Open Access

Monthly-averaged hourly solar diffuse radiation models for world-wide locations

Future Cities and Environment20151:5

https://doi.org/10.1186/s40984-015-0008-5

Received: 15 November 2014

Accepted: 1 May 2015

Published: 24 August 2015

Abstract

Monthly-averaged daily global irradiation data are now easily available from NASA website for any global location. Using established models it is then possible to decompose the daily to averaged-hourly global irradiation. The missing link so far has been hourly averaged diffuse irradiation. In this article data 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 regressions are distinctly different from previously available hour-by-hour regressions.

Keywords

Solar radiation Averaged-hourly solar diffuse fraction Insolation Solar diffuse radiation

Introduction

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://eosweb.larc.nasa.gov/cgi-bin/sse/retscreen.cgi?email=rets@nrcan.gc.ca) 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.
Table 1

Climatic data for Easthampstead (Bracknell) with the NASA reported irradiation data and averaged measured data for the period 1981-1983

 

Unit

Climate data location

       

Latitude

°N

51,42

       

Longitude

°E

–0,75

       

Elevation

m

58,00

       

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

 

°C

%

kWh/m2/day

kPa

m/s

°C

°C-d

°C-d

kWh/m2/day

January

4,2

83,90

0,77

100,8

6,3

3,1

426

1

0,71

February

4,3

80,20

1,39

101,0

5,8

3,6

380

1

1,28

March

6,4

76,80

2,34

100,9

6,0

6,2

353

4

2,18

April

8,6

69,80

3,59

100,7

5,1

9,1

279

21

3,55

May

12,7

64,00

4,57

100,9

4,7

13,8

168

92

4,11

June

16,1

60,80

4,84

100,9

4,4

17,7

75

177

4,86

July

18,6

60,20

4,80

100,9

4,4

20,4

25

261

4,77

August

18,6

61,20

4,23

100,9

4,3

20,3

26

264

4,23

September

15,5

66,30

2,86

100,9

5,0

16,5

83

164

2,85

October

11,7

74,10

1,73

100,7

5,5

11,5

191

73

1,57

November

7,3

83,20

0,96

100,7

5,9

6,4

318

11

0,80

December

4,9

85,00

0,60

100,8

6,1

3,8

404

3

0,60

Annual

         
 

10,7

72,10

2,72

100,8

5,3

11,0

2728

1072

 

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.
Fig. 1

Comparison between NASA reported irradiation data and ground-based averaged measured data for Bracknell, kWh/m2-day

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 − k t plot) and monthly-averaged hourly regressions (Fig. 3: \( \overline{k}-{\overline{k}}_t \)). 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.
Fig. 2

Hourly diffuse ratio versus clearness index for UK locations

Fig. 3

Monthly-averaged hourly plot for UK locations (arranged in an increasing order of latitude: Camborne 50.21° N, Aldergrove 54.65° N)

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 hourly \( \overline{k}-{\overline{k}}_t \) regressions

Fourteen worldwide locations were chosen for this study, details of which are shown in Table 2.
Table 2

The 14 worldwide locations that were presently investigated

Country

Location

Latitude

Longitude

Period of observation

India

Chennai

13.08

80.18

1990–1994

Pune

18.32

73.85

1990–1994

Kingdom of Bahrain

Bahrain

26.03

50.61

2000–2002

State of Kuwait

Kuwait

29.22

47.98

1996–2000

Spain

Almeria

36.83

−2.38

1993–1998

Portugal

Faro

37.02

−7.96

1982–1986

Lisbon

38.71

−9.15

1982–1990

Spain

Madrid

40.40

−3.55

1999–2001

Girona

41.97

2.76

1995–2001

United Kingdom

Camborne

50.21

5.30

1981–1995

Bracknell

51.42

0.75

1992–1994

Aberporth

52.13

4.55

1975–1995

Finningley

53.48

0.98

1982–1995

Stornoway

58.22

6.39

1982–1995

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 ratio \( \left(\overline{k}\right) \) and the corresponding clearness index \( \left({\overline{k}}_t\right) \) were calculated from sunrise to sunset. The following conditions were used in each case to remove erroneously recorded data.
$$ {k}_T=\frac{I_G}{I_E}\to {I}_G<{I}_E $$
(1)
$$ k=\frac{I_D}{I_G}\to {I}_D\le {I}_G $$
(2)
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.
Fig. 4

Monthly-averaged hourly diffuse ratio (y-axis) versus clearness index (x-axis) fot two locations. One Indian and other a South European

Fig. 5

Averaged values of diffuse ratio for the locations between latitude 13-20° North

Figures 6 and 7 respectively show the regressions for locations in a narrower range of latitudes (20-42° N) and worldwide sites with a more diverse range of latitudes (13-58°N).
Fig. 6

Averaged values of diffuse ratio for the locations between latitude 20-42° North

Fig. 7

Averaged values of diffuse ratio for the all locations

Note that Fig. 6 shows the potential for a single regression model. Figure 7 on the other hand indicates the existence of different sub-models and these shall now be explored further.

Figures 8, 9 and 10 respectively present regressions models that were obtained by pooling data from locations with a latitude range of 13-20° N, 20-42° N and 50-58° N.
Fig. 8

Averaged values of diffuse ratio for the locations between latitude 13-20° North (Chennai and Pune)

Fig. 9

Averaged values of diffuse ratio for the locations between latitude 20-42° North (Bahrain, Kuwait, Almeria, Faro, Lisbon, Madrid and Girona)

Fig. 10

Averaged values of diffuse ratio for the locations between latitude 50-58° North (Camborne, Bracknell, Aberporth, Finningley and Stornoway)

Table 3 presents regressions equations and coefficient of determination (R2) for each location.
Table 3

The regressions equations and coefficient of determination (R2) for each location

Country

Location

Regression equations

R2

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

Three points are worthy of note from Figs. 8, 9 and 10:
  1. i.

    A strong correlation is observed between \( \overline{k} \) and \( {\overline{k}}_t \) 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),

     
  2. ii.

    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

     
  3. iii.

    it is not possible to produce a single regressed curve for worldwide locations.

     
The latter point is reinforced via Fig. 11.
Fig. 11

Monthly-averaged hourly regressions for three ranges of latitudes

Conclusions

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.

Declarations

Authors’ Affiliations

(1)
Edinburgh Napier University
(2)
University of Granada

References

  1. Collares-Pereira M, Rabl A (1979) The average distribution of solar radiation correlations between diffuse and hemispherical and between daily and hourly insolation values. Solar Energy 22:155View ArticleGoogle Scholar
  2. Erbs DG, Klein SA, Duffie JA (1982) Estimation of the diffuse fraction of hourly, daily and monthly-averaged global radiation. Solar Energy 28:293View ArticleGoogle Scholar
  3. Hawas M, Muneer T (1984) Study of diffuse and global radiation characteristics in India. Energy Convers Manage 24:143View ArticleGoogle Scholar
  4. Liu YH, Jordan RC (1960) The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Sol Energy 4:1–19View ArticleGoogle Scholar
  5. Lloyd PB (1982) A Study of Some Empirical Relations Described by Liu and Jordan. Report no. 333, Solar Energy Unit, University College, CardiffGoogle Scholar
  6. Mani A, Rangarajan S (1983) Techniques for the precise estimation of hourly values of global, diffuse and direct solar radiation. Solar Energy 31:577View ArticleGoogle Scholar
  7. Muneer T (2004) Solar Radiation and Daylight Models, 2nd edn., ElsevierGoogle Scholar
  8. Muneer T, Hawas M (1984) Correlation between daily diffuse and global radiation for India. En Conv Mgmt 24:151View ArticleGoogle Scholar
  9. Muneer T, Saluja GS (1996) Correlation between hourly diffuse and global solar irradiation for the UK. Building Services Engineering Research & Technology 7, 1Google Scholar
  10. Muneer T, Hawas MM, Sahili K (1984) Correlation between hourly diffuse and global radiation for New Delhi. Energy Conv Mgmt 24:265View ArticleGoogle Scholar
  11. Saluja GS, Muneer T, Smith ME (1988) Methods for estimating solar radiation on a horizontal surface. Ambient Energy 9:59View ArticleGoogle Scholar
  12. Stanhill G (1966) Diffuse sky and cloud radiation in Israel. Solar Energy 10:96View ArticleGoogle Scholar

Copyright

© The Author(s) 2015

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.