Direct-normal solar irradiance (DNSI), the energy in the solar spectru
m incident in unit time at the Earth's surface on a unit area perpendi
cular to the direction to the Sun, depends only on atmospheric extinct
ion of solar energy without regard to the details of the extinction, w
hether absorption or scattering. Here we report a set of closure exper
iments performed in north central Oklahoma in April 1996 under cloud-f
ree conditions, wherein measured atmospheric composition and aerosol o
ptical thickness are input to a radiative transfer model, MODTRAN 3, t
o estimate DNSI, which is then compared with measured values obtained
with normal incidence pyrheliometers and absolute cavity radiometers.
Uncertainty in aerosol optical thickness (AOT) dominates the uncertain
ty in DNSI calculation. AOT measured by an independently calibrated Su
n photometer 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 w
ithin the combined uncertainties in the measurement (0.3-0.7%) and mod
el calculation (1.8%), albeit with a slight average model underestimat
e (-0.18 +/- 0.94)%; for a DNSI of 839 W m(-2) this corresponds to -1.
5 +/- 7.9 W m(-2). The agreement is nearly independent of air mass and
water-vapor path abundance. These results thus establish the accuracy
of the current knowledge of the solar spectrum, its integrated power,
and the atmospheric extinction as a function of wavelength as represe
nted in MODTRAN 3. An important consequence is that atmospheric absorp
tion of short-wave energy is accurately parametrized in the model to w
ithin the above uncertainties.