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Based on results of numerical simulation and processing of real satellite data, a method is proposed for automatically estimating the quality of MODIS meteorological data, used for atmospheric correction of satellite IR measurements of land surface temperature.

The description of the complex measurement and computation system for monitoring and forecasting the meteorological situation at the airport is presented. The system consists of the meteorological temperature profiler MTP-5PE, Vaisala Weather Transmitter WXT520, main and remote control terminals, network data storage, two high-resolution meteorological models, server, and SKIF Cyberia complex at Tomsk State University. The paper presents the results of the measurements and forecasts of the atmospheric temperature profile and surface values of the wind velocity and direction, pressure, humidity and temperature of the previous winter, characterized by various extreme weather events observed at the airport Bogashevo. It is shown that the measured and calculated temperature profiles for the lower part of the atmospheric boundary layer have a good qualitative and quantitative agreement of the results.

Errors in lidar measurements of the air density in the middle atmosphere are analyzed. A lidar was placed onboard the ISS. A solid-state Nd:YAG-laser, operating at the 3rd and 4th harmonics with wavelengths of 355 and 266 nm, was used as a lidar transmitter. Calculations were performed for the lidar with reasonable parameters: pulse energy of 0.4 (355 nm) and 0.2 J (266 nm), pulse repetition frequency of 20 Hz, accumulation time of 60 s, radius of the receiving mirrors of 0.3 and 0.5 m, field of view of the receiving telescope of 1 and 0.1 mrad, filter bandwidth of 0.5, 1, and 10 nm, and spatial resolution of 1 km. The results showed that radiation at a wavelength of 355 nm can cover altitude range, on average, from 75 km at night and from 55 km in the daytime to 10 km depending on the parameters of the lidar with 10% measurement errors (calculations were not carried out below 10 km). When operating with radiation at 266 nm for 10% measurement error, the sensing range can be expanded to the upper mesosphere at 90 km and penetrate deeper into the atmosphere to 38 km. Thus, the use of two harmonics allows the altitude range of air density measurements from the ISS to be expanded from 90 km down to the troposphere.

The results of photo-acoustic measurements of the laser pulses with a wavelength of 266 nm by water vapor mixed with nitrogen on laser radiation intensity are presented. The laser radiation intensity varies from 0.5 till 10 mW/cm² and water vapor partial pressure changes with 0–10 mbar. It is shown that with laser intensity increase the absorption is linear for H₂O partial pressure increase from 0 to 5 mbar and becomes ruther stable at H₂O partial pressure increase from 5 till 10 mbar.

A probabilistic method for regularization is proposed. This method enables one to obtain a non-negative solution to systems of linear algebraic equations. A theorem of existence of the best possible solution is proved. A numerical example of the method application is given.

In this paper, some aspects of numerical realization of algorithms from the software package for solving problems of minimization of nonlinear functions including non-smooth functions with allowance for the linear constraints set by sparse matrices are considered. Examples of the solution of test problems are presented.

A new method for constructing efficient monotone numerical schemes for solving direct, adjoint, and inverse atmospheric chemistry problems is presented. It is a systhesis of a variational principles combined with splitting and decomposition methods and a constructive realization of the Eulerian integrating factors (EIM) by means of the local adjoint problem technique. To provide the efficiency of calculations, a method to decompose the multi component substances transformation operators in terms of mechanisms of reactions is also proposed. With the analytical EIMs, the decomposed systems of stiff ODEs are reduced to the equivalent systems of integral equations. To solve them, non-iterative multistage algorithms of given order of accuracy are developed. An original variational method for constructing of mutually consistent algorithms for direct and adjoint problems, and sensitivity studies for complex models with constraints is developed.

The problem of isolation of discrete random values and vectors with discrete distributions having a given average value and a minimum dispersion is solved. The vector model is associated with statistical methods of calculation of multiple integrals and solutions to systems of the integral equations.

An iterative algorithm with an efficient preconditioner for the numerical solution of an elastic problem in approximation of plate theory with mixed boundary conditions is proposed and substantiated. Exact constants of energy equivalence for optimization of iteration method are obtained. Inversion of the preconditioner is equivalent to the double inversion of a discrete analog of the Laplace operator with the Dirichlet boundary conditions.

This paper presents the results of studies of the scalar linear functional-differential equation of a delay type x˙ (t) = a(t)x(t − 1) + b(t)x(t/q) + f(t), q > 1. The main attention is being given to the original problem with the initial point, when the initial condition is specified at the initial point, and the classical solution, whose substitution into the original equation transforms it into the identity, is sought for. The method of polynomial quasi-solution, based on representation of an unknown function x(t) as polynomial of degree N is applied as the method of investigation. Substitution of this function in the original equation results in the residual Delta( t)=O(t^{N}), for which an accurate analytical representation is obtained. In this case, the polynomial quasi-solution is understood as exact solution in the form of polynomial of degree N, disturbed because of the residual of the original initial problem. The theorems of existence of polynomial quasi-solutions for the considered linear functional-differential equation and exact polynomial solutions have been proved. The results of the numerical experiment are presented.