The vertical temperature distribution in the permanently shaded region (PSR) has a significant impact on the temporal and spatial distribution of the cold trap. To obtain the vertical temperature profile of the PSR, an inversion method that fuses microwave and infrared brightness temperature (TB) data is proposed. In the inversion process, the infrared data were initially used to derive the optimal value of the H-parameter that controls the density profile. Subsequently, high-frequency (37 and 19.35 GHz) microwave TB data were used to ascertain the range of surface density, whereas low-frequency (3 GHz) microwave TB data were used to determine the range of bottom density. A fixed correction was applied to the 3-GHz brightness temperature data to account for the calibration error. Due to the inherent uncertainties associated with the thermal model, both the Hayne and Woods' models were used in the inversion process, yielding disparate results. The PSR in the Haworth impact crater was selected as a case study for the inversion. The Woods' model was found to provide a superior explanation for the microwave observation. The optimal surface density of the PSR of the Haworth crater was determined to be within the range of 1200-1300 kg m(-3), while the bottom density was within the range of 2100-2200 kg m(-3). The inverted vertical temperature distribution in the PSR of Haworth crater indicates that the depth of the cold trap can reach approximately 8.5 m. In addition, the impact of heat flow on microwave TB is discussed.

A microwave radiation model with coherent surface scattering is developed for analyzing the topographic effects of the lunar permanently shadowed region (PSR) on microwave radiometric observations. The coherent surface scattering to the observer, which comes from the nearby surface due to the variation in the surface slope, is quantified by the ray-tracing method. In addition, the vertical distribution of temperatures of the PSR is estimated by a 1-D thermal model with 3-D shading and scattering effects. The impact of coherent scattering on microwave brightness temperatures (TBs) by a nadir-look radiometer becomes more noticeable with high-resolution microwave TB data, such as 4 pix/degrees by 4 pix/degrees in this study. The rise in TB at certain locations in PSR may reach up to similar to 8 K at 37 GHz. However, when compared with the low resolution of the TB by Chang'E-2, the averaged contribution of coherent surface scattering is less than 1 K. Meanwhile, there is a discrepancy between the model-generated microwave TB and the measured TB of Chang'E-2, both in small and large craters. This discrepancy may be explained by a calibration issue or the uncertainty of model parameters. Nonetheless, the trend in the model-generated TB is consistent with the measurements, indicating that the proposed model has the potential to predict TB effectively within the PSR.

The uncertainty of passive microwave retrievals of snowfall is notoriously high where high-frequency surface emissivity is significantly reduced and varies markedly in response to the changes in snowpack physical properties. Using the dense media radiative transfer theory, this article studies the potential effects of terrestrial snow-cover depth, density, and grain size on high-frequency channels 89 and 166 GHz of the radiometer onboard the Global Precipitation Measurement (GPM) core satellite, which are commonly used to capture snowfall scattering signals. Integrating the inference across all feasible grain sizes, ranges of snowpack density and depth are identified over which snowfall scattering signatures can be time-varying and potentially obscured. Using ten years of reanalysis data, the seasonal vulnerability of snowfall retrievals to the changes in snowpack emissivity in the Northern Hemisphere is mapped in a probabilistic sense and connections are made with the uncertainties of the GPM passive microwave snowfall retrievals. It is found that among different snow classes, relatively light Arctic tundra snow in fall, with a density below 260 kg m(-3), and shallow prairie snow during the winter, with a depth of less than 40 cm, can reduce the surface emissivity and obscure the snowfall passive microwave signatures. It is demonstrated that during winter, the highly vulnerable areas are over Kazakhstan and Mongolia with taiga and prairie snow. In the fall, these areas are largely over tundra and taiga snow in north of Russia and the Arctic Archipelagos as well as prairies in Canada and the Great Plains in the United States.

Near-surface temperatures of permanently shadowed regions (PSRs) on the Moon provide fundamental information for water ice exploration. Seasonal temperature variations of PSRs are found in both Chang'E-2 microwave radiometer data and Diviner Lunar radiometer observations. Furthermore, unusual microwave brightness temperature variations between February 2011 and May 2011 of double-shaded PSRs are shown in the Chang'E-2 observational data, i.e., that the minimum microwave brightness temperature occurs before the time when the infrared brightness temperature reaches the minimum in double-shaded PSRs. To interpret this phenomenon, the 1-D thermal model and the microwave radiation transfer model are used. In the thermal model, the reradiation energy from the illuminated area is estimated by effective solar irradiance, which is an analytic solution for the radiative equilibrium temperature in the shadowed area of a spherical bowl-shaped crater. In the simulation, an assumed internal 0.4 W/m(2) heat flow beneath the lunar surface made a plausible fit to the unusual variations during some lunations. However, this is a huge value compared with the well-known heat flow value of about 0.018 W/m(2). Furthermore, it is difficult to obtain this extra heat energy by lateral conduction below the surface in a large impact crater due to the small thermal conductivity of the lunar regolith. Finally, the unusual microwave brightness temperature (TB) changes are concluded to be caused by a calibration problem after excluding other possible reasons. In addition, a statistical correction method is applied to revise the problematic TB data to obtain the proper variation trend of the brightness temperature.