P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For example, a second order polynomial that contains 3 free parameters was presumed based on in-situ SMP data. The polynomial is currently parameterized based on 3 backscatter observations provided by AirMOSS (i.e. one frequency at three polarizations of HH, VV and HV). In this paper, a more realistic, physically-based SMP model containing 3 free parameters is derived based on a solution to Richards’ equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

Secondary forests (SF) are important carbon sinks, removing CO₂ from the atmosphere through the photosynthesis process and storing photosynthates in their aboveground live biomass (AGB). This process occurring at large-scales partially counteracts C emissions from land-use change, playing, hence, an important role in the global carbon cycle. The absorption rates of carbon in these forests depend on forest physiology, controlled by environmental and climatic conditions as well as on the past land use, which is rarely considered for retrieving AGB from remotely sensed data. In this context, the main goal of this study is to evaluate the potential of full polarimetric ALOS-2 PALSAR-2 data for estimating AGB by taking into account the past-land use of SF areas in the Brazilian Amazon. We surveyed a chronosequence of 42 SF plots (20 ha) near the Tapajós National Forest in Pará state to quantifying AGB growth rates. We explored the full polarimetric data testing three regression models including non-linear (NL), multiple linear regressions models (MLR), and the semi-empirical extended water cloud model (EWCM). The results showed that the intensity of previous use has affected the structure of SF by reducing the AGB accumulation and being noticeable by several polarimetric attributes. The combination of multiple prediction variables with MLR improved the AGB estimation by 70% comparing amongst other models (R² adj. = 0.51; RMSE = 13.2 Mg ha^-1) bias = 2.1 ± 37.9 Mg ha^-1. The error propagation of the MLR model was estimated to be 15%.

We employ hierarchy of models (HoM) with 2, 3 and 4 parameters to reanalyze the nucleation kinetics in the electrodeposition as quantified by n(t) - “the number of nuclei vs. time” data obtained at different overvoltages from precise experiments on electrodeposition of Hg on two different types of Pt-cathodes by Ivan V. Markov and Evgenia Stoycheva [1]. The obtained two scales, nmax and , are used to rescale the original data mapping it on a master curve in coordinates . Our main result is obtained by studying further the dependence of these two scales on the overvoltage (analogue of supersaturation). Surprisingly, for one of the two cathode types - the “hemispherical single-crystal electrode” (as defined by the authors), there is discontinuity in the “ vs. overvoltage” dependence – an almost horizontal jump from 85 to 86 mV accompanied by a change in the slope of the dependence - it is ~ -1 and ~ -0.5 after. For the other cathode - “plane structureless platinum electrode”,  decreases smoothly. Combined, these two behaviors point at the so called “cusp catastrophe”. We compare our findings with published results on protein nucleation.