solar spectral irradiance in the visible and infrared regions

Photochemistry and Phorobioiogy Val. 48. NO. 4, pp. 477-486, 1988 Printed in Great Britain. All rights reserved

0031-8655/88 $03.00+0.00 Copyright @ 1988 Pergaman Press plc

SOLAR SPECTRAL IRRADIANCE IN THE VISIBLE AND INFRARED REGIONS

ALEX E. S. GREEN'.* and SHUN-TIE CHAI' 'Department of Mechanical Engineering and *Department of Engineering Sciences, University of

Florida, Gainesville, FL 3261 1, USA

(Received 2 December 1987; accepled 16 May 1988)

Abstract-The analytical formulas previously developed for estimating the spectral irradiance reaching the ground in the ultraviolet are extended into the visible and infrared (35C3000 nm). This approach has two distinct features: (1) all physical inputs for calculating the direct irradiance are given in analytical form, and (2) the diffuse spectral irradiance (skylight) is calculated using dimensionless ratios which relate it to the direct irradiance. In common with other approaches, the global spectral irradiance for arbitrary ground reflectivity is calculated from the sum of the direct and diffuse spectral irradiances and a divisor which depends upon the ground and air spectral reflectivities. The global spectral irradiance on a tilted surface may also be calculated in terms of the above quantities and two angles. As in the case of the ultraviolet. the formulas presented are intended for photobiological applications.

1. INTRODUCTION

Early measurements and calculations of visible and infrared radiation (VIR)? reaching the ground are summarized in a number of specialized studies (Elsasser, 1942; Goody, 1964; Green and Wyatt, 1965; Kondratyev, 1969). Following the launching of Sputnik 1 in 1957, a tremendous increase of effort began which is mainly recorded in specialized reports by aerospace firms and national laboratories and in highly distilled form in the archival literature. The most comprehensive methodology which has emerged is now based upon the Air Force Geophysi- cal Laboratory (AFGL) atmospheric absorption line parameter compilations, (Rothman et al., 1982a,b) a data bank which described several hundred thou- sand molecular transitions. A model and computer

*To whom correspondence should be addressed. ?Abbreviations: D, the downward direct spectral irradiance; G, global irradiance; H, extraterrestrial solar spectral irradiance; I , , the absorption intensities; IR, infrared; K,, aerosol extinction coefficient; K,, ozone absorption coefficient; Kh, mixed gas absorption coefficient; M , the ratio of the diffuse irradiance at 0 = 0" to the direct irradiance at 0 = 0"; M,,, sun-earth distance; N . the day of the year (1-365); R , ground reflectivity; r , air reflectivity; S , diffuse sky irradiance; Y, the ratio of the diffuse irradiance to the diffuse; irradiance at 0 = 0"; T , , air scattering transmittance function; T2. aerosol scattering transmittance function; T3, ozone absorption transmittance function; T.,, aerosol absorption transmittance function; Ts. water vapor absorption transmittance function; T6. mixed gas absorption transmittance function; t,, small characteristic numbers; UV, ultraviolet; V, visible; VIR, visible and infrared; W , wavenumber; W,, aerosol thickness; W,, the band centers; W,, total ozone thickness; Z, , the aerosol optical depth at 500 nm; z , the angle of incidence of the direct beam on the tilted surface; A , wavelength; p, cos 6; p,, generalized cosine function; T,, Rayleigh scattering optical depth; T ~ , aerosol scattering optical depth; T,. ozone absorption optical depth; T ~ , aerosol absorption optical depth.

code FASCODE (Fast Atmospheric Signature Code, Smith et al., 1978) performs, with a major computer, line by line calculations calling upon these atlases. Such procedures are useful for the purposes of high resolution detection systems and remote sensing with lasers.

For moderate resolution purposes, a FORTRAN computer code LOWTRAN has been developed through several versions (Kneizyo et al., 1983). These programs and modest data sets (Perluissi and Maragoudakis, 1984), with large computers, provide estimates of atmospheric transmittance and radiance from 350 to 40 000 cm-I (0.25 to 28.5 pm) averaged over 20 cm-' in 5 cm-' steps. Their results are useful for many applications in atmospheric science, climatology and meteorology. For photobiologists, solar radiation and illumination engineers, and other applied scientists lower resolution atmospheric spectral transmittance and solar spectral irradiances reaching the ground are more useful (the forest vs the trees problem!). Such needs have been addressed by Leckner (1978), Bird and Rior- dan (1986) and others who have developed simpler numerical programs and smaller data sets, suitable for desk type microprocessors. In the present work we further simplify such applied or engineering type calculations in the 0.35 to 3 pm region by adapting some features of work previously developed (Green, 1966; Green et al., 1974; Shettle and Green, 1974; Green et a l . , 1975) to estimate UV radiation effects (Green et al., 1975; Calkin, 1982). The most recent form of this approach (Green et al. , 1975; Calkin, 1982). The most recent form of this approach (Green et al., 1980; Schippnick and Green, 1982; Green, 1983) has been published as a BASIC program (Bjorn and Murphy, 1985) for use by plant physiologists. The equations have also been used to estimate ultraviolet irradiation of human cornea, lens and retina (Hoover, 1986).

477

478 ALEX E. S. GREEN and SHUN-TIE CHAI

One distinct feature of this ultraviolet approach is that all physical inputs for calculating direct irradiance are given in analytical form. This pro- vides unambiguous inputs at all intermediate wavelengths whereas tabular inputs are defined only at the given wavelengths. A second distinct feature is that the diffuse spectral irradiance (skylight) is calculated using dimensionless ratios which relate it to the direct irradiance. This simplifies estimating diffuse spectral irradiance which in the ultraviolet is usually comparable or greater in magnitude than the direct spectral irradiance. The ratio approach should also be useful in estimating visible and infrared diffuse spectral irradiances which are usually much smaller than the direct spectral irradiance. In extending the analytic-ratio method to the visible and infrared (VIR) we draw upon the work of Bird and Riordan (1986) and Leckner (1978) and their sources (Neckel and Labs, 1981; Frohlich and Shaw, 1980; Hay and Davies, 1978; Dickinson and Cher- emisinoff, 1980) both for inputs and for validation.

2. DIRECT IRRADIANCE

Extending our previous work (Green, 1983), the downward direct spectral irradiance D(A, 8 ) as a function of wavelength (A) and zenith angle (8) at the ground is placed in the basic form

D(A, 0) = P ff~(A)DseTl T2T3T4TSTb (1) where p. = cos 8, &(A) is the extraterrestrial solar spectral irradiance at one astronomical unit, D,, is a sun-earth distance factor, T I , T2, T3, T4 , Ts and Th denote transmittance functions for, (1) air scattering, (2) aerosol scattering, (3) ozone absorption, (4) aerosol absorption, (5) water vapor absorption and (6) mixed gas absorption respectively. For i = 1 to 4 T, = exp -al, the absorbance a,(A,8) = ~,/p., where T, is the corresponding optical depth. For i = 5 and 6 the absorbances obey band model formulas (see sections 7 and 8). The symbols pI, p2 (= p4), p3, k5, and k6 which allow approximately for earth roundness denote

p.1 = [(F2 + W ( 1 + G)1"2 (2)

where the t,'s are small numbers which depend upon the altitude distribution of the species. (Table 5a)

3. THE EXTRATERRESTRIAL SOLAR SPECTRAL IRRADIANCE

The extraterrestrial solar spectral irradiance H&) used here is essentially the 10 nm resolution version of the Neckel and Labs (1981) solar spec- trum as listed in Bird and Riordan's Table 2-1 (1986) for 122 wavelengths. To fit these data, we extend our U V approach in which we used a black body formula with a series of Gaussian modifiers to simu- late the Fraunhofer structure in the extraterrestrial solar spectral irradiance. Here we use an empirical distribution function which contains the Planck

function as a special case together with a series of Gaussian modifiers

[ 1 + xiAiexp(, - w)] (3)

where KO = 2300 W/m2 km, q = 728.5 nm, a g = 4.8, and Po = 2.0. Note that for a 5000 K Planck function ciO = 5, P o = 1, q = c2/T = 28 779 nm where c2 is the second radiation constant and KO depends upon the solar area, emissivity, geometric factors and the first radiation constant. The Gaus- sian.modifier parameters are given in Table 1. Fig- ure 1 illustrates the analytic function and the exper-

Table 1. Gaussian modifiers

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

10.

386.640 391.138 410.280 456.000 672.941 827.330 837.350 934.950

1377.200 2669.790

Ai

-0.18841 -0.11838

0.22462 0.14190

- 0.02772 - 0.04920 -0.01382 -0.0805 1

-0.34589 0198830

c,

38.9360 2.6710 9.3381

15.4584 20.9260 80.6520 12.0810 19.8210

320.8600 320.1900

2100 r

0 I I I I 1

350 900 1450 ZOO0 2550 3100

WAVELENCTB (nm)

Figure 1. The extraterrestrial spectral irradiance. The curve is the analytic representation and the circles are representative points from the Neckel and Labs compi-

lation.

Solar spectral irradiance in the visible and infrared regions 419

WAVELENGTE (ad

Figure 2. Analytical representations of the optical depths for Rayleigh scattering (7,). aerosol scattering ( T ~ ) and absorption (TJ. and ozone absorption ( T ~ ) for T, = 0.3

and W , = 0.344 atm-cm.

imental data. At wavelengths longward of, 3 pm, thermal atmospheric radiation comes into play, the equations for radiative transfer become much more complex and direct photobiological effects are small.

4. RAYLEIGH OPTICAL DEPTH

To incorporate the Rayleigh scattering optical thickness over this extended range, we use a formula proposed previously (Green, 1983)

n ( X ) = K~(p/p~)(AtJA)'exp[al(ho/X)~l (4)

but with parameters K1 = 0.1380, a, = 0.05022, At) = 500 nm and = 1013 mb. Figure 2 illustrates this function which is within the line width of the function used by Bird and Riordan and varies by about 1% from the function of Frohlich and Shaw (1980). The main purpose of this figure is to illus- trate the relative roles of the Rayleigh scattering vis- a-vis aerosol scattering and absorption and ozone absorption at various visible and infrared wavelengths.

5. AEROSOL OPTICAL DEPTH

The aerosol optical depth is one of the most highly variable inputs needed for VIR calculations and measurement interpretation. Shettle and Fenn (1979) have proposed a series of models for the properties of aerosols of the lower atmosphere and the effects of humidity variations on these optical properties. They consider aerosols which are representative of those found in rural, urban, and mari- time air masses and in the troposphere at various humidities. Using model size distributions and complex indices of refraction they computed extinction coefficients for wavelengths between 0.2 and 40 pm.

For the purpose of this study between 0.35 and 3.1 pm, we concentrate our attention on their rural

model at 50% relative humidity. We take the Shettle-Fenn extinction coefficients computed for the 14 VIR wavelengths as input data and simplify and modify our previous formulas to

ke(h) = ke(An)(l + Pz) '{P2 + e x p [ ( A - W k l ) ( 5 )

(6)

7 2 = (1-r)W,k,(A) (7)

= r W, k,(A) (8)

r(A) = r2(h&)"z

where W , is the aerosol thickness, r = r(A) relates the absorptive to the scattering components, A. = 500 nm, P2 = -0.8174, A2 = 2475 nm, r2 = 0.067, a2 = -0.9369 and k&) = 0.1678.

The values of k,(X,) are fixed using the Shettle-Fenn diagrams for An = 500 nm at 50% relative humidity and 15 000 (particles/cm') particle number density. For different particle number den- sities one should proportion the parameter k,(Ao) accordingly. In this work we refer aerosol parameters to the aerosol optical depth at 500 nm using

T , = k, (A") W, (9)

Thus using Eqs. 5-8, we may tie .*(A) and T'(X) to the number T , obtainable with a sun photometer and the assignment of a few parameters P2, A2, r2, and a2 which depend somewhat upon the nature of the aerosols and the relative humidity (Shettle and Fenn, 1979). Aerosol optical depths 'r2(h) and T ~ ( A ) for a rural aerosol at a representative turbidity T ,

= 0.3 are shown in Fig. 2.

6. THE OZONE OPTICAL THICKNESS

In our UV studies, we consider the Hartley and Huggins bands which are strong ozone absorption bands in the ultraviolet from 180 to 345 nm. In the present work we allow for the Chappuis band which is a weak band from 440 to 740 nm. Here we approximately fit the ozone absorption coefficient data (Leckner, 1978) for the visible wavelengths with the double exponential

where K," = 0.1274 atm-cm, A, = 594.0 nm, A3 = 35.2 nm.

The ozone optical thickness is given by

T g = W&3(A) (111 where W, is the total ozone thickness. In general, W3 is variable averaging 0.38 cm at high latitudes and 0.24 cm towards the equator. The ozone optical depth vs wavelength for a representative ozone thickness is illustrated in Fig. 2.

7. WATER VAPOR ABSORPTION

Many studies have been published on the absorption properties of water vapor and we refer the


Table 2a. The big bands of water vapor

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

3755.9 5331.9 7249.9 8807.0

1061 3.4 12151.3 13830.9 15348.0 16899.0

2662.5 1875.5 1379.3 1135.5 942.2 823.0 723.1 698.3 591.7

241000 .0 27800.0 21000.0

1498.0 877.0 46.0 50.0 16.6 5.0

1 0.52 0.62

1 1 1 1 1

0.40

Table 2b. The secondary bands of water vapor

1. 3657.1 2734.5 16600.0 7.0 2. 5234.9 1910.2 573.0 1 3. 6871.4 1455.3 1896.0 1 4. 9000.1 1111.1 66.0 1 5. 11032.4 906.4 103.0 1

reader to the general works on this topic (Herzberg, 1945; Elsasser, 1942; Goody, 1964; Kondratev, 1969). In the wavelength range of our interest, bands of increasing intensity lie at 600, 700, 800, 900, 1100, 1400, 1900 and 2662 nm. Various band models have been developed for water vapor transmittance when the monochromator band width is large compared to rotational line widths and spacings, but small compared to vibrational spacings. Here we use the phenomenological IR transmission model of Green [Green and Wyatt, 1965, Eqs. 8-4 (38)] in the simplified form proposed by Leckner (1978)

(12) and x5 = 0.2385, .E5 = 20.07, a5 = 0.45. Rather than use numerical tables for the spectral function k,(A), we incorporate the big band centers and big band intensities of Green and Mann (1987) into a function which represents the water absorption coefficient vs wavelength. Thus we write

where

w = lo7/& w, = 1071h, (14) y = 0.07389 and 6 = 0.005. Here wn denotes the wave numbers of the band centers and I , the absorption intensities as given by the formulas of Green and Mann, Sn denotes the empirical factors which modify some of these band intensities to give agreement with atmospheric observations. Table 2a gives these constants. Table 2b also gives the corresponding constants for secondary bands of H20 vapor which are apparent in atmospheric absorption measurements and which are included to match the table of absorption constants listed by Bird and Riordan. Figure 3a gives the comparison between the BR table and our analytic function.

8. UNIFORMLY MIXED GAS ABSORPTION

In the VIR region of concern here (350-3000 nm), molecuIar band absorption by the uniformly mixed gas, 02, C 0 2 , and CH4 also contribute to optical absorption. Only three oxygen bands at

wAvELEK;TH ( m 1 WAVELENCTH ( mn )

Figure 3 . (a) Water absorption vapor coefficient. (b) Mixed gas absorption coefficient. The curves are the analytic representation (AR). The points are from Bird and Riordan (BR).

Solar spectral irradiance in the visible and infrared regions 48 1

Table 3. Parameters for mixed gas absorption coefficients

W" L I,,.% 6,

- 0 2 1. 14526.4 688.4 33.0 0.0032 2. 13121.6 762.1 286.8 0.0032 3. 7884.6 1268.3 45.0 0.0040

-co, 4. 6973.0 5. 6350.0 6. 6221.8 7. 5100.0 8. 4978.1 9. 4853.2

10. 3714.7 11. 3611.7

1434.1 1574.8 1605.7 1960.8 2008.8 2060.5 2692.0 2767.8

1 .0 0.0020 2.3 0.0020 2.3 0.0020

66.7 0.0020 300.0 0.0020

16.7 0.0020 1666.2 0.0020 3333.3 0.0020

-CH4 12. 6004.9 1665.3 0.02 0.0035

688.4, 762.1, and 1268.3 nm are noticeable in atmospheric optics. Eight C 0 2 bands are observable, the shortest wavelength band is at 1434 nm, and the longest and strongest band lies near 2700 nm. An observable CH4 absorption band at 1667 nm is also included.

To generate the transmittance function T, for the uniformly mixed gases, we use the same formulas (Eqs. 12-14) to determine the spectral function k6 as in the case of water vapor but input the w,, s,, I , , and 6, in tabular form. We also set w6 = 1, in effect, incorporating this thickness constant into the k6 function. The transmission function parameters for the uniform gases given by Leckner are x6 = 1.41, i6 = 115.3 and c.6 = 0.45. Table 3 gives a set of parameters and Figure 3b gives a comparison of the analytic absorption coefficients with tabular data.

9. DIFFUSE AND GLOBAL IRRADIANCES

Skylight, the scattered solar radiation, arises from Rayleigh scattering, aerosol scattering, and multiple scattering between the ground and air. In the absence of a theoretical analytical form, we represent the diffuse irradiance on a horizontal surface at the ground in terms of ratios which relate the diffuse component to the direct component (Green, 1983). This device tends to minimize the dynamic ranges of the important dependent variables and is adaptable to the new VIR physical inputs.

While skylight is a major component of the total irradiance in the UV, at longer wavelengths in the visible and infrared, skylight makes decreasingly smaller contributions, which favors the ratio method.

The diffuse sky irradiance is expressed as

S(h,B) = Y(A,B)M(A)H(A)D(h,O") (15) where

Y(h ,@) = S(A,B)/S (A,@) ( 16)

and

M ( h ) = S(h,O")/D(h,O") (17) These ratios have relatively limited dynamic range whereas the sky irradiance itself, as a function of wavelength and angle, can vary over many orders of magnitude. In this work, we preserve these basic aspects of the ratio method but generalize the func- tional forms chosen to represent Y (h,0) and M(h) . Thus we have proceeded in a systematic way from zero to large zenith angle and from the aerosol free models to the models with aerosols, letting the multidimensional empirical formulas successively evolve.

The Y has been generalized to

Empirical functions which lead to satisfactory VIR results are given in Table 4.

The M ( h ) function has been generalized to the form

M ( h ) = IA.r~~~maFa3 + A,2~2~.(1 + Aa1~lm~Fa3>] F a d

where the functions are also given in Table 4. Figure 4a illustrates this function.

Another contribution to skylight depends on the ground and air reflectivities, the color of adjacent objects and the angle of illumination. To allow for this contribution, we write the global irradiance in the forms

(19)

Table 4. Empirical formulas


100

10-1

10-2

10-3

3% 3W 1 4 1 2608 3SE 9W I I E ZOW 2551

WAVFLENCTH (rm) WAVELENCTH (m)

Figure 4. (a) M ( A ) function. (b) r(X) function.

G(X,B,O) = D(A,6) + S(A,B) (21)

where r,(X) is the effective air reflectivity and R is ground reflectance (assumed diffuse). The air

between our calculation and Bird-Riordan's for the same atmospheric conditions.

reflectivity is expressed by 10. GLOBAL IRRADIANCE ON HORIZONTAL AND TILTED SURFACES

r,(X) = [ A b i 7 1 m h F b 3 + A b 2 7 2 P b ] F h 4 (22)

where Fh3, Fh4 and the other functions and parameters are also given in Table 4. All parameters are listed in Table 5a and Table 5b. Figure 4b illustrates the r,X,B) at three aerosol turbidities coefficients. The abrupt drops in the curves are caused by water vapor absorption.

Now we have a complete set of formulas to calculate direct, diffuse and global irradiances on a horizontal surface. Figures 5-7 show comparisons

Several algorithms have been proposed that con- vert the global irradiance on a horizontal plane to a tilted surface. Bird and Riordan obtained the best agreement with rigorous modeled data for clear-sky conditions using the Hay-Davis (1978) algorithm. We can also use the spectral direct, diffuse, and then global irradiance on a horizontal-plane as calculated in previous sections as basic inputs to this algorithm.

Table 5a. Numerical parameters

1 2 3 4 5 6

0.0018 0.5700 0.5205 0.5248 0.3712

-2.7705 0.1440 0.1440 1.8181

- 13.3850

0.0003

1.4004 0.7561

7.9911 1.1703 1.2660

15.8591

-

- 0.2276

-7.0712

0.0074 0.0003 0.0009 0.0018 1.1597 - 0.1830 0.057 0.0813 - 0.3575 0.5023 0.3413 36.552 5.4876 4.2504 0.0001 0.0802 0.2014 0.7406 3.9642 0.3238

Table 5b. Numerical parameters

m, P3 qo v ,

i = a 1.0713 1.0635 0.3240 0.0060 i = b 0.8096 1.1565 0.3698 0.1728

a = 87.41 q = 2.6768 t = 0.041


350 9w 1450 zoo0 350 goo 14sa 2006 2550

wAva.lwrtl ( m 1 WAVFLWG'IH ( m

Figure 5 . (a) Direct Irradiance ( T ~ = 0.1, W , =0.31 atm-cm, W , = 2.93 cm, 8 = 0". Solid line-AR, dashed line-BR. (b) Direct irradiance (T.~ = 0.3, W , = 0.344 atm-cm W , = 1.42 cm. 8 = 60". Solid

line-AR, dashed line-BR.

(a)

Figure 6. Diffuse irradiance. Solid line-AR, dashed line-BR. (a) for T, = 0.3, W , = 0.344 atm- cm, W , = 1.42 cm, 8 = 60". (b) for T , ~ = 0.5, W , = 0.31 atm-cm, W , = 2.93 cm, 8 = 30".

Thus the spectral global irradiance on an inclined surface is represented by

G(A,B,R,f) = D(A,O")COS(Z) + [G(A,B,R) -

D( A ,B)] [D( A ,O")cos(z)/H( A) + 0.5(1 +cos(t))(l- D(A,O")/H(A)] + 0.5R( 1 - cos(t))G( A ,€I ,R)

(23) where z is the angle of incidence of the direct beam on the tilted surface and t is the tilt angle of the inclined surface. The tilt angle is zero for a horizontal surface and 90" for a vertical surface.

The first term in the above equation is the direct component on the inclined surface. The second term has two components: the first is the aureole and the second is a diffuse skylight component. The third term accounts for the isotropically reflected radiation from the ground. Figure 8 shows the agreement between our calculations and those of Bird and Riordan based upon the Hay-Davis algorithm.

Now we have completely developed the analytic formulas to calculate the irradiance reaching the ground in visible and near infrared regions. By vary- ing input parameters such as solar zenith angle, ozone total amount, water vapor total amount,


Figure 7. Global irradiance. Solid line-AR, dashed line-BR. (a) for 5, = 0.1, W , = 0.344 atm-cm, W , = 1.42 cm, 8 = O", R = 0.2 (b) for T , ~ = 0.3, W , = 0.31 atm-cm, W , = 1.93 cm, 8 = 70", R =

0.2.

0

2

v

0 s

0

T In

r I

I I I

9W 1 6 0 2000 2550 350 900 1150 2000 351

HAVELENC'IH ( nm 1 HAVLUC;TH ( l l ~ 1

Figure 8. Global irradiance on a tilted surface. Solid line-AR, dashed line-BR. (a) for T , ~ = 0.3. W, = 0.344 atm-cm, W , = 1.42 cm, 8 = 50". t = 30", R = 0.2. (b) for T , = 0.3, W , = 0.344 atm-

cm, W , = 1.42 cm, 8 = 30", t = 60", R = 0.2.

atmospheric turbidity, surface pressure, ground albedo, and the collector tilt angle, we can calculate direct and diffuse and then, global irradiances for different atmospheric conditions. Adequate corrections for sun-earth distance variations can also be included by using in Eq. 1 the relative sun-earth distance factor.

D,, = (1 + 0.0167 cos [(2~/365.25)(N - 3.4)]}-*

where N represents the day of the year. More accu- rate corrections are given in the literature (Bird and

Riordan, 1986; Spencer, 1971; Bjorn and Murphy, 1985; Duffet-Smith, 1985).

Bjorn and Murphy (1985) have published a computer program in BASIC which gives the solar spectral irradiance in the UVB region based upon the formulas of Green (1983). The first block of this program calculates the solar angle given the lati- tude, month, date and time of day based upon formulas recommended by Diffey (1977). This block can also be utilized in conjunction with a program by M. Kawejsza et al. , (1987-unpublished) which


calculates the VIR irradiances using the equations ,

of this paper. This program is available upon request to one of us (AESG).

I I . DISCUSSION AND CONCLUSIONS

The methodology given in this report extends the analytic input method for direct irradiances and the ratio method for estimating diffuse irradiances into the visible and infrared. In effect we have shown that even the complex attenuating role of water vapor and other molecular absorbers can be handled by a tractable set of equations not much more diffi- cult than those for U V irradiance estimation. The fact that some of the parameters in these molecular spectral functions can be related to fundamental molecular vibrational properties (Green and Mann, 1987) is an additional valuable feature. The reader should also refer to the more numerical approaches of Bird and Riordan (1984) and Leckner (1984) which also treat this complex problem with a ‘user friendly’ approach. Our analytic inputs for direct irradiances may have some advantages since, because of the specific connections which can be made to fundamental molecular properties, it should be possible to add absorption bands for other species e.g. NzO, CO in regions of high air pol- lution. Furthermore, the input parameters for lower resolution studies can be estimated from the 10 nm resolution spectral functions or higher resolution spectral functions (Green et al., 1988). Our ratio functions for obtaining diffuse irradiances would not be expected to change greatly with resolution since these depend mainly upon Rayleigh and aerosol scattering which change relatively slowly with wavelength. In any event, we hope that these simple approaches to the estimation of natural VIR irradiance will be useful for broader studies of photobiological mechanisms.

Acknowledgements-This work was sponsored by the Corning Glass Works. We particularly thank Herbert L. Hoover and Thomas J . Loomis for encouraging the initiation of this effort and the publication of our results. We also thank Dr. Ady Mann for helpful discussions and Michael Kawejsza and David Milum for assistance with the calculations.

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