the sun’s total and spectral irradiance for solar energy applications and solar radiation models

Solar Energy 76 (2004) 423–453

www.elsevier.com/locate/solener

The sun’s total and spectral irradiance for solarenergy applications and solar radiation models

Christian A. Gueymard 1

Solar Consulting Services, 2959 Ragis Rd, Edgewater, FL 32132, USA

Received 29 May 2003; received in revised form 29 August 2003; accepted 29 August 2003

Communicated by: Associate Editor David Renne

Abstract

Using the most recent composite time series of total solar irradiance spaceborne measurements, a solar constant

value of 1366.1 Wm�2 is confirmed, and simple quadratic expressions are proposed to predict its daily value from the

Zurich sunspot number, the MgII index, or the 10.7 cm radio flux index. Whenever these three indices are available on a

daily basis (since 1978), it is possible to predict the sun’s irradiance within 0.1% on average, as accurately as current

measurements.

Based on this value of the solar constant, an improved approximation of the extraterrestrial solar spectrum from 0 to

1000 lm is proposed. It is obtained by dividing the spectrum into nine bands and selecting representative (and recent)

spectra, as well as appropriate scaling coefficients for each band. Comparisons with frequently used spectra are dis-

cussed, confirming previous findings of the literature.

This synthetic and composite spectrum is proposed at 0.5-nm intervals in the UV (280–400 nm), 1-nm intervals

between 0–280 and 400–1705 nm, 5-nm intervals between 1705 and 4000 nm, and progressively larger intervals beyond 4

lm, for a total of 2460 wavelengths.

� 2003 Published by Elsevier Ltd.

Keywords: Radiation; Spectral distribution; Solar constant and extraterrestrial radiation; Solar spectrum

1. Introduction

The magnitude and variations of the solar energetic

output directly or indirectly affects many atmospheric

and biological processes on Earth. For all applications

where spectral solar radiation needs to be evaluated

from the top of the atmosphere down to ground level,

precise knowledge of the extraterrestrial spectrum (ETS)

is of primarily importance.

Terrestrial spectra can be calculated through the use

of radiative transfer models (RTMs), which describe

atmospheric extinction processes on a spectral basis. A

E-mail address: [email protected] (C.A.

Gueymard).1 ISES member.

0038-092X/$ - see front matter � 2003 Published by Elsevier Ltd.

doi:10.1016/j.solener.2003.08.039

description of these atmospheric processes is beyond the

scope of this contribution, except for one important

aspect: their spectral resolution. All RTMs are devel-

oped around a specific spectral resolution and accord-

ingly calculate each process’ extinction at more or less

regular spectral intervals or ‘‘step size’’. These intervals

can vary from very narrow and essentially monochro-

matic at one extreme––in the case of ‘‘line-by-line’’

atmospheric codes such as FASCOD or LBLRTM

(Clough et al., 1981, 1992)––to very coarse at the other

extreme, in the case of engineering-type models such as

SPCTRAL2 (Bird, 1984; Bird and Riordan, 1986). An

intermediate case is worth mentioning here for the sake

of subsequent discussions. SMARTS is a ‘‘medium-res-

olution’’ (0.5–5 nm) spectral radiative model, versatile

enough to cover a variety of solar energy applications

(Gueymard, 2001, 2003; Gueymard et al., 2002). Three

resolutions and spectral intervals are now used in

mail to: [email protected]

Nomenclature

Ek spectral irradiance (Wm�2 nm�1)

RZ daily Zurich sunspot number

SC solar constant (Wm�2)

TSI total solar irradiance (Wm�2)

MG daily MgII index

RF daily 10.7 cm radio flux index

k wavelength (nm)

424 C.A. Gueymard / Solar Energy 76 (2004) 423–453

SMARTS: 0.5 nm in the UV (280–400 nm), 1 nm in the

visible and part of the near infrared (400–1702 nm) and

5 nm beyond, up to 4000 nm. These same intervals will

also be used here in the development of the proposed

ETS, so that it can accommodate the SMARTS model

among others.

During the five decades that followed the seminal

publication of the ‘‘Johnson curve’’ (Johnson, 1954),

considerable progress has been made in the determina-

tion of the ETS, but most of this progress dates back

only 30 years. In a 1965 review paper on then current

developments in ETS determination (Thekaekara, 1965),

its author pointed out ‘‘that the results from different

sources have wide discrepancies, that no new experi-

mental data have been taken in recent years, and that

the conventional technique of extrapolation to zero air

mass leaves large uncertainties’’. These problems were

addressed in later years through the development of

better instrumentation that could be deployed at

increasingly higher altitudes, thus eliminating much, if

not all, atmospheric interference and the associated er-

rors introduced by the extrapolation to zero air mass.

These platforms include high-altitude observatories

(e.g., Burlov-Vasiljev et al., 1995, 1998; Kurucz et al.,

1984; Lockwood et al., 1992; Neckel and Labs, 1981,

1984), research aircraft (e.g., Thekaekara, 1973; The-

kaekara and Drummond, 1971), stratospheric balloons

(e.g., Anderson and Hall, 1989), parachute launched

from a rocket (Mentall et al., 1981), rockets (e.g., Mount

and Rottman, 1981), and finally spacecraft (e.g., Brue-

ckner et al., 1996; Cebula et al., 1996; Floyd et al., 1999;

Thuillier et al., 1998a; VanHoosier et al., 1988; Woods

et al., 1996). In recent years, the new developments in

measuring the solar constant and ETS were driven in

great part by the realization that, to some extent, their

variation could explain various features of the Earth’s

climate and its short-term or long-term fluctuations. The

magnitude of this ‘‘solar forcing’’ is still discussed in the

current debate about the global climate change. For a

more thorough background information and historical

perspective, see, e.g., Hoyt and Schatten (1997).

Most of the experimental results mentioned above

concentrated on a few parts of the solar spectrum.

Spectral measurements are performed with instruments

whose spectral range is usually very limited. As a result,

a complete ETS must be obtained as a combination of

various spectra sensed by different instruments, in dif-

ferent spectral bands, with different resolution and cal-

ibration methods, on different platforms, and at different

moments in time. All these issues introduce noticeable

uncertainties in the resulting ETS. To address this, new

instruments with extended spectral range and refined

calibration techniques are being developed and sent in

orbit for long-term observations. One such instrument,

SOLSPEC (Thuillier et al., 1998b, 2003a), covers the

range 200–3000 nm and has been flown on various space

platforms since 1983. A more recent instrument is the

solar irradiance monitor (SIM). Even though its spectral

range (300–2000 nm) appears reduced, it offers the im-

mense advantage of an exceptionally low uncertainty,

�0.1% (Rottman et al., 2004). SIM is part of the Solar

Radiation and Climate Experiment (SORCE), now in

orbit, and has started producing data in mid-2003

(http://lasp.colorado.edu/sorce/data_access.html), dur-

ing the reviewing process of this paper. These new

datasets will help assess the accuracy of the ETS dis-

cussed here, and will certainly provide the basis for

updated spectra. The SORCE mission also includes two

spectral instruments that are monitoring the sun’s out-

put in the 1–34 and 115–320 nm bands (Woods et al.,

2000). Therefore, most of the spectrum below 2000 nm

will be monitored with great accuracy from a single

platform, and hopefully for a long time.

Different ETS distributions have been used in the

past for solar radiation modeling, astrophysical re-

search, or other applications (e.g., Arvesen et al., 1969;

Burlov-Vasiljev et al., 1995; Colina et al., 1996; Johnson,

1954; Lockwood et al., 1992; Neckel and Labs, 1984;

Nicolet, 1989; Simon, 1981; Smith and Gottlieb, 1974;

Thekaekara, 1973), but most were only partial spectra.

An important milestone was the adoption by the World

Meteorological Organization (WMO) of the World

Radiometric Center (WRC) spectrum (Wehrli, 1985),

more generally known as the ‘‘Wehrli spectrum’’. It was

developed as a composite of four existing datasets,

concatenated to cover most of the spectrum (200 nm–10

lm), and smoothed, scaled and forced in such a way that

the resulting total irradiance equals the WMO-recom-

mended value for the solar constant, 1367 Wm�2.

More recently, the American Society for Testing and

Materials (ASTM) standardized an updated four-band

spectrum, using more recent sources for some of its

C.A. Gueymard / Solar Energy 76 (2004) 423–453 425

parts, along with a wider spectral range (120 nm–1000

lm), and different resolution and spectral intervals

(ASTM, 2000). Some scaling and adjustments were also

necessary so that the integrated irradiance could be

obtained as 1366.1 Wm�2, the ASTM-recommended

value for the solar constant.

A revised ETS is proposed here for the following

reasons.

ii(i) Some problems have been discovered in the still

widely used Wehrli spectrum. These include anom-

alous dips around 940, 1270, and 2300 nm (Gao

and Green, 1995; Green and Gao, 1993), and inac-

curacies or biases due to the brute smoothing/scal-

ing process used to concatenate datasets obtained

with vastly different methods (personal communica-

tions with Claus Fr€ohlich, 1992, Eric P. Shettle,

1993, and Bo-Cai Gao, 1994).

i(ii) Even though the ASTM spectrum represents an

improvement over Wehrli’s, it also shows slight

problems, which will be discussed later (Section

4). Furthermore, its resolution is limited to 1 nm

below 630 nm, and 2 nm below 2500 nm, which is

not sufficient for many applications––considering

the important spectral structure at shorter wave-

lengths, particularly below 600 nm.

(iii) New datasets have been published recently. They

are based on modern instrumentation undergoing

sophisticated and frequent calibration and data

quality control. These recent data are therefore of

potentially better quality and accuracy than some

of the older data used in the Wehrli and ASTM

spectra.

Even though this contribution’s emphasis is about

spectral irradiance, it is by essence tied to the determi-

nation of the broadband solar irradiance often referred

to as the ‘‘solar constant’’, which will be discussed in

Section 2. The importance of this discussion stems from

the obvious constraint that the spectral integration of

any ETS should coincide with the solar constant. Be-

cause of the slight variations of solar output during an

11-year sunspot cycle, the ETS will be defined here for

the same average solar activity conditions as the solar

constant.

To respect the different spectral bands and resolu-

tions described above, the derivation of the proposed

ETS will be made band-by-band in Section 3. The

resulting spectrum is compared to existing ‘‘reference’’

spectra in Section 4.

2. Solar constant and total solar irradiance

The determination of the ‘‘solar constant’’ and its

possible variations was of considerable interest at the

turn of the 20th century and became the main driving

force that motivated pioneers such as Langley and Ab-

bott in those early days of solar radiation research (Hoyt

and Schatten, 1997). After a few decades of constant

monitoring by sensors on board various satellites, it is

now recognized that this ‘‘solar constant’’ is misnamed

because the solar energetic output does vary over time,

albeit by a small amount. Nowadays, this varying solar

output should be referred to as total solar irradiance

(TSI), whereas the term ‘‘solar constant’’ should be used

only to describe the long-term average TSI. For more

details on the history of TSI measurement from satel-

lites, experimental challenges, and scientific advances in

understanding the TSI variability, the reader is referred

to recent reviews (Fr€ohlich, 2004; Hoyt and Schatten,

1997; Willson, 1994).

It is now established that TSI is directly affected by

solar activity, which follows the well-documented

Schwabe (11-year) cycle. In particular, when the sun’s

activity increases at the onset of a new cycle, different

phenomena occur and have opposite effects. The ‘‘sun-

spot blocking’’ effect tends to lower TSI, whereas facu-

lae, plages and flares tend to increase it. Therefore, from

one day to the next, TSI can vary in one way or the

other depending on the relative strength and location

(on the sun’s disc) of these phenomena, which are also

influenced by the 27-day sun’s rotation cycle.

Various spaceborne radiometers have been monitor-

ing TSI since 1978. Because of calibration and degra-

dation problems, overlapping datasets were originally

not in perfect quantitative agreement, even though they

did agree qualitatively on the shape and magnitude of

the TSI variations during successive solar cycles. Con-

siderable effort was devoted to correcting each individ-

ual dataset and developing a unique composite time

series from the best available data (Fr€ohlich, 2004;

Fr€ohlich and Lean, 1998). The most recent version of

this composite dataset was ‘‘d25-05-0301’’ as of this

writing. It has been obtained from WRC in Davos,

Switzerland (http://www.pmodwrc.ch/) and used in what

follows.

Fig. 1 shows the measured TSI time series, consisting

of mean daily values, as well as a 27-day running mean

to dampen short-term effects. For the duration of this

dataset (November 1978 to January 2003, or 24.2 years),

the absolute minimum and maximum daily TSI were

1363 and 1368 Wm�2, respectively. Using the 27-day

smoothing filter, these numbers become 1365.0 and

1367.2 Wm�2, respectively, yielding a mean value

[(min+max)/2] of 1366.1 Wm�2 and a half-amplitude of

1.1 Wm�2 (i.e., ±0.08% of the mean). This value of the

mean TSI confirms the solar constant value, SC, whichhas been recently standardized (ASTM, 2000). It is also

only 0.9 Wm�2 less than the value of 1367 Wm�2 rec-

ommended by the World Meteorological Organization

(WMO) in 1981, and which has been widely used thus

1363

1364

1365

1366

1367

1368

0

100

200

300

1978 1983 1988 1993 1998 2003

Dai

ly T

SI (

Wm

-2)

Daily S

unspot Num

berYear

Total Solar Irradiance and Sunspot NumbersDaily values, 1978–2003

Fig. 1. Daily TSI for the period 11/1978–1/2003 (top panel) and

daily sunspot number for the same period (bottom panel). The

thicker lines indicate the smoothed 27-day running mean.

1362

1363

1364

1365

1366

1367

1368

1369

0 50 100 150 200 250 300

Daily TSI vs Daily Sunspot Numbers, 1978-2002

Dai

ly T

SI (

Wm

-2)

Daily Sunspot Number

Fig. 2. Daily TSI vs sunspot number for the period 11/1978–1/

2003.


far. Because of the inherent absolute uncertainty of at

least 0.1% or 1.4 Wm�2 in TSI measurements, it can be

argued that the difference between the two SC values just

mentioned is not significant, so that the WMO value can

still be considered valid. Nevertheless, the latest deter-

mination of SC (1366.1 Wm�2) will be used here in all

what follows.

Fig. 1 also shows the variability in the daily Zurich

sunspot number, RZ, as obtained from solar observato-

ries around the world since 1749 and distributed by the

Sunspot Index Data Center (SIDC), which is the world

data center for the Sunspot Index (http://sidc.oma.be).

During the same period (1978–2003) as above, RZ varied

between 0 and 302, with a similar wave pattern as TSI.

Even though a correlation exists between the two phe-

nomena, and can be expressed as

TSI ¼ 1365:5þ 0:012461RZ � 4:6078� 10�5R2Z ð1aÞ

or

TSI=SC ¼ 0:99956þ 9:1216� 10�6RZ � 3:37296

� 10�8R2Z ð1bÞ

it is not as strong as could be expected, with a correla-

tion coefficient of only 0.491 (Fig. 2). [The important

scatter produced by Eq. (1) was previously noticed

(Solanki and Fligge, 1999), and led to slightly different

coefficients, because of the shorter and older dataset

used by these authors.] The pronounced curvature can

be explained by the dynamic balance between the facu-

lae (brightening) effect and the sunspot blocking (dark-

ening) effect, which is not directly or only a function of

the number of sunspots.

A slightly better correlation is obtained when con-

sidering the MgII index, MG, as the independent vari-

able. This index has been specifically developed to

monitor changes in the UV irradiance (Heath and

Schlesinger, 1986), and has been calculated by NOAA’s

Space Environment Center (http://sec.noaa.gov/Data/

solar.html) from spectral measurements around 280 nm

using spaceborne sensors since 1978. A quadratic rela-

tionship is again obtained

TSI ¼ 1164:6þ 1426:4MG � 2521:3M2G ð2aÞ

or

TSI=SC ¼ 0:8525þ 1:04414MG � 1:84562M2G ð2bÞ

with a correlation coefficient of 0.592 (Fig. 3).

It has been also argued (Fligge and Solanki, 1998a,b)

that the 10.7 cm radio flux index, RF, would be a good––

if not the best––proxy for faculae brightening. Even

though this might be true on a longer time scale (which

was the main focus of the above-mentioned studies), its

correlation with the daily TSI is not as good as that

obtained with Eq. (2). Nevertheless, a combination of

RZ;MG and RF explains more variance in TSI than any

1362

1363

1364

1365

1366

1367

1368

1369

1362 1363 1364 1365 1366 1367 1368 1369

Daily TSI Correlation Model

Pre

dict

ed T

SI (

Wm

-2)

Measured TSI (Wm-2)

Fig. 4. Predicted TSI using Eq. (3) vs measured TSI (daily

values) for the period 11/1978–1/2003. The horizontal line

indicates the solar constant value defined here (1366.1 Wm�2),

and the dashed lines represent the limits for an uncertainty of

±0.1% around the perfect 1:1 line.


of them independently. This effect can be simply mod-

eled as

TSI ¼ 1327:87� 0:0038269RZ þ 143:1027MG

� 2:87203� 10�5R2F ð3aÞ

or

TSI=SC ¼ 0:97202� 2:80133� 10�6RZ

þ 0:104753MG � 2:10236� 10�8R2F ð3bÞ

with a correlation coefficient of 0.744. The ‘‘adjusted’’

Ottawa RF index used here has been obtained from the

Dominion Radio Astrophysical Observatory (http://

www.drao-ofr.hia-iha.nrc-cnrc.gc.ca/). Nearly all of the

predicted TSI values with Eq. (3) are within ±0.1% of

the measured TSI, as shown with the scatterplot in

Fig. 4.

Because measurements of the MgII index are rela-

tively recent, Eq. (3) cannot be used to reconstitute TSI

before its own measurements started in space. To esti-

mate the daily TSI between 1947 and 1978, a 2-variable

fit with lesser accuracy (R ¼ 0:576) may be used:

TSI ¼ 1364:0� 2:4008� 10�3RZ þ 0:026452RF

� 6:5502� 10�5R2F ð4aÞ

or

TSI=SC ¼ 0:99846� 1:7574� 10�6RZ þ 1:9363

� 10�5RF � 4:7948� 10�8R2F ð4bÞ

1362

1363

1364

1365

1366

1367

1368

1369

0.26 0.265 0.27 0.275 0.28 0.285 0.29 0.295

Daily TSI vs NOAA's MgII index, 1978-2002

Dai

ly T

SI (

Wm

-2)

MgII index

Fig. 3. Daily TSI vs MgII index for the period 11/1978–1/2003.

Future predictions and longer-term historical reconsti-

tutions––with possibly more accurate estimates than Eq.

(1) [which can be used for periods from 1749 to pres-

ent]––would require substantially more sophisticated

models of the solar cycle (e.g., Fligge and Solanki, 2000;

Fligge et al., 1998; Foukal and Lean, 1990; Fr€ohlich,2002; Fr€ohlich and Lean, 1998; Lean, 2000; Lean et al.,

1997; Solanki and Fligge, 1998; Tobiska et al., 2000;

Unruh et al., 1999).

3. Spectral irradiance

All wavelengths are not affected by solar activity

equally. Theoretical studies as well as a variety of

experimental measurements have revealed that most of

the sun’s output variation––at least in relative terms––

occurs in the far and extreme UV (below 200 nm), as

documented elsewhere (Floyd et al., 1998; Lean, 1991,

1997; Rottman, 1999; Rottman et al., 2004; Woods and

Rottman, 2002). The variability there considerably in-

creases with decreasing wavelength, to the point where

the ratio of maximum to minimum irradiance reaches an

estimated factor of 100 at 0.5 nm (Woods and Rottman,

2002). Short-term variations are of the same order of

magnitude as long-term variations (Brueckner et al.,

1996; Chandra et al., 1995; Lean, 1991; Rottman, 1988),

with 27-day amplitudes normally lower than 11-year

amplitudes (Woods and Rottman, 2002). Because for


UV to near infrared (NIR) wavelengths (300–4000

nm)––of most interest here––the solar variability has

normally only a very small amplitude of about �0.1%

and possibly less (i.e., an order of magnitude below the

precision of current spectral measurements), this vari-

ability will not be taken into consideration in what fol-

lows. In other words, a single spectrum, corresponding

to average activity conditions will be developed and

proposed. The spectral irradiance Ek, is therefore related

to the solar constant through

SC ¼Z 1

0

Ek dk ð5Þ

It must be acknowledged, however, that the ETS vari-

ability can be very important at a few specific wave-

lengths in the visible and NIR corresponding to some

solar absorption lines, such as the Ca K line around

393.5 nm, and the He line at 1083 nm. The solar cycle

modulation for the latter reaches 200% (Livingston,

1992), but it is unlikely that such spikes can explain the

±2–3 Wm�2 maximum daily variability in SC, so that

there might be either other strong localized effects or

small, smooth and spectrally broad variations falling

under the detection limit of current instrumentation.

Two essentially different sources of spectral data are

available and need be considered to assemble an ETS

because they complement each other. The first source is

from ground observatory telescopes pointing to the sun

center (Burlov-Vasiljev et al., 1995, 1998; Kurucz et al.,

1984; Neckel and Labs, 1981, 1984). These measure-

ments are made with either high-performance spec-

trometers or with a Fourier transform spectrometer

(FTS) at extremely high resolution (e.g., 0.0005 nm).

Such a high resolution is an asset to this method, but it

also has two drawbacks: (i) the raw disk-center radiance

measurements have to be converted into disk-average

irradiance, and this requires more or less empirical

spectral corrections to take the sun’s spatial inhomo-

geneity into consideration (the limb-darkening effect in

particular); (ii) because of strong absorption bands by

ozone, water vapor, carbon dioxide and other gases, no

reliable data can be directly obtained below �300 nm or

in strong NIR absorption bands, even when the obser-

vatory is at relatively high altitude––unless precise and

thorough atmospheric corrections are expressly made,

see, e.g. Burlov-Vasiljev et al. (1998). (The effect of this

atmospheric interference on spectral accuracy will be

discussed further in Section 4.)

The second source of data is from spectrometers

deployed on space platforms. They normally sense the

complete solar disk, thus integrating all possible sources

of inhomogeneity (limb-darkening, sunspots, flares, and

faculae) without the need for any correction. Another

asset is that they directly observe the ‘‘air mass zero’’

spectrum for long periods of time, without any atmo-

spheric interference or resulting spectral limitations. On

the other hand, they also have some drawbacks: (i) their

half-angle field-of-view is normally larger than that of

the sun disk to allow small variations in the satellite

orbit or pointing; their resolution is thus limited to

about 0.1–1 nm, due to the inverse relationship between

resolution and field-of-view (Jacquinot, 1954); (ii)

instrumentation tends to degrade noticeably because of

harsh conditions in space; (iii) monitoring this degra-

dation is difficult, and most of the time must be esti-

mated a posteriori; (iv) maintaining proper calibration

over long periods of time is an issue in unmanned

spacecraft, therefore better results are usually achieved

during short missions on a space shuttle.

Because of the strong interest in solar UV monitoring

associated with concerns in climate change and strato-

spheric ozone depletion, long continuous records of

daily extraterrestrial UV irradiance now exist. As more

instruments are sent to space, there are also more

occurrences ofmultiple overlaps in datasets (Cebula et al.,

1996; Lean et al., 1997; Thuillier et al., 1998a; Woods

et al., 1996), which permit intercomparisons and better

quality control. Two of these instruments in particular,

SUSIM and SOLSPEC, have also been deployed during

the three shuttle missions known as ATLAS-1 (1992),

ATLAS-2 (1993) and ATLAS-3 (1994). [More details

about these missions can be found elsewhere (Kaye and

Miller, 1996).] These relatively short missions increased

the accuracy of the measurements by (i) permitting

careful manipulation by the crew, (ii) avoiding long-term

degradation in space, and (iii) allowing for post-flight

calibration. All these efforts helped decrease the mea-

surement uncertainty, which has been studied in detail

(Thuillier et al., 1998a; Woods et al., 1996).

3.1. Selected sources of data

An exhaustive survey of the existing sources of data

is beyond the scope of this contribution, but the inter-

ested reader can find detailed reviews elsewhere (e.g.,

Nicolet, 1989; Smith and Gottlieb, 1974; Thuillier et al.,

1998b, 2003a, 2004). In what follows, 23 spectra have

been selected, in great part as a result of this review of

literature, and will constitute the pool of data from

which a synthetic spectrum will be assembled. They are

first rapidly presented in alphabetical order in the three

following sections.

3.1.1. Partial spectra

This category corresponds to a variety of experi-

mental spectra that, by essence, do not cover the whole

solar spectrum for reasons explained in Section 1.

However, they have generally been used in various

combinations to assemble complete spectra.

The Arvesen spectrum has been obtained in 1967

from a series of flights with an instrumented aircraft at


about 12 km altitude (Arvesen et al., 1969). This spec-

trum extends from 300 to 2495 nm and has been used in

the subsequent construction of composite spectra (Co-

lina et al., 1996; Nicolet, 1989; Smith and Gottlieb, 1974;

Wehrli, 1985). Even though these measurements were

done at high altitude, it seems that telluric absorption

features, and possibly instrument-related problems, are

still present in this spectrum between 1.2 and 2.5 lm at

least (Gao and Green, 1995; Thuillier et al., 2004).

The ATLAS-3 spectrum (VanHoosier, 1996) has

been measured by the SUSIM instrument on November

13, 1994. Of the three ATLAS missions mentioned

above, ATLAS-3 is considered to have generated the

best dataset, partly because of grating drive and read-

out improvements performed on SUSIM before

launch (Personal communication with Linton Floyd,

NRL, 2003). The original dataset covers the range

150–408 nm at 0.05-nm intervals, with a 0.15-nm reso-

lution.

The Burlov-Vasiljev spectrum (Burlov-Vasiljev

et al., 1995, 1998) has been recently measured from a

high-altitude observatory. Only the radiance of the disk

center was observed, but a number of sophisticated

corrections were introduced to remove terrestrial

absorption features. This spectrum extends from 310 to

1070 nm at 1-nm intervals with some overlap. For

later use in this study (Section 3.4), a separation at

650 nm between the two original spectra has been

considered, and the disk center’s radiance has been

converted into disk-center irradiance, and then into

disk-average irradiance using recent spectral ratios

(Neckel, 1997).

The Colina spectrum (Colina et al., 1996) is a com-

posite using both experimental data (120–960 nm) and

modeled data in the IR (960–2500 nm). It has been

developed as a reference model for astrophysical appli-

cations.

The Harrison spectrum (Harrison et al., 2003) has

been obtained with a rotating shadowband spectrora-

diometer (RSS) using careful zero air mass extrapolation

and corrections, from 360 to 1050 nm. However, it has

not been corrected for terrestrial absorption features.

The Kitt Peak ‘‘solar flux atlas’’ (Kurucz et al., 1984)

is a high-resolution spectrum from 296 to 1300 nm,

which has been largely used by astrophysicists even

though it has not been corrected for terrestrial absorp-

tion features.

The Lockwood spectrum (Lockwood et al., 1992) has

been obtained with an original methodology: rather

than using a telescope to point to the sun’s center, a

small image of it was obtained with a 30-lm pinhole. Its

irradiance between 329 and 850 nm was then absolutely

calibrated by comparison with the spectrum of a similar

star, Vega. However it reportedly contains strong ter-

restrial absorption features beyond 600 nm (Thuillier

et al., 1998b).

The Neckel & Labs spectrum (Neckel and Labs,

1984), hereafter NL84, has been one of the most cited

spectra for about two decades. It has been derived from

measurements of the disk-center radiance in the range

330–1250 nm. Specific corrections were considered to

remove terrestrial absorption features. It has been used

in various composite spectra (ASTM, 2000; Colina

et al., 1996; Nicolet, 1989; Wehrli, 1985). However, the

results of some comparative studies (Burlov-Vasiljev

et al., 1995; Harrison et al., 2003; Thuillier et al., 1998b,

2004) suggested that NL84 was most probably too low

below �450 nm and too high above 850 nm. When

incorporating the spectral corrections proposed subse-

quently (Neckel, 2003), a corrected spectrum has been

obtained here and will be referred to as NL03 in what

follows.

The SOLSPEC spectrum, version 13c from 200 to

2400 nm, has been proposed recently (Thuillier et al.,

2003a) as an improvement over previous versions

(Thuillier et al., 1997, 1998a,b). As mentioned in the

Introduction, it is––as of this writing––the only opera-

tional spaceborne instrument with a spectral range

extending to the infrared, which is an important

advantage.

This SOLSPEC spectrum has been used in part to

assemble the composite Thuillier ‘‘reference’’ spectra

(Thuillier et al., 2004), hereafter T03. Two spectra,

which both extend from 0 to 2400 nm, have been defined

to represent an active sun and a quiet sun, respectively.

An elaborate methodology has been used in their deri-

vation, involving multiple spectral adjustment factors.

The spectrum corresponding to an active sun, based on

the ATLAS-1 data, is used here.

From the multitude of spectra recorded by satellite-

based instruments in the UV over many years, only three

have been retained here for practical reasons. The spe-

cific UARS-SOLSTICE spectrum selected here has been

obtained with the SOLSTICE instrument onboard the

UARS satellite on November 11, 1994, i.e., in parallel

with the ATLAS-3 mission. Results from the latest ver-

sion (17) of the retrieval algorithm, which has been used

here, provide spectral data at 0.05 nm intervals in the

range 119–420.5 nm. The SOLSTICE instrument and

original calibration technique are described elsewhere

(Rottman et al., 1993, 2004; Woods et al., 1993).

The specific UARS-SUSIM spectrum retained here

originates from the same satellite, but with another

spectrometer, SUSIM. It has similar optical character-

istics and spectral range as SOLSTICE, but uses a more

conventional calibration technique. More details on this

experimentation and its results can be found elsewhere

(Brueckner et al., 1993, 1996; Floyd et al., 1998; Rottman

et al., 2004; Woods et al., 1996). The representative spec-

trum selected here has been measured on April 15, 1993

(i.e., in parallel with the ATLAS-2 mission), and has

been produced with the improved version-20 algorithm.


This spectrum covers the range 115–410 nm at 0.05-nm

intervals.

Finally, the composite Woods ‘‘reference’’ spectrum

for the UV during Solar Cycle 22 (Woods and Rottman,

2002) is used because it covers an extended spectral

range of 0–420 nm at 1-nm intervals. The latest version

(Personal communication with Tom Woods, 2003) has

been modified in October 2002 to include new extreme

UV data.

3.1.2. MODTRAN spectra

The MODTRAN RTM (Anderson et al., 1993; Berk

et al., 1999) has become a de facto standard in a variety

of atmospheric applications. An interesting characteris-

tic in the framework of this study is that it offers different

ETS options. Besides the Wehrli spectrum that will be

further discussed in the next section, five spectra are

available to perform irradiance calculations. They are all

derived from the modeled Kurucz spectrum (Kurucz,

1995), all cover the range 50–50,000 cm�1 (200 nm–200

lm) at 1 cm�1 intervals, and therefore constitute essen-

tially complete spectra at an apparent high resolution.

(In fact, linear interpolation has been used extensively to

fill in some of the spectra within different bands, so that

the true resolution is frequently different from the step

size.) They will be referred to here with the file names

used in MODTRAN: cebchkur, chkur, newkur, oldkur,

and thkur. Whereas oldkur refers to an older version of

the Kurucz spectrum, the four other spectra are based

on a more recent version (Kurucz, 1995), with various

alternatives in the UV and visible. More precisely, chkur

refers to the use of the Chance spectrum (Chance and

Spurr, 1997) below 800 nm, cebchkur is a variant of

chkur that additionally uses the Cebula UV spectrum

(Cebula et al., 1996) obtained during the ATLAS-1

mission, and thkur uses the Thuillier spectra (Thuillier

et al., 1997, 1998b), also from the ATLAS-1 mission, but

for wavelengths up to 877 nm. All these options also

incorporate other spectra over limited spectral ranges

(e.g., Anderson and Hall, 1989), but the details of their

assemblage have not been published. Despite this, it is

argued that, because of the prominent importance of

MODTRAN in atmospheric studies and related appli-

cations, it is worthwhile to consider and intercompare

these optional spectra.

3.1.3. Complete composite spectra

In the era posterior to the Johnson curve (Johnson,

1954), only four complete ETS have been in wide cir-

culation, and they are reviewed here. For reasons ex-

plained above, any ETS is necessarily assembled by

combining a number of basic spectra from different

sources, instruments, etc.

The ASTM spectrum is the latest in this series, and

has been elevated to standard status (ASTM, 2000). It is

assembled from four parts. From 119 to 380 nm, the

ATLAS-2 validation spectrum combining measurements

from SUSIM and SOLSTICE onboard UARS (Woods

et al., 1996) has been used and scaled by 0.968443. NL84

was used between 380 and 825 nm without scaling.

Modeled Kurucz data were used in the 825–4000 nm

range and scaled by 1.00085. The synthetic Smith and

Gottlieb spectrum (see below; Smith and Gottlieb, 1974)

was used between 4 and 1000 lm and scaled by 0.99437.

Finally, all data points were scaled by 0.99745 to force

the integrated irradiance to equal the solar constant

value of 1366.1 Wm�2. No mention is made of the

irradiance at wavelengths below 119 nm, but it would

amount to less than 0.1 Wm�2 and therefore would not

change the scaling necessary to match the integrated

irradiance and the solar constant.

The Smith and Gottlieb spectrum (Smith and Gott-

lieb, 1974) has been assembled from a variety of sources,

using curve fitting to smooth the differences in data. The

resulting ETS is of too low resolution to be used here

(except where noted), but has been used in the ASTM

spectrum as mentioned above, and, to even a larger

extent, in the Wehrli spectrum discussed below.

The Thekaekara/NASA spectrum (Thekaekara,

1973; Thekaekara and Drummond, 1971; Thekaekara

et al., 1971) was the first serious revision to the Johnson

curve and resulted in the adoption of a noticeably re-

duced solar constant (1353 Wm�2, compared to 1396

Wm�2 for Johnson). It has been in wide use until the

release of the Wehrli spectrum (discussed below). Most

of the Thekaekara spectrum (between 300 and 15,000

nm) relied on aircraft-based measurements. Later it be-

came apparent that terrestrial absorption features were

still present in the spectrum, as well as impacts from

calibration and other experimental problems (Fr€ohlich,1983; Thuillier et al., 1998b, 2004).

These problems were addressed in great part in the

Wehrli spectrum (Wehrli, 1985), which replaced an

earlier 1981 version by Fr€ohlich and Wehrli. Whereas

the latter only had limited circulation (Bird, 1984; Iqbal,

1983; Riordan, 1987), the 1985 Wehrli spectrum has

been in wide use since its release. It was assembled from

four different parts: 199–310 nm (Brasseur and Simon,

1981), 310–330 nm (Arvesen et al., 1969), 330–869 nm

(Neckel and Labs, 1984), and 870–10075 nm (Smith and

Gottlieb, 1974). Uniform scaling was used to force the

total irradiance within 199–10075 nm to the WMO-

recommended solar constant value of 1367 Wm�2. (This

obviously assumed that the irradiance below 199 nm and

above 10075 nm can be neglected.) As mentioned above,

however, a few problems were discovered later, both in

the visible and NIR.

3.2. General corrections

Because all spectra recorded in space use vacuum

wavelengths, whereas the intended applications of this


contribution are exclusively terrestrial, these vacuum

wavelengths have been first converted to air wave-

lengths. A 5-coefficient dispersion formula for the index

of refraction (Peck and Reeder, 1972) has been used for

this conversion. (This formula was devised by its authors

as an updated and improved version of the classic Edl�enformula still used by most astronomers; although these

two formulae assume standard air composition, pressure

and temperature, it is unlikely that non-standard

atmospheric conditions would introduce any significant

change to the medium-resolution spectrum proposed

here.) Note, however, that the spectrum below 280 nm

has not been converted to air wavelengths because it is

completely absorbed in the upper layers of the earth’s

atmosphere.

In order to compare spectra of extremely differ-

ent resolution wavelength-by-wavelength, appropriate

smoothing was performed whenever possible. It consists

in applying a filter with a triangular shape, and with a

bandwidth (full width at half maximum) equal to the

desired target resolution, e.g., 0.5 nm in the interval 280–

400 nm.

3.3. Total irradiance in selected spectral bands

With due consideration for the spectral limits of the

spectra reviewed in Section 3.1.1 in particular, the whole

solar spectrum has been divided into nine unequal bands

for easier manipulation and discussion. These are

• Band 1: 0–200 nm

• Band 2: 200–280 nm

• Band 3: 280–400 nm

• Band 4: 400–700 nm

• Band 5: 700–1000 nm

• Band 6: 1.0–1.705 lm• Band 7: 1.705–2.390 lm• Band 8: 2.390–4.0 lm• Band 9: 4.0 lm–1.

For each of the above bands, the total irradiance

was calculated for all the spectra just reviewed, pro-

vided that they were defined over the whole band.

These results appear in Table 1, showing some inter-

esting features when comparing individual band irra-

diances to the band average: (i) the standard deviation

of all results is near 1% in Bands 4–6; (ii) the most

recent complete spectrum, ASTM, has a Band-2 irra-

diance lower by 2–5% compared to recent spaceborne

measurements; (iii) the Wehrli spectrum is possibly too

high in Band 6 and too low in Bands 7 and 8, com-

pared to the mean values; (iv) NL84 is possibly too

high in Band 5; (v) T03 is possibly too high in Bands 6

and 7. Moreover, the total irradiance, i.e., the solar

constant, of the complete spectra integrates to between

1353 and 1376.3 Wm�2 ()0.23% and +0.75% compared

to 1366.1 Wm�2, respectively––a margin substantially

larger than the currently accepted uncertainty of about

±0.1%).

These findings suggest that a synthetic spectrum can

be constructed band-by-band through proper selection

of a high-quality base spectrum for that band, followed

by proper individual band scaling, defined in such a way

that two conditions are simultaneously met: (i) each

band irradiance must be reasonably close to the average

value listed in Table 1, and (ii) the total spectrum must

integrate to 1366.1 Wm�2. The scaling factors thus de-

rived are described in more detail in what follows.

3.4. Synthetic spectral irradiance for each band

• Band 1 (below 200 nm) and Band 2 (200–280 nm)

Together, these extreme UV regions account for

only a very small part of TSI (<1%). They are both

completely absorbed by the upper atmosphere and thus

cannot play any role in terrestrial applications such as

solar energy utilization. For completeness and proper

calculation of the solar constant, however, a represen-

tative spectrum is needed. The spectral region 0–280

nm (at 1 nm intervals) from the Woods spectrum re-

viewed above is selected here. Because average solar

activity conditions must be met, an average spectrum

has been derived from the reported minimum and

maximum activity conditions. After conversion from

photons s�1 cm�2 to Wm�2 nm�1, this average-activity

spectrum yields a total irradiance of 0.11 Wm�2 below

200 nm, and 7.00 Wm�2 for the 200–280 nm spectral

range.

• Band 3 (280–400 nm)

A primary dataset, consisting of the ATLAS-3

spectrum, has been selected because of its highly re-

garded status. A secondary dataset has been assembled

as the arithmetic mean of four different spectra: UARS-

SOLSTICE, UARS-SUSIM, Kitt Peak (for wavelengths

above 327 nm only, to avoid interference with ozone

absorption), and the Harrison spectrum above 362 nm.

The resulting synthetic spectrum (at 0.5-nm intervals) is

obtained as a weighted average, with weights of 0.6 and

0.4 applied to the primary and secondary spectrum,

respectively. The resulting spectrum is plotted in Fig. 5.

The UV irradiance in this band integrates to 103.76

Wm�2 or 7.6% of SC.• Band 4 (400–700 nm)

T03 is selected here as the base spectrum. Because the

corresponding band irradiance appears slightly too high,

some scaling is required. To lessen the difference of its

spectral irradiance with that of the ASTM, Burlov-

Vasiljev, Harrison, NL03, and SOLSPEC spectra, a

progressively decreasing correction with wavelength, k,is applied: 1.09217–0.000172k, resulting in a +2.3%

correction at 400 nm and a )2.8% correction at 700 nm.

A few individual data points are also corrected (by no

Table 1

Integrated irradiance of various spectra calculated for nine bands of the solar spectrum

Spectral range (nm) Total

0–200 200–280 280–400 400–700 700–1000 1000–1705 1705–2390 2390–4000 4000–1Band

1 2 3 4 5 6 7 8 9

Partial spectra

1. Arvesen – 7.28 111.64 546.68 311.94 289.71 77.89 – – –

2. ATLAS-3/

SUSIM

– 6.83 104.16 – – – – – – –

3. Burlov-

Vasiljev/Neckel

– – – 535.54 310.14 – – – – –

4. Colina – – 103.57 532.04 308.46 282.09 77.87 – – –

5. Harrison – – – 542.41 [284.8] – – – – –

6. Kitt Peak – – – 529.51 [289.2] – – – – –

7. Lockwood – – – 532.34 – – – – – –

8. Neckel &

Labs 1984

– – – 531.43 314.23 – – – – –

9. Neckel &

Labs 2002

– – – 539.84 313.57 – – – – –

10. SOLSPEC-

Thuillier

– 6.73 104.99 529.20 307.53 285.62 81.12 – – –

11. Thuillier

reference

0.11 6.85 103.51 535.35 311.65 289.62 82.24 –- –

12. UARS-

SOLSTICE

– 7.07 104.18 – – – – – – –

13. UARS-

SUSIM

– 6.78 102.39 – – – – – – –

14. Woods &

Rottman

0.11 7.11 103.66 – – – – – – –

MODTRAN spectra

15. Cebchkur 0.10a 6.92 103.55 531.08 306.67 283.67 78.33 40.01 11.90 1362.2

16. Chkur 0.10a 7.25 100.96 530.96 306.67 283.67 78.33 40.01 11.90 1359.9

17. Newkur 0.10a 7.58 105.04 532.82 308.64 283.67 78.33 40.01 11.90 1368.1

18. Oldkur 0.10a 6.90 104.51 530.84 311.70 288.41 78.65 40.09 11.90 1373.1

19. Thkur 0.10a 6.82 106.09 536.81 312.60 283.67 78.33 40.01 11.90 1376.3

Complete spectra

20. ASTM 0.10 6.62 99.87 530.11 311.17 287.92 78.57 40.04 11.74 1366.1

21. Smith &

Gottlieb

0.08 7.48 96.61 527.20 310.82 288a 70a 45a 13a 1358.0

22. Thekaekara/

NASA

0.11 7.53 110.42 516.23 305.57 282.30 74.20 43.89 12.75 1353.0

23.Wehrli/WRC 0.01 7.04 101.64 532.10 310.10 290.60 76.75 38.50 10.25 1367.0

AVERAGE

(Wm�2)

0.09 7.05 103.93 532.76 310.09 285.91 78.38 40.32 11.78 1370.3

St. Dev.

(Wm�2)

0.04 0.30 3.50 6.30 2.59 3.14 1.98 1.54 0.69 –

St. Dev./mean

(%)

45.4 4.2 3.4 1.2 0.8 1.1 2.5 3.8 5.9 –

24. This work 0.11 7.00 103.76 534.64 308.58 283.68 78.10 39.27 11.00 1366.1

[ ] Spectrum strongly affected by terrestrial absorption features in this band; these underestimated values are not considered in the

average.a Estimated value.


more than ±4%) when deviations to Burlov-Vasiljev and

NL03 appear too large. The resulting spectrum (at 1-nm

intervals) is plotted in Fig. 6. The visible irradiance in

this band integrates to 534.64 Wm�2 or 39.1% of SC.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

280 290 300 310 320 330 340 350 360 370 380 390 400

Synthetic Spectrum

Irra

dian

ce (

Wm

-2 n

m-1

)

Wavelength (nm)

Fig. 5. Proposed synthetic spectrum for Band 3, 280–400 nm.

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

700 720 740 760 780 800 820 840 860 880 900 920 940 960 980 1000

Synthetic Spectrum

Irra

dian

ce (

Wm

-2 nm

-1)

Wavelength (nm)



• Band 5 (700–1000 nm)

As in Band 4, the selected base spectrum is T03, but

it is scaled by 0.9904 to match the band irradiance of

the newkur spectrum, 308.58 Wm�2, or 22.6% of SC.A few data points are also corrected, as for Band 4.

The resulting spectrum (at 1-nm intervals) is shown in

Fig. 7.

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700

Synthetic Spectrum

Irra

dian

ce (

Wm

-2 nm

-1)

Wavelength (nm)


• Band 6 (1.0–1.705 lm)

T03 is selected here too as the base spectrum, but a

progressive correction is applied to obtain a better

match with newkur: 1.0467–0.052389 k, for k here in lm.

The resulting spectrum (at 1-nm intervals) integrates to

283.68 Wm�2 (20.8% of SC) and is shown in Fig. 8.

• Band 7 (1.705–2.390 lm)

An initial base spectrum (at 5-nm intervals) is ob-

tained here as a weighted average of T03 (weight: 0.6),

newkur (weight: 0.3) and Colina (weight: 0.1). To better

match the newkur and Colina spectra, the base spectrum

is scaled by 0.9686 and results in a band irradiance of

78.10 Wm�2, or 5.7% of SC.• Band 8 (2.39–4.0 lm)

The selected base spectrum (at 5-nm intervals) is here

newkur. It is scaled by 0.9814 to match the average band

irradiance of ASTM and Wehrli, which results in a band

irradiance of 39.27 Wm�2, or 2.9% of SC.• Band 9 (4 lm–1)

ASTM is selected for the initial base spectrum. It is

scaled by 0.932 for 4 < k < 5 mm and by 0.942 for

5 < k < 1000 lm to better match the average of ASTM

and Wehrli, and to take into consideration recent find-

ings (Thuillier et al., 2004) that ASTM appears slightly

too high around 4.5 lm. The corrected irradiance totals

11.00 Wm�2 in this band, or 0.8% of SC. The spectrum

beyond 1000 lm is not known precisely, but can be

approximated by Planck’s law, and its irradiance is

negligible.

With the individual band corrections described

above, the total irradiance obtained for the whole

0.15

0.25

0.35

0.45

0.55

0.65

0.75

1000 1100 1200 1300 1400 1500 1600 1700

Synthetic Spectrum

Irra

dian

ce (

Wm

-2 nm

-1)

Wavelength (nm)

Fig. 8. Proposed synthetic spectrum for Band 6, 1.0–1.705 lm.

0

10

20

30

Irradiance Comparisonswith Synthetic Spectrum

Per

cent

Diff

eren

ce


spectrum is exactly 1366.1 Wm�2 (Table 1), so that no

further spectrum-wide scaling is necessary, contrarily to

the ASTM and Wehrli spectra.

As mentioned earlier in this section, the reference

spectrum just described is representative of periods of

moderate solar activity. As a first approximation, the

actual spectral irradiance for any day, E�k, can be ob-

tained from the reference irradiance in Appendix A, Ek,

through

E�k ¼ EkðTSI=SCÞ ð6Þ

where the ratio (TSI/SC) can be estimated from Eqs.

(1b), (2b), (3b) or (4b), depending on the available input

data. There are indications, also mentioned above, that

a more precise correction would involve an intricate UV-

weighted spectral dependence, but it is still too uncertain

to be formulated explicitly. An additional correction is

well known, however: E�k needs to be corrected for the

actual sun–earth distance, a deterministic astronomical

quantity.

-30

-20

-10

280 300 320 340 360 380 400

ASTM

Wehrli

Wavelength (nm)

Fig. 9. Percent difference between the ASTM and Wehrli irra-

diance, and the proposed synthetic spectrum in Band 3.

4. Comparison with existing spectra

Even though the integrated band irradiances dis-

played in Table 1 show relatively limited scatter, there

are important differences in the case of small spectral

ranges or, even more so, single wavelengths. These dif-

ferences may be caused by calibration problems, inter-

ferences with atmospheric absorbers, or wavelength

accuracy around Fraunhofer lines and other solar

absorption features. The latter experimental error may

induce important spikes in the relative difference be-

tween two spectra, particularly below 1000 nm because

of the abundance of this kind of sharp structure in the

solar spectrum (Figs. 5–8). It is therefore nearly impos-

sible to establish the wavelength-by-wavelength uncer-

tainty of the proposed synthetic spectrum, or of any

other that preceded it. Nevertheless, important infor-

mation can be gained by comparing different spectra on

the same basis. Such intercomparisons have been fre-

quently used in the literature (e.g., Burlov-Vasiljev et al.,

1995, 1998; Thekaekara et al., 1971; Thuillier et al.,

1998b, 2004). However, these earlier contributions

elected to show only smoothed differences between

spectra, using a relatively large averaging interval (e.g., 5

nm), whereas differences will be displayed here at the

maximum resolution of the proposed spectrum to

demonstrate the very frequent wavelength-shift prob-

lem.

Fig. 9 shows the relative difference between two

earlier composite spectra, ASTM and Wehrli, and the

proposed synthetic spectrum for Band 3. As was noted

before, the ASTM UV spectrum is consistently lower

than those of Wehrli or this work. Important differences

also exist between Wehrli and this work. Because the

present synthetic spectrum is mostly based on the AT-

LAS-3 data in this band, and because the latter dataset

is considered to have an excellent wavelength accuracy,

it is argued that most of these differences and spikes are

-30

-20

-10

0

10

20

30

280 300 320 340 360 380 400


chkur

Thuillier 03

Per

cent

Diff

eren

ceWavelength (nm)

Fig. 11. Percent difference between the chkur and T03 irradi-

ance, and the proposed synthetic spectrum in Band 3.


due to inadequacies in the three original spectra that

have been assembled by Wehrli in Band 3. The lower

ASTM irradiance seems to be due to the low overall

scaling factor (0.96596) affecting the UARS/ATLAS-2

spectrum used below 380 nm, to its wavelength accu-

racy, and to the relatively low NL84 irradiance below

450 nm, already noticed above.

Similarly, Figs. 10 and 11 show the relative difference

between the newkur, cebchkur, chkur or T03 spectra,

and the proposed synthetic spectrum in the UV. The

cebchkur spectrum, obtained from spaceborne mea-

surements in this band, is consistent with the proposed

spectrum, even though a persistent wavelength shift is

noticeable. In comparison, newkur appears less consis-

tent, particularly around 385 nm. The chkur spectrum

also seems to have some inconsistencies below 330 nm.

The T03 spectrum, on average, is remarkably consistent

with the proposed spectrum, but a wavelength shift is

obvious here too. Although the ATLAS-3 data used

here are believed to have better wavelength alignment

than the ATLAS-1 data––basis for the ‘‘high activity’’

Thuillier spectrum––there is no way of knowing which

one is really closer to the truth.

Fig. 12 compares the spectral irradiance from Arve-

sen and Thekaekara to that of the proposed spectrum

for the visible, Band 4. The Arvesen spectrum seems to

become progressively too high above 560 nm, whereas

Thekaekara’s reveals a significant drop between 520 and

610 nm, at which point its resolution becomes too coarse

for meaningful comparisons.

-30

-20

-10

0

10

20

30

280 300 320 340 360 380 400


newkur

cebchkur

Per

cent

Diff

eren

ce

Wavelength (nm)

Fig. 10. Percent difference between the newkur and cebchkur

irradiance, and the proposed synthetic spectrum in Band 3.

Similarly, but for a spectral range extending to 900

nm, Fig. 13 compares the Smith & Gottlieb and SOL-

SPEC spectra to the proposed synthetic spectrum. The

former is based on NL84 in this band and appears rel-

atively low below 550 nm. As could be expected, the

-20

-15

-10

-5

0

5

10

15

20

400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700


Arvesen

Thekaekara

Per

cent

Diff

eren

ce

Wavelength (nm)

Fig. 12. Percent difference between the Arvesen and Thekae-

kara irradiance, and the proposed synthetic spectrum in Band 4.

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

400 500 600 700 800 900


newkurthkur

Per

cent

Diff

eren

ceWavelength (nm)

Fig. 14. Percent difference between the newkur and thkur

irradiance, and the proposed synthetic spectrum in Bands 4–5.

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

400 500 600 700 800 900


Smith & Gottlieb

SOLSPEC-Thuillier

Per

cent

Diff

eren

ce

Wavelength (nm)

Fig. 13. Percent difference between the Smith & Gottlieb and

SOLSPEC irradiance, and the proposed synthetic spectrum in

Bands 4 and 5.

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

400 500 600 700 800 900


Neckel & Labs 1984Neckel & Labs 2003

Per

cent

Diff

eren

ce

Wavelength (nm)

Fig. 15. Percent difference between two versions of the Neckel

& Labs irradiance, and the proposed synthetic spectrum in

Bands 4–5.


SOLSPEC and proposed spectra are mutually consistent

because they rely on very closely related datasets.

An irradiance intercomparison in Bands 4 and 5 is

proposed in Figs. 14 and 15, showcasing the newkur,

thkur, NL84 and NL03 spectra. Whereas newkur ap-

pears too low between 400 and 500 nm, thkur appears

too high in the 820–870 nm range, demonstrating that

the SOLSPEC data underwent significant changes be-

tween version 8 as used in thkur (Personal communi-

cation with G�erard Thuillier, 1998) and version 13c as

used in the more recent SOLSPEC spectrum (Thuillier

et al., 2003a). As illustrated in Fig. 15, the comparison

between the two versions of the Neckel & Labs spectrum

shows that the newer version effectively corrected the

tendency of the older version to underestimate below

about 510 nm. However, both versions are possibly too

high in the 560–700 nm range.

Figs. 16 and 17 cover Bands 4, 5 and

6 (in part). They show two similar comparisons of

spectra measured from the ground, but with [Colina

and Burlov-Vasiljev] or without [Harrison and Kitt

Peak] atmospheric correction. The two latter spectra

exhibit characteristic sudden drops exactly where the

atmospheric gaseous absorptance increases sharply, as

calculated with the SMARTS code (Gueymard, 2001)

for a US Standard Atmosphere and a site at 2-km

altitude. These perturbations are not present in the

Colina spectrum (based in this spectral range on NL84,

and thus showing the same trends as noted just above,

which are absent in Harrison’s spectrum) or in the

Burlov-Vasiljev radiance spectrum coupled with Nec-

kel’s disk-center to disk-average function.

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

0

0.2

0.4

0.6

0.8

1

400 500 600 700 800 900 1000 1100 1200 1300

Irradiance Comparisons with Reference Spectrum

ColinaHarrison

Per

cent

Diff

eren

ce

Gaseous A

bsorptanceWavelength (nm)

Gaseous Absorptance at 2-km altitude

Fig. 16. Percent difference between the Colina and Harrison

irradiance, and the proposed synthetic spectrum in Bands 4–6

(top panel), and gaseous absorptance of the earth’s atmosphere

as predicted by the SMARTS code for an elevated site (bottom

panel).

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

0

0.2

0.4

0.6

0.8

1

400 500 600 700 800 900 1000 1100 1200 1300

Irradiance Comparisons with Synthetic Spectrum

Burlov-Vasiljev/Neckel

Kitt Peak atlas

Per

cent

Diff

eren

ce

Gaseous A

bsorptance

Wavelength (nm)

Gaseous Absorptance at 2-km altitude

Fig. 17. Percent difference between the Burlov-Vasiljev/Neckel

and Kitt Peak irradiance, and the proposed synthetic spectrum

in Bands 4–6 (top panel), and gaseous absorptance of the

earth’s atmosphere as predicted by the SMARTS code for an

elevated site (bottom panel).

-20

-15

-10

-5

0

5

10

1700 1800 1900 2000 2100 2200 2300 2400


ASTM

Wehrli

Per

cent

Diff

eren

ceWavelength (nm)

Fig. 18. Percent difference between the ASTM and Wehrli


-4

-2

0

2

4

1700 1800 1900 2000 2100 2200 2300 2400


Colina

newkur

Per

cent

Diff

eren

ce

Wavelength (nm)

Fig. 19. Percent difference between the Colina and newkur



Finally, Figs. 18 and 19 provide a comparison of

spectra (ASTM, Wehrli, Colina and newkur) to the

synthetic spectrum for Band 7. ASTM is here consistent

with the proposed spectrum, whereas Wehrli’s spectrum


displays a wide valley between 2050 and 2400 nm, thus

confirming previous findings (Gao and Green, 1995). In

this spectral region, Wehrli based his spectrum on Smith

& Gottlieb, and hence on older spectra (Arvesen et al.,

1969; Pierce, 1954) in which atmospheric interferences

were likely. In turn, Colina based his spectrum on Ku-

rucz’s modeled results, explaining the similitude with

newkur, even though the latter appears about 0.5%

higher than the former––apparently because two differ-

ent versions of the Kurucz model were used.

5. Conclusion

The solar constant of 1366.1 Wm�2 obtained here

from 24 years of irradiance measurements in space is

identical to the value now standardized by ASTM. Day-

to-day variations in solar activity (sunspots, faculae,

etc.) are responsible for detectable structure in the TSI

time series. For the solar conditions that prevailed

during this 24-year period at least, the daily TSI can be

simply predicted with relatively good accuracy from

three important solar indices, the Zurich sunspot num-

ber, the MgII index, and the 10.7 cm radio flux. Eqs. (1),

(4), and (3) can be used for simple estimates of the daily

TSI for the periods 1749–1947, 1947–1978 and 1978–

present, respectively.

Twenty-three existing measured or modeled spectra

were analyzed within nine spectral bands, covering the

whole solar spectrum. From this analysis, a synthetic/

composite spectrum has been assembled. For each

band, a single spectrum (or a weighted average of

different spectra) was selected as the base case. A

scaling factor (close to 1) was applied––if necessary––so

that the total irradiance in that band could better

match other representative spectra, and moreover, so

that the total integrated irradiance becomes exactly

equal to the solar constant value mentioned above.

This result is achieved without a spectrum-wide ren-

ormalization, contrarily to previous 4-band composite

spectra (ASTM and Wehrli). Because of current limi-

tations in instrumentation and calibration techniques

[which are such that the accuracy in spectral mea-

surements (1–3% at best) is an order of magnitude

larger than that in TSI (�0.1%)], scaling of measured

spectra appears necessary to constrain a complete

spectrum to the solar constant value. The methodology

used here, however, limits such scaling to 1.7% on

average over the 2460 wavelengths considered.

An intercomparison study has been conducted to

gain more insight into the strengths and weaknesses

of each original or composite spectrum. Four types of

problems have been identified in these spectra: (i)

localized inaccuracy around a specific wavelength, the

cause of which is unknown; (ii) large-band underesti-

mations or overestimations (e.g., NL84 below 510 nm or

in the 560–700 nm region; newkur possibly too low

around 385 nm and between 400 and 500 nm; Wehrli too

low between 2050 and 2400 nm), confirming previous

studies; (iii) sharp underestimation structure corre-

sponding to atmospheric absorption interference in

uncorrected spectra, particularly in the near infrared

(e.g., Harrison, Kitt Peak, Lockwood); and (iv) rapid

wavelength-to-wavelength fluctuations of a few percents

close to solar Fraunhofer lines or other solar absorption

features, particularly in the UV and visible, caused by

slight spectral shift between spectra, themselves resulting

from differences in wavelength accuracy of �0.1 nm or

less.

The selection of the ATLAS-3 spectrum in the 280–

400 nm band should limit the uncertainty in the pro-

posed spectrum because this dataset is considered

to have one of the best wavelength accuracies ever

achieved in space. Nevertheless, radically new instru-

mentation with absolute accuracies comparable to the

radiometers measuring TSI (�0.1%)––such as the Solar

Irradiance Monitor which has been recently launched

as part of the SORCE mission––will be necessary to

assess the accuracy of existing spectra or of this newly-

proposed synthetic spectrum, and to improve these

spectra in both resolution and accuracy. Furthermore,

new spaceborne instruments will be necessary to mon-

itor the solar spectrum in the infrared beyond 2.5 lmor so.

The new spectrum (tabulated in Appendix A and

available from http://rredc.nrel.gov/solar/spectra/am0/

special.html) has a resolution roughly equal to the step

size, i.e., 1 nm for 0–280 and 400–1705 nm, 0.5 nm be-

tween 280 and 400nm, 5 nm between 1705 and 4000 nm,

and increasing intervals beyond 4 lm.

It is felt that the 0.5- and 1-nm constant intervals

used here over the most important part of the spec-

trum (0–1705 nm) constitutes a good compromise be-

tween resolution and ease of use in solar radiation

models.

Acknowledgements

The author is particularly thankful to all the indi-

viduals who contributed largely to this work by pro-

viding basic data or valuable discussions: Gail P.

Anderson, Linton E. Floyd, Bo-Cai Gao, Dianne K.

Prinz, Gary J. Rottman, Eric P. Shettle, G�erard Thuil-

lier, Michael E. VanHoosier, and Tom Woods. Permis-

sion to use unpublished data from the VIRGO

Experiment on the cooperative ESA/NASA Mission

SOHO, and TSI data from PMOD/WRC is acknowl-

edged.

Appendix

Extraterrestrial spectruma

k Ek k Ek k Ek k Ek k Ek k Ek

0.5 2.278E)06 345 9.981E)01 700 1.413E+00 1110 5.823E)01 1520 2.852E)01 2830 3.200E)021.5 1.219E)04 345.5 1.018E+00 701 1.410E+00 1111 5.778E)01 1521 2.813E)01 2835 3.182E)022.5 1.513E)05 346 8.640E)01 702 1.402E+00 1112 5.739E)01 1522 2.812E)01 2840 3.148E)023.5 2.519E)05 346.5 9.766E)01 703 1.408E+00 1113 5.725E)01 1523 2.838E)01 2845 3.133E)024.5 3.708E)05 347 1.044E+00 704 1.422E+00 1114 5.775E)01 1524 2.815E)01 2850 3.111E)025.5 4.610E)05 347.5 8.414E)01 705 1.424E+00 1115 5.728E)01 1525 2.823E)01 2855 3.093E)026.5 4.367E)05 348 9.597E)01 706 1.410E+00 1116 5.732E)01 1526 2.843E)01 2860 3.074E)027.5 3.115E)05 348.5 9.591E)01 707 1.407E+00 1117 5.757E)01 1527 2.843E)01 2865 3.047E)028.5 2.828E)05 349 8.876E)01 708 1.410E+00 1118 5.703E)01 1528 2.836E)01 2870 2.994E)029.5 1.652E)05 349.5 8.760E)01 709 1.396E+00 1119 5.625E)01 1529 2.755E)01 2875 2.977E)0210.5 6.771E)06 350 1.081E+00 710 1.403E+00 1120 5.626E)01 1530 2.735E)01 2880 2.988E)0211.5 3.362E)06 350.5 1.138E+00 711 1.396E+00 1121 5.663E)01 1531 2.812E)01 2885 2.973E)0212.5 1.756E)06 351 1.014E+00 712 1.385E+00 1122 5.685E)01 1532 2.800E)01 2890 2.953E)0213.5 1.958E)06 351.5 9.808E)01 713 1.377E+00 1123 5.676E)01 1533 2.773E)01 2895 2.938E)0214.5 2.140E)05 352 1.053E+00 714 1.382E+00 1124 5.636E)01 1534 2.748E)01 2900 2.918E)0215.5 1.636E)05 352.5 8.210E)01 715 1.356E+00 1125 5.481E)01 1535 2.780E)01 2905 2.899E)0216.5 3.398E)05 353 1.032E+00 716 1.363E+00 1126 5.535E)01 1536 2.792E)01 2910 2.883E)0217.5 5.008E)04 353.5 1.102E+00 717 1.382E+00 1127 5.580E)01 1537 2.767E)01 2915 2.862E)0218.5 2.875E)04 354 1.143E+00 718 1.360E+00 1128 5.558E)01 1538 2.738E)01 2920 2.843E)0219.5 2.038E)04 354.5 1.158E+00 719 1.335E+00 1129 5.497E)01 1539 2.719E)01 2925 2.813E)0220.5 1.958E)04 355 1.152E+00 720 1.361E+00 1130 5.508E)01 1540 2.694E)01 2930 2.803E)0221.5 9.410E)05 355.5 1.038E+00 721 1.346E+00 1131 5.536E)01 1541 2.725E)01 2935 2.790E)0222.5 1.025E)04 356 1.084E+00 722 1.345E+00 1132 5.538E)01 1542 2.732E)01 2940 2.770E)0223.5 2.287E)05 356.5 9.246E)01 723 1.357E+00 1133 5.447E)01 1543 2.748E)01 2945 2.747E)0224.5 4.762E)05 357 7.635E)01 724 1.346E+00 1134 5.501E)01 1544 2.754E)01 2950 2.733E)0225.5 1.173E)04 357.5 9.338E)01 725 1.337E+00 1135 5.503E)01 1545 2.758E)01 2955 2.719E)0226.5 4.025E)05 358 7.391E)01 726 1.339E+00 1136 5.510E)01 1546 2.740E)01 2960 2.704E)0227.5 8.475E)05 358.5 6.309E)01 727 1.348E+00 1137 5.454E)01 1547 2.681E)01 2965 2.689E)0228.5 8.556E)05 359 8.815E)01 728 1.324E+00 1138 5.383E)01 1548 2.679E)01 2970 2.671E)0229.5 4.375E)05 359.5 1.122E+00 729 1.297E+00 1139 5.402E)01 1549 2.691E)01 2975 2.655E)0230.5 6.252E)04 360 1.188E+00 730 1.329E+00 1140 5.359E)01 1550 2.678E)01 2980 2.635E)0231.5 1.190E)04 360.5 9.484E)01 731 1.319E+00 1141 5.367E)01 1551 2.704E)01 2985 2.620E)0232.5 1.593E)04 361 8.627E)01 732 1.322E+00 1142 5.388E)01 1552 2.708E)01 2990 2.601E)0233.5 1.566E)04 361.5 9.897E)01 733 1.318E+00 1143 5.401E)01 1553 2.660E)01 2995 2.581E)02

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Appendix (continued)


34.5 6.937E)05 362 8.526E)01 734 1.332E+00 1144 5.351E)01 1554 2.645E)01 3000 2.560E)0235.5 5.933E)05 362.5 1.176E+00 735 1.313E+00 1145 5.395E)01 1555 2.644E)01 3005 2.555E)0236.5 8.039E)05 363 1.053E+00 736 1.307E+00 1146 5.433E)01 1556 2.646E)01 3010 2.539E)0237.5 1.383E)05 363.5 9.672E)01 737 1.317E+00 1147 5.418E)01 1557 2.674E)01 3015 2.522E)0238.5 5.931E)06 364 1.180E+00 738 1.295E+00 1148 5.383E)01 1558 2.660E)01 3020 2.505E)0239.5 5.832E)06 364.5 1.007E+00 739 1.273E+00 1149 5.373E)01 1559 2.645E)01 3025 2.489E)0240.5 9.781E)06 365 1.024E+00 740 1.292E+00 1150 5.358E)01 1560 2.664E)01 3030 2.469E)0241.5 1.810E)05 365.5 1.283E+00 741 1.271E+00 1151 5.354E)01 1561 2.681E)01 3035 2.432E)0242.5 4.798E)06 366 1.356E+00 742 1.265E+00 1152 5.311E)01 1562 2.661E)01 3040 2.393E)0243.5 1.101E)05 366.5 1.271E+00 743 1.295E+00 1153 5.341E)01 1563 2.633E)01 3045 2.415E)0244.5 4.389E)06 367 1.236E+00 744 1.287E+00 1154 5.351E)01 1564 2.648E)01 3050 2.414E)0245.5 4.824E)06 367.5 1.281E+00 745 1.284E+00 1155 5.321E)01 1565 2.641E)01 3055 2.397E)0246.5 1.738E)05 368 1.119E+00 746 1.290E+00 1156 5.304E)01 1566 2.612E)01 3060 2.383E)0247.5 6.925E)06 368.5 1.127E+00 747 1.292E+00 1157 5.305E)01 1567 2.612E)01 3065 2.362E)0248.5 1.155E)05 369 1.215E+00 748 1.289E+00 1158 5.291E)01 1568 2.590E)01 3070 2.351E)0249.5 3.965E)05 369.5 1.293E+00 749 1.274E+00 1159 5.169E)01 1569 2.595E)01 3075 2.343E)0250.5 1.680E)05 370 1.376E+00 750 1.273E+00 1160 5.182E)01 1570 2.620E)01 3080 2.324E)0251.5 5.743E)06 370.5 1.066E+00 751 1.260E+00 1161 5.084E)01 1571 2.641E)01 3085 2.306E)0252.5 9.808E)06 371 1.137E+00 752 1.265E+00 1162 5.220E)01 1572 2.623E)01 3090 2.296E)0253.5 7.458E)06 371.5 1.421E+00 753 1.271E+00 1163 5.216E)01 1573 2.610E)01 3095 2.282E)0254.5 4.843E)06 372 9.422E)01 754 1.274E+00 1164 5.147E)01 1574 2.523E)01 3100 2.266E)0255.5 2.165E)05 372.5 1.128E+00 755 1.267E+00 1165 5.175E)01 1575 2.498E)01 3105 2.258E)0256.5 6.578E)06 373 1.145E+00 756 1.266E+00 1166 5.134E)01 1576 2.475E)01 3110 2.240E)0257.5 6.528E)06 373.5 7.436E)01 757 1.268E+00 1167 5.169E)01 1577 2.417E)01 3115 2.201E)0258.5 3.689E)05 374 1.079E+00 758 1.253E+00 1168 5.177E)01 1578 2.546E)01 3120 2.208E)0259.5 7.776E)06 374.5 8.919E)01 759 1.249E+00 1169 5.065E)01 1579 2.587E)01 3125 2.201E)0260.5 3.112E)05 375 8.660E)01 760 1.249E+00 1170 5.160E)01 1580 2.600E)01 3130 2.188E)0261.5 9.737E)06 375.5 1.292E+00 761 1.245E+00 1171 5.175E)01 1581 2.560E)01 3135 2.177E)0262.5 4.209E)05 376 1.070E+00 762 1.223E+00 1172 5.161E)01 1582 2.502E)01 3140 2.163E)0263.5 1.060E)05 376.5 1.108E+00 763 1.246E+00 1173 5.156E)01 1583 2.521E)01 3145 2.150E)0264.5 2.442E)06 377 1.171E+00 764 1.239E+00 1174 5.132E)01 1584 2.535E)01 3150 2.125E)0265.5 1.916E)06 377.5 1.368E+00 765 1.226E+00 1175 4.988E)01 1585 2.555E)01 3155 2.119E)0266.5 1.709E)06 378 1.482E+00 766 1.176E+00 1176 5.072E)01 1586 2.533E)01 3160 2.112E)0267.5 1.750E)06 378.5 1.400E+00 767 1.216E+00 1177 5.071E)01 1587 2.490E)01 3165 2.095E)0268.5 6.027E)06 379 1.155E+00 768 1.221E+00 1178 5.012E)01 1588 2.395E)01 3170 2.079E)02

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69.5 4.452E)06 379.5 1.055E+00 769 1.209E+00 1179 5.085E)01 1589 2.318E)01 3175 2.075E)0270.5 1.172E)05 380 1.096E+00 770 1.209E+00 1180 5.097E)01 1590 2.379E)01 3180 2.058E)0271.5 5.120E)06 380.5 1.325E+00 771 1.201E+00 1181 5.061E)01 1591 2.433E)01 3185 2.049E)0272.5 3.833E)06 381 1.325E+00 772 1.198E+00 1182 5.000E)01 1592 2.521E)01 3190 2.039E)0273.5 4.995E)06 381.5 1.048E+00 773 1.205E+00 1183 4.855E)01 1593 2.543E)01 3195 2.027E)0274.5 6.155E)06 382 9.288E)01 774 1.198E+00 1184 4.998E)01 1594 2.551E)01 3200 2.008E)0275.5 9.412E)06 382.5 7.899E)01 775 1.188E+00 1185 5.043E)01 1595 2.508E)01 3205 2.001E)0276.5 2.379E)05 383 7.300E)01 776 1.202E+00 1186 5.032E)01 1596 2.439E)01 3210 1.991E)0277.5 2.156E)05 383.5 7.020E)01 777 1.186E+00 1187 5.031E)01 1597 2.515E)01 3215 1.975E)0278.5 3.043E)05 384 7.734E)01 778 1.179E+00 1188 4.847E)01 1598 2.528E)01 3220 1.967E)0279.5 1.429E)05 384.5 1.136E+00 779 1.180E+00 1189 4.839E)01 1599 2.499E)01 3225 1.954E)0280.5 1.468E)05 385 1.125E+00 780 1.173E+00 1190 4.980E)01 1600 2.477E)01 3230 1.943E)0281.5 1.668E)05 385.5 1.046E+00 781 1.174E+00 1191 5.011E)01 1601 2.449E)01 3235 1.929E)0282.5 2.465E)05 386 8.946E)01 782 1.181E+00 1192 4.986E)01 1602 2.466E)01 3240 1.916E)0283.5 4.209E)05 386.5 1.173E+00 783 1.160E+00 1193 4.981E)01 1603 2.475E)01 3245 1.904E)0284.5 3.061E)05 387 9.740E)01 784 1.165E+00 1194 4.972E)01 1604 2.457E)01 3250 1.900E)0285.5 3.409E)05 387.5 1.093E+00 785 1.158E+00 1195 4.911E)01 1605 2.454E)01 3255 1.886E)0286.5 3.613E)05 388 1.008E+00 786 1.172E+00 1196 4.916E)01 1606 2.427E)01 3260 1.874E)0287.5 4.301E)05 388.5 9.949E)01 787 1.167E+00 1197 4.795E)01 1607 2.448E)01 3265 1.863E)0288.5 4.915E)05 389 1.073E+00 788 1.161E+00 1198 4.742E)01 1608 2.459E)01 3270 1.854E)0289.5 5.978E)05 389.5 1.298E+00 789 1.167E+00 1199 4.691E)01 1609 2.385E)01 3275 1.841E)0290.5 7.044E)05 390 1.301E+00 790 1.165E+00 1200 4.886E)01 1610 2.336E)01 3280 1.827E)0291.5 5.389E)05 390.5 1.196E+00 791 1.149E+00 1201 4.907E)01 1611 2.380E)01 3285 1.816E)0292.5 1.922E)05 391 1.406E+00 792 1.138E+00 1202 4.880E)01 1612 2.400E)01 3290 1.800E)0293.5 1.685E)05 391.5 1.433E+00 793 1.123E+00 1203 4.676E)01 1613 2.415E)01 3295 1.763E)0294.5 1.201E)05 392 1.206E+00 794 1.110E+00 1204 4.788E)01 1614 2.409E)01 3300 1.760E)0295.5 6.964E)06 392.5 1.078E+00 795 1.136E+00 1205 4.845E)01 1615 2.352E)01 3305 1.774E)0296.5 7.241E)06 393 5.989E)01 796 1.140E+00 1206 4.851E)01 1616 2.317E)01 3310 1.768E)0297.5 1.296E)04 393.5 4.347E)01 797 1.139E+00 1207 4.842E)01 1617 2.371E)01 3315 1.751E)0298.5 1.474E)05 394 8.837E)01 798 1.138E+00 1208 4.595E)01 1618 2.402E)01 3320 1.721E)0299.5 2.274E)05 394.5 1.122E+00 799 1.139E+00 1209 4.687E)01 1619 2.372E)01 3325 1.732E)02100.5 9.215E)06 395 1.368E+00 800 1.129E+00 1210 4.713E)01 1620 2.306E)01 3330 1.729E)02101.5 1.065E)05 395.5 1.389E+00 801 1.132E+00 1211 4.730E)01 1621 2.337E)01 3335 1.718E)02102.5 9.719E)05 396 1.203E+00 802 1.127E+00 1212 4.787E)01 1622 2.374E)01 3340 1.706E)02103.5 1.004E)04 396.5 7.019E)01 803 1.122E+00 1213 4.781E)01 1623 2.407E)01 3345 1.700E)02104.5 1.470E)05 397 5.261E)01 804 1.120E+00 1214 4.782E)01 1624 2.387E)01 3350 1.688E)02105.5 1.244E)05 397.5 1.069E+00 805 1.106E+00 1215 4.780E)01 1625 2.377E)01 3355 1.679E)02

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y76(2004)423–453

441



106.5 1.184E)05 398 1.497E+00 806 1.121E+00 1216 4.772E)01 1626 2.386E)01 3360 1.672E)02107.5 1.257E)05 398.5 1.546E+00 807 1.112E+00 1217 4.759E)01 1627 2.400E)01 3365 1.658E)02108.5 2.109E)05 399 1.670E+00 808 1.110E+00 1218 4.741E)01 1628 2.401E)01 3370 1.644E)02109.5 1.419E)05 399.5 1.663E+00 809 1.101E+00 1219 4.721E)01 1629 2.373E)01 3375 1.640E)02110.5 1.513E)05 400 1.727E+00 810 1.104E+00 1220 4.735E)01 1630 2.363E)01 3380 1.631E)02111.5 1.388E)05 401 1.769E+00 811 1.115E+00 1221 4.716E)01 1631 2.366E)01 3385 1.623E)02112.5 1.512E)05 402 1.861E+00 812 1.116E+00 1222 4.698E)01 1632 2.353E)01 3390 1.617E)02113.5 1.181E)05 403 1.763E+00 813 1.118E+00 1223 4.683E)01 1633 2.315E)01 3395 1.596E)02114.5 7.990E)06 404 1.733E+00 814 1.111E+00 1224 4.696E)01 1634 2.326E)01 3400 1.575E)02115.5 1.313E)05 405 1.730E+00 815 1.105E+00 1225 4.681E)01 1635 2.340E)01 3405 1.582E)02116.5 1.484E)05 406 1.697E+00 816 1.103E+00 1226 4.660E)01 1636 2.290E)01 3410 1.575E)02117.5 6.311E)05 407 1.665E+00 817 1.099E+00 1227 4.567E)01 1637 2.251E)01 3415 1.561E)02118.5 1.671E)05 408 1.729E+00 818 1.077E+00 1228 4.642E)01 1638 2.197E)01 3420 1.559E)02119.5 5.556E)05 409 1.847E+00 819 1.071E+00 1229 4.651E)01 1639 2.207E)01 3425 1.550E)02120.5 1.687E)04 410 1.610E+00 820 1.064E+00 1230 4.626E)01 1640 2.212E)01 3430 1.541E)02121.5 8.119E)03 411 1.740E+00 821 1.063E+00 1231 4.611E)01 1641 2.200E)01 3435 1.537E)02122.5 5.962E)05 412 1.863E+00 822 1.065E+00 1232 4.589E)01 1642 2.224E)01 3440 1.529E)02123.5 4.230E)05 413 1.816E+00 823 1.076E+00 1233 4.598E)01 1643 2.235E)01 3445 1.520E)02124.5 3.217E)05 414 1.834E+00 824 1.073E+00 1234 4.574E)01 1644 2.217E)01 3450 1.512E)02125.5 3.050E)05 415 1.834E+00 825 1.070E+00 1235 4.569E)01 1645 2.234E)01 3455 1.503E)02126.5 4.499E)05 416 1.861E+00 826 1.078E+00 1236 4.583E)01 1646 2.255E)01 3460 1.496E)02127.5 2.361E)05 417 1.813E+00 827 1.076E+00 1237 4.577E)01 1647 2.256E)01 3465 1.487E)02128.5 1.932E)05 418 1.777E+00 828 1.070E+00 1238 4.567E)01 1648 2.239E)01 3470 1.476E)02129.5 2.273E)05 419 1.797E+00 829 1.063E+00 1239 4.510E)01 1649 2.230E)01 3475 1.468E)02130.5 1.817E)04 420 1.787E+00 830 1.060E+00 1240 4.519E)01 1650 2.236E)01 3480 1.462E)02131.5 2.964E)05 421 1.866E+00 831 1.054E+00 1241 4.538E)01 1651 2.232E)01 3485 1.454E)02132.5 2.270E)05 422 1.771E+00 832 1.057E+00 1242 4.492E)01 1652 2.242E)01 3490 1.446E)02133.5 2.163E)04 423 1.727E+00 833 1.024E+00 1243 4.453E)01 1653 2.243E)01 3495 1.437E)02134.5 2.023E)05 424 1.825E+00 834 1.029E+00 1244 4.497E)01 1654 2.237E)01 3500 1.431E)02135.5 4.616E)05 425 1.818E+00 835 1.045E+00 1245 4.509E)01 1655 2.241E)01 3505 1.424E)02136.5 2.997E)05 426 1.765E+00 836 1.050E+00 1246 4.481E)01 1656 2.251E)01 3510 1.416E)02137.5 3.188E)05 427 1.730E+00 837 1.045E+00 1247 4.475E)01 1657 2.246E)01 3515 1.407E)02138.5 3.158E)05 428 1.684E+00 838 1.029E+00 1248 4.493E)01 1658 2.237E)01 3520 1.399E)02139.5 9.267E)05 429 1.590E+00 839 1.026E+00 1249 4.488E)01 1659 2.230E)01 3525 1.392E)02

442

C.A.Gueymard

/SolarEnerg

y76(2004)423–453

140.5 7.694E)05 430 1.389E+00 840 1.043E+00 1250 4.473E)01 1660 2.248E)01 3530 1.385E)02141.5 4.532E)05 431 1.377E+00 841 1.037E+00 1251 4.441E)01 1661 2.247E)01 3535 1.374E)02142.5 4.897E)05 432 1.773E+00 842 1.028E+00 1252 4.410E)01 1662 2.229E)01 3540 1.367E)02143.5 5.708E)05 433 1.780E+00 843 1.016E+00 1253 4.432E)01 1663 2.218E)01 3545 1.364E)02144.5 5.554E)05 434 1.652E+00 844 1.009E+00 1254 4.433E)01 1664 2.213E)01 3550 1.356E)02145.5 5.972E)05 435 1.725E+00 845 1.033E+00 1255 4.421E)01 1665 2.194E)01 3555 1.344E)02146.5 7.424E)05 436 1.938E+00 846 1.027E+00 1256 4.404E)01 1666 2.187E)01 3560 1.336E)02147.5 9.217E)05 437 1.906E+00 847 1.004E+00 1257 4.402E)01 1667 2.174E)01 3565 1.333E)02148.5 9.396E)05 438 1.732E+00 848 1.003E+00 1258 4.398E)01 1668 2.152E)01 3570 1.324E)02149.5 8.473E)05 439 1.795E+00 849 9.749E)01 1259 4.408E)01 1669 2.183E)01 3575 1.318E)02150.5 9.444E)05 440 1.848E+00 850 9.330E)01 1260 4.410E)01 1670 2.190E)01 3580 1.309E)02151.5 1.021E)04 441 1.910E+00 851 9.939E)01 1261 4.385E)01 1671 2.149E)01 3585 1.303E)02152.5 1.286E)04 442 2.046E+00 852 9.844E)01 1262 4.375E)01 1672 2.105E)01 3590 1.298E)02153.5 1.429E)04 443 1.995E+00 853 9.427E)01 1263 4.391E)01 1673 2.144E)01 3595 1.290E)02154.5 2.543E)04 444 2.034E+00 854 8.179E)01 1264 4.349E)01 1674 2.142E)01 3600 1.283E)02155.5 2.101E)04 445 1.991E+00 855 8.930E)01 1265 4.357E)01 1675 2.100E)01 3605 1.279E)02156.5 2.113E)04 446 1.894E+00 856 9.783E)01 1266 4.365E)01 1676 2.104E)01 3610 1.272E)02157.5 1.910E)04 447 2.042E+00 857 9.964E)01 1267 4.322E)01 1677 2.120E)01 3615 1.266E)02158.5 1.837E)04 448 2.077E+00 858 9.905E)01 1268 4.292E)01 1678 2.103E)01 3620 1.260E)02159.5 1.836E)04 449 2.077E+00 859 9.894E)01 1269 4.337E)01 1679 2.063E)01 3625 1.252E)02160.5 2.064E)04 450 2.131E+00 860 9.896E)01 1270 4.352E)01 1680 1.990E)01 3630 1.245E)02161.5 2.419E)04 451 2.208E+00 861 9.847E)01 1271 4.341E)01 1681 1.971E)01 3635 1.239E)02162.5 2.778E)04 452 2.125E+00 862 9.994E)01 1272 4.330E)01 1682 2.024E)01 3640 1.231E)02163.5 3.047E)04 453 1.996E+00 863 1.023E+00 1273 4.310E)01 1683 2.069E)01 3645 1.222E)02164.5 3.391E)04 454 2.079E+00 864 9.716E)01 1274 4.293E)01 1684 2.092E)01 3650 1.214E)02165.5 5.295E)04 455 2.091E+00 865 9.627E)01 1275 4.310E)01 1685 2.093E)01 3655 1.204E)02166.5 3.695E)04 456 2.138E+00 866 8.656E)01 1276 4.309E)01 1686 2.089E)01 3660 1.201E)02167.5 4.362E)04 457 2.172E+00 867 9.032E)01 1277 4.298E)01 1687 2.089E)01 3665 1.198E)02168.5 4.852E)04 458 2.100E+00 868 9.827E)01 1278 4.279E)01 1688 2.086E)01 3670 1.190E)02169.5 6.357E)04 459 2.086E+00 869 9.621E)01 1279 4.245E)01 1689 2.065E)01 3675 1.182E)02170.5 7.352E)04 460 2.092E+00 870 9.894E)01 1280 4.191E)01 1690 2.088E)01 3680 1.167E)02171.5 7.377E)04 461 2.138E+00 871 9.760E)01 1281 3.958E)01 1691 2.100E)01 3685 1.166E)02172.5 7.963E)04 462 2.150E+00 872 9.723E)01 1282 3.749E)01 1692 2.102E)01 3690 1.166E)02173.5 7.993E)04 463 2.136E+00 873 9.703E)01 1283 4.051E)01 1693 2.098E)01 3695 1.149E)02174.5 9.816E)04 464 2.095E+00 874 9.587E)01 1284 4.164E)01 1694 2.093E)01 3700 1.133E)02175.5 1.209E)03 465 2.063E+00 875 9.395E)01 1285 4.182E)01 1695 2.088E)01 3705 1.136E)02176.5 1.310E)03 466 2.079E+00 876 9.496E)01 1286 4.199E)01 1696 2.081E)01 3710 1.132E)02

C.A.Gueymard

/SolarEnerg

y76(2004)423–453

443



177.5 1.580E)03 467 2.043E+00 877 9.588E)01 1287 4.208E)01 1697 2.078E)01 3715 1.130E)02178.5 1.762E)03 468 2.066E+00 878 9.702E)01 1288 4.192E)01 1698 2.076E)01 3720 1.129E)02179.5 1.723E)03 469 2.076E+00 879 9.550E)01 1289 4.192E)01 1699 2.060E)01 3725 1.125E)02180.5 2.061E)03 470 2.010E+00 880 9.344E)01 1290 4.139E)01 1700 2.043E)01 3730 1.119E)02181.5 2.481E)03 471 2.006E+00 881 9.231E)01 1291 4.172E)01 1701 2.039E)01 3735 1.101E)02182.5 2.312E)03 472 2.114E+00 882 9.436E)01 1292 4.190E)01 1702 2.026E)01 3740 1.075E)02183.5 2.471E)03 473 2.087E+00 883 9.448E)01 1293 4.166E)01 1703 2.022E)01 3745 1.073E)02184.5 2.114E)03 474 2.094E+00 884 9.410E)01 1294 4.157E)01 1704 2.043E)01 3750 1.083E)02185.5 2.417E)03 475 2.116E+00 885 9.480E)01 1295 4.174E)01 1705 2.028E)01 3755 1.081E)02186.5 2.769E)03 476 2.058E+00 886 9.126E)01 1296 4.175E)01 1710 1.981E)01 3760 1.080E)02187.5 3.211E)03 477 2.067E+00 887 9.158E)01 1297 4.138E)01 1715 1.993E)01 3765 1.078E)02188.5 3.402E)03 478 2.121E+00 888 9.357E)01 1298 4.133E)01 1720 1.959E)01 3770 1.073E)02189.5 3.834E)03 479 2.103E+00 889 9.360E)01 1299 4.154E)01 1725 1.933E)01 3775 1.063E)02190.5 3.969E)03 480 2.102E+00 890 9.387E)01 1300 4.138E)01 1730 1.911E)01 3780 1.059E)02191.5 4.360E)03 481 2.135E+00 891 9.316E)01 1301 4.113E)01 1735 1.814E)01 3785 1.056E)02192.5 4.664E)03 482 2.140E+00 892 9.167E)01 1302 4.094E)01 1740 1.848E)01 3790 1.048E)02193.5 3.532E)03 483 2.108E+00 893 9.112E)01 1303 4.063E)01 1745 1.857E)01 3795 1.043E)02194.5 5.901E)03 484 2.062E+00 894 9.134E)01 1304 4.076E)01 1750 1.843E)01 3800 1.039E)02195.5 5.754E)03 485 1.962E+00 895 9.098E)01 1305 4.098E)01 1755 1.842E)01 3805 1.035E)02196.5 6.512E)03 486 1.712E+00 896 9.232E)01 1306 4.096E)01 1760 1.816E)01 3810 1.029E)02197.5 6.603E)03 487 1.791E+00 897 9.093E)01 1307 4.073E)01 1765 1.797E)01 3815 1.024E)02198.5 6.658E)03 488 1.965E+00 898 9.131E)01 1308 4.068E)01 1770 1.783E)01 3820 1.021E)02199.5 7.231E)03 489 1.973E+00 899 9.104E)01 1309 4.065E)01 1775 1.758E)01 3825 1.019E)02200.5 7.933E)03 490 2.072E+00 900 8.896E)01 1310 4.039E)01 1780 1.735E)01 3830 1.013E)02201.5 8.826E)03 491 2.033E+00 901 8.590E)01 1311 4.037E)01 1785 1.726E)01 3835 1.005E)02202.5 8.766E)03 492 1.919E+00 902 8.678E)01 1312 3.928E)01 1790 1.721E)01 3840 1.002E)02203.5 1.010E)02 493 1.981E+00 903 9.008E)01 1313 3.962E)01 1795 1.701E)01 3845 9.991E)03204.5 1.119E)02 494 2.000E+00 904 9.098E)01 1314 3.996E)01 1800 1.682E)01 3850 9.942E)03205.5 1.159E)02 495 2.016E+00 905 9.072E)01 1315 3.878E)01 1805 1.668E)01 3855 9.883E)03206.5 1.190E)02 496 2.028E+00 906 8.862E)01 1316 3.971E)01 1810 1.654E)01 3860 9.806E)03207.5 1.388E)02 497 2.059E+00 907 8.934E)01 1317 3.989E)01 1815 1.583E)01 3865 9.739E)03208.5 1.565E)02 498 1.962E+00 908 8.777E)01 1318 3.972E)01 1820 1.555E)01 3870 9.701E)03209.5 2.250E)02 499 1.988E+00 909 8.598E)01 1319 4.000E)01 1825 1.599E)01 3875 9.682E)03210.5 3.016E)02 500 1.932E+00 910 8.768E)01 1320 3.980E)01 1830 1.592E)01 3880 9.631E)03

444

C.A.Gueymard

/SolarEnerg

y76(2004)423–453

211.5 3.682E)02 501 1.899E+00 911 8.722E)01 1321 3.957E)01 1835 1.576E)01 3885 9.544E)03212.5 3.344E)02 502 1.878E+00 912 8.734E)01 1322 3.965E)01 1840 1.555E)01 3890 9.526E)03213.5 3.190E)02 503 1.961E+00 913 8.926E)01 1323 3.961E)01 1845 1.530E)01 3895 9.475E)03214.5 4.486E)02 504 1.933E+00 914 8.820E)01 1324 3.964E)01 1850 1.533E)01 3900 9.424E)03215.5 3.663E)02 505 1.983E+00 915 8.747E)01 1325 3.946E)01 1855 1.520E)01 3905 9.398E)03216.5 3.437E)02 506 2.048E+00 916 8.785E)01 1326 3.923E)01 1860 1.500E)01 3910 9.358E)03217.5 3.394E)02 507 1.948E+00 917 8.661E)01 1327 3.919E)01 1865 1.479E)01 3915 9.313E)03218.5 4.915E)02 508 1.881E+00 918 8.703E)01 1328 3.883E)01 1870 1.455E)01 3920 9.262E)03219.5 5.061E)02 509 1.929E+00 919 8.733E)01 1329 3.836E)01 1875 1.348E)01 3925 9.226E)03220.5 5.191E)02 510 1.915E+00 920 8.626E)01 1330 3.893E)01 1880 1.424E)01 3930 9.174E)03221.5 3.602E)02 511 1.962E+00 921 8.410E)01 1331 3.883E)01 1885 1.431E)01 3935 9.121E)03222.5 5.262E)02 512 1.981E+00 922 8.378E)01 1332 3.840E)01 1890 1.409E)01 3940 9.093E)03223.5 6.923E)02 513 1.874E+00 923 8.148E)01 1333 3.901E)01 1895 1.378E)01 3945 9.030E)03224.5 6.178E)02 514 1.859E+00 924 8.406E)01 1334 3.905E)01 1900 1.388E)01 3950 8.952E)03225.5 5.441E)02 515 1.840E+00 925 8.404E)01 1335 3.880E)01 1905 1.381E)01 3955 8.896E)03226.5 3.993E)02 516 1.836E+00 926 8.297E)01 1336 3.886E)01 1910 1.366E)01 3960 8.871E)03227.5 3.837E)02 517 1.630E+00 927 8.561E)01 1337 3.870E)01 1915 1.357E)01 3965 8.854E)03228.5 5.683E)02 518 1.714E+00 928 8.575E)01 1338 3.847E)01 1920 1.341E)01 3970 8.813E)03229.5 4.896E)02 519 1.798E+00 929 8.461E)01 1339 3.789E)01 1925 1.334E)01 3975 8.764E)03230.5 5.909E)02 520 1.864E+00 930 8.505E)01 1340 3.830E)01 1930 1.303E)01 3980 8.716E)03231.5 4.909E)02 521 1.882E+00 931 8.505E)01 1341 3.837E)01 1935 1.302E)01 3985 8.643E)03232.5 5.513E)02 522 1.885E+00 932 8.460E)01 1342 3.834E)01 1940 1.272E)01 3990 8.589E)03233.5 4.566E)02 523 1.852E+00 933 8.492E)01 1343 3.830E)01 1945 1.203E)01 3995 8.533E)03234.5 3.652E)02 524 1.921E+00 934 8.471E)01 1344 3.840E)01 1950 1.246E)01 4000 8.300E)03235.5 5.941E)02 525 1.948E+00 935 8.371E)01 1345 3.820E)01 1955 1.267E)01 4020 7.975E)03236.5 4.667E)02 526 1.862E+00 936 8.330E)01 1346 3.803E)01 1960 1.251E)01 4040 7.815E)03237.5 5.654E)02 527 1.758E+00 937 8.389E)01 1347 3.811E)01 1965 1.230E)01 4060 7.658E)03238.5 3.827E)02 528 1.862E+00 938 8.382E)01 1348 3.809E)01 1970 1.225E)01 4080 7.506E)03239.5 4.642E)02 529 1.965E+00 939 8.322E)01 1349 3.780E)01 1975 1.204E)01 4100 7.357E)03240.5 4.219E)02 530 1.938E+00 940 8.224E)01 1350 3.751E)01 1980 1.191E)01 4120 7.213E)03241.5 5.072E)02 531 1.968E+00 941 7.925E)01 1351 3.777E)01 1985 1.183E)01 4140 7.071E)03242.5 7.710E)02 532 1.901E+00 942 8.090E)01 1352 3.791E)01 1990 1.182E)01 4160 6.933E)03243.5 6.826E)02 533 1.845E+00 943 8.189E)01 1353 3.775E)01 1995 1.162E)01 4180 6.798E)03244.5 6.614E)02 534 1.898E+00 944 8.079E)01 1354 3.753E)01 2000 1.159E)01 4200 6.667E)03245.5 5.095E)02 535 1.937E+00 945 8.160E)01 1355 3.716E)01 2005 1.147E)01 4220 6.538E)03246.5 5.134E)02 536 1.953E+00 946 8.189E)01 1356 3.699E)01 2010 1.144E)01 4240 6.413E)03247.5 5.980E)02 537 1.874E+00 947 8.207E)01 1357 3.704E)01 2015 1.134E)01 4260 6.290E)03

C.A.Gueymard

/SolarEnerg

y76(2004)423–453

445



248.5 4.587E)02 538 1.906E+00 948 8.214E)01 1358 3.732E)01 2020 1.114E)01 4280 6.171E)03249.5 5.894E)02 539 1.890E+00 949 8.207E)01 1359 3.696E)01 2025 1.108E)01 4300 6.054E)03250.5 6.228E)02 540 1.813E+00 950 8.149E)01 1360 3.699E)01 2030 1.091E)01 4320 5.941E)03251.5 4.689E)02 541 1.831E+00 951 8.105E)01 1361 3.728E)01 2035 1.081E)01 4340 5.829E)03252.5 4.114E)02 542 1.891E+00 952 8.112E)01 1362 3.688E)01 2040 1.076E)01 4360 5.721E)03253.5 5.376E)02 543 1.866E+00 953 8.038E)01 1363 3.670E)01 2045 1.077E)01 4380 5.614E)03254.5 5.853E)02 544 1.903E+00 954 7.792E)01 1364 3.685E)01 2050 1.064E)01 4400 5.511E)03255.5 8.455E)02 545 1.896E+00 955 7.660E)01 1365 3.694E)01 2055 1.053E)01 4420 5.409E)03256.5 1.020E)01 546 1.909E+00 956 7.984E)01 1366 3.671E)01 2060 1.037E)01 4440 5.311E)03257.5 1.274E)01 547 1.904E+00 957 7.922E)01 1367 3.659E)01 2065 1.029E)01 4460 5.214E)03258.5 1.355E)01 548 1.879E+00 958 8.008E)01 1368 3.645E)01 2070 1.023E)01 4480 5.119E)03259.5 1.116E)01 549 1.883E+00 959 8.016E)01 1369 3.621E)01 2075 1.022E)01 4500 5.026E)03260.5 9.016E)02 550 1.905E+00 960 7.903E)01 1370 3.619E)01 2080 1.006E)01 4520 4.936E)03261.5 8.884E)02 551 1.881E+00 961 7.941E)01 1371 3.626E)01 2085 9.972E)02 4540 4.847E)03262.5 1.119E)01 552 1.894E+00 962 7.873E)01 1372 3.656E)01 2090 9.874E)02 4560 4.761E)03263.5 1.631E)01 553 1.861E+00 963 7.834E)01 1373 3.654E)01 2095 9.729E)02 4580 4.677E)03264.5 2.743E)01 554 1.906E+00 964 7.831E)01 1374 3.622E)01 2100 9.745E)02 4600 4.594E)03265.5 2.761E)01 555 1.911E+00 965 7.800E)01 1375 3.593E)01 2105 9.684E)02 4620 4.513E)03266.5 2.617E)01 556 1.887E+00 966 7.737E)01 1376 3.577E)01 2110 9.573E)02 4640 4.434E)03267.5 2.701E)01 557 1.830E+00 967 7.804E)01 1377 3.607E)01 2115 9.489E)02 4660 4.356E)03268.5 2.623E)01 558 1.819E+00 968 7.793E)01 1378 3.612E)01 2120 9.370E)02 4680 4.281E)03269.5 2.421E)01 559 1.788E+00 969 7.788E)01 1379 3.619E)01 2125 9.285E)02 4700 4.207E)03270.5 2.975E)01 560 1.812E+00 970 7.780E)01 1380 3.604E)01 2130 9.277E)02 4720 4.134E)03271.5 2.451E)01 561 1.838E+00 971 7.756E)01 1381 3.592E)01 2135 9.165E)02 4740 4.064E)03272.5 1.956E)01 562 1.828E+00 972 7.774E)01 1382 3.562E)01 2140 9.141E)02 4760 3.994E)03273.5 2.249E)01 563 1.882E+00 973 7.692E)01 1383 3.577E)01 2145 9.059E)02 4780 3.926E)03274.5 1.265E)01 564 1.834E+00 974 7.598E)01 1384 3.583E)01 2150 9.007E)02 4800 3.859E)03275.5 1.850E)01 565 1.821E+00 975 7.690E)01 1385 3.564E)01 2155 8.921E)02 4820 3.794E)03276.5 2.680E)01 566 1.797E+00 976 7.647E)01 1386 3.565E)01 2160 8.778E)02 4840 3.731E)03277.5 2.625E)01 567 1.835E+00 977 7.630E)01 1387 3.558E)01 2165 8.270E)02 4860 3.668E)03278.5 1.709E)01 568 1.829E+00 978 7.619E)01 1388 3.570E)01 2170 8.508E)02 4880 3.607E)03279.5 7.821E)02 569 1.807E+00 979 7.555E)01 1389 3.550E)01 2175 8.562E)02 4900 3.547E)03280 7.846E)02 570 1.803E+00 980 7.594E)01 1390 3.529E)01 2180 8.491E)02 4920 3.488E)03280.5 1.023E)01 571 1.786E+00 981 7.635E)01 1391 3.553E)01 2185 8.458E)02 4940 3.431E)03

446

C.A.Gueymard

/SolarEnerg

y76(2004)423–453

281 1.716E)01 572 1.843E+00 982 7.609E)01 1392 3.541E)01 2190 8.358E)02 4960 3.375E)03281.5 2.410E)01 573 1.865E+00 983 7.554E)01 1393 3.528E)01 2195 8.337E)02 4980 3.320E)03282 2.916E)01 574 1.862E+00 984 7.544E)01 1394 3.511E)01 2200 8.258E)02 5000 3.266E)03282.5 3.142E)01 575 1.832E+00 985 7.550E)01 1395 3.505E)01 2205 8.068E)02 5050 3.197E)03283 3.429E)01 576 1.815E+00 986 7.494E)01 1396 3.518E)01 2210 8.048E)02 5100 3.078E)03283.5 3.223E)01 577 1.833E+00 987 7.479E)01 1397 3.521E)01 2215 8.019E)02 5150 2.964E)03284 3.211E)01 578 1.800E+00 988 7.489E)01 1398 3.516E)01 2220 7.969E)02 5200 2.854E)03284.5 2.514E)01 579 1.798E+00 989 7.371E)01 1399 3.478E)01 2225 7.868E)02 5250 2.751E)03285 1.185E)01 580 1.818E+00 990 7.402E)01 1400 3.429E)01 2230 7.827E)02 5300 2.652E)03285.5 1.377E)01 581 1.817E+00 991 7.415E)01 1401 3.455E)01 2235 7.761E)02 5350 2.558E)03286 3.006E)01 582 1.842E+00 992 7.438E)01 1402 3.473E)01 2240 7.656E)02 5400 2.467E)03286.5 3.581E)01 583 1.839E+00 993 7.418E)01 1403 3.447E)01 2245 7.616E)02 5450 2.380E)03287 3.778E)01 584 1.850E+00 994 7.418E)01 1404 3.449E)01 2250 7.541E)02 5500 2.298E)03287.5 3.782E)01 585 1.802E+00 995 7.385E)01 1405 3.455E)01 2255 7.456E)02 5550 2.218E)03288 2.504E)01 586 1.765E+00 996 7.379E)01 1406 3.447E)01 2260 7.414E)02 5600 2.143E)03288.5 3.588E)01 587 1.810E+00 997 7.376E)01 1407 3.446E)01 2265 7.347E)02 5650 2.071E)03289 4.201E)01 588 1.793E+00 998 7.351E)01 1408 3.446E)01 2270 7.318E)02 5700 2.001E)03289.5 4.911E)01 589 1.646E+00 999 7.317E)01 1409 3.452E)01 2275 7.264E)02 5750 1.935E)03290 6.177E)01 590 1.716E+00 1000 7.307E)01 1410 3.435E)01 2280 7.142E)02 5800 1.871E)03290.5 6.459E)01 591 1.782E+00 1001 7.352E)01 1411 3.364E)01 2285 7.103E)02 5850 1.810E)03291 6.097E)01 592 1.780E+00 1002 7.320E)01 1412 3.365E)01 2290 7.064E)02 5900 1.751E)03291.5 6.020E)01 593 1.784E+00 1003 7.233E)01 1413 3.384E)01 2295 6.909E)02 5950 1.695E)03292 5.728E)01 594 1.781E+00 1004 7.100E)01 1414 3.398E)01 2300 6.918E)02 6000 1.641E)03292.5 4.965E)01 595 1.752E+00 1005 6.779E)01 1415 3.409E)01 2305 6.897E)02 6050 1.589E)03293 5.672E)01 596 1.779E+00 1006 7.078E)01 1416 3.387E)01 2310 6.843E)02 6100 1.539E)03293.5 5.760E)01 597 1.767E+00 1007 7.208E)01 1417 3.408E)01 2315 6.760E)02 6150 1.491E)03294 5.039E)01 598 1.751E+00 1008 7.203E)01 1418 3.393E)01 2320 6.671E)02 6200 1.445E)03294.5 5.434E)01 599 1.746E+00 1009 7.199E)01 1419 3.368E)01 2325 6.534E)02 6250 1.401E)03295 5.160E)01 600 1.737E+00 1010 7.188E)01 1420 3.368E)01 2330 6.561E)02 6300 1.358E)03295.5 5.821E)01 601 1.715E+00 1011 7.167E)01 1421 3.336E)01 2335 6.509E)02 6350 1.318E)03296 6.210E)01 602 1.702E+00 1012 7.141E)01 1422 3.311E)01 2340 6.487E)02 6400 1.278E)03296.5 4.926E)01 603 1.727E+00 1013 7.141E)01 1423 3.318E)01 2345 6.461E)02 6450 1.241E)03297 4.241E)01 604 1.754E+00 1014 7.091E)01 1424 3.320E)01 2350 6.351E)02 6500 1.204E)03297.5 5.976E)01 605 1.743E+00 1015 7.050E)01 1425 3.301E)01 2355 6.220E)02 6550 1.168E)03298 5.577E)01 606 1.732E+00 1016 7.023E)01 1426 3.280E)01 2360 6.246E)02 6600 1.134E)03298.5 3.788E)01 607 1.745E+00 1017 7.045E)01 1427 3.293E)01 2365 6.230E)02 6650 1.102E)03299 5.767E)01 608 1.722E+00 1018 6.999E)01 1428 3.303E)01 2370 6.157E)02 6700 1.070E)03

C.A.Gueymard

/SolarEnerg

y76(2004)423–453

447



299.5 5.214E)01 609 1.722E+00 1019 6.914E)01 1429 3.247E)01 2375 6.089E)02 6750 1.040E)03300 4.166E)01 610 1.706E+00 1020 6.972E)01 1430 3.287E)01 2380 6.055E)02 6800 1.011E)03300.5 4.391E)01 611 1.713E+00 1021 6.951E)01 1431 3.291E)01 2385 5.856E)02 6850 9.825E)04301 4.939E)01 612 1.706E+00 1022 6.920E)01 1432 3.341E)01 2390 5.906E)02 6900 9.552E)04301.5 5.295E)01 613 1.683E+00 1023 7.000E)01 1433 3.308E)01 2395 5.884E)02 6950 9.290E)04302 3.743E)01 614 1.657E+00 1024 6.976E)01 1434 3.301E)01 2400 5.847E)02 7000 9.036E)04302.5 5.437E)01 615 1.690E+00 1025 6.971E)01 1435 3.310E)01 2405 5.813E)02 7050 8.790E)04303 6.767E)01 616 1.632E+00 1026 6.957E)01 1436 3.303E)01 2410 5.769E)02 7100 8.553E)04303.5 6.886E)01 617 1.627E+00 1027 6.939E)01 1437 3.307E)01 2415 5.596E)02 7150 8.324E)04304 5.771E)01 618 1.688E+00 1028 6.930E)01 1438 3.304E)01 2420 5.622E)02 7200 8.102E)04304.5 6.481E)01 619 1.670E+00 1029 6.853E)01 1439 3.272E)01 2425 5.602E)02 7250 7.888E)04305 6.729E)01 620 1.681E+00 1030 6.876E)01 1440 3.142E)01 2430 5.580E)02 7300 7.681E)04305.5 6.124E)01 621 1.686E+00 1031 6.859E)01 1441 3.225E)01 2435 5.515E)02 7350 7.481E)04306 5.422E)01 622 1.670E+00 1032 6.831E)01 1442 3.184E)01 2440 5.501E)02 7400 7.287E)04306.5 5.857E)01 623 1.648E+00 1033 6.730E)01 1443 3.218E)01 2445 5.429E)02 7450 7.100E)04307 6.442E)01 624 1.617E+00 1034 6.728E)01 1444 3.206E)01 2450 5.337E)02 7500 6.918E)04307.5 6.515E)01 625 1.613E+00 1035 6.749E)01 1445 3.248E)01 2455 5.297E)02 7550 6.743E)04308 6.563E)01 626 1.638E+00 1036 6.791E)01 1446 3.222E)01 2460 5.311E)02 7600 6.572E)04308.5 6.802E)01 627 1.665E+00 1037 6.678E)01 1447 3.223E)01 2465 5.299E)02 7650 6.407E)04309 5.619E)01 628 1.663E+00 1038 6.710E)01 1448 3.242E)01 2470 5.217E)02 7700 6.248E)04309.5 5.133E)01 629 1.663E+00 1039 6.710E)01 1449 3.231E)01 2475 5.207E)02 7750 6.094E)04310 4.648E)01 630 1.628E+00 1040 6.684E)01 1450 3.188E)01 2480 5.100E)02 7800 5.944E)04310.5 7.144E)01 631 1.629E+00 1041 6.716E)01 1451 3.154E)01 2485 5.065E)02 7850 5.799E)04311 8.236E)01 632 1.604E+00 1042 6.670E)01 1452 3.186E)01 2490 5.079E)02 7900 5.658E)04311.5 7.643E)01 633 1.638E+00 1043 6.652E)01 1453 3.180E)01 2495 5.050E)02 7950 5.522E)04312 6.417E)01 634 1.611E+00 1044 6.679E)01 1454 3.145E)01 2500 5.034E)02 8000 5.389E)04312.5 6.965E)01 635 1.631E+00 1045 6.592E)01 1455 3.141E)01 2505 4.997E)02 8050 5.261E)04313 7.110E)01 636 1.603E+00 1046 6.523E)01 1456 3.151E)01 2510 4.919E)02 8100 5.137E)04313.5 7.252E)01 637 1.625E+00 1047 6.586E)01 1457 3.171E)01 2515 4.894E)02 8150 5.015E)04314 7.931E)01 638 1.633E+00 1048 6.627E)01 1458 3.197E)01 2520 4.881E)02 8200 4.898E)04314.5 5.927E)01 639 1.611E+00 1049 6.608E)01 1459 3.184E)01 2525 4.856E)02 8250 4.784E)04315 7.536E)01 640 1.591E+00 1050 6.583E)01 1460 3.165E)01 2530 4.826E)02 8300 4.673E)04315.5 6.800E)01 641 1.587E+00 1051 6.580E)01 1461 3.154E)01 2535 4.779E)02 8350 4.566E)04316 5.180E)01 642 1.576E+00 1052 6.559E)01 1462 3.127E)01 2540 4.700E)02 8400 4.462E)04

448

C.A.Gueymard

/SolarEnerg

y76(2004)423–453

316.5 6.628E)01 643 1.597E+00 1053 6.514E)01 1463 3.114E)01 2545 4.685E)02 8450 4.361E)04317 8.224E)01 644 1.588E+00 1054 6.536E)01 1464 3.134E)01 2550 4.657E)02 8500 4.263E)04317.5 8.798E)01 645 1.593E+00 1055 6.549E)01 1465 3.113E)01 2555 4.619E)02 8550 4.166E)04318 6.342E)01 646 1.569E+00 1056 6.536E)01 1466 3.135E)01 2560 4.587E)02 8600 4.073E)04318.5 6.820E)01 647 1.577E+00 1057 6.524E)01 1467 3.129E)01 2565 4.556E)02 8650 3.983E)04319 7.530E)01 648 1.591E+00 1058 6.372E)01 1468 3.116E)01 2570 4.535E)02 8700 3.895E)04319.5 6.829E)01 649 1.560E+00 1059 6.389E)01 1469 3.135E)01 2575 4.527E)02 8750 3.809E)04320 8.363E)01 650 1.529E+00 1060 6.384E)01 1470 3.083E)01 2580 4.473E)02 8800 3.727E)04320.5 9.076E)01 651 1.586E+00 1061 6.382E)01 1471 3.080E)01 2585 4.365E)02 8850 3.646E)04321 7.151E)01 652 1.568E+00 1062 6.426E)01 1472 3.067E)01 2590 4.405E)02 8900 3.567E)04321.5 6.749E)01 653 1.566E+00 1063 6.370E)01 1473 3.033E)01 2595 4.376E)02 8950 3.491E)04322 8.146E)01 654 1.543E+00 1064 6.442E)01 1474 3.028E)01 2600 4.354E)02 9000 3.417E)04322.5 7.013E)01 655 1.509E+00 1065 6.419E)01 1475 3.036E)01 2605 4.334E)02 9050 3.344E)04323 6.399E)01 656 1.321E+00 1066 6.274E)01 1476 3.049E)01 2610 4.297E)02 9100 3.273E)04323.5 6.829E)01 657 1.356E+00 1067 6.361E)01 1477 3.034E)01 2615 4.257E)02 9150 3.205E)04324 7.812E)01 658 1.509E+00 1068 6.240E)01 1478 3.035E)01 2620 4.179E)02 9200 3.138E)04324.5 8.264E)01 659 1.513E+00 1069 6.036E)01 1479 3.075E)01 2625 3.984E)02 9250 3.073E)04325 7.840E)01 660 1.517E+00 1070 6.262E)01 1480 3.055E)01 2630 4.101E)02 9300 3.010E)04325.5 9.411E)01 661 1.527E+00 1071 6.297E)01 1481 3.044E)01 2635 4.141E)02 9350 2.948E)04326 1.052E+00 662 1.537E+00 1072 6.272E)01 1482 3.038E)01 2640 4.059E)02 9400 2.887E)04326.5 9.968E)01 663 1.504E+00 1073 6.168E)01 1483 3.012E)01 2645 4.071E)02 9450 2.829E)04327 1.009E+00 664 1.512E+00 1074 6.265E)01 1484 3.054E)01 2650 4.055E)02 9500 2.771E)04327.5 9.959E)01 665 1.506E+00 1075 6.132E)01 1485 3.060E)01 2655 4.003E)02 9550 2.716E)04328 9.529E)01 666 1.504E+00 1076 6.271E)01 1486 3.021E)01 2660 3.996E)02 9600 2.661E)04328.5 9.132E)01 667 1.499E+00 1077 6.270E)01 1487 2.896E)01 2665 3.917E)02 9650 2.608E)04329 1.024E+00 668 1.496E+00 1078 6.177E)01 1488 2.793E)01 2670 3.943E)02 9700 2.557E)04329.5 1.139E+00 669 1.517E+00 1079 6.143E)01 1489 3.008E)01 2675 3.907E)02 9750 2.507E)04330 1.162E+00 670 1.509E+00 1080 6.229E)01 1490 3.026E)01 2680 3.899E)02 9800 2.457E)04330.5 9.725E)01 671 1.507E+00 1081 6.057E)01 1491 3.013E)01 2685 3.883E)02 9850 2.410E)04331 1.005E+00 672 1.493E+00 1082 6.003E)01 1492 3.011E)01 2690 3.854E)02 9900 2.363E)04331.5 9.815E)01 673 1.514E+00 1083 5.994E)01 1493 3.028E)01 2695 3.823E)02 9950 2.317E)04332 1.006E+00 674 1.507E+00 1084 6.140E)01 1494 3.032E)01 2700 3.806E)02 10000 2.272E)04332.5 9.721E)01 675 1.492E+00 1085 6.176E)01 1495 2.980E)01 2705 3.776E)02 11000 1.540E)04333 9.790E)01 676 1.501E+00 1086 6.100E)01 1496 2.938E)01 2710 3.745E)02 12000 1.085E)04333.5 9.164E)01 677 1.485E+00 1087 5.893E)01 1497 2.974E)01 2715 3.726E)02 13000 7.856E)05334 9.417E)01 678 1.488E+00 1088 6.024E)01 1498 2.975E)01 2720 3.700E)02 14000 5.831E)05334.5 1.040E+00 679 1.463E+00 1089 6.015E)01 1499 2.976E)01 2725 3.669E)02 15000 4.418E)05

C.A.Gueymard

/SolarEnerg

y76(2004)423–453

449



335 9.537E)01 680 1.474E+00 1090 6.095E)01 1500 2.993E)01 2730 3.650E)02 16000 3.401E)05335.5 1.072E+00 681 1.464E+00 1091 6.065E)01 1501 2.975E)01 2735 3.629E)02 17000 2.666E)05336 7.396E)01 682 1.462E+00 1092 6.009E)01 1502 2.825E)01 2740 3.597E)02 18000 2.120E)05336.5 9.049E)01 683 1.459E+00 1093 5.811E)01 1503 2.783E)01 2745 3.584E)02 19000 1.705E)05337 7.526E)01 684 1.452E+00 1094 5.568E)01 1504 2.745E)01 2750 3.554E)02 20000 1.385E)05337.5 9.392E)01 685 1.463E+00 1095 5.835E)01 1505 2.742E)01 2755 3.502E)02 25000 5.699E)06338 8.864E)01 686 1.456E+00 1096 5.830E)01 1506 2.871E)01 2760 3.460E)02 30000 2.760E)06338.5 9.904E)01 687 1.474E+00 1097 5.839E)01 1507 2.916E)01 2765 3.465E)02 35000 1.488E)06339 9.808E)01 688 1.457E+00 1098 5.759E)01 1508 2.869E)01 2770 3.456E)02 40000 8.770E)07339.5 9.380E)01 689 1.454E+00 1099 5.892E)01 1509 2.910E)01 2775 3.425E)02 50000 3.608E)07340 1.133E+00 690 1.444E+00 1100 5.927E)01 1510 2.938E)01 2780 3.409E)02 60000 1.743E)07340.5 1.016E+00 691 1.433E+00 1101 5.848E)01 1511 2.926E)01 2785 3.387E)02 80000 5.539E)08341 9.640E)01 692 1.420E+00 1102 5.772E)01 1512 2.872E)01 2790 3.376E)02 100000 2.280E)08341.5 8.880E)01 693 1.422E+00 1103 5.885E)01 1513 2.865E)01 2795 3.353E)02 120000 1.102E)08342 1.060E+00 694 1.426E+00 1104 5.865E)01 1514 2.868E)01 2800 3.325E)02 150000 4.531E)09342.5 9.903E)01 695 1.426E+00 1105 5.863E)01 1515 2.882E)01 2805 3.302E)02 200000 1.441E)09343 1.084E+00 696 1.438E+00 1106 5.845E)01 1516 2.857E)01 2810 3.287E)02 250000 5.916E)10343.5 1.017E+00 697 1.432E+00 1107 5.824E)01 1517 2.871E)01 2815 3.263E)02 300000 2.779E)10344 7.664E)01 698 1.412E+00 1108 5.827E)01 1518 2.874E)01 2820 3.242E)02 400000 9.514E)11344.5 7.515E)01 699 1.431E+00 1109 5.821E)01 1519 2.867E)01 2825 3.218E)02 1000000 3.184E)12

k: Wavelength (nm); Ek: Irradiance (Wm�2 nm�1).a Also available as a text file from http://rredc.nrel.gov/solar/spectra/am0/special.html.

450

C.A.Gueymard

/SolarEnerg

y76(2004)423–453


References

Anderson, G.P. et al., 1993. MODTRAN2: suitability for

remote sensing. In: Kohnle, A., Miller, W.B. (Eds.), Proc.

Atmospheric Propagation and Remote Sensing II, vol. 1968.

SPIE, Orlando, pp. 514–525.

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