Solar radiation data are essential for the design of very many energy systems. These data are needed for obtaining solar energy resource assessment, its transmission and also to obtain the efficiency of energy delivery. A few examples are solar water heating, and space PV systems, daylighting, building air conditioning load and solar-driven ventilation. The starting point for the above computational chain is almost always global and diffuse horizontal radiation. Usually, the computations are carried out using hourly or sub-hourly data.
Note that not always it is possible to obtain a long-term series of hourly or sub-hourly data for the above parameters.
The most commonly measured solar data are global irradiation and these are available for a limited number of stations within any given country at an hourly, daily or monthly frequency. For example within the UK and Spain a historical records of hourly data are available for 71 and 31 stations, respectively.
Of these stations due to higher operational costs associated with diffuse radiation measurements the respective meteorological offices tend to record the latter variable at much fewer locations. For example, since the year 2002 within the UK the diffuse radiation is recorded at only two locations, at North latitudes of Camborne (50.21°) and Lerwick (60.80°).
On the contrary, through the work of NASA (http://firstname.lastname@example.org) it is now possible to obtain daily-averaged irradiation data for virtually any location in the world. A sample table of climatic data for Easthampstead (Bracknell) is provided in Table 1.
|Unit||Climate data location|
|Heating design temperature||°C||–1,74|
|Cooling design temperature||°C||22,96|
|Earth temperature amplitude||°C||14,35|
|Frost days at site||day||37,00|
|Month||Air temperature||Relative humidity||Daily solar radiation-horizontal||Atmospheric pressure||Wind speed||Earth temperature||Heating degree-days||Cooling degree-days||Average measured radiation|
|Measured at (m)||10,0||0,0|
This information was downloaded from the above-mentioned NASA website. The NASA reported irradiation data were compared by the present research team against averaged measured data for one UK location for the period 1981–1983 (three complete years) (see Fig. 1). The statistics within the latter figure shows that there is a close concordance between the satellite-based NASA irradiation and the UK Meteorological Office measured data set.
Following the original work of Liu and Jordan (Liu & Jordan 1960) a great many number of research teams from around the world have produced regressions relating diffuse ratio (k) and clearness index (kt) regressions at an hourly, daily, monthly and annual frequency. Each of the above four category of regression is unique and statistically different as shown in the work of Muneer (Muneer 2004) and Saluja et al. (Saluja et al. 1988).
The present article was pooled from 14 world-wide locations to obtain a regression model to complete the above missing link. It was presently shown that the averaged–data based regressions are distinctly different from previously available hour-by-hour regressions.
The unique nature of solar radiation regressions
Historically speaking, a large number of research teams from around the world have produces k-kt regressions that were based on an hour-by-hour, daily, monthly or annual data. Examples that may be cited here, are Liu and Jordan (daily, and monthly-averaged daily) (Liu & Jordan 1960), Erbs et al. (hourly, daily and monthly-averaged daily) (Erbs et al. 1982), Hawas and Muneer (hour-by-hour, daily, monthly- and annual-averaged daily) (Hawas & Muneer 1984; Muneer & Hawas 1984; Muneer et al. 1984) and Stanhill (monthly- and annual-averaged daily) (Stanhill 1966).
Presently, Figs. 2 and 3 show the unique nature of hour-by-hour (Fig. 2: k − kt plot) and monthly-averaged hourly regressions (Fig. 3: ). An important point to note is that while Fig. 2 shows a convex profile, Fig. 3 demonstrates a concave behaviour. The latter two figures are based on data from common UK locations.
While there are established models for data of Fig. 2 there are no regressions available in literature for averaged-hourly data such as those shown in Fig. 3. The object of this article is to present the latter type of regressions.
Presently developed monthly-averaged hourlyregressions
Fourteen worldwide locations were chosen for this study, details of which are shown in Table 2.
|Country||Location||Latitude||Longitude||Period of observation|
|Kingdom of Bahrain||Bahrain||26.03||50.61||2000–2002|
|State of Kuwait||Kuwait||29.22||47.98||1996–2000|
Data consisted of hourly global and diffuse irradiation values for several years for each location, covering most of the range of latitude for the country. The location names have been arranged in an increasing order of latitude.
Monthly-averaged hourly values were calculated for the global and diffuse radiation considering the data period for each location. For each of them, the monthly-averaged hourly diffuse ratioand the corresponding clearness index were calculated from sunrise to sunset. The following conditions were used in each case to remove erroneously recorded data.
The monthly-averaged clearness index was then regressed against the monthly-averaged diffuse ratio for each location. Figure 4 shows one such scatter plot for Chennai and Lisbon. Furthermore, for each increment at bandwidth of clearness index of 0.05 width, the corresponding values of averaged diffuse ratio shown in Fig. 5 were obtained, shown here for pooled data from two Indian locations.
Table 3 presents regressions equations and coefficient of determination (R2) for each location.
|India||Chennai||y = 0.5124x2-0.9809x + 0.8733||0.83|
|Pune||y = 0.4083x2-0.873x + 0.853||0.92|
|Kingdom of Bahrain||Bahrain||y = 1.4455x2-2.113x + 1.1262||0.98|
|State of Kuwait||Kuwait||y = 0.7088x2-1.3237x + 0.8299||0.96|
|Spain||Almeria||y = 1.9414x2-2.9329x + 1.3637||0.98|
|Portugal||Faro||y = 0.9184x2-2.2173x + 1.3654||0.99|
|Lisbon||y = 0.0721x2-1.3001x + 1.1246||0.99|
|Spain||Madrid||y = 0.9087x2-2.0465x + 1.1808||0.99|
|Girona||y = 0.1781x2-1.0867x + 0.887||0.98|
|United Kingdom||Camborne||y = 0.8188x2-1.1127x + 0.9365||0.96|
|Bracknell||y = 1.4394x2-1.5414x + 0.9878||0.97|
|Aberporth||y = 0.9797x2-1.3032x + 0.9403||0.95|
|Finningley||y = 0.451x2-0.876x + 0.9267||0.99|
|Stornoway||y = 7441x2-1.1382x + 1.0147||0.98|
- A strong correlation is observed between and with the respective coefficient of determination of 0.87, 0.80 and 0.83 (corresponding values of coefficient of correlation are 0.93, 0.89 and 0.91),
- In each case the shape of the regressed curve is concave, contrary to the convex profile for hour-by-hour regressions reported by research teams from around the world, and
- it is not possible to produce a single regressed curve for worldwide locations.
The latter point is reinforced via Fig. 11.
Monthly-averaged daily global irradiation data are now easily available from NASA website for any terrestrial location. Using established models such as those presented by Liu and Jordan (Liu & Jordan 1960), Collares-Pereira and Rabl (Collares-Pereira & Rabl 1979), Mani and Rangarajan (Mani & Rangarajan 1983), Muneer and Saluja (Muneer & Saluja 1996) and Lloyd (Lloyd 1982) it is then possible to decompose the daily–to averaged-hourly global irradiation. The missing link so far has been hourly averaged diffuse irradiation. The authors report a regression model to complete the above missing link for 14 world locations and show that the averaged–data regressions are distinctly different from previously available hour-by-hour regressions.