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Accurate thermal infrared (TIR) fast-forward models are critical for weather forecasting via numerical weather prediction (NWP) satellite radiance assimilation and operational environmental data record (EDR) retrieval algorithms. The thermodynamic and compositional data about the surface and lower troposphere are derived from semi-transparent TIR window bands (i.e., surface-sensitive channels) that can span into the far-infrared (FIR) region under dry polar conditions. To model the satellite observed radiance within these bands, an accurate a priori emissivity is necessary for the surface in question, usually provided in the form of a physical or empirical model. To address the needs of hyperspectral TIR satellite radiance assimilation, this paper discusses the research, development, and preliminary validation of a physically based snow/ice emissivity model designed for practical implementation within operational fast-forward models such as the U.S. National Oceanic and Atmospheric Administration (NOAA) Community Radiative Transfer Model (CRTM). To accommodate the range of snow grain sizes, a hybrid modeling approach is adopted, combining a layer scattering model based on the Mie theory (viz., the Wiscombe–Warren 1980 snow albedo model, its complete derivation provided in the Appendices) with a specular facet model. The Mie-scattering model is valid for the smallest snow grain sizes typical of fresh snow and frost, whereas the specular facet model is better suited for the larger sizes and welded snow surfaces typical of aged snow. Comparisons of the model against the previously published spectral emissivity measurements show reasonable agreement across zenith observing angles and snow grain sizes, and preliminary observing system experiments (OSEs) have revealed notable improvements in snow/ice surface window channel calculations versus hyperspectral TIR satellite observations within the NOAA NWP radiance assimilation system. [ABSTRACT FROM AUTHOR]

We are devoted to the study of a non-local non-homogeneous time fractional Timoshenko system with frictional and viscoelastic damping terms. We are concerned with the well-posedness of the given problem. The approach relies on some functional analysis tools, operator theory, a priori estimates and density arguments. This work can be considered as a contribution to the development of energy inequality methods, the so-called a priori estimate method inspired from functional analyses and used to prove the well-posedness of mixed problems with integral boundary conditions. [ABSTRACT FROM AUTHOR]

This paper considers a theoretical substantiation of the influence of a perturbation of a moving singular point on the analytical approximate solution to the Van der Pol equation obtained earlier by the author. A priori estimates of the error of the analytical approximate solution are obtained, which allows the solving of the inverse problem of the theory of error: what should the structure of the analytical approximate solution be in order to obtain a result with a given accuracy? Thanks to a new approach for obtaining a priori evaluations of errors, based on elements of differential calculus, the domain, used to obtain an analytical approximate solution, was substantially expanded. A variant of optimizing a priori estimates using a posteriori estimates is illustrated. The results of a numerical experiment are also presented. [ABSTRACT FROM AUTHOR]

The article considers the Van der Pol equation nonlinearity aspect related to a moving singular point. The fact of the existence of moving singular points and the uniqueness of their solution for complex domains have been proved. An answer to the question about the existence of moving singular points in the real domain was obtained. The proof of existence and uniqueness is based on an author's modification of the technology of the classical Cauchy theorem. A priori estimates of the analytical approximate solution in the vicinity of a moving singular point are obtained. Calculations of a numerical experiment are presented. [ABSTRACT FROM AUTHOR]

The paper considers the specifics of nonlinear differential equations that have applications in different areas. Earlier, the authors proved the existence and uniqueness theorem for a solution to a class of non-linear differential equations in a neighborhood of a moving singular point. In this paper, we consider the first problem of studying a third-order nonlinear differential equation in the domain of analyticity. An analytical approximate solution is built, taking into account the solution search area. A priori estimates of the analytical approximate solution are obtained, and the technology of their optimization using a posteriori ones is illustrated. The result of a numerical experiment is presented. The presented results allow to expand the class of nonlinear differential equations for describing various phenomena and processes. [ABSTRACT FROM AUTHOR]

We obtained results on the existence and uniqueness of a mild solution for a fractional-order semi-linear differential inclusion in a Hilbert space whose right-hand side contains an unbounded linear monotone operator and a Carathéodory-type multivalued nonlinearity satisfying some monotonicity condition in the phase variables. We used the Yosida approximations of the linear part of the inclusion, the method of a priori estimates of solutions, and the topological degree method for condensing vector fields. As an example, we considered the existence and uniqueness of a solution to the Cauchy problem for a system governed by a perturbed subdifferential inclusion of a fractional diffusion type. [ABSTRACT FROM AUTHOR]