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**Modeled Vs. Measured Direct-Normal Solar Irradiance**

Schwartz, S. E., Brookhaven National Laboratory

Radiation Processes

Radiative Processes

Halthore R. N., Schwartz, S. E., Michalsky, J. J., Anderson, G. P., Ferrare R. A., Holben B. N., and ten Brink H. M. 1997. "Comparison of Model Estimated and Measured Direct-Normal Solar Irradiance," *J. Geophys. Res.* 102(D25): 29991-30002

Direct-normal solar irradiance (DNSI), the total energy in the solar spectrum incident in unit time on a unit area at the earth's surface perpendicular to the direction to the Sun, Figure 1, depends only on atmospheric extinction of solar energy without regard to the details of the extinction—whether absorption or scattering.

Here we report a set of closure experiments performed in north-central Oklahoma in April 1996, under cloud-free conditions, wherein measured atmospheric composition and aerosol optical thickness are input to a radiative transfer model, MODTRAN-3, to estimate DNSI, which is then compared with measured values obtained with normal incidence pyrheliometers and absolute cavity radiometers. MODTRAN-3 is a medium resolution radiative transfer program that uses band models for atmospheric absorption that represent current knowledge of absorption by atmospheric gases in the solar spectrum. Uncertainty in aerosol optical thickness (AOT) dominates the uncertainty in DNSI calculation. AOT measured by an independently calibrated sunphotometer and a rotating shadow-band radiometer agree to within the uncertainties of each measurement.

For 36 independent comparisons, the agreement between measured and model estimated values of DNSI falls within the combined uncertainties in the measurement (0.3 - 0.7%) and model calculation (1.8%), albeit with a slight average model underestimate. Image 2 shows MODTRAN-3 estimated DNSI plotted against measured values; the least-squares fit is shown by the dashed line. The 1:1 line (solid) is shown for comparison. The variation in DNSI is due mainly to variation in solar zenith angle. The correlation exhibits a slight bias. The linear fit to the data yields a slope of 0.995 and an offset of 10.3 W m.-2 (Figure 2). (The square of the Pearson product-moment correlation coefficient, R-squared, is 0.996).

The agreement between measured and modeled DNSI is nearly independent of air mass and water-vapor path abundance. Figure 3 shows fractional difference between the model estimated and measured DNSI, (modeled-measured/modeled), plotted as a function of air mass to examine the effect of increasing column abundance of attenuators, especially gases. The spread in ordinate values at low air mass (open circles) is attributed to atmospheric non-uniformity and atmospheric radiance effects in the field of view of the detector. At large air mass (filled circles, defined as air mass greater than 1.7) slope of the linear fit is 0.05% per air mass. Figure 4 shows Percent difference between the model estimated and measured DNSI plotted against the amount of water along the path. The slope of data points (filled circles corresponding to "high air mass" points) is -0.05% per cm path water(Figures 3 and 4).

Comparison of the measured and model estimated direct normal solar irradiance constitutes a simple yet robust closure experiment. The simplicity arises from the need to know only the extinction properties of the atmosphere without regard to scattering properties. The robustness arises from the relatively low uncertainties in the measurement of DNSI and other atmospheric quantities that are used in the prediction of DNSI. DNSI and the atmospheric variables required as model inputs, AOT, water vapor and ozone, were measured, with quantified uncertainties. For 36 independent measurements, the model slightly underestimated the measured DNSI by -0.18 ± 0.94% (one standard deviation). This degree of disagreement is well within the combined uncertainties of model calculation (1.8%) and DNSI measurement (0.3 - 0.67%). The data base on which MODTRAN-3 band model parameters are based is therefore suitable for incorporation into global and climate and weather models, either directly or as the basis for subsequent parametrization as may be required by particular models. The uncertainty in the model calculation of 1.8% is dominated by the effect (1.6%) of uncertainty in AOT measurement of 0.01 at airmass of 1. In view of the diverse nature of measurements that are employed in this rather simple closure experiment, the disagreement is surprisingly small. The bias (-0.18%) and the standard deviation (0.94%) of the difference between model calculation and the measurement could be due to an unknown combination of factors that may include the solar constant used in the model which contributes the maximum correction to the DNSI measurement and the uncertainty in the AOT measurement, which is the main contributor to the uncertainty in model calculation of DNSI.

These results allow us to establish a limit on the atmospheric absorption that is unaccounted for in MODTRAN-3. The linear fit of the difference between model estimated and measured DNSI vs. airmass for airmass greater than 1.7 translates to an unaccounted absorption of about 6 ± 4 W m-2. Work by others has suggested that a general circulation model (GCM) representative of many GCMs currently in use, underestimates the globally averaged solar flux absorbed in the atmosphere by 25 to 30 W m-2, which corresponds to 50 to 60 W m-2 in the instantaneous flux for a dayside average solar zenith angle of 60° or ~0.025 in vertical optical thickness (compare with 0.0038, the average unaccounted attenuation). The discrepancy has been attributed principally to inadequate parameterization of absorption by water vapor or other components such as aerosols that spectrally correlate with water vapor. If MODTRAN-3 suffered the same inadequacies in parameterization, the resulting effect on DNSI would be readily apparent as a bias that would increase with increasing airmass (slope ~ 2.5% per airmass) or water path abundance. Clearly, this is inconsistent with the present finding. Thus the MODTRAN-3 calculation of DNSI, and by extension its treatment of atmospheric absorption, does not appear to exhibit underestimated clear-sky absorption that has been ascribed to GCMs.