SERI/TR-215-2525

UC Categories: 59, 62

DE86010737

Measuring and Modeling Solar

Irradiance on Vertical Surfaces

E. L. Maxwell

T. L. Stoffel

R. E. Bird

July 1986

Prepared under Task No. 3738.10

FTP No. 468

Solar Energy Research Institute

A Division of Midwest Resear ch Inst itute

1617 Cole Boulevard

Golden, Colorado 80401

Prepared for the

U.S. Department of Energy

Contract No. DE-AC02-83CH10093
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1
TR-2525

PREFACE

This report presents the first evaluations of five algorithms for converting

the solar energy parameters most widely available from the national climatic

data archives (global horizontal and direct normal solar irradiance) to global

irradiance on tilted surfaces using measurements from the Solar Radiation

Research Laboratory (SRRL) at the Solar Energy Research Inst i tute (SERI).

This evaluation was prepared by the Resource Assessment and Instrumentation

Branch, Solar Electric Research Division. Support for this research was

provided by the U.S. Department of Energy through the Passive Solar Program at

the SERT Solar Heat Research Division.

The authors wish to recognize the following people for constructive technical

review: Jay Burch, Roland Hulstrom, Kerri Hunter, and Claude Robbins of SERI;

John Hay of the University of British Columbia; and Richard Perez of the State

University of New York at Albany.

Approved for the

SOLAR ENERGY RESEARCH INSTITUTE

filL:jL/~ Roland L. Hulstrom, Manager

Resource Assessment and

Instrumentation Branch

~~. Stone, Director

L..----Solar Electric Research Division

iii
TR-2525

SUMMARY

Objective

This report presents the first evaluations of five algorithms for converting

global horizontal and direct normal solar irradiance components to global

i r r ad i ance on tilted surfaces using measurements from the Solar Radiation

Research Laboratory (SRRL) at the Solar Energy Research Institute (SERI).

Discussion

High resolution (l5-min) measurements from eight thermopile radiometers

oriented vertically in the four cardinal directions were available for a

169-day period ending 31 December 1984. Concurrent measurements of global

horizontal and direct normal solar irradiance components were also used for

the analysis. The pyranometers used in the experiment were intercompared on

horizontal, north-facing, and south-facing vertical orientations before their

deployment. The conversion algori thms each attempt to account for very

complex atmospheric interactions with incoming solar radiation. The sky and

ground radiance contributions to tilted surface irradiance are assumed to be

isotropic, anisotropic, or a combination of the two regimes depending on the

algorithm.

Conclusions

Results from the analysis of solar irradiance measurements on vertical

surfaces for the period 22 July through 4 September indicate a general

overestimate (18%-46.5%) of solar irradiance on north-facing surfaces by all

five algorithms. The best agreement with measured data was demonstrated for

south-facing surfaces where all but one algorithm were within the present

measurement accuracy (±5%). Estimates of global irradiance on east- and westfacing vertical surfaces ranged from slightly underpredicting (-3%) to

overpredicting by as much as 23% of the observed IS-min data. Future research

should emphasize the collection of data similar to that being obtained at

SRRL, which will lead to greater understanding of atmospheric processes and

diffuse sky irradiance distributions.

LV
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TABLE OF CONTENTS

1.0 Introduction . 1

2.0 Algorithm Descriptions•••••••••••• 2

Ground-Reflected Term ••••••••••••••••••••••••••••••

2

2

2

3

4

4

4

5

6

6

Isotropic ..

Perez ..

Klucher ..

Hay ..

Temps and Coulson.

2.3.1

2.3.2

Direct Solar Beam Term....................... ••••••••••••••••

Diffuse Sky Terms • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

2.2.1 Isotropic.................................... . . 2.2.2 Temps and Coulson •••••••••••••••••••••••••••••••••••••••

2.2.3

2.2.4

2.2.5

2.3

2.1

2.2

3.0 Measurements at SRRL •••••••••••••••••••••••••••••••••••••••••••••••• 7

3.1

3.2

3.3

Sensor Calibrations••••••••••••••••••••••••••••••••••••••

Data Collection and Processing......................... • •••••

Data Plots " ..

7

13

13

4.0 Evaluation of the Algorithms ••••••••••••••••••••••••• 17

4.1

4.2

4.3

Intercomparisons of the Algorithms •••••••••••••••••••••••••••

Summary of Work by Perez ••••••••••••••••••••••••••••••••••

Evaluations Using Data Collected at SRRL ••••••••••••••••••

17

17

18

5.0 Summary and Conclusions••••••••••••••••••••••••••••••••••••••••••••• 25

6.0 References .. 27

v
TR-2525

LIST OF FIGURES

3-1 The Radiometer Tower at the SERI Solar Radiation Research

Laboratory on South Table Mountain, Golden, Colo................... 8

3-2 Locations of Pyranometers on Radiometer Tower for Measuring Solar

Irradiance on Vertical Surfaces.................................... 9

3-3 Pyranometer Comparisons using Tilt Table Mounting Platform in a

(a) Horizontal Position and (b) Vertical South-Facing position..... 10

3-4 Results of Pyranometer Comparisons using Tilt Table Mounting

Platform in Horizontal (0), South-Facing (S), and North-Facing (N)

Vertical Posi t i ons s , , •••• •••• •••••••••••• ••••••••• •••• ••••• ••• ••••• 11

3-5 A Selected Clear Day (10 August 1984) of IS-min Averaged

Measurements from Data Set #1 •••••••••••••••••••••••••••••••••••••• 14

3-6 Measurements for a Selected Overcast Day (Cirrostratus Clouds)

from Data Set fF1................................................... 14

3-7 Measurements for a Selected Day from Data Set #2 ••••••••••••••••••• 15

3-8 Measurements from a Partly Cloudy Day in Data Set #2 ••••••••••••••• 16

3-9 Typical Diurnal Pattern of Ground Albedo Measurements •••••••••••••• 16

4-1a Solar Component Measurements for 6 September 1984 (Day 250) •••••••• 22

4-1b Comparison of Measured Data for North-Facing Vertical Surface

on September 6, 1984 and Tilt Model Estimates•••••••••••••••••••••• 22

4-2a Solar Component Measurements for 7 September 1984 (Day 251) •••••••• 23

4-2b Comparison of Measured Data for North-Facing Vertical Surface

on 7 September 1984 and Tilt Model Estimates ••••••••••••••••••••••• 23

4-3 Comparison of Measured Data for North-Facing Vertical Surface

on 6 September 1984 (clear sky) with Isotropic and Anisotropic

Model Estimates •••••••••••••••••••••••••••••••••••••••••••••••••••• 24

4-4 Comparison of Measured Data for North-Facing Vertical Surface

on 7 September 1984 (partly cloudy sky) with Isotropic and

Anisotropic Model Estimates •••••••••••••••••••••••••••••••••••••••• 24

vi
TR-2525

LIST OF TABLES

2-1 Insolation Conversion Algorithms.................................... 3

3-1 Results of Pyranometer Comparisons on Tilt Table •••••••••••••••••••• 12

4-1 Model Comparisons, North Facing-gOO Tilt •••••••••••••••••••••••••••• 17

4-2 Summary of the Models' Performance •••••••••••••••••••••••••••••••••• 19

4-3 Conversion Algorithm Performance during 41 Days ••••••••••••••••••••• 20

4-4 Average Daily Total Irradiance on Vertical Surfaces Measured at

SRRL during the Period 23 July-4 September 1984 ••••••••••••••••••••• 20

VIl
1.0 INTRODUCTION

Passive solar heating, cooling, and daylighting systems utilize building

apertures and external surfaces (walls) to collect or reject incident solar

radiation. Those surfaces can generally be characterized in design

performance simulations as flat plate collectors having a wide range of

orientations described by various combinations of azimuth and elevation

angles. Available solar radiation resource data for input to these

simulations are limited to the historical measurements of global irradiance

(direct solar beam plus diffuse sky irradiance components) on an unobstructed

horizontal surface (SERI 1981a). Therefore, algorithms are needed to convert

these measured values to estimates of the irradiance available to plane

surfaces of any orientation. Several candidate conversion algorithms exist

(Hay and McKay 1985). Their accuracy for other than south-facing orientations

and application for a variety of climates continues to be a topic of research.

The FY 1984 objectives for this task were

• To evaluate the capability of existing conversion algorithms to estimate

irradiance on N-E-S-W vertical surfaces

• To initiate the measurement of irradiance on N-E-S-W vertical surfaces to

support the evaluation and development of conversion algorithms.

Initial plans called for three approaches to the evaluation of existing conversion algorithms:

1. Intercomparison of the performance of the algori thms under various hypothetical atmospheric conditions.

2. Comparison of actual measured data collected at universities participating

in the Department of Energy's Solar Energy Meteorological Research Training

Sites (DOE/SEMRTS) program (SERI 1981b, 1982) with estimated values from

the algorithms.

3. Comparison of measured data collected at SERI' s Solar Radi a t ion Research

Laboratory (SRRL) with estimated values from the algorithms.

The first approach was abandoned because of its limited usefulness to the

variety of climates encountered in a general application of the alorithms.

Shortly after the task was undertaken it was determined that the second

approach had already been used at the Atmospheric Sciences Research Center,

State University of New York, Albany (Perez and Stewart 1984; Stewart and

Perez 1984). Rather than duplicating their effort, we put greater effort into

the collection of irradiance data at SRRL and the use of that data for the

third approach given above.
2.0 ALGORITHM DESCRIPTIONS

In general, conversion algorithms take the form

(2-1)

where

Ir(S,$) = the total irradiance on a tilted surface

I 8(B,$) = the direct solar beam irradiance on the surface

In(S,$) = the diffuse sky irradiance on the surface

IG(B,$) = the ground reflected irradiance on the surface

B = the surface tilt angle (measured from the horizontal)

$ = the surface azimuth angle relative to the sun.

The five algorithms evaluated are listed in Table 2-1, which also defines the

general character of the diffuse sky and ground terms.

2.1 Direct Solar Beam Term

The direct solar beam term for each of the five algorithms 1S identical and 1S

expressed by

I8(B,$) = I cos 8 ,

where

I = the intensity of the direct normal (beam) irradiance

a = the incidence angle of the direct normal on the surface.

(2-2)

The direct normal is measured using a tracking pyrheliometer. The 5.7 0 field

of view of most pyrheliometers encompasses the entire solar disk (0.5°) and

most of the circumsolar region around the sun, which is produced by the

forward scattering of radiation by the atmosphere.

2.2 Diffuse Sky Terms

The diffuse sky terms are different for each of the algorithms evaluated. The

simple isotropic term used by Liu and Jordan (1960) is described first, then

the anisotropic modifiers of the other models are discussed.

2.2.1 Isotropic

The diffuse sky term of the algorithm is often referred to simply as the

isotropic algorithm and is expressed as

In(a) = 1/2 In(O)(l + cos a) ,

2

(2-3)
Table 2-1. Insolation Conversion Algorithms

Algorithm

Isotropic

Temps and Coulson

K1ucher

Hay

Perez

where

Diffuse Sky Term

Clear or cloudy and isotropic

Clear only and anisotropic

Clear or cloudy and anisotropic

Clear or cloudy and anisotropic

Clear or cloudy and anisotropic

Ground Term

Isotropic

Anistropic

None

Isotropic

None

ID(O) = the measured diffuse sky irradiance on a horizontal surface (6 0)

6 = the surface tilt angle.

This expression assumes uniform radiance from each portion of the sky, i.e.,

isotropic diffuse irradiance from all directions above the surface, resulting

in no dependence on azimuth angle, ~.

2.2.2 Temps and Coulson

Temps and Coulson (1977) added a degree of complexity to the isotropic diffuse

sky term:

ID{S) (2-4)

where

a = the angle of incidence of the direct beam on the surface

Z = the solar zenith angle.

(2-5)

(2-6)

MI is an anisotropic modifier to account for horizon brightening, and M2 is an

anisotropic modifier to account for the brightening around the solar disk

{circumsolar radiation}. M2 is a potential sOurce of error since the

measurement of the direct normal beam (I) encompasses a large part of the

circumso1ar radiation. Note also that M2 does not include any means to

account for the increase in circumso1ar radiation with the onset of cloud

cover, which eventually leads to an anisotropic sky under overcast conditions.

It is for this reason that the Temps and Coulson algorithm is applicable to

only clear conditions. Under overcast skies there is horizon "darkening"--

another reason why the Temps and Coulson algorithm is inappropriate for other

than clear sky conditions.

3
TR-2525

2.2.3 Klucher

A refinement of the diffuse sky term provided by Klucher (1978) adds a cloudiness function (F) to the Temps and Coulson algorithm; i.e.,

where

M3 = [1 + F sin3( a/ 2) ]

M4 = [1 - F cos 2e sin3Z]

F = {I - [I D(O)/1T(O)]2}

(2-7)

(2-8)

(2-9)

(2-10)

An examination of the cloudiness function reveals that under overcast skies

[ID(O) = IT(O)] the Klucher diffuse sky term reduces to the isotropic term of

Liu and Jordan, as was the intent.

2.2.4 Hay

The diffuse sky term described by Hay and Davies (1978) also provides for

anisotropy by considering both circumsolar and isotropic terms. The diffuse

sky term in the Hay algorithm is expressed as

ID(8) = 1D(O)[(1 cos ell o cos Z) + 1/2(1 + cos a) (1 - 1/10 ) ] , (2-11)

where

I = the direct normal (beam) irradiance from the sun

10 = the extraterrestrial direct normal (beam).

The first term inside the brackets represents circumso1ar radiation whose

intensity is a function of atmospheric transmissivity (1/1 0 ) , the angle of

incidence of the direct beam, and the solar zenith angle. The inverse relation with cos Z represents an increase in circumso1ar radiation with an

increase in airmass (increasing solar zenith angle). The second term represents the isotropic radiation from the sky that increases with decreasing

transmissivity; i.e., with increasing turbidity or cloud cover. Note that the

Hay algorithm simplifies to the isotropic case for overcast conditions.

2.2.5 Perez

This algorithm, like the K1ucher and the Temps and Coulson algorithms,

accounts for horizon brightening as well as circumso1ar radiation (Perez and

Stewart 1984). This is accomplished by describing the sky dome as isotropic

except for a circular region of variable size around the sun and a horizontal

band of variable height at the horizon. The equation for the diffuse sky term

of the Perez algorithm is

4
TR-2525

1/2(1 + cos 8) + 2(F1 - 1)(1 - cos a)Zc

In(O) 1 + 2(F1 1)(1 cos a)Zh

(2-12)

+ 2(F2 - 1) ~/~ sin ~t

+ 1/2(1 - cos 2~)(F2 - 1) ,

where

F1 =

F2

Ct. =

~' =

Zc =

the ratio of the radiance in the circumsolar region to isotropic sky

radiance

the ratio of the radiance in the horizon band to the isotropic sky

the half angle width of the circumsolar region

the angular width of the horizon band

the altitude angle of the apex of the horizon band with respect to the

tilted surface

cos 6 [0 < 6 < (~/2 - Ct.)]

(Xc Sln Xc)

Zc (~/2 - Ct.) < a < (~/2 + ex)]

Ct.

Zc 0 [8 > (~/2 + Ct.)]

Xc = (~/2 + ex - 6)/2

6 = angle of incidence of circumsolar radiation on a tilted surface

Zh = cos Z [0 < Z < (~/2 - Ct.)]

Zh

(XhsinXh) = [Z > (~/2 - a)]

ex

Xh = (~/2 + ex - Z)/2

Z = angle of incidence of circumsolar radiation on a horizontal surface.

The terms F1 and F2 are empirically derived from measured data at the location

of interest. They are a function of the solar zenith angles, ID(O) and 1(0),

and are available in the form of 5 x 6 x 7 matrices. The empirlcal nature of

these terms is a distinct limitation of data sets similar to those at the

State University of New York at Albany.

2.3 Ground-Reflected Term

The approach for estimating the contribution of ground-reflected solar

irradiance can be classified as either isotropic (uniform with respect to

direction) or anisotropic (directional). The Klucher algorithm was developed

from data collected from pyranometers shielded from this radiation component

by artificial ground planes and therefore does not account for either case.

With the exception of the Temps and Coulson algorithm, which accounts for the

azimuthal dependence of the ground-reflected components, the remaining

algorithms assume isotropy for this term in Eq. 2-1.

5
TR-2525

2.3.1 Isotropic

The ground-reflected term for these algorithms is given by

IC(S) = 1/2 IT(O)RC(1 - cos S) ,

where

IT(O) = the measured global horizontal irradiance

RC = the ground albedo.

(2-13)

This algorithm assumes the ground is a homogeneous Lambertian surface (perfect

diffuser) surrounding the tilted surface.

2.3.2 Temps and Coulson

The Temps and Coulson term for ground-reflected radiation 1S given by

(2-14)

where

MS = [1 - cos 2( s/ 2) ]

M6 = [1 + sin2(Z/2) Icos ~I] = the titled surface azimuth angle relative to the sun (~ = 0 when the

surface is pointed toward the sun).

The equation represents a ground surface exhibiting forward scattering, which

increases with the solar zenith angle.

6
3.0 MEASUREMENTS AT SRRL

Pyranometers were installed at the Solar Radiation Research Laboratory (SRRL)

using the radiometer tower designed for monitoring solar irradiance on vertical surfaces oriented in the four cardinal directions (Figure 3-1). The

instruments were positioned to measure the global irradiance on each of the

four vertical surfaces as well as the diffuse sky and ground-reflected components for the north- and south-facing orientations. Global horizontal and

ground-reflected i r r ad i ance on downward-facing horizontal surfaces complete

the list of ten Eppley PSP pyranometers deployed for the experiment. The

arrangement of sensors, artificial horizons, and radiation baffles to

accomplish the measurements is shown in Figure 3-2.

In addition to the array of sensors set up for this task, SRRL routinely monitors global horizontal, di rect normal, and diffuse horizontal irradiances.

These data provide the inputs corresponding to each term in the conversion

algorithm (Eq. 2-1). In addition to the irradiance values, ground albedo is

calculated by ratioing the downward-looking horizontal data wi th the global

horizontal data.

3.1 Sensor Calibrations

All of the Eppley PSPs used for this task were calibrated and intercompared by

plac ing them on a large tilt table wi th SERI t S working standard PSP and

collecting simultaneous global data for horizontal, south-facing vertical, and

north-facing vertical planes as shown in Figure 3-3. Note the presence of

white "collars," which were installed around the instrument body below the sun

shade. These units provide additional shielding of the instrument body, which

serves as the reference cold junction for the thermopile sensor, from the

direct radiation. This reduces the presence of thermal gradients when the

pyranometer is mounted in other than a horizontal position. The collars were

used during all intercomparisons and final installation on the radiometer

tower. Several days of I-min data were obtained and analyzed for each

orientation. The calibration results are summarized in Table 3-1.

From these data, the selection of PSPs for each position on the radiometer

tower was made so as to minimize differences among sensors for which data comparisons would be critical. A minimum of two days of measurements for each

tilt table orientation (horizontal, vertical north-facing, and vertical southfacing) was analyzed. Instrument selection was based on the minimum relative

variance of the I-min ratios of the output signal from the test pyranometer

(millivolts) to the irradiance measured by the SERI reference pyranometer

(watts per square meter). The calibration factor for each instrument was

determined from this ratio. The mean value (calibration factor) and standard

deviation of this ratio were computed for three groups of data determined by

the tilt table orientations. The relative variance of the calibration factor

was computed for each instrument using the formula: Relative Variance = 100 x

Standard Deviation/Mean.

The relative performance of the test pyranometers with respect to the reference unit is shown in Figure 3-4. The varability of the calibration

7



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10 12 14

Vertical

north-facing

\

2

..--....,.-....,...-.,....---,--..,....---,~-.,..-...,---....,.-....,...-.,....-'"

0.8

0.4

3.2

PSP INTERCOMPARISONS: TILT TABLE

APRIL 4-139 1984

INSTRUMENT

NUMBER

1

2

3

4

5

6

7

8

9

10

11

12

13

SERIAL

NUMBER

13674F3

17798F3

17799F3

17800F3

17362F3

17879F3

18035F3

18036F3

18039F3

lR040F3

18078F3

200h8F3

20079F3

MEASUREMENT

PARAMETER

(Not Used)

South-Sky

North-sky

North-Ground

South-Ground

South-Global

Albedo

'Illest-G1oba1

North-Global

Diffuse Horizontal

East-Global

(Not Used)

Global Horizontal

Figure 3-4. Results of Pyranometer Comparisons using Tilt Table Mounting

Platform in Horizontal (0), South-Facing (S), and Horth-Facing

(H) Vertical positions. Installation of instruments of the

radiometer tower (measurement parameter) was determined from

these data.

11
Table 3-1. Results of Pyranometer Comparisons on Tilt Table

Calibration Factor (~V!Wm-2) % Difference Pyranometer

Serial No.

Measurement

Parameter Factory Horizontal South North South North

17799

17800

18039

18078

17798

17862

17879

18036

18035

20079

18040

13674

20068

North-sky

North-ground

North-global

East-global

South-sky

South-ground

South-global

West-global

Albedo

Horizontal

Diffuse

Not used

Not used

8.50

9.17

8.37

10.17

8.35

8.31

9.00

7.99

8.63

10.50

8.95

10.73

10.57

8.37

9.16

8.30

10.01

8.38

8.34

9.06

7.89

8.64

10.20'1~

8. 70'~

10.94

10.36

8.50

9.24

8.31

10.09"'~

8.22'·~

8.3S'·~

9.01":

7• 90"~

8.58

10.33

8.77

10.57

10.52

8.51"':

9 • 15"':

8.28*

9.69

8.28

8.19

8.87

7.80

8.45'·~

9.85

8.44

10.89

9.97

1.55

-0.87

-0 .12

-0.80

1. 91

-0.12

0.55

-0.13

0.69

-1.27

-0.80

3.40

-1.54

1.67

0.11

0.24

3.19

1.19

1.80

2.10

1.14

2.20

3.43

2.99

0.46

3.76

Measurement parameter

Factory calibration

Horizontal

South

North

% Difference

{*}

final instrument orientation for continuous monitoring

Eppley Laboratory's indoor sphere determination

comparison with SERI Reference PSP 17860, tilt table in

horizontal position

comparison with SERI Reference PSP 17860, tilt table In

south-facing vertical position

comparison with SERI Reference PSP 17860, tilt table In

north-facing vertical posltlon

100 x (horizontal - vertical}!horizontal

calibration factor used for continuous monitoring

factor depends on the particular instrument and its orientation. The ability

of the instrument to view the direct (beam) radiation component appears to

minimize the relative performance differences between all instruments and the

SERI reference pyranometer. The reference pyranometer may itself undergo

changes in sensitivity when instrument orientation, ambient air temperature,

solar irradiance levels, or other factors change. These intercomparisons cannot ensure the absolute measurement accuracy of the pyranometers. The overall

agreement of the calibrations is within the generally accepted tolerance of

±5% for these thermopile instruments (SERI 1982b).

The selection of pyranometer orientation/location on the radiometer tower was

based on the results shown in Figure 3-4. For example, the three north-facing

sensors were selected from those that compared best on a north-facing plane.

The calibration factors for the east- and west-facing pyranometers were determined from the tilt table comparisons exhibiting the least relative variance

12
TR-2525

from the reference instrument after select ing the north- and south-fac ing

instruments. The cosine response of the east- and west-facing pyranometers is

particularly important since the irradiance levels are generally high near

solar noon when the sun is setting or rising (incidence angle = 900 ) on these

instruments.

3.2 Data Collection and Processing

Plans called for the simultaneous collection of I-min data from all nine sensors in the test array, plus the three baseline monitors. However, this task

was initiated during the transition period between the operation of an interim

research laboratory and the establishment of a permanent facility at SRRL.

SRRL has yet to become fully operational; and therefore, data collection has

been limited to IS-min data from seven sensors at a time. At this time, the

following data sets have been collected:

Data Set No.1

(from 22 July to 4 Sept. 1984)

Global horizontal

Direct normal

Global north vertical

Global east vertical

Global south vertical

Global west vertical

Ground reflected horizontal

Data Set No.2

(from 5 Sept. to 30 Sept. 1984)

Global horizontal

Direct normal

Diffuse horizontal

Global south vertical

Global north vertical

Sky north vertical

Ground north vertical

In the near future, a much improved data acquisition capability will be in

operation at SRRL. This will permit the collection of data from all sensors

at the same time with any desired integration time. The results in this

report have been derived from the two data sets noted above.

3.3 Data Plots

Figures 3-5 and 3-6 are plots of typical data from data set No.1. Figure 3-5

shows the symmetry of a very clear day on 10 August 1984. It is particularly

interesting to note that in the absence of the direct beam because of surface

orientation, the irradiance on all four surfaces is about the same. Furthermore, on this midsummer day, the daily total energy received on east, south,

and west vertical surfaces is about the same (17.9, 13.5, and 17.5 MJ/m2,

respectively).

The irradiance received on a cloudy day, 6 August 1984, is shown in Figure 3-6. Some direct beam irradiance was recorded between 0500 and 0800; but

thereafter, the sun did not shine on the SRRL. Between 0800 and 1030, a low

heavy overcast developed. This cloud cover thinned out between 1030 and 1330,

but was more or less uniform across the sky dome. These recorded observations

are confirmed by the variations in irradiance shown in Figure 3-6.

Data for a clear day and partly cloudy day from the second data set are shown

in Figures 3-7 and 3-8, respectively. On the clear day, an interesting relationship is observed between the north-vertical diffuse sky irradiance and the

13

TR-2525

north-vertical ground-reflected irradiance. In early morning and late afternoon the diffuse sky irradiance reaches a maximum and is greater than the

ground-reflected irradiance. By midmorning, the ground-reflected irradiance

is about twice the diffuse sky. This is, of course, consistent with the

gradual increase in the i rradiance on horizontal surfaces as shown on the

figure. The region around the tower was a natural surface with grass, forbs,

and some bare soil showing. At this time of year, the vegetation is mostly

senescent. The measured albedo just two days earlier is shown in Figure 3-9.

Figure 3-8 presents an even more interesting situation. Early in the morning

a cold front moved through the area producing a dark layer of a I to-stratus

clouds that moved from the northwest early in the morning until most of the

sky was covered by 0830. These stratus clouds produced a sky irradiance that

was approximately double the ground-reflected component, just the opposite of

the relative levels observed on the previous clear day. At about 1230, this

stratus condition began to break up, and at about 1315, we noted a crossover

of the sky and ground components. The presence of alto-cumulus in the afternoon produced the jagged appearance of the direct normal and maintained the

diffuse sky irradiance at about the same level as the ground-reflected term.

CD

o

c::

co

:0 400

col...

l...

/-----\ I'. r

~/' 'v v \

/ I

/ f,--.,

/ Global \

, horizontal '\ / \

, \ / I

,/ \~'" / North-sky '\

I

I North-ground vertical Nor~h-global •

, vertical_.__._\-....·_·~~.L. \. ~.-:::.::- 1-·-'-1:. -e:- _ _ _ _ - - - -t--

- - - - - ~~. "-

- 7 9 11 13 15 17

Mountain standard time

19

Figure 3-7. Measurements for a Selected Day from Data Set #2. Clear sky in

the morning with thin cirrus clouds in the afternoon.

15

4.0 EVALUATION OF THE ALGORITHMS

The conversion algorithms described in Section 2.0 have been evaluated in

several ways. First, an intercomparison of the models under different atmospheric conditions reveals certain characteristics such as their regression to

an isotropic form under overcast skies. The comparisons with measured data,

which are reported here, include a brief summary of results reported by Perez

and Stewart (1984). Comparisons with the two data sets available from the

SRRL conclude this section.

4.1 Intercomparisons of the Algorithms

The results reported here excluded the ground term since some of the algorithms do not have such a term. The numbers in Table 4-1 are values of

irradiance for individual days that were overcast, partly cloudy, or clear.

Measured data were available for these atmospheric conditions for the direct

normal, global horizontal, and diffuse sky components. This particular data

set, used at the start of this task, did not include measurements on vertical

surfaces. Hence, the model s could be intercompared but not compared in

absolute terms.

The results show up to 30% differences under clear skies in June and almost

identical results under overcast skies any time of the year. This is a result

of all the models regressing to the isotropic model under overcast conditions.

4.2 Summary of Work by Perez

The State University of New York at Albany (SUNYA) collected an accurate data

base of solar radiation measurements from 1977 to 1981 under the DOE-funded

Solar Energy Meteorological Research Training Sites (SEMRTS) program. The

data included measurements on vertical surfaces with N-E-S-W azimuths and measurements on other tilted south-facing surfaces. An artificial horizon

shielded the sensors from the ground-reflected radiation.

Perez and Stewart used that data base to evaluate the isotropic (Liu and

Jordan), Klucher, and Hay algorithms, as well as a new model they developed

Table 4-1. Model Comparisons, North Facin¥-900 Tilt

(Daily Total Irradiance - kJ/m )

Month Condition Isotropic Klucher Hay Perez

June Clear 8349 9648 6882 7479

June Partly cloudy 4375 4487 4332 4000

June Overcast 1525 1528 1525 1531

December Clear 3182 3448 2912 3148

December Partly cloudy 1865 1967 1796 1679

December Overcast 632 633 632 629

17
TR-2S2S

(4-1)

and called the Perez model. In their analysis, they removed the direct beam

component from the global measurements to permit evaluation of the diffuse sky

component by itself.

A summary of the results of their evaluation is given in Table 4-2. It is

apparent that the isotropic, Klucher , and Hay algorit hms perform better on

south-facing surfaces than on east, west, or north surfaces. The Perez model

does better on the E-W surfaces, but still seems to overestimate on a northvertical surface, although still exhibiting a lower RMS error. North-facing

surfaces produce the largest relative errors for all the algorithms as might

be expected for the lower irradiance levels associated with this orientation.

4.3 Evaluations Using Data Collected at SRRL

As described in Section 3.2, data set No.1 contains 41 days of data with

global measurements on N-E-S-W vertical surfaces. Table 4-3 gives average

root mean square (RMSE) and mean bias errors (MBE) for the entire 41 days of

data, where the measured values were compared with estimates from each

algorithm. The measured data are IS-min integrals.

The percent mean bias error is defined by

n

%MBE = 100[n-1. L (Yi - Xi>]/Y , 1=1

where n is the sample size, Yi is the model generated value for time interval

i, x . is the corresponding measured value, and x is the mean measured value 1. for a given time frame.

The percent root mean square error 1.S given by

n

%RMSE = 100[n-1 L (Y' - x·)2]O.S/x i=1 1 1 ,

where the parameters are the same as those defined for Eq. 4-1.

(4-2)

One should note that the horizontal diffuse irradiances used as input to the

models were calculated from global horizontal and direct normal beam values

using

10(0) = 1T(O) - I cos Z , (4-3)

where all the terms are defined in Section 2.0. These calculated diffuse

values are generally thought to be more accurate than diffuse measurements

us ing a pyranometer wi th a shadow band (Ryznar and Portman 1983; LeBaron,

Peterson, and Oirmhirn 1980).

The evaluations using measurements from data set No. 1 were based on the

observed ground albedo values. The isotropic ground term computation method

was added to the Klucher and Perez algorithms to complete the comparisons.

18
Table 4-2. Summary of the Models' Performance

February 1980 June 1980

Azimuth South South North East West South South North East West

Tilt 430 900 900 900 900 430 900 900 900 90

Energy (kJ/m2/h) 1606 1361 190 593 581 778 407 124 346 356

RMS Errors

Isotropic 12.2 18.6 47.3 26.8 23.7 7.3 12.4 38.9 27.6 32.4

-

"" Klucher 6.2 11.5 66.2 22.0 21.1 4.9 17.0 56.8 24.6 29.9

Hay 7.0 10.2 48.5 17.2 16.5 6.8 19.5 32.3 19.1 24.4

Perez 4.5 7.4 22.1 10.5 10.6 3.6 10.4 13.3 10.0 13.5

Accumulated Errors

Isotropic -8.8 -13.7 24.3 -9.8 -6.3 -4.1 -1.3 13.9 -6.3 -7.3

Klucher -2.2 2.7 38.4 3.0 2.4 -1.5 9.6 30.6 3.3 3.2

Hay -2.0 -4.2 -4.7 -8.8 -6.2 -4.3 -9.3 -5.4 -7.1 -10.7

Perez 1.1 0.9 10.4 -1.9 0.6 -1.3 -1.5 0.1 -1.6 -2.2

~(Data from State University of New York at Albany

III

III

-V

-II I

~-"
S=~II.I TR-2525

Table 4-3. Conversion Algorithm Performance during

41 Days (from 22 July to 4 September 1984)

Vertical Surfaces

Azimuth North East West South

Hourly RMS Errors (%)

Isotropic 61.6 29.1 33.0 17.9

Temps & Coulson 96.5 31.4 50.9 31.9

K1ucher 68.9 29.6 34.5 20.5

Hay 60.4 28.3 32.4 18.0

Perez 55.5 26.6 32.2 19.6

Mean Bias Error (%)

Isotropic 18.5 -3.0 3.4 1.5

Temps & Coulson 46.5 9.5 23.1 15.3

Klucher 29.2 2.1 11.1 6.8

Hay 14.6 -3.0 2.9 0.9

Perez 18.0 1.9 10.6 6.7

The RMS errors given in Table 4-3 are lowest for a south-facing surface, much

higher on E-W surfaces, and very high on north surfaces. This can be attributed in part to the effect of generally lower levels of irradiance available

on north-facing slopes on this relative error calculation (see Table 4-4).

The mean bias errors show reasonable performance on E-S-W surfaces with the

exception of Temps and Coulson, which has no cloud cover term.

The Perez algorithm was used with FI and F2 values derived from data at

SUNYA. Considering that fact, it may be that the F terms are spatially and

temporally conservative based on the results for the SRRL.

Table 4-4. Average Daily Total Irradiance on

Vertical Surfaces Measured at the

SRRL during the Period 23 July4 September 1984

Orientation

North

East

South

West

Irradiance

(kJ/m2/day)

4967

13950

10495

8832

20

Percent

of North

100

320

241

312
TR-2525

Data from two days were taken from data set No.2 for a more detailed evaluation of all of the algorithms, except the isotropic, since these data included

north sky and north ground separation. Day 250, September 6, 1984, was

generally clear although scattered clouds did develop in the afternoon. This

is apparent from Figure 4-1(a), which shows the direct normal beam, global

horizontal, and diffuse horizontal (calculated from Eq , 4-]) components on

that day.

The comparison in Figure 4-1(b) between measured and estimated values of

irradiance on a north-vertical surface is very revealing. During the morning,

under clear skies, the measured values are about twice the estimated values.

Since data set No. 2 did not contain observations of ground-reflected

irradiance, the albedo input to the algorithms was adjusted each hour

according to Figure 3-9. In general, the model results are well behaved, with

Klucher and Temps and Coulson being inseparable and giving the best performance. In the afternoon, the scattered clouds produced very erratic results

until late afternoon when the skies apparently cleared again. Scattered

clouds are obviously not handled well by any of the algorithms.

Figures 4-2a and b are similar plots for a generally cloudy day, 7 September

1984, which was previously described with reference to Figure ]-6. On this

day, all of the models overestimated the irradiance on a north-vertical surface, except during relatively clear periods during the early morning and late

afternoon hours. The Perez model performed the best, and the Temps and

Coulson model gave the worst results.

Figures 4-3 and 4-4 provide comparisons between measured and estimated groundreflected irradiance on a north-vertical surface. Relatively good agreement

is indicated between the isotropic and anisotropic methods under clear and

cloudy sky conditions for north-facing surfaces.

21



and west vertical

surface by 14.6%.

5.0 SUMMARY AND CONCLUSIONS

Five algorithms for converting global horizontal and direct normal solar irradiance to global irradiance on tilted surfaces were evaluated using measurements from monitoring equipment newly installed at the Solar Radiation

Research Laboratory. High resolution (15-min) measurements from eight thermopile radiometers oriented vertically in the four cardinal directions were

available for a 169-day period ending 31 December 1984. Concurrent measurements of global horizontal and direct normal were also available for the

analyses. The pyranometers used in the experiment were intercompared on horizontal, north-facing, and south-facing vertical orientations before their

deployment.

The conversion algorithms each attempt to account for very complex atmospheric

interactions with incoming solar radiation. The sky and ground radiance

contributions to tilted surface irradiance are assumed to be isotropic

(independent of direction), anisotropic (direction dependent), or a combination of the two regimes depending on the algorithm.

Results from the analysis of measurements for the period 22 July through

4 September indicate the following algorithm performances:

• Isotropic (Liu & Jordan)--Within measurement accuracy (±5%) for east, south,

and west vertical surfaces. Overpredicts irradiances of north-facing

surface by 18.)%.

• Temps & Coulson--Overpredicts irradiance for all orientations from 9.5% to

46.5%.

• Klucher--Overpredicts irradiance for all orientations from 2.1% to 29.2%.

• Hay--Within measurement accuracy for east, south,

surfaces. Overpredicts irradiance of north-facing

Demonstrated least overall mean bias errors.

• Perez--Within measurement accuracy for east orientation. Overpredicts 1rradiance of south (6.7%), west (10.6%), and north (18.0%) orientations.

The performance of all the algorithms was poorest for the north-facing vertical surfaces. The irradiance levels measured on this orientation were between

two and three times less than that observed for the others on an average daily

total basis. This would help explain the larger relative errors, but this

orientation also places the greatest demands upon the models to account for

the anisotropic distribution to diffuse sky and ground irradiances.

Because of the limited data available at this time, these results must be considered preliminary and inconclusive. Nevertheless, a fairly clear picture is

emerging that indicates significant deficiencies in the diffuse sky component

of all of the models. Future research should emphasize the collection of data

similar to that being obtained at SRRL, which will lead to greater

understanding of atmospheric processes and diffuse sky i r r ad i ance , A very

desirable addition at SRRL would be the installation of an all-sky camera to

photograph the sky every 15 minutes. This would improve our understanding of

the data and would likely suggest modifications of the conversion algorithms.

25
TR-2525

The collection of data during the coming months, with the change of seasons

and the concomitant changes in atmospheric and ground cover conditions, should

provide greater insight into the problems with the algorithms. The

development of improved models should be realized in the near future if

support for this kind of research continues.

26
6.0 REFERENCES

Hay, J. E., and J. A. Davies, (1978), "Calculation of the Solar Radiation

Incident on an Inclined Surface," Proc. 1st Canadian Solar Radiation Data

Workshop, J. E. Hay and T. K. Won (eds.), Toronto, Canada.

Hay, J. E., and D. C. McKay, (1985), "Estimating Solar Irradiance on Inclined

Surfaces, A Review and Assessment of Methodologies," International Journal

of Solar Energy, Vol. 3, pp. 203-240.

Klucher, T. M., (1978), Evaluation of Models to Predict Insolation on Tilted

Surfaces, NASA TM-78842.

Liu, B. Y. H., and R. C. Jordan, (1960), "The Inter-relationship and

Characteristic Distribution of Direct, Diffuse, and Total Solar Radiation,"

Solar Energy, Vol. 4, pp. 1-19.

Perez, R., and R. Stewart, (1984), "Real Time Comparison of Models Estimating

Irradiation on Sloping Surfaces," preprint from Progress in Solar Energy,

Vol. VII, American Solar Energy Society.

SERI, (1981a), Solar Radiat ion Resource Atlas of the Uni ted States, SERII

SP-642-1037, Golden, co: Solar Energy Research Institute, 183 pp.

SERI, (1981b), Solar Energ Meteorological Research and Trainin Site Pro ram:

First Annual Report, SERI SP-642-947, Golden, CO: Solar Energy Research

Institute, 87 pp.

SERI, (1982a), Solar Energy Meteorological Research and Training Site Program:

Second Annual Report, SERl/sP-290-1478, Golden, co: Solar Energy Research

Institute, 109 pp.

SERI, (1982b), International Energy Agency Conference

Measurements, 16-20 March 1981, Boulder, Colorado,

Golden, co: Solar Energy Research Institute, 431 pp.

on Pyranometer

SERI!TR-642-1156,

Anisotropic Model

in Solar Energy,

Stewart, R., and R. Perez, (1984), "Validation of an

Estimating Insolation on Tilted Surfaces," _P_r_o.:.::g_r_e_s_s

Vol. VII, American Solar Energy Society.

Temps, R. C., and K. L. Coulson, (1977), "Solar Radiation Incident upon Slopes

of Different Orientations," Solar Energy, Vol. 19, pp. 179-189.

27
TR-2525

INTERNAL ABO EXTERNAL REVIEWERS FOR

PASSIVE REPORT

Richland Perez, State Un i v, of N.Y. at Albany; John Hay, Un i v , of B.C.,

Vancouver; Gene Clark, Trinity Univ., San Antonio, Tex.; Ross McCluney,

Florida Solar Energy Center, Cape Canaveral, Fla.; Bob Jones Los Alamos Labs.,

Los Alamos, N.M.

Claude Robbins

Kerri Hunter

Jay Burch

28
Document Control 11. S.ERI R.eport No. 12. NTIS Accession No.

Page S£RI/TR~215-2525

4. Title and Subtitle

Measuring and Modeling Solar Irradiance on Vertical

Surfaces

7. Author(s)

E. L. Maxwell, T. L. Stoffel, R. E. Bird

9. Performing Organization Name and Address

Solar Energy Research Institu~e

1617 Cole Boulevard

Golden, Colorado 80401

12. Sponsoring Organization Name and Address

15. Supplementary Notes

3. Recipient's Accession No.

5. Publication Date

6.

8. Performing Organization Rept. No.

10. Project/Task/Work Unit No.

3738.10 11. Contract (C) or Grant (G) No.

(C)

(G)

13. Type of Report & Period Covered

Technical Report

14.

16. Abstract (Limit: 200 words) This report presents the first evaluations of 5 algorithms for

converting global horizontal and direct normal solar irradiance components to global

irradiance on tilted surfaces using measurements from the Solar Radiation Research

Laboratory (SRRL) at SERI. High resolution (15~min) measurements from 8 thermopile

radiometers oriented vertically in the 4 cardinal directions were available for a

169-day period ending 31 December 1984. Concurrent measurements of global horizontal and direct normal solar irradiance components were also used. The pyranometers

used were intercompared on horizontal, north-facin~, and south-facing verticalorientations. The conversion algorithms each attempt to account for the very complex

atmospheric interactions with incoming solar radiation. The sky and ground radiance

contributions to tilted surface are assumed to be isotropic, anisotropic, or a combination of the two depending on the algorithm. Results from the analysis of measurements on vertical surfaces for 22 July through 4 September indicate a general

overestimate (18%-46.5%) of solar irradiance on north-facing surfaces by all 5 of

the algorithms. The best agreement with measured data was demonstrated for southfacing surfaces where all but one algorithm were within the present measurement by

as much as 23% of the observed 15-min data.

17. Document Analysis

a.Descriptors Algorithms; Data; Diffuse Solar Radiation; Direct Solar Radiation;

Pyranometers; Solar Radiation

b. IdentifiersiOpen·Ended Terms Vertica1 Surfaces

c. UC Categories

59, 62

18. Availability Statement

National Technical Information Service

U. S. Department of Commerce

5285 Port Royal Road

Springfield, Virginia 22161

Form No. 0069 (3w25-82)

19. No. of Pages

38

20. Price

AD3

'it U.s.GOVERNMENT PRINTI NG OFFICE: 1986-676-099140049