records of sunshine duration. Regional regression coefficients are obtained and used for prediction of global solar irradiance. The agreement with measurements is better than 5% and 1% on monthly and yearly basis respectively. Estimation of diffuse solar irradiance by Page's and also Liu and Jordan's correlations, as well as the direct beam component are also performed and the results are examined and presented. The abundance of solar energy in Jordan is evident from the daily average global solar irradiance which ranges between 5 and 7 kWh/m². A correlation of Angstrom type of the form: H/Ho = 0.448+0.203 S/So is found suitable for Jordan with correlation coefficient r = 0.93.     

Comparative study of various correlations in estimating hourly diffuse fraction of global solar radiation

Proper design and performance predictions of solar energy systems require accurate information on the availability of solar radiation. The diffuse-to-global solar radiation correlation, originally developed by Liu and Jordan, has been extensively used as the technique providing accurate results, although it is latitude dependent. Thus, in the present study, empirical correlations of this type were developed to establish a relationship between the hourly diffuse fraction (k_d) and the hourly clearness index (k_t) using hourly global and diffuse irradiation measurements on a horizontal surface performed at Athalassa, Cyprus. The proposed correlations were compared against 10 models available in the literature in terms of the widely used statistical indicators, rmse, mbe and t test. From this analysis, it can be concluded that the proposed yearly correlation predicts diffuse values accurately, whereas all candidate models examined appear to be location-independent for diffuse irradiation predictions.     

Correlation between hourly diffuse and global radiation for New Delhi

Estimation of hourly insolation on tilted surfaces is required in simulation of solar energy systems. This necessitates splitting of hourly global horizontal insolation into diffuse and direct components. Many models have been developed for this purpose, and the aim of this study is to develop a correlation between hourly diffuse ratio and clearness index for New Delhi. The correlation is developed on the basis of measured data for two years. The performance of this correlation was checked by calculating the difference between computed and measured diffuse radiation. The correlation proved to perform quite well. A comparison of the present correlation with those for other locations showed that such correlations are location dependent.     

Global,direct and diffuse solar radiation on horizontal and tilted surfaces in Jeddah,Saudi Arabia

The measured data of global and diffuse solar radiation on a horizontal surface, the number of bright sunshine hours, mean daily ambient temperature, maximum and minimum ambient temperatures, relative humidity and amount of cloud cover for Jeddah (lat. 21°42′37′′N, long. 39°11′12′′E), Saudi Arabia, during the period (1996–2007) are analyzed. The monthly averages of daily values for these meteorological variables have been calculated. The data are then divided into two sets. The sub-data set I (1996–2004) are employed to develop empirical correlations between the monthly average of daily global solar radiation fraction (H/H₀) and the various weather parameters. The sub-data set II (2005–2007) are then used to evaluate the derived correlations. Furthermore, the total solar radiation on horizontal surfaces is separated into the beam and diffuses components. Empirical correlations for estimating the diffuse solar radiation incident on horizontal surfaces have been proposed. The total solar radiation incident on a tilted surface facing south H_t with different tilt angles is then calculated using both Liu and Jordan isotropic model and Klucher’s anisotropic model. It is inferred that the isotropic model is able to estimate H_t more accurate than the anisotropic one. At the optimum tilt angle, the maximum value of H_t is obtained as ∼36 (MJ/m² day) during January. Comparisons with 22 years average data of NASA SSE Model showed that the proposed correlations are able to predict the total annual energy on horizontal and tilted surfaces in Jeddah with a reasonable accuracy. It is also found that at Jeddah, the solar energy devices have to be tilted to face south with a tilt angle equals the latitude of the place in order to achieve the best performance all year round.     

Estimation of daily diffuse solar radiation in China

Applying the measured global and diffuse solar radiation data from 78 meteorological stations in China, a countrywide general correlation model for calculating the daily diffuse radiation was derived on the basis of Liu and Jordan method. Two widely used statistics: root mean square error and mean bias error were used to assess the performance of the correlation. And the correlation shows good behavior when applied to most of the stations. Subsequently, with the measured data from the 78 stations, an analysis of geographical distribution of solar energy resource in China was also presented in the form of clearness index (the ratio of global solar radiation to extraterrestrial radiation) percentage frequency, and results show that the solar energy resource in western and northern China is relatively abundant.