Reference

NATL INST. OF STAND & TECH

NBS

Publications

AlllOS T7mi5

tit ^ v^ ii ^ ^ NBS TECHNICAL NOTE 1148

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

-QC

100

.U5753

No.mS

JL. _?>—"-.

Solar Radiation

and Illumination
NATIONAL BUREAU OF STANDARDS

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MAriOMAL BiriUBAt'

Soiar Radiation and Illumination tto"i'i m\

CK. for

If- S. Treado

T. Kusuda

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

Prepared for:

Naval Facilities Engineering Command

U.S. Navy

Washington, DC 20330

Directorate of Civil Engineering

U.S. Air Force Washington, DC 20330

Office of Chief of Engineers

U.S. Army

Washington, DC 20314

U.S. Department of Energy

Office of Buildings and Community Systems

Washington, DC 20585

if_ Oa

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued November 1981
National Bureau of Standards Technical Note 1 148

Nat. Bur. Stand. (U.S.), Tech. Note 1 148, 31 pages (Nov. 1981) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1981
SOLAR RADIATION AND ILLUMINATION

S. Treado

T. Kusuda

ABSTRACT

Experimental data were collected and analyzed under various cloud cover conditions to establish the relationship between solar irradiance and

illuminance. Empirically derived equations are presented for estimating

diffuse and total illuminance as a function of total and diffuse solar

radiation.

Key Words: daylighting; illuminance; illumination; irradiance; solar

radiation

111
Table of Contents

1

Introduction 1

2Solar Radiation and Illumination 3

3

Diffuse Illuminance 4

4. Total Illuminance 7

5

Summary and Conclusions 10

6. References 11

IV
1 . INTRODUCTION

Illumination conditions, both outdoors and indoors, are of interest in

building design and energy analysis. Except for clear and completely overcast sky conditions, very few data are available concerning levels of outdoor

illuminance under realistic sky conditions. Under the randomly changing outdoor illuminance levels frequently encountered, it is difficult to obtain an accurate prediction of daylighting conditions. Various procedures have been

proposed and utilized for predicting outdoor illuminance levels; some are based on fundamental principles of atmospheric science [1] while others use empirical relationships [2,3]. These procedures vary in complexity and accuracy and require a variety of input parameters from which illuminance levels

are calculated. The accuracy of many of these procedures has not been

validated for a complete range of illumination conditions.

Many building design and energy analysis procedures provide irradiance

information, either from weather data tapes or from calculation. Thus,

correlations between solar radiation conditions and the resulting illumination

conditions would enable outdoor illumination levels to be calculated. Since

illuminance (visible light, e.g., CLE. photopic response ~ 0.38 to 0.78 ym)

is largely dependent upon irradiance (full-spectrum solar radiation ~ 0.2 to

3 lim) it was desirable to establish a procedure for calculating illuminance

as a function of irradiance.

While the measured outdoor illuminance data are limited in scope and in

available locations, large amounts of solar radiation data are available from

data routinely recorded at weather stations throughout the country for many

years.

It has been customary to relate the illuminance to the total irradiance in

terms of luminous efficacy, which is defined as follows:

0.780

Kju / V(X)E(X)dX

0.380 n =

/ E(A)dX

where

K^ = maximum spectral luminous efficacy or luminosity factor

= 680 £m/w

V(X) = standard relative luminous efficacy of monochromatic

radiation of wave length X

E(X) = monochromatic solar spectral irradiance
Several researchers have published the values of n for selected and typical

sky conditions. W. Chroscicki [4], for example, developed the following

equation for clear sky.

n = 59.3 hO-1252 ^^i/w

where

h = solar altitude angle in degrees.

Rosenfeld and Selkowitz [5], on the other hand, suggest ri = 106 ± 2 £m/w for

the direct solar component and 116 ± 7 iim/w for the diffuse sky component for

clear sky conditions.

For the cloudy sky, Krochmann [6] suggests an approximate value of 115 £m/w.

While these solar luminous efficacy data are affected by the presence of

atmosphere and cloud cover, the extraterrestrial data have been estimated as 93.7 £m/w [7].

None of the data presented above permit the evaluation of outdoor illumination

under partially cloudy conditions which prevail during the course of a year,

and which are very important for the annual energy analyses.

Shikuyu and Kimura [8] have presented a relation to combine the Chroscicki

equation with Krochmann data in conjunction with cloud amount factor, Cp,

which ranges from 10 for a completely cloudy sky to for a clear sky as recorded by meteorological stations. The suggested equation is

n = 115 (-£-) + 59.3 h°°^252 ^ _ _E]

10 10

The disadvantage of this equation is that the cloud amount parameter Cp is

very subjective to the observer and not well defined.

An alternative cloud amount factor is utilized in this paper based upon the

ratio of observed diffuse and total solar radiation levels. This new cloud

amount factor is then used to compute the luminous efficacy of a cloudy sky.
2. SOLAR RADIATION AND ILLUMINATION

Solar radiation at the earth's surface Is composed of two components, diffuse

and direct. Various combinations of diffuse and direct Irradiance occur due

to different sky conditions. The sum of diffuse and direct Irradiance equals

total Irradiance. Under completely overcast conditions, diffuse Irradiance

Is equal to total Irradiance, while under very clear sky conditions the diffuse component Is approximately 10 percent or less of the total Irradiance.

The ratio of diffuse to total Irradiance can be described as the cloud ratio,

or:

Cloud Ratio = CR = Diffuse Irradiance = _d_ q)

Total Irradiance I^

Similarly, outdoor Illuminance Is composed of diffuse and direct components.

Traditionally, In the dayllghtlng community, diffuse Illuminance Is of Interest, since It represents visible light from the sky, enabling Indoor Illuminance to be subsequently calculated. Most Interior locations do not receive

direct Irradiance or Illuminance, since the sun Is usually not visible through

the window. In those cases where direct Irradiance (and consequently direct

Illuminance) Is present. It Is usually viewed as being undesirable, from the

standpoint of glare and occupant comfort. Under these conditions, frequently

a shade or other sun control device Is utilized.

The direct and total Illuminance components are of Interest when determining

the level of Illumination Incident upon an exterior surface (such as the ground

or a building), when skylights are considered, or when reflective louvers are used to bring the direct beam Illumination deep Indoors.

Since solar Illuminance Is a portion of the full solar spectrum. Illuminance

and Irradiance levels are obviously related. The relative contributions of

the ultra-violet, Infrared, and visible portions of the solar spectrum vary

with different atmospheric conditions. Thus the level of Irradiance may

change while the Illuminance remains constant, due to a change In the Intensity

outside of the visible spectrum.

Measurements were made of the levels of total Irradiance and Illuminance on a horizontal surface, along with concurrent measurements of diffuse Irradiance

and Illuminance. The diffuse components were measured using shading bands.

(See figure 1). These measurements were made at the NBS daylight research

facility near Washington, D.C. ('- 39° lat.).
3. DIFFUSE ILLUMINANCE

Earlier measurements of diffuse Illuminance indicated a strong sensitivity to

sky condition [9]. Diffuse illuminance levels were low for clear skies

and completely overcast skies. Highest diffuse illuminance levels occurred

under partially overcast conditions, when the sun was relatively unobstructed

and the remainder of the sky cloudy. Overcast conditions produced the highest

levels of diffuse illuminance per unit total irradiance, but total irradiance

levels were usually low at these conditions.

Analysis of the measured data indicated two possible procedures for

calculating diffuse illuminance based on irradiance data. The simplest

method requires a correlation between measured levels of diffuse irradiance

and diffuse illuminance. Figure 2 presents a plot of diffuse illuminance as

a function of diffuse irradiance. From this plot, it is seen that diffuse

illuminance can be calculated using the following relation:

Ed = 119 . Id (2)

where

Ejj = diffuse illuminance (lux)

—2

I J = diffuse irradiance (Wm )

Equation 2 indicates a luminous efficacy for diffuse illumination of 119

lumens/watt. A comparison of measured diffuse illuminance versus calculated

(from eq. 2) is presented in figure 3.

The average calculation error for the sample day presented is 7 percent, with

the greatest error occurring at the lower illuminance levels. On this sample

day, solar radiation and sky condition covered a large range.

The second method for calculating diffuse illuminance is based on a correlation of that parameter with total irradiance and cloud ratio. Due to

the wide variations in sky condition, diffuse illuminance does not vary

directly with total irradiance, as shown in figure 4. However, if the cloud

ratio is known, or can be estimated, this information can be combined with

information concerning the level of total irradiance to calculate diffuse

illuminance.

Figure 5 presents a typical plot of diffuse illuminance as a function of

total irradiance for different types of sky conditions. Large increases in

total irradiance cause only small increases in diffuse illuminance under

clear skies, while under overcast conditions diffuse illuminance changes

dramatically with total irradiance.
Figure 5 suggests that for a fixed cloud ratio, diffuse illuminance can be

represented as a function of total irradiance in the form:

Ed = M • It (3)

where

2 I^ = total irradiance (w/m )

The value of the slope M would be dependent upon the cloud ratio at that

particular time.

Combining equations 1 and 2 enables a correlation between diffuse illuminance

and total irradiance and cloud ratio to be obtained as follows:

E(j = 119 • CR • It (4)

From eq. (4) the slope M in eq. (3) is seen to be equal to 119 CR.

To investigate the accuracy of eq. (4) the relation between measured diffuse

illuminance and total irradiance was examined.

Figures 6a through 6o present measured diffuse illuminance as a function of

total irradiance for the full range of cloud ratios. Fifteen groups of points

are plotted, each corresponding to a small range of cloud ratios as labeled.

A least-squares best-fit line forced through zero is also drawn for each plot.

Diffuse illuminance is seen to vary linearly with total irradiance for each

fixed cloud ratio range, as would be predicted by eq. (4). The slope of each

least-squares plot should agree with the slope predicted by eq. (3), namely:

119 • CR should equal slope of least-squares line for each range of

cloud ratios.

This comparison is made in Table 1, and good agreement is seen, considering

that the least-squares calculations are based on points obtained for a range

of cloud ratios.

The accuracy of diffuse illuminance values calculated using eq. (4) would

be the same as that using eq. (2), since in each case the level of diffuse

irradiance, or the cloud ratio, is known. However, the level of diffuse

irradiance is not always known. If a value for diffuse irradiance is not

available, it may be possible to estimate the percentage of cloud cover to
enable subsequent calculation of diffuse illuminance using eq. (4). The U.S.

weather service records a "cloud cover factor", which is an estimate of cloud

cover. While this procedure has not been evaluated in this report, it may be

possible to convert the value of cloud cover factor to cloud ratio for use in

calculating the diffuse illuminance using eq. (4).

Table 1 Calculated Slope* versus Measured Slope**

Cloud Ratio Average Least-Squares Calculated = 119 • CR

Range Cloud Ratio Slope Slope

0.90 < CR < 1.0 0.966 111 115

0.80 < CR < 0.90 0.857 101 102

0.70 < CR < 0.80 0.750 85 89

0.60 < CR < 0.70 0.651 81 77

0.50 < CR < 0.60 0.5 47 74 65

0.45 < CR < 0.50 0.475 65 57

0.40 < CR < 0.45 0.430 56 51

0.35 < CR < 0.40 0.375 47 45

0.30 < CR < 0.35 0.320 41 38

0.25 < CR < 0.30 0.271 35 32

0.20 < CR < 0.25 0.230 29 27

0.167 < CR < 0.20 0.181 25 22

0.133 < CR < 0.167 0.155 22 18

0.100 < CR < 0.133 0.112 14 13

< CR < 0.100 0.083 13 10

* from eq. (4) ** from fig. (5)
4. TOTAL ILLUMINANCE

The level of total illumination is most easily calculated on the basis of the

level of total solar radiation. Figure 7 presents total illuminance on a horizontal surface as a function of total irradiance on a horizontal surface.

The effect of variations in cloud ratio is small, producing scatter about a best-fit line:

Et = 110 • Ix (5)

Equation (5) indicates a luminous efficacy for total solar radiation of 110

lumens/watt. Figure 8 compares measured total illuminance versus that calculated using total irradiance and eq. (5) for a typical sample day. The average error for the calculations is 8 percent, with the largest errors occurring

at lowest illuminance levels.

The luminous efficacy of extraterrestrial solar radiation is approximately 94

lumens/watt. This radiation is composed only of a direct component since

there is no atmosphere to produce a diffuse component. At the earth's surface, the intervening atmospheric layer causes some of the solar radiation to

scatter, resulting in sky or diffuse radiation. Since the atmosphere transmits solar radiation preferentially in the visible region, and due to the

longer path length of diffuse radiation as compared to direct radiation, the

percentage of the visible component of diffuse solar radiation is greater than

that of direct solar radiation. Thus the luminous efficacy of diffuse solar

radiation should be greater than the luminous efficacy of direct solar radiation. Also, the luminous efficacy of direct radiation at the earth's surface

would be greater than the extraterrestrial value, due to influence of the

atmosphere. The luminous efficacy of direct solar radiation was estimated

from the ratio of direct illuminance to direct irradiance, each of which in

turn was calculated from the difference between the measured levels of total

and diffuse illuminance and irradiance.

The average value for the luminous efficacy of direct solar radiation at the

earth's surface was determined from measurements to be 105 lumens/watt. Considerable variation in this value can occur with different atmospheric conditions and cloud ratios, since under completely overcast sky conditions the

direct irradiance component is actually completely diffused.

Since total solar radiation includes both diffuse and direct irradiance, its

luminous efficacy should fall somewhere between the two. This pattern is

reflected in eqs. (2) and (5), where the luminous efficacy of diffuse irradiance is seen to be greatest, while that of total irradiance falls between the

values for direct and diffuse irradiance. However, the luminous efficacy of

total solar radiation would vary slightly as the percentages of diffuse and

direct irradiance vary. This would be the case with different cloud ratios.

The value of 110 lumens/watt efficiency for total irradiance is an average

value representing all types of cloud conditions. When clear sky conditions

prevail, the actual luminous efficacy would probably be slightly less. As
conditions become increasingly overcast, the luminous efficacy of total

irradiance would approach that of diffuse irradiance.

The difference between the luminous efficacies of diffuse and total irradiance

leads to an inconsistency concerning the correlations presented in eqs. (2),

(4), and (5). When the cloud ratio exceeds 92 percent, the calculated values

of diffuse illuminance will be greater than the calculated values of total

illuminance, an obvious impossibility. When this situation occurs, the larger

value should be used for total and diffuse illuminance, since sky conditions

would be overcast, and the luminous efficacy of total irradiance would be the

same, or nearly the same, as that for diffuse irradiance. Since levels of

irradiance are usually low when the sky is overcast, differences between the

illuminances as calculated from eqs. (2) and (5) should be small.

Another procedure can be used for calculating total illuminance which

eliminates the previously described inconsistencies. Since total illuminance

is composed of diffuse and direct components, E-j can be expressed by the

relation:

Et - Ed + Ej

where

Ej) = direct illuminance

Using the value of 105 lumens/watt luminous efficacy for direct irradiance

and eq. 2, this yields:

Et = (105 . Id) + (119 . Id)

where

Id = direct irradiance

Since Id = (1-CR) • I^ and l^ = CR • I^,

Ex = It [105 • (1-CR) + 119 • (CR)]

This equation can be rearranged to yield:

Et = [105 + (CR • 14)] • It (6)
Equation 6 produces a weighted average between the diffuse and direct

illuminance components. Thus, the luminous efficacy of total irradiance,

according to eq. 6, would increase with increasing cloud ratio.

Under completely overcast conditions, cloud ratio equals one and eq. 6 reduces

to eq, 2.
5. SUMMARY AND CONCLUSIONS

Levels of total and diffuse illuminance can be calculated from solar

radiation data according to the following relations:

a) Ed = 119 . Id

b) Ed = 119 • CR • Ix

c) Ej = 110 • Ix for CR < 0.92, Ex = E^ from a or b for CR > 0.92

d) Ex = [105 + (CR • 14)] • Ix

The average uncertainty in the calculated values is approximately 8

percent. This is due to a combination of measurement error and variations

in the relative contribution of the visible band to the full solar spectrum.

The calculation procedures are sufficiently accurate to permit illuminance

levels to be calculated from concurrent irradiance levels, as long as 100

percent accuracy is not required.

10
6. REFERENCES

1. The Availability of Daylight ; CLE. Technical Report T.C.-4.2 1980.

2. Kusuda, T. and Collins, B., Simplified Analysis of Thermal and Lighting

Characteristics of Windows; Two Case Studies , BSS 109, National Bureau

of Standards, Feb. 1978.

3. Lynes, J., Principles of Natural Lighting , Applied Science Publishers

Ltd., London, 1968.

4. Chroscicki, W., from reference 6.

5. Rosenfield, A.H., and Selkowitz, S.E., "Beam Daylighting, An Alternative

Illumination Technique," Energy and Buildings , May 197 7.

6. Krochmann, J., "Quantitative Data on Daylight for Illuminating Engineering,'

Lighting Research and Technology, Vol. 6, No. 3, 1974.

7. Smithsonian Phys . Tables, 1954, p. 96.

8. Shukuya, M. and Kimura, K., "Research of Planning and Energy Evaluation

of Natural Illumination with Direct Sunlight: Part 1: Effect of Outside

Reflective Louvers," Transactions of Architectural Institute of Japan,

No. 283, Sept. 1979 (Japanese).

9. Treado, S. and Kusuda, T., Daylighting, Window Management Systems and

Lighting Controls, NBSIR Sept. 80-2147, December 1980.

11
r^m

Mi^---'

Figure 1. NBS Daylight Research Facility

12
DIFFUSE IRRADIANCE (W/m )

Figure 2. Diffuse Illuminance as a Function of Diffuse Irradiance

13
-• c alculated — measured

I t r I I I I I I 9 10 11 12 13 14 15 16 17 18 19

TIME rhnnr^

Figure 3. Diffuse Illuminance - Measured vs. Calculated

14
o

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00'

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r^.

9 10 11 xlO^

TOTAL IRRADIANCE (W/m )

Figure 4. Diffuse Illuminance as a Function of Total Irradlanpe

15
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TOTAL IRRADIANCE

Figure 5. Characteristic Plot of Diffuse Illuminance as a Function of

Total Irradiance

16
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TOTAL IRRADIANCE (W/m )

Figure 7. Total Illuminance as a Function of Total Irradiance

25
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calculated

measured

9

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Figure 8. Total Illuminance - Measured vs. Calculated

26
NBS-n4A (REV. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO,

NBS TN 1148

2. Performing Organ, Report No 3. Publication Date November 1981

4. TITLE AND SUBTITLE

Solar Radiation and Illumination

5. AUTHOR(S)

S. Treado and T. Kusuda

6, PERFORMING ORGANIZATION (If joint or other tlian NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D,C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

JLLual

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

Tri-Services: U.S. Navy, NFEC, Washington, DC 20330; U.S. Air Force, Directorate

of Civil Engr., Washington, DC 20330; U.S. Army, Off. Chief of Engrs., Washington,

DC 20314; and U.S. Dept. of Energy, Off. of Bldgs . & Community Systems, Washington,

DC 20585

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Experimental data were collected and analyzed under various cloud cover conditions to establish the relationship between solar irradiance and

illuminance. Empirically derived equations are presented for estimating

diffuse and total illuminance as a function of total and diffuse solar

radiation.

12. KEY WORDS (S/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

daylighting; illuminance; illumination; irradiance; solar radiation

13. AVAILABILITY

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\J[\ Order From National Technical Information Service (NTIS), Springfield. VA. 22161

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PRINTED PAGES

31

15. Price

USCOMM-DC 6043-P80

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(both government and non-government). In general, initial dis- tribution is handled by the sponsor; public distribution is by the National Technical Information Services, Springfield, VA 22161,

in paper copy or microfiche form.
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