NASA's Soil Moisture Active Passive (SMAP) mission objective is global mapping of surface volumetric soil moisture at 10-km resolution every two to three days and with accuracy of 0.04 cm3 cm-3 (one sigma). In order to achieve this resolution and accuracy, the SMAP utilizes L-band radar and L-band radiometer measurements. The instruments share a rotating 6-m mesh reflector antenna that scans across a 1000-km swath in order to meet the required data refresh rate. The Level-2 Active-Passive soil moisture product (L2_SM_AP) at 9 km is retrieved from the disaggregated/downscaled brightness temperature obtained by merging of active and passive L-band observations. The baseline L2_SM_AP algorithm disaggregates the coarse-resolution (~36 km) brightness temperatures of the SMAP L-band radiometer using the high-resolution (~3 km) backscatter data from the SMAP L-band radar with unfocused synthetic aperture processing. The inversion of brightness temperature to estimate surface soil moisture is more mature when compared with inversions of radar backscatter. This is the primary driver of the brightness temperature disaggregation approach to the combined active-passive surface soil moisture product. Furthermore, this approach allows some consistency with the coarse-resolution radiometer-only surface soil moisture product since the disaggregated brightness temperatures sums to the radiometer measurement. The disaggregated brightness temperature contains instrument errors (~0.7 dB for co-pol backscatter and ~1.0 dB for cross-pol backscatter, and ~1.3 K in brightness temperature) inherent in the radar and radiometer. Furthermore, the algorithm has two critical parameters that add uncertainty. Finally, correction of the land brightness temperature (used in the inversion) for water body contributions is a source of uncertainty. In this paper, we introduce analytical expressions for the SMAP downscaled brightness temperature due to all these sources of uncertainty. The expressions al...