Direct-normal solar irradiance (DNSI), the energy in the solar spectrum incident in unit time at the Earth's surface on a unit area perpendicular to the direction to the Sun, 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. Uncertainty in aerosol optical thickness (AOT) dominates the uncertainty in DNSI calculation. AOT measured by an independently calibrated Sun 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 within the combined uncertainties in the measurement (0.3--0.7%) and model calculation (1.8%), albeit with a slight average model underestimate (-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 represented in MODTRAN 3. An important consequence is that atmospheric absorption of short-wave energy is accurately parametrized in the model to within the above uncertainties. ¿ 1997 American Geophysical Union