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2026 year, number 9
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V.A. Banakh, I.V. Zaloznaya, A.V. Falits
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: parabolic equation, wave equation, spatial coherence, turbulent atmosphere, path integral
Abstract >>
Based on the representation of the solution of the stochastic wave equation for a point source as a path integral, a formula for the spatial coherence function of a spherical wave propagating in the atmosphere is derived, taking into account the entire set of virtual paths in the path integral. For the Kolmogorov turbulence spectrum model, the spatial coherence of a spherical wave is calculated for various path-length-to-wavelength ratios. The results are compared with calculations in the parabolic approximation. Conditions are determined under which the coherence function calculations based on the wave and parabolic equations coincide. A geometrical-optical approximation is rigorously justified in calculating the spatial coherence function based on a path integral. It is established that a virtual trajectory in the form of a straight line connecting the source and receiver, the only one considered in the geometrical-optical approximation, completely determines the coherent properties of a wave in a turbulent atmosphere. The results of this work can be used to solve problems of radio wave propagation in random media.
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V.A. Banakh, I.V. Zaloznaya, A.V. Falits
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: parabolic equation, wave equation, intensity fluctuations, turbulent atmosphere, path integral
Abstract >>
An expression for the spatial correlation function of weak intensity fluctuations of a spherical wave propagating in a turbulent atmosphere is derived for the first time based on the stochastic Helmholtz wave equation. Solution of the Helmholtz equation as a path integral is used for that. Using this expression, the spatial correlation function of intensity is calculated for the Kolmogorov turbulence spectrum model for various path-to-wavelength ratios. The comparison with calculations in the parabolic approximation is performed. It is shown that calculations of the intensity correlation function using formulas derived from the wave and parabolic equations yield virtually identical results regardless of the path-length-to-wavelength ratio. This proves the applicability of the parabolic equation for calculating weak intensity fluctuations of a spherical wave with a wavelength significantly longer than optical wavelengths.
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T.A. Nevzorova, A.S. Dudaryonok, N.N. Lavrentieva, L.N. Sinitsa
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: line profile parameters, line broadening, halfwidth, line shift, nitrous oxide
Abstract >>
Nitrous oxide ranks among the top five most significant greenhouse gases driving the global warming of the Earth's atmosphere. Furthermore, nitrous oxide acts as a depletor of stratospheric ozone. Therefore, the study of N2O broadening by atmospheric gases is of particular importance. This paper presents the calculated N2O line broadening and shift coefficients under N2O and air pressure, corresponding to vibrational-rotational transitions in the 3ν1 + 4ν3 band, at room temperature with the rotational quantum number | m | varying from 3 to 72. The calculations were performed using a semi-empiric method based on a semi-classical approach modified by introducing a correction factor into the calculation scheme. The N2O line self- and airbroadening coefficients are compared with published data; the vibrational dependence of the calculated values is examined. The results can be used for refining spectroscopic information in HITRAN database.
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V.I. Starikov
Tomsk State University of Control Systems and Radioelectronics, Tomsk, Russia
Keywords: HO, line broadening, line shift, hydrogen, temperature dependence
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Collision-broadening (γ) and shift (δ) coefficients are calculated for water vapor broadened by H2 in the spectral range 0.6-12160 cm-1 with the use of the semi-classical Robert and Bonamy formalism with exact trajectories. It is shown that calculated function γ( T ) depends on the used isotropic potential of the intermolecular interaction. Temperature parameters for 26 rotational transitions from the terahertz range were determined. An analytical model is presented that makes it possible to calculate the temperature dependence of the broadening coefficients in a wide spectral range. The temperature dependence of the average line shift was also determined. The results can be used in astrophysical application.
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V.P. Lukin, I.P. Lukin
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: turbulence, atmosphere, fluctuations, turbulence spectrum model, non-Kolmogorov turbulence, outer and inner turbulence scales, wind velocity, adaptive correction
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This paper examines current issues related to deriving analytical expressions for calculating fluctuations in optical wave parameters as they propagate through turbulent media with a non-Kolmogorov turbulence spectrum. The primary goal of this paper is to derive formulas for the dependence of optical wave parameter fluctuations on medium parameters. The primary analysis method utilizes theoretical calculations, supplemented by numerical computations using atmospheric models. Assuming that the integral turbulent energy is independent of the turbulence spectrum type, relationships between the structural parameters of the refractive index of the medium for different turbulence types are obtained. The results of this study allow the parameters of optical waves propagating in a random medium with a certain turbulence spectrum to be recalculated for media with different spectra. The results of this work can be used in the development of adaptive optics systems and in the study of turbulence along atmospheric optical paths.
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P.N. Antokhin, M.Yu. Arshinov, B.D. Belan, S.B. Belan, D.K. Davydov, G.A. Ivlev, A.V. Kozlov, O.O. Marchenko, T.M. Rasskazchikova, D.V. Simonenkov, T.K. Sklyadneva, G.N. Tolmachev, A.V. Fofonov
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: atmosphere, vertical distribution, carbon dioxide, concentration, mesoscale, methane, ozone, carbon monoxide, impurity transport, atmospheric composition
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Global warming, caused by the greenhouse effect, continues, and despite the extensive research into greenhouse gas concentrations in the Earth's atmosphere, estimates of their atmospheric budgets still remain uncertain at a level of 5-7%. To reduce this uncertainty, the present study investigates mesoscale inhomogeneities in gas components at different altitudes based on aircraft atmospheric sounding data. It is found that concentration differences for three gases, CH4, CO2, and CO, decrease with altitude. No such pattern was observed for ozone. These dependencies are shown to be stable over time. Concentration gradients are within the following ranges: 0.19-0.32 ppb/km for O3, 0.12-0.99 ppb/km for CH4, 0.02-0.17 ppm/km for CO2, 0.60-2.23 ppb/km for CO. The differences between the minimum and maximum altitudes are reduced by a factor of 4-9. The results of this study expand our understanding of greenhouse gas dynamics in the atmosphere at the mesoscale level and can be useful in developing requirements for both measurement accuracy and scaling of atmospheric greenhouse gas budget calculations.
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V.A. Korshunov, D.G. Sakhibgareev, V.P. Ustinov
Russian Federal Service on Hydrometeorology and Environmental Monitoring Research and Production Association «Typhoon», Obninsk, Russia
Keywords: ozone layer, stratosphere, polar stratospheric vortex, dynamic processes, lidar sensing, satellite measurements
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The stratospheric ozone layer plays a vital role in protecting the Earth's biosphere from the harmful effects of the ultraviolet solar radiation. Therefore, monitoring the state of the ozone layer in specific regions of the Earth and studying its changes under the influence of various factors are urgent tasks. This paper analyzes the influence of atmospheric dynamic processes on the ozone content in the layer from 12 to 35 km above Obninsk (55° N) using lidar and satellite measurement data from 2012 to 2025. It was established that, during the period from January to March, a significant factor in intraseasonal variations in the ozone content in the middle stratosphere (20-35 km) is the shift of the polar stratospheric vortex. In the lower stratosphere (12-20 km), ozone variations are caused by changes in the direction of meridional advection. Interannual variations in February ozone levels correlate with quasi-biennial variations in equatorial winds and solar activity. The effects of these factors on stratospheric ozone levels are assessed. The results can be useful in developing numerical models of the ozone layer and predicting its future changes under the climate change.
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Yu.A. Shtabkin1, K.B. Moiseenko1, I.B. Belikov1, V.A. Belousov1, A.V. Vasileva1, N.S. Kirillova1, D.A. Pestunov2, B.D. Belan2, M.D. Kravchishina3
1Federal state budgetary scientific institution Obukhov Institute of Atmospheric Physics of the Russian Academy of Sciences, Moscow, Russia
2V.E. Zuev Institute of Atmospheric Optics, Siberian Branch of the Russian Academy of Sciences, Tomsk, Russia
3Shirshov Institute of Oceanology of Russian Academy of Sciences, Moscow, Russia
Keywords: atmospheric composition, shipborne measurements, Arctic, methane emission, backward trajectory, model simulation, numerical assessment
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Quantifying methane emissions from Arctic shelf seas is one of the most poorly studied issues of global greenhouse gas budget, largely due to the sparse observational network at high latitudes. This paper presents the results of continuous shipborne measurements of near-surface CH4 and CO2 concentrations in Kara and Barents Seas during the 93rd cruise of the scientific research vessel Akademik Mstislav Keldysh (8 November - 7 December 2023). For episodes of high methane mixing ratios (> 2050 ppb), backward trajectories of air masses were calculated, and in situ data were compared with simulations using the regional WRF-Chem model. This approach enabled spatial localization of emission sources and assessment of methane fluxes at water - atmosphere interface. The highest emissions, with median and peak values of 55.5 and 363 mg/(m2 h), respectively, and a near-surface concentration of up to 2118 ppb, were found in southwestern Kara Sea (Baydaratskaya Bay), in good qualitative agreement with floating chamber flux measurements (86.4 and 483 mg/(m2 h)). These values are comparable to or exceed wintertime methane fluxes from tundra and wetland ecosystems in Western Siberia (40-270 mg/(m2 h)), thus pointing out to the potentially significant contribution of shelf emissions to regional atmospheric methane budget. The proposed approach for retrieving fluxes from near-surface concentration data can be applied to regionalization of point measurements and refining flux estimates in other Arctic areas where observational data are limited.
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K.N. Pustovalov1,2, P.V. Nagorskiy1, S.V. Smirnov1,2, A.E. Kalimullin1,2
1Institute of Monitoring of Climatic and Ecological Systems of the Siberian Branch of the Russian Academy of Sciences, Tomsk, Russia
2National Research Tomsk State University, Tomsk, Russia
Keywords: cloudiness, atmospheric electricity, electric field potential gradient, air temperature, air humidity, radiation transmission by clouds, frost
Abstract >>
The electric field potential gradient is a key parameter of atmospheric electricity, wich determines the state of the global electric circuit (GEC). The study of factors affecting its local variability is particularly relevant in the context of ongoing climate change. The statistical analysis of the relationship between the electric field potential gradient and meteorological conditions in the surface air layer, including extremely low temperatures (down to -45 °C) has been performed based on long-term data from the geophysical observatory of the IMCES SB RAS. It has been established that the mean values of the potential gradient increase with a decrease in temperature to -45 °C, and the data variance half reduces. In the behavior of the median values of the potential gradient as a function of frost intensity, three temperature ranges have been identified (0 to -15 °C, -15 to -30 °C, and below -30 °C). This pattern is explained by the predominance of anticyclonic conditions with low clouds, as well as occurrence of sub-inversion ice fogs or haze during severe frosts. The results can be used for the development and improvement of GEC models and atmospheric models, including those applied in numerical weather prediction and environmental forecasting.
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V.P. Gorbatenko1, L.I. Kizhner1, L.G. Ananova1, D.P. Mordus2
1National Research Tomsk State University, Tomsk, Russia
2"Aviamettelekoma Roshydromet", West Siberian Branch, Novosibirsk, Russia
Keywords: Western Siberia, intra-mass thunderstorm, frontal thunderstorm, mesoscale convective system, DMRL-S, radar parameter, synoptic conditions, nowcasting
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An increase in the accuracy of forecasting thunderstorms and hail in the intra-mass convective clouds in Western Siberia is an urgent problem. A modern Doppler meteorological radars DMRL-S is apparently a promising instrument for solving this problem. This study analyzes the radar parameters of intramass cumulonimbus cloud cover based on DMRL-S Novosibirsk data, observations from 18 meteorological stations within a radius of 200 km of the DMRL-S, and synoptic maps for June - August 2021-2023. The radar cloud characteristics of intramass and frontal thunderstorms are compared. Intra-mass thunderstorms are shown to be more often form under anticyclonic conditions, but are characterized by lower radar parameters. Higher reflectivity and water content are observed during thunderstorm development under cyclonic conditions and in diffuse baric fields. Intramass thunderstorm clouds generally exhibit weaker variability of their parameters compared to frontal clouds. The results can be used to refine diagnostic criteria and improve very short-range forecasts of thunderstorms and hail.
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E.A. Sosnin1,2, V.A. Panarin1, V.S. Skakun1, D.V. Beloplotov1, D.A. Sorokin1,2
1High Current Electronics Institute of the Siberian Branch of the RAS, Tomsk, Russia
2National Research Tomsk State University, Tomsk, Russia
Keywords: apokamp discharge, Venus, thundercloud, blue jet, giant jet, positive streamer, starter, transient luminous event
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Discharge phenomena in the Earth’s middle atmosphere are the source of the corresponding transient light events (transients): so-called starters, blue and giant jets. There are no direct methods for measuring the parameters of these transients; therefore, remote sensing methods, theoretical modeling, and experimental measurements of laboratory discharge parameters, which are analogues of natural phenomena, are used. The work reviews the results of laboratory simulation of transients in conditions of apokamp discharge from 2020 to the present. The energy threshold for triggering transients has been experimentally revealed: the maxima of energy release and electroluminescence in the UVB range in an apokamp discharge in air are attained in the pressure range from 70 to 100 torr, which approximately corresponds to the altitudes of transient formation at the troposphere - stratosphere interface (12-18 km). A similar criterion obtained by igniting an apokamp discharge in carbon dioxide predicts the altitudes where analogues of transients are to be observed in the atmosphere of Venus (70-75 km). Recording the propagation dynamics of plasma plumes of an apokamp discharge with nanosecond resolution confirms these conclusions, and, moreover, allows us to formulate a new hypothesis: the type of transient of the middle atmosphere starting from the dome of a thundercloud depends on the intra-cloud discharges and the ratio of the positive charge of the dome top and the negative charge of the outer layer. It is noted that the streamer head of an atmospheric transient should have a complex luminescence structure. The results can be used for refining models of transients of the middle atmosphere and choosing optical instruments for their observations.
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V.A. Dimaki, V.O. Troitskii
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: second harmonic generation, set of reduced nonlinear equations, fast Fourier transform, nonlinear process optimization, telescope aspect ratio, amplitude profile
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The paper continues the theoretical study [1]. Unlike [1], this work analyzes situations where the power of fundamental radiation and, hence, the SHG efficiency are sufficiently high, but the preset field approximation (PFA) is not applicable. Estimates are made with the use of numerical methods for solving the full set of reduced nonlinear wave equations. It is shown that the abandonment of PFA does not qualitatively change the main conclusions of [1]. If restrictions on the beam damage threshold of a nonlinear medium are neglected, the maximum possible SHG efficiency is achieved upon optimal focusing of laser radiation at the center of a crystal. In the cases where the pump power density should be reduced to prevent crystal damage, telescope systems are preferable to long-focus lenses.
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Abstract >>
On September 12, 2026, at the age of 85, Yuri Mikhailovich Timofeev passed away. He was one of our country’s most prominent scientists in the field of planetary atmosphere research, a Doctor of Physical and Mathematical Sciences, a professor, and the head of the Department of Atmospheric Physics at Saint Petersburg State University.
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