The tau -omega model is expanded to properly simulate L -band microwave emission of the soil-snow-vegetation continuum through a closed -form solution of Maxwell's equations, considering the intervening dry snow layer as a loss -less medium. The error standard deviations of a least -squared inversion are 0.1 and 3.5 for VOD and ground permittivity, over moderately dense vegetation and a snow density ranging from 100 to 400 kg m -3 , considering noisy brightness temperatures with a standard deviation of 1 kelvin. Using the Soil Moisture Active Passive (SMAP) satellite observations, new global estimates of VOD and ground permittivity are presented over the Arctic boreal forests and permafrost areas. In the absence of dense in situ observations of ground permittivity and VOD, the retrievals are causally validated using ancillary variables including ground temperature, above -ground biomass, tree height, and net ecosystem exchange of carbon dioxide. Time -series analyses promise that the new data set can expand our understanding of the land-atmosphere interactions and exchange of carbon fluxes over Arctic landscapes.

This paper presents a convolutional autoencoder deep learning framework for probabilistic characterization of the ground freeze-thaw (FT) dynamics in the Northern Hemisphere to enhance our understanding of permafrost response to global warming and shifts in the high-latitude carbon cycle, using Soil Moisture Active Passive (SMAP) satellite brightness temperatures (TB) observations. The autoencoder recasts the FT-cycle retrieval as an anomaly detection problem in which the peak winter (summer) represents the normal (anomaly) segments of the TB time series. The results demonstrate that the new framework outperforms the widely used fixed-thresholding of the Normalized Polarization Ratio (NPR) by learning the land surface structural and radiometric complexities that might arise in TB times series due to snow cover and vegetation. Validation against ground-based measurements over Alaska shows that the accuracy of the FT-cycle retrievals can be improved by 12%, primarily due to a marked reduction in false detection of short snowmelt episodes as ground thawing by the NPR thresholding approach.