3D RADIATIVE-TRANSFER IN WEAKLY INHOMOGENEOUS-MEDIUM - PART I - DIFFUSIVE APPROXIMATION

The solution of the three-dimensional radiative transfer equation in w eakly horizontally inhomogeneous medium has been obtained in the diffu sion approximation using the expansion of the three-dimensional delta- Eddington approximation. The solution approach, referred as the gradie nt correction (GC) method, expands the horizontal fluxes and the sourc e function in terms of the horizontal gradient of the extinction coeff icient and/or the cloud-top boundary. In the transfer equation, only t he zeroth- and first-order gradient terms are retained and hence the f ollowing limitations apply. First, the length of the horizontal variat ions of optical properties of the medium should be large in comparison to the mean radiative transport length. Second, the ratio of the vert ical to horizontal scales should be small enough so that fluxes from b oundaries may be neglected. Since there are no restrictions to the amp litude of the optical properties variations, this method may even be a pplicable to a medium with strong horizontal variations of optical pro perties, as long as scales of the variations are large enough in compa rison to the radiative transport length. The analytical solutions are in excellent agreement with the more accurate numerical solutions. The solution also shows the solar zenith angle dependence of the albedo, similar to that observed in analyses of satellite imagery. The GC appr oach may be useful as a fast and computationally inexpensive method bo th for the correction of the independent pixel approximation used for extraction of cloud fields from satellite imagery and possibly for the calculation of the radiation fluxes in climate models.