1. Introduction
Aerosol particles, for example, desert dust, smoke from biomass burning, and urban–industrial pollution (Kaufman et al. 1997a), can affect the radiation budget and the temperature field by changing the energy balance and distribution of solar radiation in the atmosphere. To understand this radiative forcing of climate, we need to determine the effect of aerosol on absorption and partition of spectral solar radiation between the earth's surface and atmosphere. Aerosol increases atmospheric absorption of solar radiation and reflection of sunlight back to space. Both of these processes reduce the solar radiation reaching the earth's surface. The reflection of radiation to space may counteract the greenhouse warming by cooling the earth system (Charlson et al. 1992). The redistribution of radiation is expected to change the temperature profiles (Alpert et al. 1998), atmospheric stability and possibly cloud formation (Ackerman et al. 2000).
Satellite spectral measurements are used for remote sensing of the presence of aerosol, for example, the effective aerosol optical thickness derived from Advanced Very High Resolution Radiometer (AVHRR) (Husar et al. 1997) and the absorbing aerosol index derived from Total Ozone Mapping Spectrometer (TOMS) (J. R. Herman et al. 1997). New efforts with present satellites [AVHRR; Ocean Color and Temperature Scanner (OCTS); Polarization and Directionality of the Earth's Reflectances (POLDER)] and new satellite missions [Earth Observing System (EOS) moderate resolution imaging spectroradiometer (MODIS); EOS multiangle imaging spectroradiometer (MISR); Advanced Earth Observing Satellite (ADEOS) Global Imager (GLI)] work toward quantification of remote sensing of aerosol loading (Kaufman et al. 1997a; Tanré et al. 1997; M. Herman et al. 1997; Nakajima et al. 1999; Higurashi and Nakajima 1999). Spectral fluxes are also derived from the measured radiation field by the MODIS instrument on EOS Terra (Tanré et al. 1997; Kaufman et al. 1997b). These measurements will provide spectral fluxes at the top of the atmosphere and should be supplemented by measurements of the aerosol attenuation of the spectral solar flux reaching the earth's surface (King 1979; Bird and Riordan 1986; Harrison et al. 1994, Eck et al. 1998).
The difference between the aerosol forcing at the surface and at the top of the atmosphere is the rate of aerosol heating of the lower atmosphere (Satheesh and Ramanathan 2000). Substantial advancement has been made in regard to the broadband partition of solar radiation and measurements of the flux reaching the surface (Charlock and Alberta 1996; Pinker and Laszlo 1992; Christopher et al. 1998). But in order to resolve the present discrepancies between measured and calculated solar fluxes reaching the surface (Li et al. 1995; Arking 1996; Ramanathan et al. 1995; Cess et al. 1995), spectral measurements of the partition of sunlight are required (e.g., Stephens and Tsay 1990; Vogelmann et al. 1998; Pilewskie et al. 1998), see also review by Li et al. (1997). Spectral partition can be used to decide if the additional absorption is due to unresolved water vapor absorption in the near-IR (e.g., Belmiloud et al. 2000), or due to new molecular absorption not detected before, or wrong aerosol absorption model in a specific spectral region.
Here we introduce a new technique to derive the spectral diffuse radiation reaching the surface. This diffuse flux of scattered sunlight in the sky is derived from sky measurements in the principal plane. The method is suitable for the existing measurements by the 50–100 instrument strong global Aerosol Robotic Network (AERONET) of sun/sky radiometers, which began operation in 1992 (Holben et al. 1998; http://aeronet.gsfc.nasa.gov). It is very different from present flux measurements, thus introducing “a second opinion” on the effect of aerosol on attenuation of downward spectral radiation, and an inexpensive method to expand the coverage of the spectral flux measurements. We first describe the pros and cons of the new method and its application to several AERONET prime sites.
2. The remote sensing approach
Derive the aerosol optical thickness, τa′ from the AERONET measured attenuation of direct sunlight.
Calculate an arbitrary sky illumination La(τ, ρ, θ, ϕ) assuming a given aerosol model, for example, a lognormal distribution of spherical homogenous aerosol particles with mean particle radius of Rg = 0.06 μm, standard deviation of σ = 0.6, single scattering albedo of ω = 0.98, refractive index of 1.53−0.003i, and constant surface reflectance of ρ = 0.1. In the single scattering approximation La(τ, ρ, θ, ϕ) is La(θ, θϕ, ϕ) = F0ω0aPa(Θ)τa/4 cos(θ), where ωϕa and Pa(Θ) are the results of the arbitrary aerosol model and τa is the optical thickness derived from the solar measurements.
- Convert the arbitrary sky radiance, La(τ, ρ, θ, ϕ), into the true sky radiance, Ls(τ, ρ, θ, ϕ), by scaling it with the radiance measured in the principal plane, Lpp-m(Θ):where Lpp-a(Θ) is the value of La in the principal plane, and Θ is scattering angle for θ, ϕ [see Eq. (1)]. In the single scattering approximation Eq. (5) meanswhich is the “true” 2D distribution of sky brightness. Here ω0m and Pm(θ, ϕ) are the exact, though unknown, quantities in the sky. Therefore, in the single scattering approximation the scaling removed any memory of the assumed aerosol properties. Multiple scattering can be expected to retain some of the memory for these properties.
- Integrate the measured radiance Ls(τ, ρ, θ, ϕ) to get the derived or measured diffuse sunlight flux reaching the surface:
The effect of multiple scattering on errors in the scaling [Eq. (5)] is proportional to the aerosol optical thickness. Therefore a sensitivity study is performed for optical thickness of 1.0, using rigorous radiative transfer model, to calculate the residual error. Smaller optical thicknesses are expected to generate proportionally smaller errors. Table 1 summarizes the results. Assuming that the errors are independent, the total error is expected to be smaller than 2.5%. This is substantially smaller than calibration errors of radiometers, or errors introduced in direct spectral flux measurements. Therefore the new method, of deriving the diffuse solar flux on the earth's surface from the measured principal-plane sky radiation is very attractive. As in any method that derives properties of the atmosphere in cloud-free conditions, cloud screening is a critical element. It is described in the next section.
3. Cloud screening
4. Application
Are the fluxes derived from the AERONET principal plane measurements in agreement with direct flux measurements and with the aerosol physical models? The next several figures address this issue for several aerosol types: smoke, dust, and urban–industrial pollution. Figure 3 shows a comparison between two measurements and one estimate of the spectral diffuse solar flux reaching the surface in Cuiabá, Brazil, during the Smoke, Clouds And Radiation-Brazil (SCAR-B) experiment, in 1995:
shadow band measurements (open symbols),
smoke aerosol model [Remer et al. (1998)—full symbols], and
fluxes derived from the AERONET data (abscissa).
We consider it a partial experimental confirmation (for optical thickness <0.6) of the method to derive the fluxes from the AERONET principal plane measurements, since the smoke aerosol model was heavily verified against in situ and radiation measurements (Remer et al. 1998). Remer et al. model is based also on AERONET measurements in Brazil, but in a different time period and on analysis of the almucantar measurements.
A very interesting behavior of the downward diffuse solar flux is shown in Fig. 4. As the aerosol optical thickness increases, it can be expected that the diffuse solar flux to the ground will first increase, reaching a maximum and then decrease. For optical thicknesses less than 1.0, atmospheric scattering transfers photons from the direct solar beam to the diffuse flux, giving the sky its brightness and color. For higher optical thickness, aerosol absorption and backscatering to space decreases the already large diffuse flux, eventually reaching darkness experienced under a heavy dust storm or smoke from a wild fire. The optical thickness for which the sky brightness reaches the maximum value is determined by the aerosol single scattering albedo and backscatering coefficient (Kaufman and Holben 1996). The data indicate higher diffuse sunlight than the model, mainly for high optical thickness. This may be due to higher single scattering albedo, or smaller backscattering coefficient. Sky heterogeneity, discussed later, may also contribute to this difference.
The data in GSFC deviate significantly from the urban–industrial model of Remer and Kaufman (1998) and therefore require further analysis. To decide if the discrepancy between the model and the AERONET data can be due to residual, unresolved clouds, the spectral dependence of the sky fluxes, given by the sky Ångström exponent, αL: αL = ln(F1/F2)/ln(λ1/λ2) is shown in Fig. 6. For AERONET and the model we use λ1 = 0.44, λ2 = 1.02 μm. A very good agreement is found between the values of the sky Ångström exponent for AERONET and the model. The Ångström exponent should be zero, or even negative for clouds. So it is not possible that the differences observed in Fig. 5 are due to unresolved clouds in the field of view. We ruled out the effect of uncertainty in the real refractive index that is strongly affected by the inclusion of liquid water in high humidities. Note that the attenuation of solar radiation reaching the surface in Créteil show much better agreement with the urban–industrial model (Fig. 7) than the GSFC data. The main difference in the data from Créteil and GSFC is the presence of broken cloudiness in GSFC that caused a rejection of 55% of the data versus 10% in Créteil. The GSFC data are further analyzed in the discussion section.
5. Aerosol radiative impact at the surface
The results are summarized in Table 3, for the spectrally averaged values of the exponent bλ. Both the model value of bλ and the measured values are used in the calculations. The calculations were performed for solar zenith angles every 10°. Assuming equal probability of all solar zenith angles, the table also averages the aerosol radiative impact over the 24 hours. The results are plotted in Fig. 7 as a function of the spectrally average value of bλ. In all cases the measured flux attenuation is smaller than in the model, but the difference is striking for measurements of urban–industrial pollution in GSFC. The radiative impact by the aerosol due to the attenuation of total sun light for unit optical thickness as measured (or modeled) is −81 (−105) W m−2 for smoke, −80 (−90) W m−2 for dust, and −80 (−98) W m−2 for urban–industrial aerosol in France but only −48 (−98) W m−2 for urban–industrial aerosol in Maryland. Note the large difference from the modeled results for the Maryland site.
6. Discussion and conclusions
A new technique was demonstrated to derive the solar diffuse spectral flux reaching the surface from principal-plane radiances measured by the AERONET sun/sky radiometers. While this is not a direct measurement of the flux, the flux can be derived from the principal-plane radiation field within 2.5%. This is in addition to the calibration error estimated to be around 5%. The advantage of the technique is the use of an existing network with 6 years of data from 50–100 instruments, better cloud screening that allows the derivation of the aerosol effect also in the presence of some cloudiness and smaller sensitivity to horizon uniformity and instrumental angular response. Application of the technique to several sites show some interesting differences from aerosol models.
While our models predict that the attenuation of total sunlight reaching the surface should be between −90 and −105 W m−2, with the lowest attenuation for dust and highest for smoke, the measurements indicate −80 W m−2 in all the cases except for GSFC near Washington, D.C. The fact that observations of varying aerosol type give the same attenuation is surprising. Apparently the differences between these aerosol types in single scattering albedo cancel out the differences in particle effective radius. For example, smoke—due to its small particle size (effective radius of 0.14 μm; Remer et al. 1998)—does not interact effectively with solar radiation for wavelengths above 1 μm, while dust interacts with the whole solar spectrum (effective radius of 1–3 μm; Tanré et al. 2000). However, smoke single scattering albedo is 0.85 to 0.90 (Kaufman et al. 1998), while dust single scattering albedo is close to 1.0 for the solar spectrum above 0.55 μm (Tanré et al. 2001). The smaller dust absorption reduces its effect on the solar radiation near the surface. Apparently these two processes cancel each other in the present case. The value of −80 W m−2 is similar also to the forcing measured in the Indian Ocean Experiment (INDOEX) (Satheesh and Ramanathan 2000). The higher modeled radiative forcing at the surface (Table 3) is the result of the higher attenuation coefficients (Table 2). These theoretical attenuation coefficients are uncertain. An uncertainty in the single scattering albedo of Δω0 = ±0.05 corresponds to an uncertainty in the attenuation coefficient bλ = ±0.04 for solar zenith angle of 50° or ±7 W m−2 in the daily flux at the surface (based on the equation in Fig. 7). Uncertainty in the particle size and dust nonsphericity will add to these uncertainties. In the case of smoke (see Figs. 3 and 4) the model underestimates the diffuse flux to the surface for high optical thickness. This is expected due to the increase of the smoke single scattering albedo and particle size as a function of the smoke optical thickness (Kaufman et al. 1998).
In GSFC we measured much lower attenuation than expected from the model calculations and much smaller than the attenuation in Créteil near Paris. We attribute this difference to the presence of broken clouds in the GSFC and the entire northeast United States in the summer, with a cloud fraction that is correlated with the presence of the aerosol (or optical thickness). These clouds, although eliminated from the direct field of view, can illuminate the principal plane from the side, and trap sunlight between the cloud layer and the surface, thereby increasing the solar flux reaching the surface. Monte Carlo calculations for a similar cloud effect on the brightness of a cloud-free region observed from space was presented by Kobayashi et al. (2000). The cloud fraction increases from 0.05 for low optical thickness to 0.2 for aerosol optical thickness of 0.6 at 0.67 μm (Fig. 8). We simulated the scattering among the aerosol layer, the clouds and the surface in the presence of variation in the cloud fraction, using a simple back of the envelop model (see appendix) that models the effect of the change in the cloud fraction as a function of the aerosol optical thickness. Clouds scattered direct sunlight and sunlight reflected from the surface. The extra photons that are scattered from the clouds illuminated the aerosol and molecular column in the cloud-free region, and contributed the extra energy that compensated partially for the aerosol attenuation. The increase in the cloud fraction and the cloud effect, compensates partially for the reduction in the irradiance of the surface by the increase in aerosol backscattering to space and aerosol absorption. The results are demonstrated in Fig. 9 and compared with the measurements. The cloud effect reduced the aerosol attenuation coefficient on average by factor of 2. This lower value is similar to the present measurements in GSFC and represents an interesting interaction among change in haziness, correlated change in fraction of broken cloudiness and the radiation field, that we did not find in other locations.
In calculating the integral on the solar spectrum, we assumed that we can use spectrally constant values of the Ångström exponent α and of the aerosol attenuation coefficient b. Spectral measurements of the sky radiance in a wider spectral range are needed to improve beyond this assumption. However, in most cases the aerosol forcing for wavelengths >1 μm is small and the assumptions are not expected to introduce a significant errors.
Acknowledgments
We would like to acknowledge the AERONET and PHOTON networks that provided the data. We also wish to express our gratitude to the director of the Servico National de Meteorologia e Geophysica (SNMG), Cape Verde for hosting and maintaining the AERONET site.
REFERENCES
Ackerman, A. S., Q. B. Toon, D. E. Stevens, A. J. Heymsfield, V. Ramanathan, and E. J. Welton, 2000: Reduction of tropical cloudiness by soot. Science, 288 , 1042–1047.
Alpert, P., Y. J. Kaufman, Y. Shay-El, D. Tanre, A. da Silva, S. Schubert, and Y. H. Joseph, 1998: Quantification of dust-forced heating of the lower troposphere. Nature, 395 , 367–370.
Arking, A., 1996: Absorption of solar energy in the atmosphere: Discrepancy between model and observations. Science, 273 , 779–782.
Belmiloud, D., R. Schermaul, K. M. Smith, N. F. Zobov, J. W. Brault, R. C. M. Learner, D. A. Newnham, and J. Tennyson, 2000: New studies of the visible and near-infrared absorption by water vapour and some problems with the HITRAN database. Geophys. Res. Lett, 27 , 3703–3706.
Bird, R. E., and C. Riordan, 1986: Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes at the earth's surface for cloudless atmospheres. J. Climate Appl. Meteor, 25 , 87–97.
Bush, B. C., and F. P. J. Valero, 1999: Comparison of ARESE clear sky surface radiation measurements. J. Quant. Spectrosc. Radiat. Transfer, 61 , 249–264.
Cess, R. D., and and Coauthors, 1995: Absorption of solar radiation by clouds—Observations versus models. Science, 267 , 496–499.
Charlock, T. P., and T. L. Alberta, 1996: The CERES/ARM/GEWEX experiment (CAGEX) for the retrieval of radiative fluxes with satellite data. Bull. Amer. Meteor. Soc, 77 , 2673–2683.
Charlson, R. J., S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley Jr., J. E. Hansen, and D. J. Hofman, 1992: Climate forcing of anthropogenic aerosols. Science, 255 , 423–430.
Christopher, S. A., M. Wang, T. A. Berendes, R. M. Welch, and S. K. Yang, 1998: The 1985 biomass burning season in South America: Satellite remote sensing of fires, smoke, and regional radiative energy budgets. J. Appl. Meteor, 37 , 661–678.
Dave, J. V., and J. Gazdag, 1970: A modified Fourier transform method for multiple scattering calculations in a plane parallel Mie atmosphere. Appl. Opt, 9 , 1457–1466.
Dubovik, O., A. Smirnov, B. N. Holben, M. D. King, Y. J. Kaufman, T. F. Eck, and I. Slutsker, 2000: Accuracy assessment of aerosol optical properties retrieval from AERONET sun and sky radiance measurements. J. Geophys. Res, 105 , 9791–9806.
Eck, T. F., B. N. Holben, I. Slutsker, and A. Setzer, 1998: Measurements of irradiance attenuation and estimation of aerosol single scattering albedo for biomass burning aerosols in Amazonia. J. Geophys. Res, 103 , 31865–31878.
Hansen, J. E., and L. D. Travis, 1974: Light scattering in planetary atmospheres. Space Sci. Rev, 16 , 527–610.
Harrison, L., J. Michalsky, and J. Berndt, 1994: Automatic multifilter rotating shadow-band radiometer: An instrument for optical depth and radiation measurements. Appl. Opt, 33 , 5118–5125.
Hegg, D. A., J. Livingston, P. V. Hobbs, T. Novakov, and P. Russell, 1997: Chemical apportionment of aerosol column optical depth off the mid-Atlantic coast of the United States. J. Geophys. Res, 102 , 25293–25303.
Herman, J. R., P. K. Barthia, O. Torres, C. Hsu, C. Seftor, and E. Celarier, 1997: Global distribution of UV absorbing aerosol from Nimbus 7 TOMS data. J. Geophys. Res, 102 , 16911–16922.
Herman, M., J. L. Deuzé, C. Devaux, P. Goloub, F. M. Bréon, and D. Tanré, 1997: Remote sensing of aerosol over land surfaces including polarization measurements and application to POLDER measurements. J. Geophys. Res, 102 , 17039–17050.
Higurashi, A., and T. Nakajima, 1999: Development of a two-channel aerosol retrieval algorithm on a global scale using NOAA AVHRR. J. Atmos. Sci, 56 , 924–941.
Holben, B. N., and and Coauthors, 1998: AERONET—A federated instrument network and data archive for aerosol characterization. Remote Sens. Environ, 66 , 1–16.
Husar, R. B., J. Prospero, and L. L. Stowe, 1997: Characterization of tropospheric aerosols over the oceans with NOAA Advanced Very High Resolution Radiometer optical thickness operational product. J. Geophys. Res, 102 , 16889–16909.
Kaufman, Y. J., and B. N. Holben, 1996: Hemispherical backscattering by biomass burning and sulfate particles derived from sky measurements. J. Geophys. Res, 101 , 19433–19445.
Kaufman, Y. J., and and Coauthors, 1997a: Passive remote sensing of tropospheric aerosol and atmospheric correction. J. Geophys. Res, 102 , 16815–16830.
Kaufman, Y. J., D. Tanré, L. Remer, E. Vermote, A. Chu, and B. N. Holben, 1997b: Remote sensing of tropospheric aerosol from EOS-MODIS over the land using dark targets and dynamic aerosol models. J. Geophys. Res, 102 , 17051–17067.
Kaufman, Y. J., and and Coauthors, 1998: The Smoke, Clouds, and Radiation—Brazil (SCAR-B) experiment. J. Geophys. Res, 103 , 31783–31808.
King, M. D., 1979: Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. Part II: Application. J. Atmos. Sci, 36 , 1072–1083.
Kobayashi, T., K. Masuda, M. Sasaki, and J. Mueller, 2000: Monte Carlo simulations of enhanced visible radiance in clear-air satellite fields of view near clouds. J. Geophys. Res, 105 , 26569–26576.
Li, Z., H. W. Barker, and L. Moreau, 1995: The variable effect of clouds on atmospheric absorption of solar radiation. Nature, 376 , 486–490.
Li, Z., L. Moreau, and A. Arking, 1997: On solar energy disposition: A perspective from observation and modeling. Bull. Amer. Meteor. Soc, 78 , 53–70.
Marshak, A., A. Davis, W. Wiscombe, and R. Cahalan, 1997: Inhomogeneity effects on cloud shortwave absorption measurements: Two-aircraft simulations. J. Geophys. Res, 102 , 16619–16637.
Nakajima, T., and and Coauthors, 1999: Early phase analysis of OCTS radiance data for aerosol remote sensing. IEEE Trans. Geosci. Remote Sens, 37 , 1575–1585.
Pilewskie, P., A. F. H. Goetz, D. A. Beal, R. W. Bergstrom, and P. Mariani, 1998: Observations of the spectral distribution of solar irradiance at the ground during SUCCESS. Geophys. Res. Lett, 25 , 1141–1144.
Pinker, R. T., and I. Laszlo, 1992: Modeling surface solar irradiance for satellite applications on a global scale. J. Appl. Meteor, 31 , 194–211.
Ramanathan, V., B. Subasilar, G. J. Zhang, W. Conant, R. D. Cess, J. T. Kiehl, H. Grassl, and L. Shi, 1995: Warm pool heat budget and shortwave cloud forcing—A missing physics? Science, 267 , 499–503.
Remer, L. A., and Y. J. Kaufman, 1998: Dynamical aerosol model: Urban/industrial aerosol. J. Geophys. Res, 103 , 13859–13871.
Remer, L. A., S. Gassó, D. Hegg, Y. J. Kaufman, and B. N. Holben, 1997: Urban/industrial aerosol: Ground-based sun/sky radiometer and airborne in situ measurements. J. Geophys. Res, 102 , 16849–16859.
Remer, L. A., Y. J. Kaufman, B. N. Holben, A. M. Thompson, and D. McNamara, 1998: Tropical biomass burning smoke aerosol size distribution model. J. Geophys. Res, 103 , 31879–31892.
Satheesh, S. K., and V. Ramanathan, 2000: Large differences in tropical aerosol forcing at the top of the atmosphere and Earth's surface. Nature, 405 , 60–63.
Shaw, G. E., 1979: Inversion of optical scattering and spectral extinction measurements to recover aerosol size spectra. Appl. Opt, 18 , 988–993.
Stephens, G. L., and S-C. Tsay, 1990: On the cloud absorption anomaly. Quart. J. Roy. Meteor. Soc, 116 , 671–704.
Tanré, D., Y. J. Kaufman, M. Herman, and S. Mattoo, 1997: Remote sensing of aerosol over oceans from EOS-MODIS. J. Geophys. Res, 102 , 16971–16988.
Tanré, D., and and Coauthors, 2001: Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data in the solar spectrum. J. Geophys. Res., 106, 18205–18217.
Vogelmann, A. M., V. Ramanathan, W. C. Conant, and W. E. Hunter, 1998: Observational constraints on non-Lorentzian continuum effects in the near-infrared solar spectrum using ARM ARESE data. J. Quant. Spectrosc. Radiat. Transfer, 60 , 231–246.
APPENDIX
Back of the Envelope Calculations of the Effect of a Broken Cloud Field on the Surface Irradiance
Cloud free
Adding clouds
Summary of the accuracy in derivation of the diffuse solar flux reaching the surface from the AERONET radiances measured in the principal plane. The errors are calculated by assuming that the atmospheric aerosol has a lognormal distribution of spherical homogenous aerosol particles with mean particle radius Rg = 0.06, std dev σ = 0.6, single scattering albedo ω0 = 0.98, refractive index 1.53–0.003i, optical thickness of 1.0, and surface reflectance ρ = 0.1. The atmosphere is simulated by changing the assumed model to Rg = 1.0, ω0 = 0.85, ρ = 0.2 one step at a time, and all steps combined. Viewing angle θ0 = 30° and λ = 0.64 μm
Attenuation of sunlight reaching the earth's surface for solar zenith angle of 50°. The fraction of solar radiation reaching the surface is fitted with an exponential function: fλ = exp (−aλ − bλτ), where aλ is attenuation by aerosol free atmosphere: a0.44 = 0.17; a0.67 = 0.033; a0.87 = 0.009; a1.02 = 0.003) and bλ is the aerosol attenuation given in the table. Results are given for the attenuation functions derived from the AERONET principal-plane radiances, and compared with dust (Tanré et al. 2000), smoke (Remer et al. 1998) and urban–industrial models (Remer and Kaufman 1998). The spectrally averaged {bλ} and the Ångström exponent, α, average and standard deviations are also shown
The attenuation of solar flux reaching the surface by the aerosol for optical thickness of 1.0 at 0.67 μm. The solar radiation reaching the surface was modeled using the tropical atmosphere gaseous attenuation. The attenuation of solar radiation is expressed in units of W m−2. The results are give for the full solar spectrum. For each model or measurement dataset the Ångström exponent α and the attenuation coefficient bλ are given