A cloudy-sky radiative transfer model suitable for calibration of satellite sensors

We present a radiative transfer model suitable for calibration of satellite instruments sensing in the solar spectrum. The model consists of two clear layers sandwiching a plane-parallel cloud layer. Clear-sky optical effects are treated with modified Beer's Law relationships and cloud optical effects are treated with the delta-Eddington method. We use a model inversion process to determine an effective cloud optical depth from surface measurements of global irradiance and then use the model to calculate the corresponding upward irradiance at the top of the atmosphere. Upward irradiances are converted into directional radiances using empirical bidirectional reflectance factors. The model radiances are then compared to simultaneous satellite measurements of radiances from the cloud tops over the surface site. We compare model results to observations of the GOES Visible and Infrared Spin Scan Radiometer. Results indicate that the VISSR band (0.55–0.75 μm) radiance is close to nominal (slope 0.9601 compared to the expected 1.0). Significant, approximately cubic-form nonlinearity of response is found (consistent with the amount of nonlinearity exhibited on prelaunch calibrations). Equivalent broad-band radiance also suffers from the same type of nonlinear response, with the best linear slope being about 80% of nominal, a result consistent with that anticipated for narrow-band to broad-band conversion. Observed root-mean-square errors for sensor calibration results are comparable to those found in direct comparison between uncalibrated and calibrated sensors on different satellites, indicating that the cloud-calibration approach has merit as a means of quantitative satellite sensor calibration.