Evaluating the First-Order Tau-Omega Model of Terrestrial Microwave Emission

We have formulated a first-order tau-omega model. Compared to the commonly-used zero-order model, this model has four new terms that each represent a scattering mechanism. We found that the first mechanism, the scattering of emission from the vegetation into the upwelling beam, is the most significant. We also found that this term does not affect the overall soil moisture sensitivity such that the zero-order and first-order models at 1.4 GHz have essentially the same sensitivity to soil moisture. Adding this scattering mechanism will allow a new relationship between tau and the amount of vegetation within the canopy that does not increase tau as rapidly with vegetation biomass. The result may be a model that better matches experimental observations of the sensitivity of terrestrial microwave emission to soil moisture while still allowing the model to produce the correct 1.4 GHz brightness temperature.