Modeling zenith-angle dependence of outgoing longwave radiation: Implication for flux measurements

As shown in previous studies, outgoing-longwave radiation (OLR) can be in error by ∼7% when evaluated from directional measurements by applying time-averaged angular distribution models (ADMs) to account for the emission anisotropy. In order to develop an insight into the problem of assessing hemispheric emission from directional measurements, we formulate the directional (monochromatic) greenhouse factor gd specified as the ratio of a longwave radiance measured above the atmosphere to that emitted from the surface at the same zenith angle θv. The explicit expressions for gd involve two atmospheric parameters, the optical thickness and the temperature-profile parameter. Our analysis indicates that under clear conditions a narrow-band radiance, if measured at θv≈57° in atmospheric windows (low values of optical thickness) and at θv≈47° in absorption bands, determines the hemispheric-average radiance to within about 1%. For broad spectral bands, whether under clear or cloudy (solid cover, or “randomly scattered” clouds) conditions, the same finding applies at θv≈50°. Thus, the, zenith angle of equivalence θeq varies by about ±5° for different values of the optical thickness; it varies only slightly for different temperature profiles (even though different temperature profiles produce quite different patterns of radiance vs. θv, that is, different ADMs apply). Measurements at or near θeq therefore constitute direct assessment of OLR, without resorting to ADMs to adjust for the variations of emission with view angle (anisotropy). The existing OLR data should be reexamined, accepting measurements only within the range 45–60% of view zenith angles.