SERI/TR-21S-3038

UC Categories: 62, 63

DE87001177

Investigation of a CloudCover Modification to

SPCTRAL2, SERI's

Simple Model for

Cloudless-Sky, Spectral

Solar Irradiance

R. E. Bird

C. J. Riordan

D. R. Myers

June 1987

Prepared under Task No. 6001.20

FTP No. S94A

Solar Energy Research Institute

A Division of Midwest Research Institute

1617 Cole Bou levard

Golden. Colorado 80401-3393

Prepared for the

U.S. Department of Energy

Contract No. DE-AC02-83CH10093
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TR-3038

PREFACE

This report describes research performed by SERI's Resource

Assessment and Instrumentation Branch to develop a cloud-cover

modification to SERI's simple model for cloudless-sky spectral

solar irradiance (SPCTRAL2). This research is part of a continuing effort to develop and verify spectral-solar-irradiance models

and to build a spectral-irradiance data base for different locations and climates.

This work was sponsored by the United States Department of Energy

(DOE). The authors thank Dave Menicucci, Sandia National Laboratory, Albuquerque; C. R. Nagaraja Rao, NOAA/NESDIS, Washington,

D.C.; and Alfred M. Powell, Jr., USAF, Offutt AFB, Nebraska, for

their useful review and comments.

Richard E. Bird

Senior Scientist

Approved for

SOLAR ENERGY RESEARCH INSTITUTE

J~~ L. Stone, Director

/~:":'Solar Electric Research Division

iii
TR-3038

SUMMARY

Objective

The objective of this research was to investigate a cloud-cover modification

to SERI' s simple model for cloudless-sky, spectral solar irradiance

(SPCTRAL2). This work contri butes to an ongoing effort in SERII S Resource

Assessment and Instrumentation Branch to develop and verify spectralirradiance models that can be used, with measurements, to build a spectralsolar-irradiance data base for different locations and climates.

Discussion

Our approach was to investigate a modification to SPCTRAL2 that did not

require detailed input on cloud properties, but relied on more commonly

acquired meteorological and broadband data available in a historical data base

(SOLMET). The method was to normalize modeled, cloudless-sky, spectral irradiance to a measured broadband-irradiance value under cloudy skies; and compare normalized, modeled data with measured spectral-irradiance data to

empirically derive spectral modifiers that improve the agreement between

modeled and measured data.

Conclusions

Results indicate the possible form of the spectral corrections; however, we

must analyze additional data to develop a spectral transmission function for

cloudy-sky conditions.

iv
TR-3038

1.0

2.0

3.0

4.0

5.0

TABLE OF CONTENTS

Introduction .

Background .

Approach ..

Results "' ..

Discussion ..

1

2

3

6

24

6.0 Summary and Conclusions •••••••• ....................................................... 26

7.0

8.0

Future Work .

Ref erences ..

v

27

28
TR-3038

LIST OF FIGURES

4-1 Case 1. Comparison of Modeled and Measured Global-Normal (a)

and Global-Horizontal (b) Spectral Solar Irradiance, and

Photograph of Sky Conditions (solar zenith angle = 28.9 0 ,

relative optical air mass = 1.14) ••••••••••••••••••••••••••••••••• 10

4-2 Case 2. Comparison of Modeled and Measured Global-Normal (a)

and Global-Horizontal (b) Spectral Solar Irradiance, and

Photograph of Sky Conditions (solar zenith angle = 29.30 ,

relative optical air mass = 1.15) ••••••••••••••••••••••••••••••••• 11

4-3 Case 3. Comparison of Modeled and Measured Global-Normal (a)

and Global-Horizontal (b) Spectral Solar Irradiance, and

Photograph of Sky Conditions (solar zenith angle = 43.7°,

relative optical air mass = 1.38) ••••••••••••••••••••.•••••••••••• 12

4-4 Case 4. Comparison of Modeled and Measured Global-Normal (a)

and Global-Horizontal (b) Spectral Solar Irradiance, and

Photograph of Sky Conditions (solar zenith angle = 44.1°,

relative optical air mass = 1.39) ••••••••••••••••••••••••••••••••• 13

4-5 Case 5. Comparison of Modeled and Measured Global-Normal (a)

and Global-Horizontal (b) Spectral Solar Irradiance (solar

zenith angle = 27.9 0 , relative optical air mass = 1.13) ••••••••••• 14

4-6 Case 6. Comparison of Modeled and Measured Global-Normal (a)

and Global-Horizontal (b) Spectral Solar Irradiance, and

Photograph of Sky Conditions (solar zenith angle = 40.6°,

relative optical air mass =1.32) ••••••••••••••••••••••••••••••••• 15

4-7 Case 7. Comparison of Modeled and Measured Global-Normal (a)

and Global-Horizontal (b) Spectral Solar Irradiance, and

Photograph of Sky Conditions (solar zenith angle = 45.4 0 ,

relative optical air mass = 1.42)••••••••••••••••••••••••••••••••• 16

4-8 Case 8. Comparison of Modeled and Measured Direct-Normal (a)

and Global-Horizontal (b) Spectral Solar Irradiance (solar

zenith angle = 56.0°, relative optical air mass = 1.78) ••••••••••• 17

4-9 Case 9. Comparison of Modeled and Measured Direct-Normal (a)

and Global-Normal (b) Spectral Solar Irradiance, and Photograph

of Sky Conditions (solar zenith angle = 28.0°, relative optical

air mass = 1.13) .........•...............•.....•.••..........••.•• 18

4-10 Case 10. Comparison of Modeled and Measured Direct-Normal (a)

and Global-Normal (b) Spectral Solar Irradiance, and Photograph

of Sky Conditions (solar zenith angle = 32.80 , relative optical

air mass = 1.19) ......•.....................•.........••..•....... 19

vi
TR-3038

4-11

4-12

4-13

4-14

LIST OF FIGURES (Concluded)

Case 11. Comparison of Modeled and Measured Global-Normal

Spectral Irradiance, and Photograph of Sky Conditions (solar

zenith angle = 30.7 0 , relative optical air mass = 1.16) ••••••••••• 20

Case 12. Comparison of Modeled and Measured Global-Normal (a)

and Global-Horizontal (b) Spectral Solar Irradiance, and

Photograph of Sky Conditions (solar zenith angle = 34.5°,

relative optical air mass = 1.21) ••••••••••••••••••••••••••••••.•• 21

Case 13. Comparison of Modeled and Measured Global-Normal (a)

and Global-Horizontal (b) Spectral Solar Irradiance, and

Photograph of Sky Conditions (solar zenith angle = 43.9°,

relative optical air mass = 1.39) ••••••••••••••••••••••••••••••••• 22

Case 14. Comparison of Modeled and Measured Global-Normal (a)

and Global-Horizontal (b) Spectral Solar Irradiance, and

Photograph of Sky Conditions (solar zenith angle = 48.40 ,

relative optical air mass = 1.50) ••••••••••••••••••••••••.•••••••• 23

LIST OF TABLES

3-1 Measurements and Documentation for Each Spectral-Irradiance

Dat a Fi 1e • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 4

4-1 Description of Measured Spectra in Figures 4-1 through 4-14 •••••••• 8

4-2 Difference Between Modeled and Measured Irradiance

below 0.55 ~m for Cases 1 and 5.................................... 9

5-1 Measurement Uncertainty for Cloudless-Sky Conditions ••••.••.••••••• 25

Vll
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1.0 INTRODUCTION

TR-3038

This report documents research performed during fiscal year (FY) 1986 by

SERI's Resource Assessment and Instrumentation Branch to extend SPCTRAL2,

SERI's simple model for spectral solar irradiance for cloudless-sky conditions [1,2], to include cloudy conditions. This effort was included in

FY 1986 activities under the Resource Assessment Project's (RAP) Solar Radiation Models task, in response to the needs expressed by the solar

community [3-5]. The specific need is for spectral-solar-irradiance data

representing a range of outdoor conditions for cloudless, partly cloudy, or

overcast skies. Our practical approach to obtain these data is to first

develop models such as SPCTRAL2 that predict solar resource characteristics

from available meteorological-type data, and then combine modeled and measured

data into a spectral-irradiance data base.

1
TR-3038

2.0 BACKGROUND

Our objective is to modify SERI's current model for cloudless-sky conditions,

SPCTRAL2, to account for the influence of clouds on total irradiance and spectral distribution. Details about the SPCTRAL2 model and its development are

found in various reports [1,2,6]. Briefly, the code calculates di rect and

diffuse irradiance on horizontal and tilted planes at the earth's surface, at

122 wavelengths ranging from 0.3 to 4.0 ~m, with a resolution of approximately

0.01 um , Inputs to the model are solar zenith angle, collector-tilt angle,

atmospheric turbidity, precipitable water, surface pressure, and ground

albedo. This code was developed using comparisons with rigorous radiative

transfer codes and limited outdoor measurements. The intent was to provide a

simple, approximate model that could be used by the solar community to calculate spectral solar irradiance using small computers and minimal input.

Validation and verification of SPCTRAL2 is ongoing in SERIfs Resource Assessment and Instrumentation Branch. Comparisons of modeled and measured data for

a limited set of cloudless-sky conditions indicate that SPCTRAL2 produces

spectra that agree with measured data to within 10% in the ultraviolet region,

5% in the visible region, and 6% in the near-infrared region of the

spectrum [7]. An uncertainty analysis of the measurement instrumentation

results in an uncertainty of approximately 6% in the ultraviolet region, 7% in

the visible region, and 10% in the near-infrared region. Hence, in view of

these instrument uncertainties, SPCTRAL2 modeled data compare favorably with

measured data.

2
TR-3038

3.0 APPROACH

Our approach to developing a cloud-cover modifier for SPCTRAL2 was to begin

with the hypothesis that clouds act as a wavelength-independent filter on

cloudless-sky solar spectra. We would then derive spectral (wave1engthdependent) modifiers, if warranted, to obtain closer agreement between

measured and modeled data. Support for the initial hypothesis is found in

Deirmendjian [8]; Guzzi, Vittori, and Tomasi [9]; and Feigelson [10]. We also

imposed the constraint that the cloud-cover modifier would not require

detailed input on cloud properties (structure, composition, etc.), but that it

would rely on more commonly acquired meteorological and broadband solarradiation data that are available in a historical data base (SOLMET) [11].

Besides, the limited data available on detailed cloud physics for input to a

model do not warrant the development of a complex cloud-cover modifier in this

case. This was illustrated by Powell [12] in his attempt to produce a model

using a fairly complex set of input data. The input data were not available

to verify his model and would not be available on a routine basis.

The procedure for acqulrIng spectral-irradiance and supporting data to develop

the cloud-cover modifier is specified in the Resource Assessment Project's

plan for collecting spectral-solar-irradiance data [13]. This plan describes

the recommended broadband solar-radiation data, meteorological data, and other

information that should be recorded with each measured spectrum to adequately

document the atmospheric conditions and solar geometry during each measurement

(see Table 3-1). The major factors that determine the spectral distribution,

such as atmospheric turbidity, are recorded so that the spectral-irradiance

data can be extended to other locations wi th simi lar, observable outdoor

conditions.

An explanation of the data-collection philosophy is given in the previously

mentioned plan; however, two of the more important points are given here.

First, the measurements and data listed in Table 3-1 allow us to calculate

some important descriptors of atmospheric conditions, such as atmospheric

transmittance of direct-beam and total solar irradiance (which are related to

cloud cover), atmospheric turbidity, and precipitable water vapor. Some of

the parameters in Table 3-1 provide redundant or correlated information, such

as relative humidity and precipitable water vapor, to provide cross checking

and the option of using more readily available data.

The second important point is the total irradiance stability check during the

30 s that is required to obtain a spectral scan with the spectroradiometers,

which is especially important under cloudy conditions. A pyranometer with a

silicon detector (for millisecond time response) monitors total solar irradiance during each spectral-irradiance measurement; if the irradiance deviates

by more than a preset amount, the scan is aborted. The purpose of this check

is to avoid distorted spectral distributions caused by variations in total

solar intensity from cloud movement and changes. We started with a cutoff of

±5% but found that we could obtain a reasonable number of spectra and avoid

spectral distortion by using a cutoff of ±2%. We also took an all-sky (fisheye) photograph to record cloud distribution and amount during each spectralirradiance scan.

3
!5::~1 IIItI TR-3038

Table 3-1. Measurements and Documentation for Each Spectra1-Irradiance Data

File

Site identifier (latitucle/longitude)a

Date (day number/year)a

Local standard time (hours/minutes)a

Collection mode for spectral-irradiance scan (e.g., global horizontal, direct

normal)

Direct-normal broadband irradiance (W m-2)b

Direct-normal broadband irradiance--silicon ~e6ector (W m-2)b,c

Global-horizontal broadband irradiance (W m- )

Global-horizontal broadband irradiance--silicon detector (W m-2)b,c

Global_~tgtal) broadband irradiance on a surface normal to the direct beam

(W m )

Global (total) broadband irradiance on a surface_2ilted at a specified angle

(usually south-facing at tilt = latitude) (W m )

Ground albedo (%)

Relative humidity (%)

National Weather Service precipitable water vapor (cm)

Ambient temperature (oe)

Surface pressure (millibars)

Average wind speed (mph)

Opaque cloud cover (tenths) and/or all-sky photograph

Multiwavelength sun phot~~ete~1values (at 0.380, 0.500, 0.862, and 0.940 ~m)d Spectral irradiance (W m ~m or equivalent)e

Operator comments

aLocation, date, and time are used to calculate solar zenith angle and relative optical air mass.

bBroadband-irradiance measurements are recorded immediately before and after

the spectral-irradiance scan to evaluate atmospheric stability.

clnstruments with silicon detectors have a fast time response and are used to

monitor atmospheric stability during the spectral-irradiance scan.

dSpectral measurements at these wavelengths are made with sun photometers with

narrow-band filters, and the values are used to calculate atmospheric turbidity and precipitable water vapor.

eThe SERI spectroradiometers used to acquire spectral-irradiance measurements

reported here have the following characteristics: a holographic grating

monochromator, a wavelength range of 0.300 to 1.100 ~m, a bandwidth of

0.006 ~m, a user-selectable scan step size, and a total scan time of 27 s at

the O.002-~m step size. SERI modified these spectroradiometers by adding

(1) integrating spheres, which improve the cosine/azimuth response of the

instruments for measuring off-normal global irradiance; (2) direct-beam

modules with a 50 field of view and which are used for measuring directnormal spectral irradiance; and (3) temperature controllers to account for

the temperature dependence of the detector response. The instruments are

calibrated against standard lamps that are traceable to the National Bureau

of Standards [14].

4
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TR-3038

The sun photometer measurements that are used to derive turbidity are obtained

only when the sun's disk is clearly visible (i.e., a cloudless line of

sight). The sun photometer data can also be used to derive precipitable water

vapor; however, we used values reported by the National Weather Service and

the Wave Propagation Laboratory in the Radio Meteorology Program of the

National Oceanic and Atmospheric Administration (NOAA) in Boulder, Colo.

Our procedure for developing the cloud-cover modifier for SPCTRAL2 was as

follows:

• Calculate cloudless-sky spectral i r r ad i anc e using SPCTRAL2 and the input

parameters, such as day of the year and time of day, corresponding to the

spectral-irradiance measurements (see Table 3-1).

• Normalize the cloudless-sky, modeled spectra to the appropriate measured

broadband-irradiance value to account for differences in bulk atmospheric

transmittance under cloudy-sky conditions.

• Compare the normalized modeled data with the measured data (spectral plots)

and derive empirical expressions (spectral modifiers) that improve the

agreement between modeled and measured data.

The broadband solar-irradiance measurements acquired during the spectral scan

are critical for evaluating the impact of clouds on total transmittance and

testing the initial assumption of a wavelength-independent filter. Two of

these measurements, total (global)-horizontal (GH) and direct-normal (DN)

solar irradiance, are recorded in the national solar radiation measurement

network [11] and fit the criterion of readily available input data for solari r r ad i ance models. Therefore, these two values were selected as the only

additional input requirements for modifying SPCTRAL2 to account for cloudcover effects. This will allow, if successful, the SOLMET and similar broadband data bases to be converted to a spectral-solar-irradiance data base.

5
TR-3038

4.0 RESULTS

Since we began with the assumption of clouds as being wavelength-independent

filters, the first step in the cloud-cover modifier is to compare the integral

under the modeled-spectral-irradiance curve with measured broadband-irradiance

values to evaluate total atmospheric transmittance. The model calculates GH

spectral irradiance, integrates this irradiance, and compares the integral to

a GH broadband measurement. If the values differ by less than 5%, no cloudcover modifications are applied to the cloudless-sky spectrum.

The 5% criterion is an arbitrary value based on measurement

uncertainty [14,15] and the accuracy of the cloudless-sky model determined

from previous evaluations [7]. The 5% criterion also allows for small errors

in the input to the model, such as atmospheric turbidity and precipitable

water vapor. The uncertainty in the modeled results is difficult to evaluate

since turbidi ty and water-vapor measurements with a sun photometer are not

obtained when clouds obscure the sun's disk. In this case, we use values for

previous or subsequent cloudless-sky periods. Since the range in turbidity

and water-vapor values for the five days in the data set is small, we do not

expect large errors in the modeled data due to incorrect values for these two

parameters. A change in turbidity has little effect in the infrared region of

the spectrum and the largest effect in the ultraviolet region. A change in

precipi table water affects only those regions where water-vapor absorption

occurs, and these regions are concentrated in the infrared region. An error

in either of these quantities will cause the modeled spectra to be skewed when

the normalization is invoked.

(4-1)

I(X)

GH,mod r(x) dX

GH,mod

If the integrals differ by more than 5%, both the ON and GH spectra are normalized to the measured broadband values for ON and GH solar irradiance,

respectively, using the equations

I(X) = IGH,meas

GH 4.0 llm

J

0.3

ION,meas and

r(x) =

ON 4.0 llm

I

0.3

ICX) dX

ON,mod

I(X)

ON,mod , (4-2)

where rGH,meas and IDN,meas are measured GH and DN broadband-irradiance

values, respectively, and r(x) and I(X) are cloudless-sky GH and ON

GH,mod ON,mod

spectra modeled using SPCTRAL2. The model then proceeds to calculate diffuse,

direct, and total (global) spectral solar irradiance on the collector surface,

which can be oriented in any direction.

We empirically derived two

between measured and modeled

spectral modifiers that improve the agreement

data when the cloud modification is invoked.

6
TR-3038

First, modeled diffuse irradiance on the collector surface is increased for

wavelengths less than or equal to 0.55 wm using the expression

Diffuse x (A + 0.45)-1.0 ,

where A is wavelength in units of wm.

(4-3)

The maximum increase using this expression is one-third of the diffuse irradiance at 0.3 wm. The second modification is the addition of a constant 7% to

the diffuse spectral irradiance at each wavelength from 0.50 to 0.926 ~m. We

did not evaluate the model beyond 1.1 ~m, since this is the wavelength limit

of the spectroradiometer used in our measurements.

Comparisons of measured and modeled spectral irradiance using SPCTRAL2 wi th

the cloud-cover modifier are shown in Figures 4-1 through 4-14. Two spectra

were measured simultaneously in 13 of the cases using two spectroradiometers,

along with the supporting information given in Table 3-1. Measured data were

acquired from 0.35 to 1.1 11m with a O.Ol-wm step size on days 108, 111,

and 112. On day 115, DN data were acquired from 0.3 to 1.1 11m, and global

data were acquired from 0.35 to 1.1 wm with a 0.002-~m step size. On day 210,

all data were measured from 0.3 to 1.1 ~m with a a.002-wm step size.

Table 4-1 lists the day number, solar zenith angle, relative optical air mass,

surface pressure, precipitable water vapor, turbidity, ground albedo, and

spectroradiometer modes, and also the ratio of measured GH and DN broadband

irradiance to integrated cloudless-sky, modeled spectral irradiance for each

measured spectrum. We used the GH ratios in the model to normalize the

modeled GH spectra, and we used the DN ratios to normalize the modeled DN in

cases where the cloud-cover modification was invoked.

A strong direct-beam component was present (DN ratio greater than 0.60) in 8

of the 13 cases (see Table 4-1), representing nearly cloudless to partlycloudy conditions. The cloud-cover modification was invoked in two of these

cases (1 and 5) with the direct beam present. In case 5, the normalization

resulted in an enhancement of the global cloudless-sky irradiance (GH ratio of

1.292). In both cases 1 and 5, the modifications provided very good agreement

between modeled and measured data (see Figures 4-1 and 4-5) from 0.55 to

1.1 um , and the model estimates are greater than measured i rradiance below

0.55 ~m, as shown in Table 4-2. In these two cases, with a strong direct beam

present, the spectral modifier in the ultraviolet (UV)-visible region does not

appear to improve the agreement between modeled and measured data.

A strong direct-beam component was present, and no normalization or spectral

corrections were invoked in cases 4 and 6 through 10. In three of these cases

(8, 9, and 10), the DN spectral irradiance was measured; agreement between

modeled and measured data was very good (see Figures 4-8 through 4-10) except

for a small difference in the region from 0.45 to 0.65 wm. In this region,

the modeled data are lower than the measured data by about 1%-7%. This may be

because the modeled data do not account for circumsolar radiation, whereas the

measured data include circumsolar radiation in a 5° field of view. The agreement between modeled and measured global normal (GN) data is within about

3%-5% in case 10, which represents nearly cloudless conditions (some haze).

7
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- Table 4-1. Description of Measured Spectraa in Figures 4-1 through 4-14 .•'

Case Day Zenith Air Surface Precipitable Turbidity Ground SpectroAngle Water Vapor Albedo radiometer GH RatioC DN Ratio C

No. No. (deg) Mass Pressure (cm) (0.5 llm) (%) Modesb

1 108 28.9 1.14 815.8 0.56 0.103 18 GN,GH 0.948 0.686

2 108 29.3 1.15 815.8 0.56 0.103 18 GN,GH 0.327 0.003

3 108 43.7 1.38 815.8 0.56 0.103 18 GN,GH 0.208 0.002

4 III 44.1 1.39 813.3 1.31 0.088 18 GN,GH 0.982 1.008

5 III 27.9 1.13 819.4 1.39 0.088 18 GN,GH 1.292 0.997

6 112 40.6 1.32 813.3 1.10 0.103 18 GN,GH 1.006 1.027

7 112 45.4 1.42 813.3 1.10 0.103 18 GN,GH 0.968 0.954

8 115 56.0 1.78 810.5 0.50 0.110 20 DN,GH 0.960 1.012

co 9 115 28.0 1.13 809.0 0.50 0.110 20 DN,GN 1.022 0.996

10 210 32.8 1.19 822.2 1.00 0.080 18 DN,GN 0.970 1.024

11 210 30.7 1.16 820.2 1.00 0.080 17 GN 0.312 0.002

12 210 34.5 1.21 820.2 1.00 0.080 17 GN,GH 0.408 0.016

13 210 43.9 1.39 819.6 1.00 0.080 17 GN,GH 0.332 0.006

14 210 48.4 1.50 819.6 1.00 0.080 18 GN,GH 0.546 0.063

aSpectral-irradiance measurements obtained at Golden, Colo., 39.74 deg N, 105.18 deg. W, elevation 1828.8 m.

bGN = 1800 field of view with aperture oriented normal to the direct beam (global normal).

GH = 1800 field of view with aperture horizontal (global horizontal).

DN = 50 field of view with aperture oriented normal to the direct beam (direct normal).

cComputed as in Eq. 4-1 and 4-2.
TR-3038

Table 4-2. Difference Between Modeled and Measured Irradiance

below 0.55 ~m for Cases 1 and 5

Global Normal Global Horizontal

Wavelength

(~m) W m-2 ~m-1 % W m-2 ~m-l %

Case 1

0.38 126 16.9 89 12.5

0.42 103 7.8 94 7.8

0.46 61 3.6 75 4.9

Case 5

0.38 251 26.0 188 20.6

0.42 245 13.7 210 13.0

0.46 172 7.5 171 8.5

However, in cases 8 and 9 the measured global irradiance is lower than modeled

by about 3%-7% beyond o. 45 urn in the GH case (8) and 8%-11% i n the GN

case (9).

In the GN and GH cases with no normalization and a strong direct-beam component (4, 6, and 7), agreement between modeled and measured data is very good

(see Figures 4-4, 4-6, and 4-7). The largest difference is in the GN spectra

of case 6, in which the modeled data are lower than the measured data by

98 W m-2 1Jm-1 (5.5%) at 0.55 um , 108 W m-2 1Jrn-1 (8%) at 0.74 um , and

122 W m-2 ].Im- 1 (9.5%) at 0.78 ~m.

The cloud-cover modifications (normalization and spectral corrections) were

invoked in cases 2, 3, and 11-14. Both GN and GH spectra were modeled and

measured for each of these cases. In all cases (except for the GN spectrum in

case 3, where the shape of the measured spectrum in the visible region indicates a possible problem with the instrumentation), the modeled data are somewhat lower than the measured, especially in the O.45-1.1-].Im region

(Figures 4-2, 4-3, and 4-11 through 4-14). However, since the spectral modifiers increase the modeled irradiance, they resulted in closer agreement

between modeled and measured data. Agreement in case 12 (see Figure 4-12) is

very good. In the other cases, agreement is generally within 5%-10% up to

0.7 um , but deviates by about 15%-20% beyond 0.7 urn in some cases. One

feature in these cases that is present in all of the measured GN spectra, and

to a lesser extent in the GH spectra, is an increased difference between

modeled and measured data from 0.7 through 1.1 urn , especially at 0.74 and

0.78 ~m. Since this feature is more pronounced for the GN cases, a possible

explanation is spectral ground albedo, which has not been taken into account

in the model (a constant broadband value is used).

It is also apparent that water-vapor absorption is underestimated when the

direct beam is obscured by clouds. This is caused by the increased path

length due to multiple scattering in the clouds, which results in a higher

probability for absorption of photons by water vapor.

9














TR-3038

5.0 DISCUSSION

We have attempted to develop a simplified cloud-cover modifier for SPCTRAL2

that accounts for the integrated effects of cloud cover on spectral i r ra-:

di ance , This simple approach was taken for two reasons. First, it is difficult to model the complex relationships and interactions among solar

radiation and cloud properties such as shape, size, and composition. Second,

if a complex model is developed, it is difficult to obtain the detailed data

on cloud properties needed to verify or use the model [12].

We realize the limitations of our simple-model approach, some of which follow:

• It does not account for differences in spectral-irradiance distribution due

to different types of clouds. We are assuming that the only available

"cloud-cover" information is atmospheric transmittance (determined from GH

and DN broadband-irradiance measurements).

• It does not account for the increased water path length due to clouds. This

affects the normalization step since the measured broadband irradiance

values include the impact of reduced irradiance caused by absorption in the

water-absorption bands.

• Turbidity must be estimated from measurements under cloudless-sky conditions

near the cloudy period. Since the change from cloudless to cloudy skies

indicates unstable atmospheric conditions, this extrapolation of the turbidity value may not be valid. The normalization that is applied when

transmittance under cloudy skies differs by more than 5% from cloudless-sky

conditions will compensate for the intensity differences due to error in

turbidity, but this will not account for spectral effects.

• The cloud modifier does not account for spectral effects of multiple reflections between the cloud base and the ground, which could be significant when

the ground albedo is high (for example, when the ground is snow-covered).

The normalization procedure will account for the impacts that these multiple

reflections have on total irradiance, but it will not account for spectral

effects.

The two spectral modifiers give closer agreement between modeled and measured

data by increasing irradiance in the region between 0.30 and 0.926 ~m. Since

the modeled data are normalized to a broadband-irradiance value before the

spectral corrections are made, there should be a corresponding decrease in

spectral irradiance beyond 1.1 ~m if the broadband-irradiance values are correct. We have not verified this through measurements since the spectroradiometer we are using for measurements has a wavelength limit of 1.1 ~m.

All of the resul t s must be examined with respect to the broadband- and

spectral-irradiance measurement uncertainty [14,15]. When the cloud-cover

modifier is applied, the modeled spectra are normalized to the broadband GH

and DN measured values, which have uncertainty limits of ±2.7% and ±1.3%,

respectively. The spectral modifiers result in closer agreement between

modeled and measured data, but the significance and accuracy must be evaluated

with respect to the uncertainty in spectral irradiance for different spectral

regions, as shown in Table 5-1. Much effort is required to determine

uncertainty limits for the measurements.

24
TR-3038 -~

Table 5-1. Measurement Uncertainty for Cloudless-Sky

Conditions (X)

Irradiance Wavelength (j.Jm)

0.35 0.65 0.90 1.30

Global Horizontal 10.7 10.0 12.3 11.9

Global Normal 6.4 7.0 9.6 15.8

Direct Normal 5.5 5.4 9.5 12.8

The uncertainty values are based on laboratory calibrations against National

Bureau of Standards (NBS) traceable standard irradiance lamps, and outdoor

tests of the integrating sphere response (in global-irradiance cases) with the

direct-beam component present. The global-horizontal uncertainty values

include an 8.5% directional bias error that is not applicable under completely

diffuse sky conditions. Uncertainty limits for anisotropic diffuse conditions

or completely diffuse conditions are under investigation. The values in this

table represent our most conservative estimates to date. Further data and

analysis are required to fully characterize all sources of error for particular measurement configurations. Accuracy of the measurements is critical for

comparisons with modeled data.

25
TR-3038

6.0 SUMMARY AND CONCLUSIONS

Our objective is to develop and evaluate a simple cloud-cover modification to

the SERl model for cloudless-sky spectral solar irradiance (SPCTRAL2). Our

approach was to begin with the hypothesis that clouds act as a wavelengthindependent filter on the cloudless-sky spectral distributions and then use

comparisons of modeled and measured data to empirically derive spectral modifiers, if necessary. The only two additional inputs to SPCTRAL2 that are

required to implement such a modifier are measurements of global-horizontal

(GH) and direct-normal (DN) broadband irradiance.

Based on comparisons of modeled and measured data, we incorporated a cloudcover modifier into SPCTRAL2 so that the model accomplishes the following:

• Calculates cloudless-sky GH and DN spectral irradiance

• Normalizes the modeled cloudless-sky, GH and DN spectral-irradiance to

broadband-irradiance measurements if the integral of the modeled GH spectrum

differs by more than 5% from the broadband value

• Calculates spectral irradiance on the collector surface (i.e., converts to

irradiance on a tilted surface if appropriate)

• Applies two spectral corrections to the calculated diffuse irradiance if the

normalization step is invoked.

In general, when a strong direct-beam component is present (under cloudlesssky or partly cloudy conditions) the cloud-cover modification (normalization

and spectral corrections) is not applied. In the two cases where the direct

beam was present and the cloud-cover modification was invoked, the agreement

between modeled and measured data was very good between 0.55 and 1.1 um ,

although the spectral correction below 0.55 llm caused the modeled values to be

higher than the measured values. It is possible that we should include

another criterion for normalization that is based on the ratio of measured to

modeled direct-beam irradiance. When the cloud-cover modification was not

invoked, the modeled DN spectrum is slightly lower than measured in the

visible region, which may be caused by circumsolar radiation that is not

included in the modeled DN data.

In cases where the cloud-cover modification was applied, the agreement between

modeled and measured data is generally within the measurement uncertainty of

5%-10% up to 0.7 llm, but can deviate by as much as 15%-20% beyond 0.7 llm in

some cases. The difference is more pronounced for GN than for GH cases, which

may indicate a relationship to spectral ground albedo. However, in some cases

(for example, case 12), the agreement between modeled and measured data is

within the measurement uncertainty of 5%-10%.

Because of the limitations of our analyses/approach, as stated in the previous

section, the cloud-cover modifier given in this report is considered to be

preliminary. This data set is not large enough to compute comprehensive error

statistics, but it allows us to examine the general form of a cloud-cover

spectral transmission function. Although our normalization approach is reasonable, we need to analyze more data to refine and investigate the spectral

corrections of the proposed cloud-cover modifier. We expect to produce a

final cloud-cover modifier by late 1987.

26
TR-3038

7 .0 FUTURE WORK

The results of our evaluation of the cloud-cover modification suggest the

following avenues for further research.

• We will collect additional data for a range of cloud types and thicknesses

and then derive a cloud-cover spectral transmission function. If resources

permit, we will use radiative transfer models to derive theoretical transmission functions for different clouds for comparison with the measurements.

Error statistics will be computed for the transmission function.

• If we continue to observe a consistent bias in the measured data to be

greater than modeled data in the region beyond 0.55 ~m (especially 0.7 to

1.111m) under overcast conditions, we will adjust the model accordingly.

Preliminary analysis of modeled data suggests that the effect may be due to

multiple reflections between the ground and cloud bases, with high spectral

ground reflectance in this region. We will evaluate the impacts of spectral

albedo on modeled spectra.

• If resources permit, we will acquire spectral measurements beyond 1.1 11m to

examine the impacts of normalization and spectral modifiers over the entire

spectrum.

• We will continue to perform error analysis and determine uncertainty limits

for the measurements that are used for comparison with modeled data. This

uncertainty determines the limits to which model modifications are valid and

significant.

27
TR-3038

8.0 REFERENCES

1. Bird, R., and C. Riordan, Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth's Surface

for Cloudless Atmospheres, SERI/TR-215-2436, Golden, co: Solar Energy

Research Institute, Dec. 1984.

2. Bird, R. E., and C. Riordan, "Simple Solar Spectral Model for Direct and

Diffuse Irradiance on Horizontal and Tilted Planes at the Earth's Surface

for Cloudless Atmospheres," Journal of Climate and Applied Meteorology,

Vol. 25, No.1, Jan. 1986, pp. 87-97.

3. Solar Energy Research Inst i tute, Photovol taics and Insolation Measurements Worksho Proceedin s; June 30 - Jul 3 1985, Vail Colorado,

SERI CP-215-2773, Golden, co: Solar Energy Research Institute.

4. Hulstrom, R. L., Final Report of the Amorphous' Silicon Measurements Task

Force, SERI/SP-215-2784, Golden, co: Solar Energy Research Institute,

Aug. 1985.

5. Hulstrom, R. L., Resource Assessment Project - User Needs Survey Results,

SERI/PR-215-2981, Golden, co: Solar Energy Research Institute (in

progress).

6. Bird, R. E., "A Simple Solar Spectral Model for Direct-Normal and Diffuse

Horizontal Irradiance," Solar Energy, Vol. 32, No.4, 1984, pp. 461-471.

7. Riordan, C. J., Com arisons of Modeled and Measured S ectral Solar Irradiance Data, SERI TR-215-2809, Golden, CO: Solar Energy Research Institute, Feb. 1986.

8. Deirmendjian, D., Electromagnetic Scattering on Spherical Polydispersions, New York: American Elsevier Publishing Company, Inc., 1969.

9. Guzzi, R., o. Vittori, and C. Tomasi, "Sun Spectra Through Optically Thin

Clouds," Journal of the Atmospheric Sciences, Vol. 31, No.1, 1974,

pp. 251-254.

10. Feigelson, E. M., Radiation in a Cloudy Atmosphere, Boston, MA: D.

Reidel Publishing Company, 1984, p. 61.

11. Hulstrom, R. L., R. E. Bird, T. W. Cannon, T. L. Stoffel, C. Riordan, and

V. Szwarc, SERI Insolation Research FY 1982 Annual Report,

SERI/PR-215-1725, Golden, co: Solar Energy Research Institute,

Sept. 1982.

12. Powell, M. Jr., A Simple Solar, Spectral Model for Studying the Effects

of Cloud Cover and Surface Albedo on the Incoming Solar Radiation, Ph.D.

Dissertation, Ann Arbor, MI: The University of Michigan, 1986.

28
,,_..;;;~

-~ II II

- ~-" TR-3038

13. Riordan, C. J., and R. L. Hulstrom, The SERI Resource Assessment Pro'-

ect's Plan for Collecting Spectral-Solar-Irradiance Data, SERI TR-21S2948, Golden, co: Solar Energy Research Institute, Dec. 1986.

14. Myers, D., Measurement Uncertainty for the SERI Spectral-Solar-Irradiance

Data Base Project, Golden, CO: Solar Energy Research Institute (in

progress).

15. Riordan, C., Sensitivity Analyses of SPCTRAL2 and Implications for Further Spectral Irradiance Measurements and Model Improvement/Validation

Verification, Golden, co: Solar Energy Research Institute (in progress).

29
Document Control \1. SERI Report No.

Page SERI/TR-2lS-3038

12. NTIS Accession No, 3. Recipient's Accession No.

4. Title and Subtitle

Investigation of a Cloud-Cover Modification to SPCTRAL2,

SERI's Simple Model for Cloudless-Sky Spectral Solar

Irradiance

7. Author(s)

R.E. Bird, C.J. Riordan, D.R. Myers

9. Performing Organization Name and Address

Solar Energy Research Institute

A Division of Midwest Research Institute

.1617 Cole Blvd.

Golden, Colorado 80401-3393

12. Sponsoring Organization Name and Address

15. Supplementary Notes

5. Publication Date

June 1987

6,

8. Performing Organization Rept. No.

10. Project/Task/Work Unit No.

6004.10

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 summarizes the investigation of a cloud-cover

modification to SPCTRAL2, SERI's simple model for cloudless-sky, spectral solar irradiance. Our approach was to develop a modifier that relies on commonly acquired meteorological and broadband-irradiance data rather than detailed cloud properties that

are generally not available. The method was to normal ize modeled, cloudless-sky,

spectral irradiance to a measured broadband-irradiance value under cloudy skies, and

then to compare the normalized, modeled data with measured spectral-irradiance data to

empirically derive spectral modifiers that improve the agreement between modeled and

measured data. Results indicate the possible form of the spectral corrections; however, we must analyze additional data to develop a spectral transmission function for

cloudy-sky conditions.

17. Document Analysis

a. Descriptors solar radiation ; insolation ; solar irradiance ; resource assessment

b. Jdentifiers/Open·Ended Terms

c. UC Categories 62, 63

18. Availability Statement

National Technical Information Service

U.S. Department of Commerce

5285 Port Royal Road

Springfield, Virginia 22161

Form No. 8~OO-13 (6-79)

19, No. of Pages

40

20. Price

A03