SERI/TR-33S-344 UC CATEGORY: UC-S9,61,62,63

DIRECT INSOLATION MODELS

RICHARD BIRD

ROLAND L. HULSTROM

JANUARY 1980

PREPARED UNDER TASK No. 3623.01

Solar Energy Research Institute 1536 Cole Boulevard Golden. Colorado 80401

A Division of Midwest Research Institute

Prepared for the U.S_ Department of Energy Contract No_ EG-77-C-01-4042

, '.

Printed in the United States of America Available from: National Technical Information Service U.S. Department of Commerce 5285 Port Royal Road Springfi e1dt VA 22161 Price:

Microfiche $3.00 Printed Copy $ 5.25

NOTICE

This report was prepared as an account of work sponsored by the United States Govern­ment. Neither the United States nor the United States Department of Energy, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process dis closed, or represents that its us e would not infringe privately owned rights.

S=�I TR-344

FOREWORD

This re port documents wo rk pe rformed by the SER I Energy Resource Assessment Branch for the Di vision of S olar Ene rgy Technology of the U . S . De pa rtment of Energy. The repo rt compa res seve ral sim ple direct insolation models with a rigorous solar t ransmission model and desc ribes an improved , s imple , d i rect insolation model .

Appro ved for:

S OLAR ENERGY RESEARCH INST ITUTE

for Res earch

i i i

Roland L . Huls t rom , Branch Chief Ene rgy Res ource Assessment

, \

S=�I TR-344

1 . 0

2 . 0

3 . 0

4 . 0

5 . 0

TABLE OF CONTENTS

Int roduction ••••••••••••••••••••••••••••••••••••••••••••••••••••••••

Descri ption of Models •••••••••••• . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 . 1 2 . 2 2 . 3 2 . 4 2 . 5 2 . 6 2 . 7 2 . 8 2 . 9 2 . 10

SOL TR.AN' Model •••••••••••••••••••••••••••••••••••••••••••••••••

Atwater and Ball Model •••••••••••••• . . . . . . . . . . . . . . . . . . . . . . . . . . Hoyt Model ••••••••••••••••••••••••••••••••••••••••••••••••••••

L acis and Hansen Model� •••••••••••••••••••••••••••••••••••••••

Macht a Model ••••••••••••••••••••••••••••••••••••••••••••••••••

AS RRAE Model ••••••••••••••••••••••••••••••••••••••••••••••••••

\V'att Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... . . . . . Majumdar Model ••••••••••••••••••••••••••••••••••••••••••••••••

Bi rd Models •••••••••••••••••••••••••••••••••••••••••••••••••••

Addit ional Models and Other Considerations ••••••••• ••• ••••••••

2 . 1 0 . 1 W ater Vapo r •••••••••••••••••••••••••••••••••••••••••••

2 . 10 . 2 Ozone •••••••••••••••••••••••••••••••••••••••••••••••••

2 . 1 0 . 3 Uniformly Mixed G ases •••••••••••••••••••••••••••••••••

2 • 1 0 . 4 Ai r Mas s ••••••••••••••••••••••••••••••••••••••••••••••

2 . 1 0 . 5 S imple T rans po rt E quation •••••••••••••••••••••••••••••

Model Compa'risons • •••••••••••••••• ••• . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Summary and C onclusions . . . . . ••••••••••••••••••••••••••••••••••••••••

Re fe rences ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••

Appendix. T abul ated Model Dat a ••••••••••••••••••••••••••••••••••••••••••

v

1

3

3 4 5 7 7 8 8

1 0 1 0 1 2 1 2 1 3 1 4 1 5 1 6

2 1

39

43

Al

S=�I IWI ________________________ _ -=T�R__=-3:!.:4�4 -� ��

LIST OF FIGURES

3-1 T ransmittance versus Secant of Solar Zenith Angle for Midlatitude Summe r Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3-2 T ransmittance ve rsus Secant of 'S olar Zenith Angle for Suba rctic Winter Model • • • • • • • • • • • • • • • • • . • . . • • • • • • • • • • • • • • • • • • 23

3-3 Ozone Abs orptance ve rsus S olar Zenith Angle for 0 . 3 1 em of Oz one ( MLS ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3-4 Ozone Abso rptance ve rsus S olar Zenith Angle for 0 . 45 em of Ozone (SA��) . . . . . . . . . .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3-5 Abso rptance ve rsus Solar Zenith Angle for 2 . 93 cm of Water Vapor (MLS ) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 27

3-6 Abso rptance ve rsus Solar Zenith Angle for 0 . 42 cm of Wate r Va por ( SAW) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 28

3-7 T ransmittance ve rsus Solar Zenith Angle for All Molecular Effects E xcept H20 Abso rption (MLS ) • • • • • • • • • • • • • • • • 29

3-8 Transmittance ve rsus Solar Zenith Angle for All Molecular Effects Except H20 Absorption ( SAW) . . . . . . . . . . . . . . . . 30

3-9 Aerosol T ransmittance ve rsus Solar Zenith Angle for 5-km Visibility Aerosol • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 3 1

3- 1 0 Ae rosol T ransmittance versus S olar Zenith Angle for 23-km Vis ibility Ae rosol • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 32

3-1 1 Solar I rradiance ve rsus S olar Zenith Angle, Vis ibility = 23 km (MLS ) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 34

3- 1 2 Solar I rradiance ve rsus Solar Zenith Angle , Visibility = 5 km (MLS ) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 35

3- 1 3 S olar Irradiance versus Solar Zenith Angle, Visibility = 23 km (SAW ) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • • 36

v i i

S;::�I ,�, ____________________________________________________ � ________ �T�R�-�3 �4 �4� - {..�

LIST OF TABLES

2-1 Sources of Data for Construct ion of Models • • • • • • • • • • • • • • • • • • • • • • • • • • 1 4

2-2 Comparisons o f Direct Normal Irradiance for Di fferent Forms o f the Trans port E quation U s ing Bird Models and SOLTRAN. . . . . . . . . . . . . . . . . . 1 7

2-3 Com parisons o f Direct Normal Irradiance for Different Forms of the Trans port Equation Using Bird Models and SOLTRAN . . . . . . . . . . . . . . . . . . 1 8

A-I Tabulated Data for the Midlatitude Summer Atmo s phere (V = 23 km) for S everal Models • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • A2

A-2 Tabulated Data for the Midlatitude Summer At mosphere (V = 5 km) for Several Models • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • A3

A-3 Tabulated Data for the Subarctic Winter Atmo s phere (V = 23 km) for Several Models • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • A4

A-4 Tabulated Data for t he Subarctic Winter At mos phere (V = 5 km) for S everal Models • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • AS

i x

TR-344

SECTION 1.0

INTRODUCTION

So lar ene rgy ( insolation) conversion systems a re different f rom systems based on othe r sources of ene rgy, because the ene rgy source is s ubject to va rying meteorological conditions . As a res ul t , rel iable insolation data a re requi red at each s ite of interest to design a solar ene rgy sys tem. Historical data have been collected by the Nat ional Weathe r Se rvice (NWS ) on a very l i mited bas is at 26 locations throughout the Uni ted S tates , and data a re currently being collected at 38 locations . Because of the small numbe r of s tations in this netwo rk and the variability of insolation, it is essential to have accu­rate models to predict insolation a t o the r locations . The accuracy of these models and e xpe rimental data affects the design, pe rfo rmance , and econo mics of sola r systems .

Nume rous s imple insolation models have been produced by d iffe rent investiga­to rs ove r the past half cent ury. The goal of these models has been to provide an uncompl i cated e s t imat ion of the available insolation. Thes e models , by ve ry diffe rent methods , account for the influence of each atmos phe ric con­s t ituent on sola r radiation. This , in turn , leads to confusion and questions of validity f rom pro s pective use rs .

This study compares several o f the mo re recent models o f the direct component of the insolation for clear sky conditions . The c ompa rison includes seven s imple model s and one rigorous model that is a bas is f o r dete rmining accu­racy. The results of the compa ri sons a re then used to formulate two s imple models of diffe ring compl e xity. The most useful formalisms of present models have been inco rpo rated into the new mode ls .

The c ri t e ria for evaluating and f o rmulating model s a re s implicity , accuracy , and the ability to use readily available meteorological dat a .

I n the future , a s imilar analys is of models for g lobal and diffuse insolation is planned . S im ple global and d if fuse models will be com pa red with a rigo rous model that uses Monte Ca rlo techniques . Add itional compa risons a re planned, with ve ry ca refully taken e xpe rimental data for both d i rect and diffuse inso­lation components . As many meteorological measurements as can reasonably be taken will be included with these data.

The goal o f this wo rk is to produce a well-documented global insolation model that includes the direct and diffuse clear sky insolation as well as cloud -and g round -reflected insolation. Thi s re po rt is the f i rst s t e p toward achieving that goal .

1

2

5=~1

!5::�1 !�l __________________________________________________________ T.R�-�3�4�4�

SECTION 2.0

DESCRIPTION OF MODELS

A rigorous atmospheric transmission model has served as a basis for comparing the accuracy of simple empirical models. The next few sections present a description of the rigorous model and the mathematical expressions that form the simplified models.

2.1 SOLTRAN MODEL

The rigorous model, called SOLTRAN, was constructed from the LOWTRAN [1-3] atmospheric transmission model produced by the Air Force Geophysics Laboratory and the extraterrestrial solar spectrum of Thekaekara [4].

The LOWTRAN model has evolved through a series of updates and continues to be improved with new data and computational capabilities. In this model, a lay­ered atmosphere is constructed between sea level and 100-km altitude by de­fining atmospheric parameters at 33 levels within the atmosphere. The actual layer heights at which atmospheric parameters are defined are: sea level (0.0 km) to 25-km altitude in 1.0-km intervals, 25 to 50 km in 5-km intervals, and at 70 km and 100 km, respectively. At each of these 33 altitudes the following quantities are defined: temperature, pressure, molecular density, �vater vapor density, ozone density, and aerosol extinction and absorption coefficients. A complete description of the standard model atmospheres incorporated in this code is given by McClatchey et al. [5J.

The absorption coefficients of water vapor, ozone, and the combined effects of the uniformlx mixed gases (C02, N20, CH4, CO, N2, and 02) ar! stored in the code at 5-cm 1 wavenumber i�tervals with a resoluti9n of 20 cm 1. The average transmittance over a 20-cm- interval as a result of molecular absorption is calculated by using a band absorption model. The band absorption model is based on recent laboratory measurements complemented by using available theo­retical molecular line constants in line-by-line transmittance calculations.

The effects of earth curvature and atmospheric refraction are included in this model. The results of earth curvature become important along paths that are at angles greater than 60° from the zenith, and refractive effects then dominate at zenith angles greater than 80°.

The scattering and absorption effects of atmospheric aerosols (dust, haze, and other suspended materials) are stored in the code in extinction and absorption coefficients as a function of wavelength. These coefficients were produced by a MIE code for defined part:i.cle size distributions and complex indices of refraction. Four aerosol models are available, representing rural, urban, maritime, and tropospheric conditions.

A user can choose any one of six standard atmospheric models incorporated in the code or can construct his own atmosphere by using a combination of para­meters from the standard models or by introducing radiosonde data.

3

S=�II*I __ ___ ____________ ____ _ -:!T�R__'-3::!.:!4:.::!_4

Some of the outputs of the LOWTRAN code include the total transmittance; the transmittance of H20, °3, and the uniformly mixed gases; and aerosol trans­mittance at each wavelength value specified. In the SOLTRAN model these transmittance values are multiplied by Thekaekara I s corresponding extrater­restrial solar irradiance at each wavelength of interest. A sum (integration) of the results of these individual multiplications is then performed over the spectral interval of interest to produce a value of the broadband terrestrial direct beam irradiance. The current version of SOLTRAN is limited to a spec­tral region between 0.25 and 3.125 ).1m because of a limited extraterrestrial solar spectral data file.

2.2 ATWATER AND BALL HODEL

A model for the direct solar insolation was published recently by Atwater and Ball [6]. This is a modification of an earlier model published by Atwater and Brown [7], which also includes a diffuse insolation formalism and the effect of clouds, neither of which are discussed here.

The equation for the direct insolation on a horizontal surface is given by:

where

(1)

IO = extraterrestrial solar irradiance,

Z = solar zenith angle,

TM = transmittance for all molecular effects except water vapor ab­sorption,

� = absorptance of water vapor,

TA = transmittance of aerosols.

The mathematical expressions for the transmittance, absorptance, and air mass M, are given by:

TM = 1.041 - 0.15[M (949 x 10-6 P + 0.051)]°·5 , * (2 )

(3)

*Atwater and Ball recently published an errata sheet in Solar Energy, Vol. 23, p. 275, changing the coefficient, 0.15, in Eq. 2 to 0.16. This change has not been incorporated in the results presented here.

4

55'11*1 ________________________ ...o:T::..ololR:....-3"""4'"-'-4

where

TA = exp ( -a M') ,

M = 35/ [(1224 cos2 Z) + 1]°·5 ,

M' = P • M/I013.

(4)

(5 )

Uw = amount of water vapor in a vertical path through the atmosphere (cm) ,

a = total broadband optical depth of the aerosol,

P = surface pressure (mb).

A brief discussion of the form of Eq. 1 is given in Paltridge and Platt [8]. The form of Eq. 2 is a slight variation ,of an empirical formula derived by Kastrov and discussed by Kondratyev [9]. Equation 3 is the form derived by McDonald [10], and Eq. 5 is a modification of a formula used by Rodgers for ozone and discussed by Paltridge and Platt [8].

Equation 4 is discussed in more detail by Atwater and Brown [7]. They used a MIE theory calculation to determine the value of a, which is not the approach that would be used in a simple, user-oriented model.

Results from using this model are presented in a later section with a compari­sons of other models.

2.3 HOYT MODEL

A model for solar global insolation that includes a model for the direct com­ponent is described by Hoyt [11]. The following equation is for the direct solar insolation on a horizontal surface:

5 I = IO(cos Z)(1 -

i�lai) TASTR (6 )

where ai represents the absorptance values for water vapor (i = 1), carbon dioxide (i = 2), ozone (i = 3), oxygen (i = 4), and aerosols (i == 5). The parameter TAS is the transmittance after aerosol scattering, and TR is the transmittance after pure air, or Rayleigh, scattering. The following formulas define these parameters:

0.110 (U' + 6.31 x 10-4)°.3 - 0.0121 , , w

a2 = 0.00235 (U� + 0.0129)°·26 - 7.5 x 10-4 ,

5

(7)

(8)

S=�II*I _________________________ ...:::T.::.::R-....; 3�4:....:...4

where

u w

, U c

t U o

M'

g(a)

(10)

M' as = O.OS[g(a)] , (ll )

M' TAS =[g(a)] , (12)

(13)

= pressure-corrected* precipitable water in the path (cm),

= pressure-corrected amount of carbon dioxide in the path [cm at standard temperature and pressure (STP) , U� = 126 cm for air mass 1.0],

= the amount of ozone in the path (cm at STP),

= pressure-corrected air mass,

= a tabulated function that is related to the angstrom tur­bidity coefficient a,

f( M') = a tabulated function of pressure-corrected air mass.

See Hoyt [11] for the tabular data.

Because the functions g(a) and f(M') are in tabular form rather than in empir­ical expressions, this model is not as flexible as it could be. The use of the tables often requires interpolation between points, and the range of air masses and turbidity coefficients listed in the tables is sometimes too limited. Results of this model will be presented in a later section.

*Hoyt calculates the pressure-corrected precipitable water by multiplying the total precipitable water from radiosonde data by 0.75 in a recent report. This correction has not been made in the analysis performed here.

6

S;55�1 '�I ________________ __________________________________________ T�R�-�3�4�4�

2.4 LACIS AND HANSEN MODEL

Lacis and Hansen [12] have described a formalism for total insolation. Since they do not separate the direct and diffuse components of the insolation, their formalism cannot be considered here. However, they derived useful empirical expressions for water vapor and ozone absorption. The water vapor absorptance is expressed by

aw = 2.9 Y [ (1 + 141.5 y) 0.635 + 5.925 y]-1 , (14)

where Y = MDw' with Dw being the precipitable water vapor (cm) in a vertical path.

The expression for ozone absorptivity in the Chappuis band is given by

vis a o = 0.02118 X (1 + 0.042 X + 0.000323 X2)-1

and for the ultraviolet band by

(15)

aUv = 1.082 X (1 + 138.6 X)-0.805 + 0.0658 X [1 + (103.6 X)3]-1 (16) o

where X = DoM with Do being the amount (cm) of ozone in a vertical path. The total ozone absorptivity is given by the sum

vis uv a = a + a o 0 0 (17)

Comparisons of the results of these expressions ,.;ith other models is shown in a later section.

2.5 MACHTA HODEL

A simple model of global insolation has been constructed by Machta [13] in the form of graphs and a worksheet. This model is an approximate method for cal­culating solar insolation at a given location without the use of mathematical expressions. A standard value of direct solar insolation is given as 887 W m-2, and a standard value of diffuse insolation is given as 142.5 W m-2 These standard values are then corrected by the use of graphs and the work­sheet. The corrections are made for station altitude, zenith angle, precipi­table water, .turbidity, and earth-sun distance. This method has greatest accuracy for very clear days and small zenith angles.

The graphs for making corrections are based on the very rigorous calculations of Braslau and Dave [14]. A few examples of calculations using this model will be illustrated in a later section.

7

S=�I' TR-344

2 . 6 AS HRAE HODEL

The American Society of Heat ing, Refrigeration and Air Condit ioning Engineers , ASHRAE, publ ishes a s imple model [ 1 5 , 1 6] f or es t imat ing solar insola t ion a t loca t ions in the Northern Hemisphere . This method represents the solar inso ­lat ion a t the earth ' s s urface , under clear sky condit ions , by us ing

where

I = A e- B s e c Z DN

A = the "apparent " extraterres trial solar radia t ion ,

B :: the "apparent" opt ical attenuation coef ficient ,

Z = the solar zenith angle.

( 1 8 )

An atmospheric clarity adjus tment , CN, called the clearnes s number , is then used to mul t iply the dire ct normal insolat ion cal culated us ing Eq. 1 8 . This clearnes s number corrects for var iations in transmit tance at a part icular location. Values of A , B, and C N are published by ASHRAE [ 1 5] as well as tables of solar insola t ion for the Nor thern Hemisphe re [1 6] resul t in g from applicat ion of these parameter value s .

A thorough dis cuss ion o f the origin o f the ASHRAE model is presented by Hulstrom [ 1 7] , and this informat ion will not be repeated here . It is suf f i­cient to say that Eq. 1 8 , commonly called Beer's Law , is strictly appl icable only f or mono chromatic radia t ion. If one takes the natural l o garithm of Eq . 1 8 , t he res ult is :

In A - B sec Z ( 1 9 )

A plot of this express ion on a In IDN versus sec Z axis sys t em results in a s traight line , with A the intercept of the lo garithmic axis and B the slope of the line . The vert ical intercept A occurs for the ext rapolation sec Z = 0 . 0 , which corresponds to zero air mas s or the e xtraterres trial ins olation .

In the model compar is ons given in a later sect ion the deviat ions of this model f rom more accurate result s are indicated . Huls t rom [ 1 7] points out that the clearness numbers published by AS HRAE corre ct only for water vapor var ia ­t ions . Moreove r , these are only average water vapor condit ions , and it is shown here in a later sect ion that var iat ions in aerosol attenuat ion are normally a much more s ignif icant factor.

2 . 7 WATT MODEL

A model for global ins olation has been cons tructed by Watt [ 1 8] , bas ed partly on the work of Moon [ 1 9]. The �xp re s s ion f or the dire ct normal insolat ion is

( 2 0 )

8

!s::�1 1�1 ______________________________________________________________ �T�R� -�3� 4� 4�

where the t rans mit t ance funct ions are Twa for water vapor absorpt ion, Ta for dry air s cat tering, To for ozone abs orpt ion, Tws for water vapor s catte�ing, TL for lower level aerosol absorp t ion and s cattering, and Tu for upper layer aerosol absorp t ion and s cattering. These t ransmit tance funct ions are defined by

= 0 . 9 3 - 0 . 0 33 log (Uw M2 )

-T M = 1 0 u 3 _ ,

TL = 0. 6 ( T 0 . 5 - 0 . 0 1 Uw - 0 . 0 3) ,

( 2 1)

( 2 2 )

( 2 3 )

( 2 4 )

( 2 5 )

( 2 6 )

( 2 7 )

( 28 )

The para meter Po is the sea level press ure; P is the pressure at the surface being cons idered; Uo and Uw are the amount of o zone and water vapor in cm in a vert ical path; TO . 5 is the ato mospheric turbidity at 0 . 5-]lm wavelength; lobs is undefined in Wat t ' s report; and 10 is the broadband extraterres trial ins o ­lation. The para meters Tu and TL are the upper and lower layer broadband t urbidity or opt ical dep th . TU can be taken from p lots in Wat t 's report for pas t years . The Hi are called path length modif iers by Wat t , and they serve the same purpose as air mass in the previous models. These path length modif iers are equal for solar zenith angles ( 70 ° and are equal to the secant of the solar zenith angle ( s ec Z ) . For solar zenith angles > 70 °, the path length modifier is def ined different ly for ea ch atmospheric cons t ituent according to the a l t itudes in the a t mosphere between which the cons t ituent is concentrated . A parameter Fz i is cal culated us ing the following express ion:

( 29 )

9

S=�I '*1 _____________________ ....::.;TR:.:....-...:::.. 34...:....:..4

where r is the earth I s radius (6.4 x 106 m) and the hi are the atmospheric altitudes (heights) between which the constituent is located. If a constitu­ent is concentrated between two altitudes, hI and h2, an F zl and F z2 are calculated corresponding to hI and h2' respectively. The values are then used in the following expression to obtain the total path length modifier:

h2 Fz2 - hI F zl M. = (30)

1 h2 - hI

The values of h used for the various constituents are:

ozone: hI = 20 km, h2 :: 40 km

dry air: hI :: ° km, h2 = 30 km

upper dust: hI = 15 km, h2 = 25 km

lower dust and water vapor: hI = ° km, h2 3 km .

When the value of h is equal to zero, the corresponding Fz can be set equal to 1.0, and Mi

= Fz2'

2.8 MAJUMDAR MODEL

A model for direct normal insolation has been constructed by Majumdar et al. [20]. This model is for clear sky conditions and minimal aerosol content, so that the effect of variable turbidity is not considered. A total of 161 sets of observations at three locations in India was used to arrive at the following regression equation:

IDN = 1331.0 (O.8644)(MP/I000)(0.8507)(UJM)0.25 (31)

where M is the air mass, P is the surface pressure, and Uw is the amount of water vapor in a vertical path.

Results generated from this model will be presented in a later section.

2.9 BIRD MODELS

As a result of comparing the simple models discussed in this section with the rigorous model (presented in a later section), the authors formulated two additional models. Where possible, these models used formalisms from the

10

S=::lI'.1 _____________________ -=-TR ..... -....... 34=:.,.4 -� ���

models previously presented. The expressions used were tuned to give the best least-squares fit to the SOLTRAN data. The first model used the following expression for direct normal insolation:

(32 )

where Tu is the transmittance of the uniformly mixed gases (C02 and O2), and the other parameters are the same as defined earlier. The 0.9662 factor was added because the spectral interval considered with SOLTRAN was from 0.3 to 3.0 �m.· The total ifradiance in the extraterrestrial solar spectrum in Zhis interval is 1307 W/m , whereas the Thekaekara solar constant of 1353 W/m is used in �ost of the other models. The factor of 0.9662 allows one to use 10 = 1353 W/m with the Bird �odels. If a higher value of this solar constant is desired (i.e., 1377 W/m ) , it can be used without changing Eq. 32. The transmittance and absorptance equations are

TR = exp [- 0.0903 (M') 0.84 (1.0 + M' - (M,)1.01) ]

To = 1.0 - 0.1611 Xo (1.0 + 139.48 Xo)-0.3035

( 2)-1 -0.002715 Xo 1.0 + 0.044 Xo + 0.0003 Xo

Tu = exp -0.0127 (M' )0.26 ,

aw = 2.4959 � [ (1.0 + 79.034 �) 0.6828 + 6.385 �J-1

LA = 0.2758 TA (0.38) + 0.35 TA(0.5)

M = [cos z + 0.15 (93.885 - Z)-1.25J-1

, (33)

(34)

(35)

(36)

(37)

(38)

(39)

where M'= tW/PO' Xo = UoM, � = UwM, Tu is the transmittance of the uniformly mixed gases, TA is the broadband atmospheric turbidity, and LA (0.38) and TA (0.5) are the atmospheric turbidity values that are measured on a regular basis by NWS at 0.38- and 0.5-�m wavelengths, respectively. If one of the turbidity values is not available, its value can be entered as a zero in Eq. 38. The values of T (0.38) and T (0.5) are obtained in practice with a turbidity meter that measures the total optical depth at each wavelength. The optical depth due to molecular scattering is then subtracted from the total

11

S=�I, �I _______________________ T=R::...-.=,.34.!....!.... 4

optical depth to obtain the turbidity (or aerosol optical depth) at each wavelength. Equation 39 is a form derived by Kasten [21]. The forms of Eqs. 34 and 36 are patterned after Lacis and Hansen (12], as shown in Eqs. 15 and 16. Some of the terms in the expression for ozone absorption used by Lacis and Hansen have been dropped in Eq. 34. This expression is still much too complicated when the relative importance of ozone is considered. The second line of Eq. 34 could be dropped without serious effeft�r The form of Eq. 33 can be simplified by removing the (l.0 + M' - (M')· ) term. This simplification provides very accurate results for Z ( 70°.

The second and simplest model is given by

(40 )

TM = 1.041 - 0.15 [M(9.368 'x 10-4 P + 0.051)]0.5 (41)

The expressions for � and TA are the same as Eqs. 36 and 37, respectively. Equation 40 was used by Atwater and Ball [6], and Eq. 41 is a slight variation of Kastrov as presented by Kondratyev [9]. The variable P is the surface pressure at the location being considered. This model will be shown to pro­vide results that are nearly as accurate as the more complex model with much less effort.

2.10 ADDITIONAL MODELS AND OTHER CONSIDERATIONS

This study is not a comprehensive comparison of simple direct insolation models. It is a comparison of the more recent models. An excellent compari­son of other models is presented by Davies and Hay [22].

For the comparison of different models it is useful to know the origin of the data used to formulate the models. An attempt will be made to trace the origins of the H20, °3, and uniformly mixed gas data used in the models described here. In addition, a discussion of air mass and the various forms of the transport equation for direct insolation will be presented.

2.10.1 Water Vapor

The LOWTRAN model is based on a band absorption model. The parameters in the band absorption model are based on comparisons with transmittance data taken by Burch et al. [23-3�1 and line-by-line transmittance calculations degraded in resolution to 20 cm • The contributors to the line data are too extensive to reference here, but are found in a report by McClatchey et al. [34].

Atwater and Ball used an empirical expression from HcDonald (10] based on old data taken by Fowle [35]. Fowle's data did not account for the weak absorp­tion bands near 0.7- and 0.8-�m wavelengths. Because of the poor documenta­tion of Fowle's data, McDonald could not claim an absolute accuracy greater than 30%.

1 2

5=�1 '

The ASHRAE model is based on work by Threlkeld. Huls trom explicates "Threlkeld determined the var iable amount of water vapor on a monthly bas is by a semiemp irical technique. He used meas urements of the broadband d irect beam ins olat ion [at Blue Hul l , Mas s . ; L incoln, Neb . ; and Madison , Wis . J in con­j unct ion with the Moon cal culat ion routine , to derive indirectly the corre­spondin g amount of precipitable water vapor" [1 7J.

Hoyt and also Lacis and Hansen used water vapor from Yamamoto [36 ]. Lacis and Hansen explain , "Absorpt ion by major water vapor bands has been measured at low spect ral resolution by Howard et ale (1 956 ) . Yamamoto (1 962 ) we ighted these absorp t ivit ies with the solar flux and summed them , including est imates for the weak absorp t ion bands near 0 . 7 and 0 . 8 Um which were not measured by Howard et ale, to obtain the total abs orp t ion as a funct ion of water vapor amount" [1 2 ]. The reference to Howard et al. is referenced here as [37].

Watt used an expres s ion for wat er vapor that he derived empirically from data in Chapter 1 6 of Valley [38 ]. He then compared this expression with measured data from several loca t ions and adj us ted the coef f icients to obtain the bes t a greement .

Ma chta bas ed his model on cal culat ions performed by Braslau and Dave [14 ] with a rigorous rad ia t ive t ransfer code . Bras lau and Dave based their cal culat ions on the database used by LOWTRAN. However , they used a mathemat ical formalism different from LOWTRAN for band absorp t ion.

2 • 10 . 2 Oz one

The LOWTRAN and t1achta models used the same original data sour ces for all the molecular ,absorbers . The references given in the previous sect ion for water vapor are the same for o zone .

A twater and Ball did not cons ider ozone separately but used a general formula that included all molecular effects except water vapor absorption.

The ASHRAE and Wat t model s are based on the ozone data used by Moon [19 ]. Moon , in turn, used data measured by Wulf [39] in the Chap puis band (0 . 5 t o 0 �7 um) and data by Lauchli [40 ] in the Hartley-Huggins band below 0 . 35 Urn wavelength.

Wat t inte grated the s pe ct ral data given by Moon to obtain broadband ozone absorption. He then modif ied an express ion that agreed with these res ults to give the bes t agreement with broadband total t ransmit tance data from other sources .

Hoyt used ozone data from Manabe and Strickler [4 1 ] to derive an empirical formula . Manabe and S trickler based the ir results on experimental data from V igroux [42 ] and Inn and Tanaka [4 3]. La cis and Hansen apparently based their empirical formula for ozone on the same original data sources that Hoyt used . They point out that the data for wavelengths greater than 0 . 34 �m were given for 1 8 °C . They used the data at -44°C for shorter wavelengths and reduced the longer wavelength data by 25% to compensate for the difference in t emperature. They produced s eparate express ions appropr iate for the ultraviolet and vis ible absorp t ion data , respect ively.

1 3

55'1 '*' _______________________ --=T..::.R-....:3::..: 4�4

2 . 1 0 . 3 Uniformly Mixed Gases

The uniformly mixed gases are CO2 and 02 . LO WTRAN and Machta are based on the same original data s ources given in the section about water vapor.

The AS HRA E and Wat t models CO2 and 0 3 in insolation abso rp t ion .

are based on Moon ' s model . but might have included

Moon did not cons ider their effect w ith H2 0

Atwater and Ball based their model on an emp irical formula that included all molecular effects except water vapor absorp t ion according to Kondratyev [9 ]. This formula was based originally on Fowle ' s data for the constant gas es .

Hoyt used Yamamoto ' s oxy gen absorp t ion data , Howard et ale [44 ]. The carbon dioxide et al. [45 J.

which in turn were taken from data were taken from Burch

A summary of the data sources used by various modelers is condensed in Table 2-1 .

Table 2 -1 . SOURCES OF DAT A FOR CONSTRUCT ION OF MODELS

}fodel H2O

SOLTRAN Burch et ale (many) Line-by-l1ne data

Atwater and Ball Fowle (McDonald)

Hoyt Howard et al. (1955) (Yamamoto)

Watt Valley & Modifications

Lacis and Hansen Howard et al. (1955) (Yamamoto)

ASHRAE

Machta

Threlkeld (Best fit 3 locations)

Burch et al. (many) Line-by-line data (Dave)

Burch et al. (many) Line-by-line data

ICastrov

Vigroux Inn and Tanaka (Manabe & Strickler)

Wulf Lauchli (Moon,)

Vigroux Inn and Tanaka (Howard et a1. 1961 Handbook)

Wulf Lauchl1 (Moon)

Burch et al. (many) Line-by-line data (Dave)

1 4

Burch et al. (many) Line-by-line data

Fowle (Kastrov)

Burch et al. (1960) Howard et al. (1955)

Moon

Moon

Burch et al. (many) Line-by-line data (Dave)

S=::!al:.' ________________________ --'T:::..:; R,:...-.::::.,.34...:.....:....4 -� ���

2 . 1 0 .4 Air Mass

The ai r mass is a coefficient that accounts for the increased path length thro ugh which light rays must pass in the atmos phere when the s un is not directly overhead . When the s un is directly overhead , the air mass is 1 .0 . The formal definition of air mass is given by Kondratyev [9] as

M � .)("�

PdS/.)("�

pdz (42 )

where dz is an increment in the vert ical direction; ds is an increment along a s lanted path; and p the dens ity of air, or whatever component of the air that is being considered . This defini tion implies that differences in alt i t ude between different s urface locations mus t be accounted f or by some means other than air mas s . In calculating atmos pheric attenuation over a slant path , for example , the optical de pth for a vertical path is multiplied by the air mas s to obtain the total optical de pth. The vert ical optical depth incl udes the effect of the alti t ude at which one is working. S o me authors inc l ude the beginning altitude in the air mas s and use the optical depth from sea level , or 1 0 1 3 mb press ure . This is called the absol ute, or pres s ure-corrected , air mass , given by

(43 )

where Po = 1 0 13 mb.

Kondratyev [9 ] z enith angle. using

s ummarizes the methods of calc ulation for different ranges of For zenith angles < 60 ° , s ufficient acc uracy can be obtained

M = sec Z ( 44 )

where Z is the zenith angle . For 6 0 0� Z � 80 ° , the effect of earth c urva t ure becomes important . Geometric considerations give

{ 2 2 } 1 /2 M = ( r/H) cos Z + 2 ( r/H ) + 1 - ( r/H ) cos Z

where r is the earth's rad i us and H the s cale height defined by

H

1 5

(45 )

(46 )

S5�1 1*1 _________________________ T=.;:R::..-.,;;:. 3..:.,.44.;..

The constant Po is the surface level density. For air or the uniformly mixed gases, H = PO/ (pog), where g is the acceleration due to gravity and Po is the surface level pressure.

For Z > 800, the effects of refractive index become important. The correct value of air mass in this region can be found in tables (Kondratyev, for example) or can be calculated with approximate expressions. An expression that this author has found to be correct to within 1% for Z < 890 is defined by Kasten [21] to be

M = {cos Z + 0.15 (93.885 - Z) -1.253} -1 (47) �

This expression was used in the results given in this report (unless otherwise noted), and is called the relative air mass by Kasten.

2.10.5 Simple Transport Equation

Several forms of the transport equation have been used in the models described here. Some possible forms of the equation are:

12

13

II = 10 TR To T u Tw TA

= 10 [TR

= 10 [TR

14 = 10

To

To

T u - a ] T w A

- aw - a ] u TA

[TM - awl TA

(48)

(49)

(50 )

(51)

where T is the transmittance due to Rayleigh scattering, To is the transmit­tance 0' ozone, Tu is the transmittance of the uniformly mixed gases CO2 and 02' Tw and � are the transmittance and absorptance of water vapor, TA is the t.ransmittance of the aerosol, and TM is the transmittance of all molecular effects except water vapor absorption.

Tables 2-2 and 2-3 were constructed using all forms of the transport equation (Eqs. 48-51) with Bird Models and the results from SOLTRAN. Two standard atmospheres that are built into SOLTRAN were used: the midlatitude summer (MLS) and the subarctic winter (SAW) models with sea level visibilities of 23 and 5 km.

Based on the results in Tables 2-2 and 2-3, it appears that Eq. 48 provides the closest agreement with SOLTRAN. The very simple form of Eq. 50 provides results that are comparable to Eq. 48. A theoretical basis for selecting any one of these forms of the transport equation as the best has not been estab­lished by the authors. However, one assumption implicit in Eq. 48 is that the attenuation by each constituent is independent of every other constituent. In other words, the transmittance measured in pure materials can be combined in the form of Eq. 48 to produce the transmittance through a mixture of

1 6

5='1'� ,, ______ ----______ ____ --=..:TR�- ..::!..:. 34::;,:;:.. 4

Table 2-2 . COMPARIS ONS OF DIRECT NORMAL IRRADIANCE FOR DIFFERENT FORMS OF THE TRANSPORT EQUATION USING BIRD MODELS AND SOLTRAN

Zenith Angle Model II 12 13 14 SOLTRAN ( de g) Atmosphere (W/m2 ) (W/m2 ) (W/m2 ) ( W/m2 ) (W/m2 )

0 . 0 MLS 8 27 . 1 8 1 2 . 5 8 1 1 . 2 8 1 6 . 6 833 . 5

2 0 . 0 V = 2 3 kIn 8 1 1 . 0 7 95 . 7 7 94 . 2 800 . 1

30 . 0 7 8 9 . 0 7 7 2 . 8 77 1 . 3 7 77 . 8

40 . 0 754 . 5 7 36 . 9 7 35 . 2 742 . 8 7 5 6 . 6

5 0 . 0 7 02 . 1 682 . 3 680 . 4 6 9 0 . 0

6 0 . 0 6 2 1 . 3 598 . 5 596 . 2 609 . 1 6 1 7 . 7

7 0 . 0 4 9 0 . 2 4 6 3 . 3 460 . 6 4 7 8 . 4

7 5 . 0 392 . 3 3 63 . 5 3 6 0. 5 380 . 5 386 . 3

8 0 .0 2 6 1 . 7 233 . 0 2 2 9 . 9 2 48 . 7 25 8 . 9

85 . 0 1 0 1 . 5 8 1 . 8 7 9 . 5 84 . 3 102 . 8

0 . 0 }ILS 545 . 8 536 . 2 535 . 3 . 5 38 . 9 530 . 6

20 . 0 V = 5 km 5 2 2 . 4 5 1 2 . 6 5 11 . 7 5 15 . 4

30 . 0 4 9 1 . 4 4 8 1 . 3 480 . 3 484 . 4

40 . 0 444 . 4 434 . 0 433 . 0 437 . 5

50 . 0 377 . 4 366 . 8 365 . 8 370 . 9

6 0 . 0 2 85 . 1 2 7 4 . 6 2 73 . 5 2 7 9 . 5 2 7 0 . 3

7 0 . 0 1 63 . 8 1 54 . 8 1 5 3 . 8 1 5 9 . 8

7 5 . 0 96 . 2 8 9 . 2 88 . 4 9 3 . 4 9 7 . 2

80 . 0 35 . 8 3 1 . 9 3 1 . 4 34 . 0 42 . 4

8 5 . 0 3 . 1 2 . 5 2 . 4 2 . 6 7 . 0

1 7

Table 2-3. COMPARISONS OF DIRECT NORMAL IRRADIANCE FOR DIFFERENT FORMS OF THE TRANSPO RT EQUATION USING BIRD MODELS AND SOLTRAN

Zenith Angle Model II 12 13 14 SOLTRAN (deg) Atmosphere (W/m2) (W/m2) (W/m2) (W/m2) (W/m2)

0.0 SAW 866.0 856.5 855.1 865.5 881.9

20.0 V == 23 km 849.4 839.5 838.0 848.9

30.0 826.8 816.3 814.7 826.4

40.0 791.2 779.7 778.0 791.1 804.3

50.0 737.2 724.0 722.0 737.5

60.0 653.0 637.9 635.6 654.7 662.5

70.0 515.9 498.0 495.1 519.6

75.0 413.0 393.7 390.5 417.2 423.3

80.0 275.3 255.9 252.6 277 .3 289.0

85.0 106.2 92.6 90.2 98.8 120.0

0.0 SAW 571.5 565.2 564.3 571.2 568.5

20.0 V = 5 km 547.2 540.8 539.8 546.9

30.0 514.9 508.3 507.4 514.7

40.0 466.0 459.2 458.2 465.9 461.1

50.0 396.2 389.2 388.1 396.4

60.0 299.6 292.7 291.6 300.4 297.8

70.0 172.3 166.3 165.4 173.6

75.0 101.3 9 6.6 9 5.8 102.3 112.0

80.0 37.6 35.0 34.5 37.9 50.5

85.0 3.3 2.8 2.8 3.0 9.0

18

TR-344

materials . One obvio us s it ua t ion that violates this ass umpt ion is when near­complete absorp t ion in a s ingle const ituent occ urs within the spectral band being cons idered . If one of the o ther cons t it uents absorbs in the same spec­tral locat ion , over attenua t ion will occur in the final res ults . The form of Eqs. 49 and 50 make this s it uat ion even worse .

1 9

sail

20

S=�I TR-344

SECTION 3.0

MODEL COMPARISONS

Where possible, each of the models was programmed on a computer to produce data for comparison. Parts of the Hoyt model were generated with a pro­grammable hand calculator, and data from the Machta model were generated by using the worksheet format presented with the model.

General transmittance data for the midlatitude summer (MLS) and the subarctic winter (SAW) atmospheric models have been generated with the SOLTRAN code. These atmospheric models are two of the standard atmospheres defined in SOLTRAN. They were chosen primarily because the amounts of ozone and water vapor defined in them represent extremes that could be encountered in the United States. The Rayleigh scattering due to molecules and the absorption of the uniformly mixed gases (C02 and 02) are relatively constant in these models. The aerosol conditions can be defined independently of the atmos­pheric model. As was mentioned previously, the results from the SOLTRAN code are for a spectral interval between 0.3 to 3.0�. If the calculations would have been made from 0.25 to 10.0 �, the results from SOLTRAN for individual atmospheric constituents could change. However, the total transmittance of all constituents should not change appreciably « 1%).

The amounts of ozone and water vapor in the SAW model are 0.45 cm of ozone and 0.42 cm of water vapor. The amounts in the MLS model are 0.31 cm of ozone and 2.93 cm of water vapor. Figure 3-1 presents a plot of the broadband (0.3 to 3. ° �) transmittance versus sec Z for all of the atmospheric components in the MLS model. Figure 3-2 presents the same type of results for the SAW model atmosphere. Both figures contain the results for a 23-km visibility aerosol at sea level. The aerosol used in this paper is the one defined in the LOWTRAN 3 version, and is representative of a continental or rural aerosol.

Figures 3-1 and 3-2 show the relative importance of each atmospheric component as an attenuater of broadband radiation (0.3-3.0 �). CO2 and 02 are the least important elements, and they are omitted from some models. The next element exhibiting increased attenuation is 03' followed by H20. The flat­tening of the curve for H20 in Fig. 3-1 with increasing zenith angle suggests that the H20 absorption bands are approaching saturation. Molecular scatter­ing (Rayleigh scattering) dominates total molecular absorption at large zenith angles and has a greater effect than most individual molecular species at all zenith angles. The one exception to this statement appears to be H20 absorp­tion for high concentrations of H20 and for air masses < 2. The most signif­icant attenuator at nearly all zenith angles is the aerosol.

An aerosol that produces a 23-km meteorological range at sea level is consid­ered to produce a relatively clear atmosphere. At higher surface altitudes and remote locations, it is not uncommon during winter months to observe meteorological ranges greater than 60 lan, which are extremely clear condi­tions. The data presented in Figs. 3-1 and 3-2 suggest that aerosol attenua­tion could be the most important attenuator at most locations throughout the United States. Unfortunately, it is also the component that is the most

2 1

S=�I �1 __________________ ____________________________ =TR �-�3� 44

1.0 0.9

0.8

0.6

0.5

CD g 0.4 tIS --

·S � 0.3 e ...

0.2

0.11...---'-_..&...---'-_-'--......... �..I.-__ ....I o 2 4 6 8 10 12

sec�

Figure 3-1. Transmittance versus Secant of Solar Zenith Angle for Midlatitude Summer Model

22

S=�II

CD U c tV -

-.-

E U) c 12 I-

0.5

0.4

0.3

0.2

CO2 + O2

�---=====03 H20

0.1��_��_-=--��� __ ..... o

Figure 3-2. Transmittance versus Secant of Solar Zenith Angle for Subarctic Winter Model

23

TR-344

S=�I '*1 ________________________ T _R-_3 _4_4

diffi c ult to meas ure and hence the least defined . It sho uld be emphas i ze d that these conc l usions are f o r broadband ( thermal) d irect insolation , and that the s i t ua t ion will change s ignificantly as the bandwidth is f urther res t ricted or global insolation is considered .

The previo us s ec tion noted that the ASHRAE model a s s umes a plot of the total t ransmittance shown in Figs . 3-1 and 3-2 will s cribe a s t raight line . The s lope of this line provides the optical depth. An examination of Figs . 3-1 and 3-2 demons trates that this ass umption is reasonable o ver a limited range of zenith angles . If the plot were o f irradiance ver s us sec Z , the vertical intercept at sec Z = 0 would provide the extra te rres trial irradiance , which i s us ually too low.

Figures 3-3 and 3-4 present 03 absorpt ion data for five of the models de­scribed earlier . Figure 3-3 is for 0 . 3 1 cm of 03 ( MLS ) , and Fig . 3-4 is for 0 . 45 cm of 03 ( SAW) . The models produce s ignificantly different res ul t s when compared in this manner . However , the differences are minor when the effec­t iveness of 03 is acco unted for. The t riangular data points are a res ul t o f performing a least sq uares fit t o the S OLTRAN data with the e quations of Lacis and Hansen (Bird model ) . The minor deviat ions of the t riangles f rom the SOLTRk� data are a res ult of attempting to fit a s imple expression to various amo unts of 03 '

Figures 3-5 and 3-6 present model compar isons of H20 absorpt ion for the two standard a tmospheres being cons idered. S ince H20 absorption plays a s ignifi­cant role in transmission cal c ula tions , the differences b etween the models sho uld be not iceable in the total transmis sion.

Fig ures 3-7 and 3-8 present plots o f transmittance vers us solar zenith angle for all molec ular effects except H20 absorption for the SAW and MLS atmos­pheric models , respectively . Some of the models did not readily lend them­selves to this particular cal c ulation and are not inc l uded . The s urprise abo ut these data is the acc uracy of the s imple expres s ion in the Atwater model.

Fig ures 3-9 and 3-10 illus t rate a comparison of aerosol t ransmittance for the MLS and SAW a tmospheric models with sea level vis ibilities of 5 and 23 km , respectively . In most cases , aerosol attenuation is independent of the a t mo­spheric model ; b ut the Watt model for aerosols is d ependent on the amo unt of H2 0 .

Hoyt ' s model provides strong agreement with SOLTRAN, b ut its tabular form is not as easily used as empirical formulas . range o f t urbidity coeffic ient s t o inc l ude data are f or aerosol s cat tering only , and aerosol absorption in th� Hoyt model.

The table covers an ins uf ficient a 5 -km visibility aerosol. Hoyt ' s there is an additional factor for

The val ue of the upper layer t urbidity Tu used in Watt ' s model was taken from historical plots that he produced . The val ue used , T = 0 . 0 2 , was an approx­imate average of the his torical data. The rest of t�e parameter values for this model were taken directly from SOLTRAN.

2 4

S=�·I I.I _______________________ TR_-_34_ 4 -� ���

0.10.----------------------,

0.09

0.08

0.07

Q) 0.06 (,) c ta

-e-0.05 o (I)

J:2

< 0.04

0.03

0.02

0.01

Lacis & Hansen

ASird

O ____ � ____ � __ � ____ � __ � ____ � __ � ____ � __ � o 10 20 30 40 50 60

Sola� Zenith Angle (degrees) 70 80 90

Figure 3-3. Ozone Absorptanee versus Solar Zenith Angle for 0.31 em of Ozone (MLS)

25

TR-344 S=�I :.J ----------------------­-� ��

G,) u

0.11.-----------------------,

0.10

0.09

0.07 A Bird

lacfs & Hansen lI--

; 0.06 -e-o � 0.05 «

'=-------::: 0.03 1-======�-=;;;:

0.02:h_---6-...... -----

0.01

O� __ � __ � ____ � __ � ____ � __ � ____ � __ � __ � o 10 20 30 40 50 90

Solar Zenith Angle (degrees)

Figure 3-4. Ozone Abso rptanee versus Solar Zenith Angle for 0.45 em of Ozone (SAW)

26

S=�I 1.11 ____________ _____ _______ T _R_-_34_4 -� ��

CD u c ta -a. .. 0 en

..c:2 <C

0.7

0.6

0.5

0.4

0.3

0.2 .

0.1

0

A Bird

10 20 30 40 50 60 70 80 90

Solar Zenith Angle (Degrees)

Figure 3-5. Absorptance versus Solar Zenith Angle for-2:93em of Water Vapor (MlS)

27

S=�I TR-344

0.16.------------------------,

CD (J

0.15

0.14

0.13

0.12

; 0.11 -Q. ... o . .a 0.10 ct

0.09

'0.07

... Bird

0.06 b=::::::::::::�---

0.05�--�--------�----------------------� ___ o 10 20 30 .40 50 60

Solar Zenith Angle (degrees) 70 80 90

Figure 3N6. Absorptanee versus Solar Zenith Angle for 0.42 em of Water Vapor (SAW)

28

5=�1 TR-344

Q) (,) r: ca --E en r: e

....

1.0 r-----------------------------------------�

0.9 r====�

0.8 ,:::--------

0.7

0.6

0.5

0.4

0.3 H20 - 2.93cm 03 - 3.1 mm

0.2

0.1

O� __ � ____ � __ � ____ � __ � ____ � __ � ____ � __ � o 10 20 30 40 50 60 70

Solar Zenith Angle (degrees) 80 90

Figure 3-7. Transmittance versus Solar Zenith Ang le for All Molecular Effects Except for H20 Absorption (MlS)

29

5='. :=}I __ ________ �--_ ______ ___ TR_- _3 4_4

1.0r-----------------------------------------�

CD U C ca

0.7

= 'E 0.5 (I) c e I- 0.4

0.3

0.2

0.1

H20- O·4�cm 03 - 4.5mm

O� __ � __ � ____ � __ � __ � ____ � __ � __ � __ _J o 10 20 30 40 50 60 70

Solar Zenith Angle (degrees) 80 90

Figure 3-8. Transmittance versus Zenith Angle for All Molecular Effects Except H20 Absorption (SAW)

30

S=�I i*I ___ � ________________ TR_-_344

CD u c CI:S -:: E en c !l

I-

1.0

, 0.9

0.8 A Bird

0.7

0.6

0.5'

0.4

, 0.3

0.2

0.1

0 10 20 30 40 50 60 70 80 90

S,?lar Zenith Angle (Degrees)

Figure 3-9. ��rosol Transmittance versus Solar Zenith Angle for S-km Visibility Aerosol

31

S=�I

CD (.) c CD --e CI) c e �

1 .0

0.9

0.8

0.7

0.6

0.5-

A Bird 0.4

0.3 Soltran

0�2

0.1

10 20 30 40 50 60 70 80 90

Solar Zenith Angle ( Degre�s)

Figu re 3-1 0. Aerosol Transmittance versus Solar Zeni th Angle for 23- km Visibility Aerosol

.

32

TR-344

S=�I TR-344

Figures 3-1 1 thro ugh 3-1 3 ill us t rate the total terrestrial s olar irradiance as a f unction of solar zenith angle for s everal models under different atmos­pheric conditions . The differences between some of the models are s ignificant . However , the difference s ill us t rated here are dominated by the aerosol attenuation, and the d if ferences d ue to molecular effects are not obvio us . If a muc h clearer atmosphere were modeled or a more res tricted bandwidth were used , the difference in molecular effects would be more evident .

In the res ul t s given for the Atwater model , the broadband o pt ical depth for the aerosol was taken from the Bird mode l . This causes close agreement with the SOLTRAN res ul t s , b ut Figs . 3-7 and 3-8 show that the b ulk of the molecular attenuation in this model agrees very well with SOLTRAN. Atwater ' s H20 ab­sorption deviates s omewhat from SOLTRAN res ults .

The res ults for Bird shown in Figs . 3-1 1 , 3-1 2 , and 3-l3 used Eq . 49 as the transport eq uat ion.

Because of the diffic ul t y of considering aerosol attenuation and Rayleigh scattering with Hoyt ' s model , it is inc l uded only in Fig. 3-12 and gives val ues that are lower than the SOLTRAN res ul t s over the applicable region.

Machta ' s model agrees with SOLTRAN within ±-5% to 6 0 ° zenith angle . It is primarily l imited to clear air condit ions and zenith angles less than 60° . The val ues shown at 70° zenith angle are beginning to deviate somewhat .

The Maj umdar model res ul ts have been g iven for the MLS a tmospheric model with V = 23 km ( see Fig. 3-1 1 ) . The Maj umdar model is for low t urbidity c onditions and has no provision for varying the t urbidity . It is evident from Fig. 3-1 1 that the t urbid i ty res ul ting from a s ea level visibility of 23 km is too large for this model . The model is very s imple , and it co uld be q uite acc urate if provisions were made to vary the aerosol a ttenuation.

Appendix A presents tabular data for each a ttenua tion element for most o f the models . Direct normal irradiance for the Bird model i s given in Tables 2-2 and 2-3 for the same atmospheric conditions modeled in Appendix A.

This comparison and eval uation of exis ting s implified models for calculating the direct solar beam energy c onsidered s ix models - Hoyt , Wat t , Lacis and Hansen, Atwater and Ball , Machta, and Maj umdar . Ideally , s uch models sho uld be c ompared according to the attenuation of each atmospheric cons tituent . By doing this , differences in cal c ulating the total broadband direct solar energy can be specifically associated with differences in how they calculate at tenuation arising from each cons tituent . However , this was impos s ible because of the variety of techniques used by the models . For example , some models considered all molecular attenuation processes in a single express ion , making it imposs ible to distinguish attenuation from speci f ic molec ular cons t i t uents . The s pecific c omparisons performed considered the following :

• absorptance d ue t o 03 ( Lacis and Hansen; Hoyt ; Wat t ) ,

• absorptance d ue to water vapor (Lacis and Hansen; Hoy t ; Watt ; Mc Donald) ,

3 3

S=�I t: � ____________________ �TR"'"_-�34_4

I

1 000 1&::=======-___ _

-N E � -

Q) u

. :; 100 =a f! ...

Maehta

.A Bird

• Maehta

V= 23 km Uw=0. 42 em Uo· 0.45 em

Majumdar

�-- Watt

�-- Soltran

�-- Atwater

1 0�--�--�--�----�--�--�--�----�� o 1 0 20 30 40 50 60 70 80 Solar Zenith Angle (Degrees)

Figure 3-1 1 . Solar Irradianee versus Solar Zenith Angle, Visibility = 23 km (M LS)

34

90

S=�I '

-COl

E � -

� u c

.! "C ftI ... ... -... ftI '0 (J)

1 000

1 00

.& Bird

V=5 km Uw =2.93 em Uo= 0.31 em

1 0�---�--�--�----�--�--�--�----�� o 1 0 20 30 40 50 60 70

Solar Zenith Angle (Deg rees)

80 90

Figure 3-1 2. Solar I rradianee versus Solar Zenith Angle, Visibili ty = 5 km (MLS)

35

TR- 34 4

TR-344 5=�1 IWI -------------------------­

-� ��

1 000

-N

E � -Q) u

1 00 c .! -0 as .. .. -.. as '0 (J)

o 1 0

A Bird

• Machta

V = 23 km : Uw = O.42 cm Uo = O.45 cm

30 40 50 60 70

Solar Zenith Angle (Deg rees)

80

Soltran

"* Atwater

90

Fig u re 3- 1 3 . Solar Irradiance versus Sola r Zenith Ang le, Visibi l ity = 23 km (SAW)

36

S5�1 '*1 ________________ � ______ ____'T_R-_3_4_4

• the atmospheric transmittance due to all molecular processes except water vapor absorption ( Atwater; Wat t ) ,

• the atmospheric transmittance due to aerosols ( Hoyt ; Wat t ) ,

• the direct solar beam irradiance versus s olar zenith angle (Machta; Hoyt ; Maj umdar; Watt ; Atwater ) .

In genera l , two sets of atmospheric conditions were considered : midlatitude summer ( ML S ) and s ubarctic winter ( SAW) . The MLS c onditions are characterized by a precipitation water vapor of 2 . 9 3 cm (high) and an ozone . amoun.t of 0 . 31 cm ( low) . The SAW conditions are distinguished by a water vapor of only 0 . 42 cm ( low) , and an ozone amount o f 0 . 4 5 cm (high) . Within these conditions , two sets of atmospheric aerosol conditions were studied : clear ( visual range = 23 km at sea level) and turbid ( visual range = 5 km at sea level) . By using these models and conditions , a reasonable range o f atmospheric s tates was considered.

3 7

38

!s::�1 ,�, ______________________________________________________________ �T�R�-�3�4�4�

SECTION 4 . 0

SUMMARY AND CONCLUSIONS

The recently developed , rigorous , spectral solar radiation transport model ( SOLTRAN) was modif ied to have the capability of calculating the broadband ( thermal solar energy) direct solar beam irradiance. Such energy is utilized by solar thermal concentrator devices . The modifications to SOLTRAN allow the prediction of the broadband solar irradiance for various atmospheric condi­tions and for various slant paths ( relative air mass ) through the atmos­phere. The atmospheric constituents considered are carbon dioxide ( C02 ) , oxygen ( 02 ) ' o zone ( 03 ) ' water vapor ( H20 ) , aerosols , and the molecular s cattering (Raylei'gh) . This modified version of S OLTRAN can be utilized to generate , the intensi ty of the direct solar beam versus time of day for various locations and atmospheric conditions . Such information is crucial to the de­s ign and performance analyses of solar concentrator sys tems and central re­ceiver systems .

After having developed the broadband-thermal version of SOLTRAN, it was then used to perform the following investigations and analyses :

• definition of the relative significance of the various atmospheric constituents to the attenuation-transmittance of the direct solar beam energy ;

• comparison and evaluation of simplified models/ algorithms ;

• development of an improved , s implified model for solar energy .

The broadband SOLTRAN calculation delineated the relative significance of the various atmospheric constituents in the transmittance of direct solar beam energy . Ae rosols appear to dominate the attenuation for a reasonable range of atmospheric conditions . Molecular scat tering (Rayleigh) is next in impor­tance , followed by water vapor absorption. These three attenuation pro­cesses s-aerosol scattering , molecular s cattering , and water vapor absorption­nearly completely determine the transmittance of the atmosphere to direc t solar energy on a clear day. Attenuation caused by CO2 , O2 , and 03 is mino r . Because aerosols and water vapor are so important in determining the available direct solar beam energy, one needs high-quality measurements of their geographic and temporal characteris tic s . In the absence o f actual measurements of the direct beam, s uch measurements could be used (with a model like SOLTRAN) to assess the availability and character of the direct solar beam energy . The SERI Energy Resource Asses sment Branch will determine the availability of the aerosol ( turbidity) and the water vapor measurements database , their quality , their applicability to assessing direct solar beam energy , and whether improved ins tnnnentation and techniques are required to meet the needs of solar energy applications .

The comparisons of the ozone absorptance revealed significant differences between the s implified models and S OLTRAN. The magnitude of the differences is a function of solar zenith angle and amount of ozone . In general , S OLTRAN predicts a lower absorptance due to ozone than the Hoyt , Watt , and Lacis and Hansen models . The total range bf the differences is determined by the Hoyt

3 9

S=�I I*I __________________________ �T.!;.!.R-.....:3::....4�4

( high) and S OLTRAN ( low) models , being approximately 30% to 50% in absorp­tan�e. The Wat t and the Lacis and Hansen models appear to give q uite s imilar res ults , which fall between the Hoyt and S OLTRAN resul t s . Although the 30% to 50% differences are certainly significant , they are not considered to be a s ignificant source of differences in calculating the total broadband direct i rradiance because the contribution of o zone to the total broadband attenua­t ion is minor .

For low amounts of water vapor ( 0 . 4 2 cm) , the comparisons of the s implified models with S OLTRAN revealed that the Lacis and Hansen and Hoyt models gave resul t s s imilar to S OLTRAN, while the McDonald and Wat t models gave s ignifi­cantly lower values for water vapor absorptance . These differences depend on solar zenith angle , but they range from 25% to 7 5 % . For high amounts of water vapor ( 2 . 92 cm) , the Hoyt , McDonald , Lacis and Hansen, and S OLTRAN models yield similar resul ts from an approximate s o lar zenith angle of 0 " to 6 0 " . At greater angles the models diverge s omewhat . The Watt model resul ts in s ig­nificantly lower values , by about 50%, than all other models . Again, the s ignificance of these differences to the calculation of the broadband direct irradiance is determined by the relative s ignificance of water vapor to the total attenuation .

The comparisons of the transmittance due to a l l molecular effects except water vapor revealed close agreement between the Atwater and SOLTRAN resul t s . The Watt model gave resul t s that were lower in t ransmittance , depending on solar zenith angle .

The comparison of aerosol t ransmittance versus solar zenith angle for the MLS conditions with turbid aerosol condit ions revealed that the Watt model gave s ignificantly higher values than the S OLTRAN model. For the SAW with clear ( visual range of 23 km) c onditions , the Hoyt and SOLTRAN models gave s imilar resul t s . The Watt model gave significantly higher t ransmittance values .

The comparisons of calculated direct beam solar irradiance versus solar zenith angle were performed for the MLS condit ions , with a clear atmosphere ( visual range = 23 km at sea leve l ) and a turbid atmosphere ( visual range = 5 km at sea level ) . The comparisons for the clear atmos phere revealed that the Macht a , Atwater , and SOLTRAN models agree fairly closely; the Hoyt model resul t s in lower values of direct irradiance , but they are within approxi­mately 1 0% of the SOLTRAN/ Atwater/Machta values . However , at large solar zenith angles ( greater than 7 0 " ) the models begin to diverge s ignificantly. The Watt model agrees favorably with the S OLTRAN/Atwater/Machta values up to a solar zenith angle of about 7 0" ; at greater angles the Watt model predicts s ignificantly higher value s . The Maj umdar model gives much higher values o f direc t irradiance versus solar zenith angle than all o ther models , by a s much as 2 0 % . The comparisons for a turbid atmosphere could only b e performed for the Watt , Atwater , and SOLTRAN model s due to l imitations in the o ther models to c lear conditions . It was shown that the Atwater and S OLTRAN model agree favorably to a zenith angle of 7 0 " . The Watt model predicts s ignificantly higher values , especially past zenith angles of 50 " . Below zenith angles of 50" , the Wat t values are within about 1 0 % of the S OLTRAN/Atwater resul t s . Comparisons were also performed for the SAW atmosphere with c lear condi­tions . This again revealed agreement between the S OLTRAN and Atwater models , and characterist ically , that the Watt model tends to predict high values .

4 0

TR-344

However , for these SAW and clear conditions , the Wat t model is in fairly good agreement to zenith angles of about 7 0 ° .

Finally , the rigorous SOLTRJU� res ults were used to develop an improved , s implified model for p redicting the direct solar beam energy as a f unct ion o f a tmospheric c onditions and solar zenith angle . The improvements consist o f higher accuracy (as compa red to the S OLTRJU� resul t s ) and the ability to handle readily available , specific inputs to characterize the a tmospheric water vapor and aerosol s . Mathematical formulations were derived by comparison with S OLTRAN res ults for the a tmos pheric transmit tance components of molecular ( Rayleigh) scattering , ozone absorption, uniformly mixed gas ( C02 and 02 ) ab­s o rption , water vapor absorpt ion, and aerosol scattering and absorption, as functions of relative air mas s ( solar zenith angle) . The inputs to the model ( Bird) are s urface pressure , precipitable ozone , precipitable water vapor , and aerosol turbidity at 0. 38 � and a t 0. 500 un. Thus the Bi rd model allows the calculation of the direct s olar beam irradiance as a function of available atmos pheric parameters , which properly consider the s ignificant water vapor and aerosol cons tituents .

The absolute accuracy o f the Bird , S OLTRAN, and o ther models can be determined only by comparisons with actual measurements of the direct solar beam irradi­ance and measurement s of the atmospheric inputs . Unfortunately , s uch compar­isons and measurements have been lacking in the pas t in the vis ible region [ 4 6-50 J ; when done , they will probably resul t in improvements in the S OLTRAN and s implified model s . The SERI Energy Resource Assessment Branch and t he Solar Energy Meteorological Res earch and Training s i tes ( university re­search programs s ponsored by DOE to collect insolation and meteorological re­search dci'ta at eight locations within the United States) will be collecting s uch data and performing research that will greatly advance the s tate of knowledge concerning the a tmospheric influences on the d irect solar beam ir­radiance . Consequently, this will lead to improved prediction models for the d irect solar beam irradiance and improved design and predict ions of solar energy conversion devices .

4 1

4 2

S=�I r;.1 _______________________ T;:.:,R:....-3=....:4:.....:...4 -� ��

1.

SECTION 5 . 0

REFERENCES

Selby, J. E. A . ; Kneizys, F . X. ; Atmospheric Transmittance/Radiance: 78-0053; 1978 .

Chetwynd, J. H. ; McClatchey, R . A . Computer Code LOWTRAN 4. AFGL-TR-

2. Selby, J. E. A . ; Shettle, E. P. ; McClatchey, R . A . Atmospheric Trans­mittance from 0 . 25 to 28 . 5� : Supplement LOWTRAN 3B. AFGL-TR-76-025 8 ; 1976.

3. Selby, J. E. A . ; McClatchey, R. A . Atmospheric Transmittance from 0 . 25 to 28 . 5� : Computer code LOWTRAN 3. AFCRL-TR-75-0255 ; 1975 .

4. Thekaekara, M . P. "Extraterrestrial Spectral Irradiance . " The Extra­terrestrial Solar Spectrtml, A . J. DrUlllmond and M . P . Thekaekara, eds . Mount Prospect: Institute of Environmental Sciences ; pp. 71-133 ; 1973.

5 . McClatchey, R . A . ; Fenn, R. W . ; Selby, J. E . A . ; Volz, F . E. ; Garing, J . S . Optical Properties of the Atmosphere (Third Edition) . AFCRL-72-0497; 1972.

6. Atwater, M . A . ; Ball, J. T . "A Numerical Solar Radiation Model Based on Standard Meteorological Observations . " Solar Energy. Vol. 21: pp . 163-170 ; 1978.

7. Atwater, M . A . ; Brown, P . S . "Numerical Computations of the Latitudinal Variation of Solar Radiation for an Atmosphere of Varying Opacity . " J . Applied Meteorology. Vol . 13: pp . 289-297; 1974.

---

8 . Paltridge, G. W . ; Platt, C . M. R . Radiative Processes in Meteorology and Climatology . New York : Elsevier; 1976.

9 . Kondratyev, K. YA . Radiation in the Atmosphere . New York: Academic Press ; 1969 .

10.

11.

Mc Donald, J. E. "Direct Absorption of Solar Radiation by Atmospheric Water Vapor . " J. Meteorology . Vol. 17: pp. 319-328 ; 196 0 .

Hoyt, D. V. Solar Energy .

"A Model for the Calculation of Solar Global Insolation. " Vol . 21: pp . 27-35 ; 1978 .

12. Lacis, A . L. ; Hansen, J . E. " A Parameterization for the Absorption of Solar Radiation in the Earth's Atmosphere . " J. Atmospheric Science . VoL 31: p p • 118-13 3 ; 1 974.

13. Machta, L. Workbook for Approximate Calibration of Solar Radiation Sensors. Silver Spring, MD: National Oceanic and Atmospheric Adminis­tration; TM-ERL-ARL-70 j 1978 .

4 3

S=�I i*1 _________ ----:: _____________ ..:::.;TR::.:;,.-....::::3....:..:...44

1 4 . Braslau, N. ; Dave , J . V . Effect of Aerosols on the Transfer of Solar Energy Through Realistic Model Atmospheres . Palo Al t o , CA : I BM Re-search; RC4 1 14 ; 1 9 7 2 .

1 5 . The American Society of Hea ting, Ref rigeration and Air Conditioning Engineers . ASHRAE HANDBOOK OF FUNDAMENTALS . 1 9 7 2 ed.

1 6 . Jordan, R . C . ; Liu , B . Y. H . , eds . Applications of Solar Energy for Heating and Cooling of Buildings . ASHRAE-GRP- 1 7 0 ; 1 9 7 7 .

1 7 . Hul strom, R . L . Insolation Models ) Da ta and Algorithms . Golden, C O : Solar Energy Research Institute; SERI/ TR-36-1 1 0 ; 1 9 7 8 .

1 8 . Watt , D . On the Na ture and Di s tribution o f Solar Radiation. U. S . Depart�ent of Energy; HCP/T255 2-0 1 ; 1 97 8 .

1 9 . Moon, P . "Proposed Standard Solar-Radiation Curves for Engineering

20 .

2 1 .

2 2 .

2 3 .

24 .

2 5 .

2 6 .

2 7 .

Use . " J . F ranklin Ins titute . Vol . 2 3 0 : pp . 583-6 1 7 ; 1 94 0 .

Majumdar , N . C . ; Mathur, B . L . ; Kaushik , S . B . "Prediction o f Di rect Solar Radiation for Low Atmospheric Turbidity . " Solar Energy . Vol . 1 3 : pp . 383-394 ; 1 97 2.

Kas ten, F . "A New Table and Approximate Formula for Relative Opt ical Air Mass . " Arch. Meteoral . Geophys . Bioklimatal . Series B , Vol . 1 4 (No . 2 ) : pp . 206-223 ; 1 96 6 .

Davie s , A . D . ; Hay , J . E . "Calculation o f the So lar Radiation Incident on a Horizontal Surface . " Proceedings , First Canadian Solar Radiation Da ta Workshop. April 1 7-1 9 , 1 9 7 8 . Canadian Atmospheric Environment Service ; 1 9 7 9 .

Burch , D . E . Semi-Annual Technical Repor t , Inves tigation of the Ab­s orption of Infrared Radiation by Atmospheric Ga s e s . Philco Ford Co rp . ; Aeronutronic Report U 4784 ; Contract No . F 1 9628-69-C-0263 ; 1 9 7 0 .

Burch , D. E . ; Gryvnak, D. A . Ab sorption by H20 Be tween 5045 and 1 4 , 485 cm- 1 ( 0 . 69 to 1 . 98 un Region) . Aeronutronic Report U-3 7 0 4 ; 1 96 6 .

Burch, D . E . ; Gryvnak, D . A . Strengths , Widths and Shapes of the Oxygen Lines Nea r 7600 Angs troms . Aeronutronic Re port U-40 76 ; 1 96 7 .

Burch, D . E . ; G��nak, D . A . ; Pat ty , R . R . Absorption by CO! Between 4500 and 5400 cm ( 2 � Region) . Aeronutronic Report U-2 955 ; 9 6 4 .

Burch, D. E . ; G�1vnak , D. A . ; Patty , R. R . Absorption by CO2 Between 6600 and 7 12 5 cm ( 1 . 4 � Region) . Aeronutronic Re port U-3 1 2 7 ; 1 965a .

i 2 8 . Burch, D. E . ; Gry��ak, D. A . ; Patty , R . R. Absorption by CO2 Between '"

8000 and 1 0 , 000 cm ( 1 to 1 . 25 � Re gion) . Ae ronutronic Report U-3 200 ; 1 965b .

4 4

S=�I f�.1 ___________ ----'-_____________ T=R�-...;;;.3....;.,44..;.. -� ���

2 9 .

3 0 .

3 1 .

3 2 .

Burch , D . E . ; Gr1vnak , D . A. ; Patty, R . R. Absorption by C02 Between 5400 and 6600 cm - (1 . 6 \.llIl Region) . Aeronutronic Report U-320 1 ; 1 965c.

Burch, D. E . ; Gr1vnak , D. A. ; Pat t y , R . R. Absorption by H�O Between 2 800 and 4500 cm- ( 2 . 7 \.llIl Region) . Aeronutronic Re port U-3 2 0 ; 1 965d .

Burch, D. E . ; Gr1vnak, D. A. ; Patty, R. R. Absorption by CO2 Between 7 1 25 and 8000 cm- ( 1 . 25 to 1 . 4 \.llIl Region) . Ae ronutronic Report U-3 9 3 0 ; 1 9 6 7 .

Burch , D. E . ; Gryvnak , D. A . ; Pa t t y , ?-. R . Ab sorption by CO2 Between 3 1 00 and 4 1 00 cm-1 ( 2 . 44 to 3 . 22 ]..m Region) . Aeronutronic ��--��������----��--�----��--�----��� Report U-4 1 3 2 ; 1 9 6 8 .

3 3 . Burch , D. E . ; Gryvnak , D. A. ; Singeleton , E . B . ; Franc e , W . F . ; Williams , D. Infrared Absorption by Carbon Dioxide , Water Vapor and Minor Atmospheric Constituents . AFCRL ; Re search Contract AF1 9 ( 6 04 ) -2 63 3 ; Ohio S tate University; 1 9 6 2 .

3 4 . McClatchey , R . A. ; Benedict , W . S . ; Clough , S . A. ; Burch , D . E . ; Calfee , R. F . ; Fox , K. ; Rothman, L. S . ; Garing , J. S . AFCRL Atmospheric Line Parameter Compilation. AFCRL-TR-73-0096 ; 1 97 3 .

3 5 . Fowle, F . Vol . 42 :

E . " The Transparency o f Aqueous Vapor . " pp . 394-4 1 1 ; 1 9 1 5 .

Astrophysics . J .

3 6 . Yamamoto , G . "Di rec t Ab sorption o f Solar Rad iation by Atmospheric Water Vapor , Carbon Dioxide and Molecular Oxygen . " J . Atmospheric Science . Vol . 1 9 : pp . 1 8 2- 1 88 ; 1 96 2 .

3 7 . Howard, J . N. ; Burch , D. E . ; Williams , D . " Infrared Transmission o f Synthetic Atmospheres , Parts I-V . " J . Optical Society of America . Vol . 46 : pp . 1 8 6- 1 90 , 237-2 4 1 , 242-245 , 334-338 , 452-455 ; 1 95 6 .

3 8 . Valley , S . L . , ed . "Solar Electromagnetic Radiation . " Chapter 1 6 in Handbook of Geophys ics and Space Environment s . Air Force Cambridge Research Laboratories ; 1 9 6 5 .

3 9 . Wulf , O. R. "The De termination of Ozone by Spectrobolometric Measure-ments . " Smithsonian Mis cellaneous Collection. Vol . 85 (No . 9 ) : p . 9 ; 1 93 1 .

40 . Lauchli , A . "Zur Ab sorption der Ul travioleten St rahlung im Ozon. " Zs . F . Phys . p . 9 2 ; 1 92 9 .

4 1 . Manabe , S . ; Strickle r , R. F . with Convective Adjus tment . " pp . 3 6 1 -385 ; 1 964.

"Thermal Equilibrium of the Atmosphere J. Atmospheric Science . Vol . 2 1 :

4 2 . Vigroux , E . "Contributions a i ' etude Experimentale de l ' absorption de l ' o zone . " Ann. de Physique . Vol . 8 : pp. 709-7 6 2 ; 1 9 5 3 .

4 5

!;::�I :�I __________________________ �-----------------------------------T�R---3�4-4--� ���

4 3 . Inn , E . C . Y . ; Tanaka , Y . "Absorption Coefficient of Ozone in the Ultra-Violet and Visible Regions . " J. Op tical Society American. Vol . 4 3 : pp . 8 7 0-873 ; 1 95 3 .

44 . Howard, J . N. ; Burch , D . E . ; Williams , D . Near-Infrared Transmiss ion Through Synthe tic Atmospheres . AFCRC-TR-55-2 1 3 ; 1 955 .

4 5 . Burch , D. E . ; Gryvnak , D. ; Williams , D. The Infrared Ab sorption by Carbon Dioxide . Ohio State University Research Foundation; Report on Project 7 7 8 ; 1 9 6 0 .

4 6 . She ttle , E . P. ; Fenn , R . W . "Models of the At"mospheric Aerosols and Their Optical Properties . " Proceeding of AGARD Conference No. 1 8 3 , Optical Propagation in the Atmosphere . pp . 2 . 1 -2 . 1 6 , presented at the Electromagnetic Wave Pro'pagation Panel Symposium, Lyngby , Denmark; 27-3 1 Oc tober 1 97 5 .

4 7 . Roberts , R . E . ; Selby , J . E . A. ; Biberman , 1 . M. " Infrared ContinulIDl Absorption by Atmospheric �vater Vapor in the 8- 1 2 ).m Window. " Applied Optic s . Vol . 1 4 : p . 2085 ; 1 97 6 .

4 8 .

4 9 .

Haught , K . M. ; Corday , D. Transmis sion Measurements :

M. "Long-Pa th High-Re s olution Atmospheric

Appl ied Optics. Vol . 1 7 : Comparison with LOWTRAN 3B Predic tions . "

pp . 2668-2 6 7 0 ; 1 97 8 .

McClatchey , R . A. ; Kneizys , F . X. pheric Transmiss ion Mea surements : tions ; Comments . " Applied Optic s .

"Long-Path High-Resolution Atmos­Comparison with LOWTRAN 3B Predic­

Vol . 1 8 : pp . 5 9 2-593 ; 1 97 9 .

5 0 . Haught , K. M. ; Cordray , D . M . "Long-Path High-Re solution Atmospheric Transmis s ion Measurements : Comparisons with LOWTRAN 3B Predictions ; Reply to Comments . " Applied Optics. Vol . 18 : p . 5 9 3 ; 1 97 9 .

4 6

5»5'1 � �, __________________ �� ____________________ �T=R-�3�4�4

APPENDIX

TABULATED MODEL DATA

A compilation of computer outputs for the Atwater and Ball , l-lat t , Bird , Lacis and Hansen, Maj umdar , and the Hoyt models are presented. The a tmospheric models used were the Hidlat itude Summer (MLS ) and the Subarctic Winter ( SAW) models with 23 km and . 5 km sea level vis ibilities for each model . The direct normal irradiance (IDN ) is not included for the Bird models s ince it was given previously in Tables 2-2 and 2-3 . The SOLTRAN output is also lis ted in Tables 2-2 and 2-3 . The IDN is not given in the Hoyt model , becaus e parts· of the calculation that required look-up tables were done on a hand calculator .

F or the MLS model , 2 . 93 cm of H20 and 0 . 31 cm of 03 was used . The SAW used 0 . 42 cm of H20 and 0 . 45 em of 03 . The turbidity at 0 . 5 and 0 . 38 lltn wavelength was 0 . 2733 and 0 . 34 6 9 , respect ively , for V = 23 km; and 0 . 9243 and 1 . 1 7 27 , respectively , for V = 5 km. In all cases , the incident extraterrestrial ir­radiance was 1353 W/m2 •

A l

Table A-1 . Tab ulated Data for the Midlatitude Summer Atmosphere (V = 23 km) for Several Models

10 13�3. 0000 Ulol 2.90300 uc . 31 0 0 PI!! 1 013. 00M T1'ItJ, • . 2733 TMJ3S- . 30,;" T1'ItJ1Ia . 1913

IiI�T� nrl!CCT I'IIIIII'!AI.

ZENITH IiIIRI'IASS TIi! All TI'I I'DIt O. 0000 1 . 0000 . a2159 . 1 063 .a901 a7'. n"iIa

20. 0000 1 . 06"1 . 91156 . 1 0S3 . S8!53 8'7.6348 30. 0000 1 . 1!14!5 .SOIS . 1 1 1 0 . 13788 832._1 40. 0000 1 .3 0!5 0 . 7"0 . 1 1 ' 1 . 36e6 n ... I .... ' 150. 0000 1 . " "8 . 7"27 • til .. . s�a9 73'. 00" 60. 0000 t . �976 \ liaa4 • lalla . sa77 643. 3732 70. 0000 2.9148 . '72!5 . 10,;' . 7a33 "';I3.2S2JII 7!5. 0000 3.S"19 . "7" . 1!592 . 7"'2 3aO. I_ 80. 0000 '.68 .... .3370 . 17'0 .;;,112 aas. _ 8S. 0000 1 0. $068 . li .. 1 . 2 177 • !5"2'; 15".'''011

IoIIiITT DIRECT ffilRI'!AI.

om. 1'''' T>lacA 1'>I2IIS Ttl3 TAIR 11111 0 . 0 .87,*, . 914;; .';1379 . 97';8 . 9 0 1 6 8'9. 1 987

3 0 . 0 . 9740 . 9137 . 9341 . 9763 . S"74 88".2390 3 0. 0 .S6159 . 9Ia, . 9287 • 97!S7 .S917 863.3708 40. 0 .S!530 . :HOS . 9 1 '" . 9747 . 8826 S3 I. 6"'56 SO. O . S3a" • "oa3 . '0" • 9724!' ._3 78a. I!! I ' 60. 0 • 79»a . 9047 . an7 . %99 .,04SI 704.3a94 :'0. 0 . 73� .s"';! • 32,H .%� . 8 029 !!73 . l a .. " i'!$� 0 . 6aaa . $,",,3 . 78 1 3 . ?'86 . 770l! "77. 0l!26 80. 0 . !!944 .88% . ii933 .'l'469 . 7144 336. 1S9 9!5. 0 .4331 . S8 0 0 .4$% . n 09 . 61a3 143. 9323

HIlYT nll!eeT MIlRM!.

ZEl'IITIt """ Atlli AIl3 AOi O. 0000 . 1 397 . 007!! • 0215S . 007:1

a:o. OOI]O . 1 426 . 0076 . 026" . 0079 30. 0000 . 1 4&4 . 0 079 . 0274 • 009!! "0. 0000 . 1�23 • alia I . 02ge . OO� !O. 0000 . 16 1 2 . ooas . 03 1 0 . Ol t O 60. 0000 . 1 747 . 0091 . 0344 . 0137 70.0000 . 1%9 . 01 0 1 .. 0401 . 0190 7!I. OOOO • a 1"7 . 0 1 09 . 0448 . 0a44 ao. 0000 . 2442 . 01U • 0�23 . 0338 85.0000 • 2938 . 0 1 .... . 0"9 • Ol!7S

I..AC I S >120 FlHII 113

nN.,.>I AIR_S """ T03 O. 0000 . 9995 . 13"1 . 9776

20. 0000 1 . 063" . 1�63 .9769 30. 0000 1 . 1'36 . 1 392 . 9761 "0.0000 1 • • 037 . 1 437 � 9747 !l0. 0000 1 . !5l525 . 1503 . 97<:5 60. 0000 1 .. 90927 . 1 000 • 968a 70.0000 2. 139'97 . 17!51 .961a 7:5. 0000 3 . S 076 . 1 9';!I • 95!52 80. 0000 '. !5790 • .!oae . �32 8!1. 0000 1 0.3163 . 2299 .. 91 ... 9

I"!AJU"DAR DIRECT "aRM!.

ZENI,... III � TT 1'>l21l 11)" 0. 0000 1 1!!0. 6024 . 9 0,,3 �31 . a'39a

ZO. OOOO 1 139 . 9371 .M67 919. 565� 30. 0000 I lZS. 0SI5' . S031 903. 5S77 "0. 0000 1 160.7170 . 7977 979. 0 1 7 1 !l0. 0000 1 06 1 . 5163 . 7997 93S.a4"!!S 60. 0000 9!'!5.:"6 . 7778 774. 3037 70. 0000 972 . 3 0S" . ;�as 061 ..-9765 7!I. 0000 764.20:53 . 744 1 :568.6819 ao. oooo :190. 3:129 . 7aa .. 4a6 ..... 91� 8:1. 0000 296. 0123 . 6W 202.6061

BIRD II IREieT "CRI'!AI.

:EI't TA Ttl3 TCII2 TR TM """ 0 .. 0 . 9122 .983" .997 .. . 9137 . 991 0 . 10.19

20. 0 . 9024 . ge46 . 9972 . 9094 . a863 . 123!5 30. a � 7990 . 99 1 6 _ .913.9 . 9033 . 8799 . 12�7 <40 .. 0 . 7672 . 97':\9 • 996!! o S�37 . a697 . 1291 SO. O . 7330 . 5'772 • 99S9 . 871.13 .8S'" . 1340 6�. 0 .�771 . 9727 . 99"9 .8S31 . 9a93 . 14 1 \ 70. 0 • !l777 . 96"3 . 9934 � a 074 • 78S6 . 1:520 7!I. 0 . 4949 • 9l5�6 • 98a2 � 7ea4 .. 7463 . 1601 ao. o . 3�94 . 9430 .9$03 . 7078 . �S67 � 1 7 1 7 95. a . 174� . � H l;; . 9770 . 61:17 . S"92 . 1907

A2

Table A- 2. Tabulated Data for the Midlatitude Summer Atmosphere (V = 5 km) for Several Models.

10 13,3. 00GO uw 2.9300 ua . 31 0 0 PR 1 01 3 . 0000 TAWl - . 9243 TAU3S- 1 . 1 727 rAUB- . ''''9

A'NATIR D I RECT J'tCRI!Al.

ZEl'IInt "U R�ASS TA AW T� IDII

0 . 0000 1 . 0000 .:5236 . 1 0,;3 . 8901 ,"�. aS9� 20. 0000 1 . 0641 .SGa4 . l oe3 . ae� S2a . I 399 30. 0000 1 . 1:54' . .. 738 . 1 1 1 0 • 87ee .�.2'62 <-0.0000 1 .30$0 . . 42"9 . 1 1:5 1 . eee,; 43a . 2 IS" '0. 0000 1 . " ,,* . 3"7 . 12 1 4 .a'29 3"1 .�9 60. 0000 1 .9976 . 27'" . 130a . a277 2S8.9480 70. 0000 2.'11<48 . 1' 1 7 . 1 "" .. t$33 1 3 1) . 7:1 1 1 ;"S.oooo 3.a41l1 . 0933 - 1'92 . 74:2 66. 0326 a o . oooo '. 6&46 . 02'3 . 1790 .,,812 1 7 . 1 770 a,. oooo 1 0.9068 . 0009 . 2 1 77 . S4a6 .3790

>JATT DIRlcr IIIJRI!Al.

ZEH TA T"aDiII TK2DS T03 TA!!! lim 0 . 0 . '�3 . 91'" . 9379 . 37�8 ,, :�Olf; 609."'83

20. 0 . '8 12 .9137 . 9341 . 9763 . S97" �aa. 03ao

30. ° . 15622 . 9 1il5 . 9287 .. 9757 .891 7 $60.8678 4". 0 . :5329 . 9 1 08 � 9 1 97 . 97017 . ee26 '19.4331 150. 0 . 4889 . 908S . 90'1 . 9729 . a.as .,9.a331 6 0 . 0 .4232 .9047 . 8797 . 9693 . S"'5 1 373.41704 70. 0 . 32 1 0 . 8992 .8291 .963' . eoa9 a'o . .. .,...o 7:5. 0 ... ,o2 . 39:53 . 7 8 1 3 . 91586 ,, 'lila 1 74. 8369 80. 0 . 11583 . aa% .6933 . .... 89 . 7142 99. '032

as. 0 . osa<- .8aoo . 48"6 . nll9 . 6 123 1 7. ""47

HOYT D I RECT NCRI!Al.

UIIIT>! ",.. ,;ca2 A03 A!l2 Q. o ooo . 1397 . 0075 . 02sa . 007S

ao. oooo . 1426 . 007.6 . 0264 . 0079 :30. 0000 .. 1464 . 0079 . oa74 . 008' 40. 0000 . 1:'$23 . 00$1 . oalla . 00" '0. 0000 . 161a . 00815 . 03 1 0 . 0 l t O 6 0 . 0000 • 1147 . 0091 . 034 .. . 0)137 70.0000 . 1969 . 01 0 1 . 04 0 1 . 0190 7:5. 0000 . .. 147 . 01 0' . 0_ . 0l!42 �o. 0000 .2422 . 012.i . 0'23 . 033a a,. 0000 . 2938 . 01 44 . 0663 . 0'78

LAC I S "21l AnD 03

ZEIIIT>! "'IRIO'ISS AW TIl3 0.<1000 . 999� . 13<-1 . 3776

ao. oooo 1 . 0634 . 1363 . j76' 3 0 . 0 0 0 0 1 . 1S36 . IS92 . 1761 40. 0000 1 . 3037 . 1437 . '747 sO. oooo 1 . ':'$2' . 1'03 .972' 6 0 . 0000 1 . -j�27 . 1 600 • • 689 70. 0000 2. 8997 . 1� 1 . % I S 7'.0000 3. 8076 . 19615 . 3"2 ao. oooo �,,!5790 . 2 028 . 943;a 8' . 00 0 0 1 0. 3 163 .a299 . 9149

I'IA�U"DAA DI1>£CT l'IOR"fII.

ZEIIITH 10 X TT TK21l tDIi 0 . 0000 l 1 S0. 60a. . a093 93 1 . ;:'298

aa.Moo 1 t3'.9371 . 9067 9a.,�" 30. 0000 1 12'. OS�9 .3031 903." 77 .. 0. 0000 1 1 00 . 7 1 7 0 . 7,n 879. 0 1 7 1 '0. 0000 1 06 1 .'163 . 79'7 838 . 2 .... " 60.0000 "S.'666 . 777$ 774. 3037 70 ... 0000 B72. 30S4 . 7SSS .6 1 . 8765 715. 0000 764. 20'3 . 7441 '69.6819 so. 0000 '<;'0. 3'2a . 7224 <a6.491' a'. 0000 2%. 0 1a3 . '34! ua.6061

III>D DIRECT NaR""'I..

Z£H TA T03 T�oa T/I TI'\ AW 0. 0 . '360 . '834 .9�74 . ' 1 3 7 .$91 0 . 1<: 1 9

20. 0 .�H69 . :ilea6 .. '$0$72 . 90'" . 8$63 . 123' �I). 0 . 4�13 . "aI6 . '?90� . 9033 . 37�' . 1257 .. 0. ° . 4l$ 1 9 . 97"" . 9'96' . 6<;>37 .36�7 . 1291 '0. 0 . 3'40 . ')772 . �e" . 8783 . 8'41 . 1340 00. 0 . 3 1 06 . 9727 . >649 . SS31 . sa93 . 1-4 1 1 70. 0 . 19�0 . 9643 . 9834 . S074 . 78:56 . IS20 7',, 0 . 12 1 " . 9:566 .. 9sea . '(6a4 . 7-483 . 1 601 ao. o . 050!!! . 9430 .'9803 . 707$ . 6867 . 1 7 1 7 8'. 0 . 00'<- . '1 16 . 9770 • .0157 . ,l59a . 1907

A3

Table A - 3. Tabulated Data for the Subarctic Winter Atmosphere (V = 23 km) for Several Models

I II Ubi \.10 Pit " TAU!5 ,. TFIO'3e_ TAU):-

13�3. eooo' ."200 . .. �oo

1 0 1 3 . 0 0 0 0 . 2733

. �""9

. 1913

IITWATER DIRECT rlDRM\.

Z!l1r1 0. 0

Zll'tlTK 0. 0 0 0 0

aO. 0090 3 0 . 0 0 0 0 40. 0 0 0 0 '0. 0 0 0 0 � o . 0 0 0 0 7 0 . 0 0 0 0 7�. 0 0 0 0 so, 0000 85. 00 0 0

m . 3498

ao. o . S4l!9 30. 0 .933" "0. 0 . S 1 8 1 5 0 . 0 . 7�O ';0. 0 . 7'''' 7J>. ,I) . 6,8,,, 7!5. 0 • ..a .... SO. O . ,a8, 95. 0 . 3'91

ZEKITH 0. 0000

20. 0000 30. 0 000 40. 0000 '0. 0000 60.0000 7 0 . 0 00 0 7�. 0000 �O. 00.)0 S�. 0000

Z!l1r1lTI<I 0. 0 0 0 0

20. 0 0 0 0 31) .. 00t)0 ,,,If),, 01)00 150 .. 01)01) <>0. '1000 70. (1001} 7!I. oooo ao� 0 0i,,1 0 3' . 0000

IIIIII'IRSS t . OOOO 1 . 0641 1 . 1 '''� 1 . 30'0 1 . " 48 1 . 9976

... 914$

:3 . a-"19

lS. 6e4li

1 0 .90.;8

TR . a2'9 . 8 1'S .. 31llS � 77';toO • �427 .6aa .. . !l72' . .. 1'9s . 3370

. 1241

WRTT DIRECT rIORlOAL

TMaOA TIEOS . 94<!" . �o<] . 94 1 5 . �03

� 941)4 .'9894

. n96 .�8al .. ·�16 1 • 98,a

� '332!5 . -E'$1 8 . 9a71 . 973!1 . 90031 . '?.o�2 0 ';' 1 74 . 9468 . 9 079 .9027

HOYT DI RECT rlDPI'IAL

A<j ACC2 • (\727 0 0(17, . 07"3 • 0076 . 01/54 . 0 073 .. 0797 . 0081 . oa"7 • ooa, . 09':2 . 0 091 . 1 0 .... . 1) 1 0 t

. 1 1 .. 6 . 01 09

. 1U'!> . 01<lZ

. 1-5e7 .. 0 1 4<4-

!.AClS "' .. 0 ""D 03

FU�"ASS AIoI . 9'�,?� . 07';1

1 . 0634 .. 0776

1 . 1'36 . 0796

1 . $0'3;' . 08;:7 1 . 5sa� • !)Bra l c '�'4:j' • Q .... I a .. a�97 . 1 051) 3. $076 . 1 131i ,' • .57�O . la�3

1 0. 3 1';3 . 14S�

AIoI . 0,9« . 0';0' . 06eo s 064-') . 0678 . 0730 . 0$IS . 08S<] . 1 00 0 . 1216

T03

. 9736 ��no . 9>721 . 9706 . '�6t.u . �6 .9�44 . '1474 . '336 .90ao

AC3 . 0301 . 1)309

. 030.:: 0

. 0337 � 0362

. 041) 1

. 0 .... 7

. 0'21

. 0';08 .. 1)77'

T03

.. 97:34 .. �726 � �71 ' . 969� . �";�7 . 'Mi'i) . '!>�2" .. ?""3� .. 92.76 . 6907

�I)l'!_ DIPECT rtORI'IAI..

ZEKITH III " TT TH2D Illrl 0. 0 0 0 0 1 1' 0 . �O2" . :37aO 1 0 1 0. 1839

eo . oooo 1 1 39 . 93 7 1 .. 3762 998. 788 1 30. 00 00 uas. �lj; . S736 ?>O3.0703 40 .. OIlOO 1 1 00 . 7 1 7 0 . 8701 957. 78� �o� 1)001) 1 0ojl .·'163 . 2643 91 7. 9'8S 60. 0 0 0 0 ?9!5 .. '6� . a 567 8' ... 91 0' 70. 0001) $, ... 30, .. .3438 736. 0339 7S. 00 0 0 7"4.aO!53 . a337 &37 .. 1483 ao. oooo ,0;.0. 3'2$ . 31S7 4$3 .. 3 1 34 as. 6000 296 .. 0 12.:3 . n1 ' 2.34 .. 4 1 '6

BI�D D1RECT NCRI'IAI..

"1'1 TA T03 TCO .. Tl1 0 . 0 .8122 . 9783 . 9874 .'7137

ao. o . :30S:4 . '?-773 . 9972 . Si'O'?04 3 0 . 0 . 7990 . ·?7'� • "?569 . 9-1):3:3 40. 0 . 76.72 . -:;737 . �a.;, .an7 .'S O. II .. 73:30 . 9702 . 31$59 . 8783 01). 0 . 6771 . ::644 . ',7$49 .a�31 fl). O . '777 . $1'334 . 9'9'34 . S 074 ��. 0 , .. 9 ... .,. . ;'4·34 . i'aaa • (,SS4-J!it) .. (,I . :36'74 . 92'36 . ',803 . 7079 s� . o . 1 7490 . 9848 . ';'770 • • 157

A4

Tl'! .8901 . ae53 . a 7as . a�a& . aS29 • san . 7933 . 7"'2 ."$12 .. S4a6

TAI� . 1'016 . 3<>74 • S'3'1 7 . Ssa6 . 3�a3 .8"'1 . 3029

• 770a . 7I4<! . 6123

FtIl2 . 007S , 0079 . ooas � OO'?' . 01 1 0 . 0 137 . 0 1'9'0 . 0242 . 0338 . 0573

IDrI 92a."3�6 9 1 0 .. 4298 996 . 1 599 947 . 7640 788.860' 696.7169

�43" "1Z4 42'. 1"52' 26:1. 0097

7 0 . 69UI

IllM 94l! ..... S>7 9-29. "'26 ?O� • • l4S3 a�. 3�76 S33 .. <i9'O 7$ 1. (2)3' ';38. 5'''2 �"'.3a46 "IS. 0 .... 5 221 . ;3 732

AW . 0759

. ono

. 1)7S?

. 0$ 1 3

. ')851

. 0907

. 1).9�

. 1 1)'a

. 1 16.)

. 1326

Table A-4. Tabulated Data for the Suba rctic Winter Atmosphere (V= 5 kml for Several Models

10 U'3 . oaoo 'JW .4200 vo . �oo PR 1 013. 0000 1'l'U! • . ,a"3 TAU3S- 1 . 17a7 TAU'- ...... 9

ilTIoUIT£R D IRIICT NIlRI'IAI..

Z'EliIT'I FURi'fRSS TFI """ TI'I llIti

0 . 0 0 0 0 1 . 0 0 0 0 . �a3' " f./5'S'4 .a,ol ,a9. ,.26 ao. oooo 1 . 0 .... 1 _ " 024 . o,;os .aaS3 �.0. 6i50i5 SO. OOOO I. IS'" . "739 • tl6ao . a?as sa3 . 6S 0 0 4 0 . 0 0 0 0 1 . 30'0 � 4a,,� . 06"3 . 369. ,..;70< "'t3 .50. 0000 1 . �i5"9 . 3';'7 . 00;79 .asas 3a9 . ... $1 60. (01)0 1 . '97� . a7 .... . 0730 .�277 oi!aO.4uH

70. 0 0 0 0 2 . 9 14$ . ISI7 . 0S l a . 7$33 144. 00S. 7'. 000. 3 . 3419 .. 0$33 . 09109 . 7�2 73. 7�"9 eo. oooo s.6a .... . oa�3 . 1 00 0 . 6S l a 19.8821 ,,15. 00 0 0 1 0.906a . 0009 . la l 6 . 15426 .411 1

!.IATT nI�ECT NIlR�

ZI!N TA TIIaDA THaos TQ3 TAIIt I D" 0 . 0 ."150 .. ioo&a4 .9909 . ·,736 . 3 0 1 6 637.73ao

z o . o .�fS!l!l: . �"IS . 9903 . 9730 . 3974 Ii 1 7.43.7 SO. O . S 4 1 1 .3404 . 9894 . �721 .391 7 S90. 4373 40 .. 0 . � 1 I 0 . 9386 . 9aSI . �71')6 . aea. �'.a333 150. 0 . 4663 . 93�1 .��s . %81 .a�3 489 . ... 37 60. 0 . 4�OO . 932' . $0$ 1 8 . %36 . S� 1 40� .. 'O83 70. 0 .an3 .9271 . 97315 . '�!I"" . s oa9 279. 0931 7'. 0 . a289 . 1'231 .%,a a 9474 . 7702 201 . 31589 80. 0 . 1407 . ' 1 74 • 94a8 . 9336 . 7142 1 1 0.1513 •

a'.o . 043' . 3079 . 9027 .90S0 • • H23 a6.(,999

HOYT D I�I!CT NOR"'*-

ZEit I TIl oW FlC02 iIQ3 F!02

0. 0000 . 0727 . 0 07' . 03 0 1 . 007$ 20. 0 0 0 0 . 0743 . O07� . 0309 . 0079 3 •• 0 0 0 0 . 0764 • 0078 . 03S0 . 008'

4 0 . 0000 . 0797 . 0081 . 0337 . 0 09' 50. 0000 . 0847 • 008' . 0362 . 01 1 0 �G. 0000 . 0322 • 0091 • e"G! • 0137 70. 0 0 0 0 . 1 046 • 6 1 0 1 . 0467 • 0190 7'5. 0000 . 1 1 .... . \) 1 09 . 0521 . 0242 ao. oooo . 1 299 . 01.:2 . 0608 . 033& S15. 0000 . 115a7 . 01 .... . 07715 . 0'78

I.FlCIS HaD AriD 03

ZENITH AIRMASS � Ta3 0 . 0 0 0 0 . 999' . O(�H .. �734

20. 0 0 0 0 1 . 0634 . 0776 .9726 �O. 0 0 0 0 1 . 11536 • 079' .97115 40. 00 0 0 1. 3037 . OS27 .96% 50. 0000 1 . "215 . 087a . S667 J$O.OOM h�*7 . 034 1 . 9�la 70. 0000 2 .. 3S':l7 . 1 0'0 � 9eia4

715. 0000 3 . a 076 . 1 136 . 94,6 $ 0 . 0 0 0 0 ,. 579. . 1263 . �76 as. 0000 1 0 . 3 163 . 14815 .9907

.... JUI'lDRR D I�IICT "�1'IFll.

ZENITH 10 X TT THaQ IDN 0. 0 0 0 0 1 1�O. 6024 . a780 1 0 1 0. IS3S

20. 0 0 0 0 1 1 39.9371 . 8762 998.7a81 3 0 . 0000 1 12'.0'1$19 • an'S 963. 0703 40. 0 0 0 0 1 1 0 0 . 7170 . &7 0 1 1'57. 7868 50. 0 0 0 0 1 06 1 . 15 1 63 .3''''8 917. 'r'S' 6 0 . 0000 ���666 . $:;67 esa. 9 1 05 70. 00 0 0 1372 .. 3 054 . a •• a 735. 0339 7'. 0000 764.2OS3 . a337 637. 1483 $0. 0 0 0 0 1590. 31526 . 3187 48 3 . 3 1 3" $5. 0 0 0 0 296. 0123 . 7919 23 •• 4198

lHRD D IREC T NORI'IAI..

ZErt TFI TOl TCIl1! T� TI'! """

0. 0 • 5J<;0 . 9783 . 9a7. . 91 3 7 .a91 0 • 07159 an. o .15169 . 9773 .9872 . 9 034 . 8863 . 0770 30. 0 . 49 1 3 ,,�7S9 . 9969 . 9 033 .. $7'9� . 0787 40. 0 .4:519 . 9737 . 996' . a937 . a697 . 08 1 3 50. 0 . :3940 .-:'702 . ,a159 . 8783 .S1541 . 08'1 60 .. 0 . 3 1 06 . %44 .0;849 .91531 . 8293 • 0907 70. 0 . 1930 . 91534 . '3834 • <l074 . 78�6 . O�

,.�. o . 1 C! 1 '" • '143 ... . %22 . 7684 • 7483 . 1 062 ao. o . 0'05 . 92�' . �303 � 7079 . �67 . 1 16 0 a15. o . 005. • S9..a . 9770 . 6 1 57 . 5'92 . 1326

AS

Document Control I ; ' SERI Report No.

Page TR- 33 5 - 344 1 2. NTIS Accession No. 3. Fiecipient's Accessio n No.

-4. Title and Subtitle 5. Publication Date

Di re ct I n so l a t i o n Mode l s 6.

7. Author(s) la. Performing Organization Rept. No.

Ri cha rd Bi rd ; Ro l a n d L . H u l s t rom i 9. Performing OrganizatiOn Name and Address 1 1 0. prOkCtlTaSk/Work Unit No.

Tas #362 3 . 01 So l a r Energy Re s e a r c h I n s t i t u te/ DOE 1 1 . Contract (C) or Grant (G) No. 1 6 1 7 Co l e Bo u l e v ard (0) Go l den , Co l o . 80401

(G)

1 2. Sponsoring Organization Name and Addres� 1 3 . Type of Report & Period Covered

Tec h n i c a l Re port

14 .

15 . Supplementa ry Notes

I I

16. Abstract (Li mit: 200 words )

S e v e ra 1 recen tl y p u b l i s he d mo d e l s o f t h e d i rect compo n e n t o f the b ro a d b a n d i ns o l a t i o n a re comp a red fo r c l ea r s ky con d i t i on s . The compa r i s o n i nc l u d e s seven s i mpl e mo de l s and o n e ri gorous mo de l t ha t i s u s e d as a bas i s fo r de -termi n i ng a c c u racy . W h e re po s s i bl e , t h e compa r i s o n i s ma d e b etween t h e res u l t s of e a c h mod e l fo r each a tmos p h e r i c c o n s t i tuent ( H20 , C02 , 03 , 02 , a e ro s o l a n d mo l e c u l a r s c a tteri n g ) s epa ra te l y as we l l a s fo r the comb i n ed effect of a l l o f t h e co n s t i t u e n ts . Two opt i mum s i mp l e mo de l s of v a ry i ng deg rees o f comp l ex i ty a re deve l o ped a s a res u l t of t h i s compa r i son . The s tu dy i nd i cate s : aero s o l s domi nate t h e atte n u a t i o n o f t h e d i rect beam fo r rea sona b l e atmo s p h e r i c con d i t i o n s ; mo l ec u l a r s catteri n g i s next i n i mportan c e ; water vapo r i s an i mportant a b s o rbe r ; a n d ca rbon d i ox i d e and o xygen a re rel a t i v e -l y un i mpo rta n t a s atten uato rs o f t h e b roa dband sol a r ene rgy .

1 7 . Document Analysis

a. Descriptors I n s o 1 a ti on ; �1at hema ti c a 1 r�ode 1 s V a po r ; Ozone ; Tra n s po rt Theory ; Gas e s

Compara t i v e Eval u a t i o n s Wa ter

b. ldentifiers/Open-Ended Terms SOL TRAN Mod e l ; Atwa ter and Sa 1 1 r'10de 1 ; H oyt Mod e l ; AS H RAE Mod e l ; Wa tt Hod e l ; Laci s and Ha n s en Mod e l ; Ma cht a Mode l ; Ma j umd a r Mod e l ; B i rd Mo d e l c . U C Categories

59 , 6 1 , 62 , 6 3

1 8 . Avai iab i l ity Statement

NT I S , U . S . Dept . of Comme rce 5285 P ort Roya l Roa d S p ri n g f i e l d , Va . 22 1 61

; 9. No. of Pages 62

20. Price $5. 25

Form N o . 8200-13 (6-79)

I

I