Comparison of brightness temperature models for layered non-isothermal bare soils with smooth boundary

DOI: 10.21046/2070-7401-2025-22-4-187-204

The article compares incoherent and coherent models of brightness temperature (BT) for layered, non-isothermal bare soils with smooth boundary. BT models include incoherent models obtained on the basis of phenomenological radiative transfer theory (with and without considering a single reflection of the wave from the lower boundary of partial layers of the layered medium), and exact coherent models: Wilheit, Njoku, Klepikov–Sharkov. As non-isothermal layered-inhomogeneous dielectric half-spaces, thawed and frozen soils are considered with modeled and synchronously measured moisture and temperature profiles in the active layer. The complex permittivity of soils is modeled using proven dielectric models. The statistical analysis is based on synchronous calculation of the BT (using all the models under consideration) at frequencies of 409 MHz and 1.4 GHz in the range of viewing angles from 0 to 60° at vertical and horizontal polarizations. As a result, it is shown that coherent BT models (Wilheit, Njoku, Klepikov–Sharkov) have the same accuracy within the limits of computation error or digitization of graphic data from third-party origins. The average absolute difference between the BT calculated by incoherent and coherent models for all considered sets of moisture and temperature profiles can reach 20 and 8 K at frequencies of 409 MHz and 1.4 GHz, respectively, if the condition of smoothness of the refractive index profile at the soil surface is not met (large scale of vertical dielectric inhomogeneities in relation to the wavelength). If this condition is met, then the error does not exceed several degrees Kelvin. It is shown that the modification of the incoherent model by introduction into the reflectivity of a coefficient of coherent reflection from the air-soil interface allows achieving accuracy close to coherent models, even for freezing soils with a sharp jump in the complex permittivity between the freezing and thawed parts of the active layer. This study corroborates the applicability of a partially coherent emission model for calculating, in a wide frequency range, the angular dependencies of BT at horizontal and vertical polarizations of bare soils with smooth boundary and virtually any moisture and temperature profiles observed in the active layer.