Journal articles: 'Atmospheric Mathematical models'

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Chatwin, P. C., D. M. Lewis, and N. Mole. "Atmospheric diffusion: some new mathematical models." Advances in Computational Mathematics 6, no. 1 (December 1996): 227–42. http://dx.doi.org/10.1007/bf02127705.

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Markiewicz, Maria. "A Review of Mathematical Models for the Atmospheric Dispersion of Heavy Gases. Part I. A Classification of Models." Ecological Chemistry and Engineering S 19, no. 3 (January 1, 2012): 297–314. http://dx.doi.org/10.2478/v10216-011-0022-y.

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A Review of Mathematical Models for the Atmospheric Dispersion of Heavy Gases. Part I. A Classification of ModelsIn this two part article in its first part models of heavy gas dispersion in the atmosphere are classified and the distinguished groups of models are characterised. In the second part the procedures for the model quality evaluation are described and the main results of model evaluation projects are summarised. Substances released to the atmosphere which have a density greater than the density of the atmospheric air are called heavy gases or dense gases. The dispersion of heavy gases is different from that encountered in the case of neutrally or positively buoyant gases. Specific models have been developed to describe it. The heavy gas dispersion models differ in the complexity and mathematical description. Based on these criteria four main groups of models are distinguished: simple/empirical models, intermediate/integral and shallow layer models, advanced/Lagrangian particle trajectory and Lagrangian puff dispersion models and sophisticated/Computer Fluid Dynamics (CFD) models. This classification is an extension of the classification proposed earlier in the literature.

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Bărbulescu, Alina, and Elena Băutu. "Mathematical models of climate evolution in Dobrudja." Theoretical and Applied Climatology 100, no. 1-2 (July 12, 2009): 29–44. http://dx.doi.org/10.1007/s00704-009-0160-7.

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Korsun, O. N., I. V. Gerilovich, and H. O. Moung. "Consideration of Atmospheric Properties when Comparing Mathematical Models of Aerodynamic Сoefficients with Flight Test Data." Herald of the Bauman Moscow State Technical University. Series Instrument Engineering, no. 4 (137) (December 2021): 152–68. http://dx.doi.org/10.18698/0236-3933-2021-4-152-168.

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Methodological approaches to the calculation of atmospheric parameters, primarily air density and velocity head, in the task of comparing flight data with the results of mathematical modeling of the aircraft motion are proposed. Models with different degrees of using onboard measurements and standard atmosphere models are considered. The models are compared according to the data of flight experiments performed on a modern aircraft for such flight modes as horizontal platform, turn, climb, descentin, and acceleration. The comparison results are given the form of absolute and relative discrepancies in temperature, static pressure and air density. It is shown that the difference between the properties of the real atmosphere and the standard atmosphere is the main source of mismatches, compared to which the influence of the type of flight modes, altitude, speed is insignificant. In addition, a comparison of the standard atmosphere model with the data of atmospheric meteorological sounding is made, which gave similar results. It is concluded that the calculation of air density and velocity head through the standard atmosphere, widespread in practice, in the general case creates a significant error, which may lead to erroneous conclusions in assessing the correspondence of the aircraft mathematical model and the real object

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Garger, E. K., F. O. Hoffman, K. M. Thiessen, D. Galeriu, A. I. Kryshev, T. Lev, C. W. Miller, S. K. Nair, N. Talerko, and B. Watkins. "Test of existing mathematical models for atmospheric resuspension of radionuclides." Journal of Environmental Radioactivity 42, no. 2-3 (January 1999): 157–75. http://dx.doi.org/10.1016/s0265-931x(98)00052-6.

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Eshagh, Mehdi. "Spherical Harmonics Expansion of the Atmospheric Gravitational Potential Based on Exponential and Power Models of Atmosphere." Artificial Satellites 43, no. 1 (January 1, 2008): 25–43. http://dx.doi.org/10.2478/v10018-009-0005-8.

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Spherical Harmonics Expansion of the Atmospheric Gravitational Potential Based on Exponential and Power Models of AtmosphereSpherical harmonic formulation of gravitational potential of the atmosphere depends on the analytical model of the atmospheric density which is used. Exponential and power models are two well-known mathematical tools which are used in atmospheric applications. This paper presents simple formulas for the harmonic coefficients of internal and external types of the atmospheric potential based on these models which can be used in most of the gravimetric aspects. It considers the atmospheric effect on the satellite gravity gradiometry data as an example for numerical investigations. The numerical studies on these data show that the maximum atmospheric effect is about 2 mE over Fennoscandia based on both models, and their differences are less than 0.1 mE. The difference between indirect atmospheric effects reaches 2 cm and 0.02 mGal on the geoid and gravity anomaly, respectively in this region.

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Tikhonov, V. A., V. M. Kartashov, O. V. Kartashov, and V. А. Pososhenko. "Mathematical models of non-stationary random processes in the SVVP representation." Radiotekhnika, no. 210 (September 28, 2022): 167–76. http://dx.doi.org/10.30837/rt.2022.3.210.14.

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The work examines methods and mathematical models that provide the possibility of researching the statistical characteristics of complex and non-stationary random processes describing a wide class of physical phenomena. The proposed models can be used to study the processes observed in various fields of human activity, namely, to analyze the trajectories of unmanned aerial vehicles, their acoustic signals, meteorological processes reflecting the state of the atmosphere. Real and simulated non-stationary random processes considered in the work are represented by the complex vector random process (CVRP) model. In this case, the length of the subvector is equal to the period of the seasonal component. In fact, in such a representation, the time series readings are replaced by their aggregate, i.e. subvectors. Statistical relationships are analyzed for subvectors, and not, as usual, for process counts. If the length of the subvector is equal to one, all operations in the SVVP representation are equivalent to the usual operations for time series. The mathematical apparatus developed in the article was used to analyze changes in time series of atmospheric temperature observed over a long period of time; average annual temperatures were estimated with subsequent smoothing with a low-pass filter. The results obtained can be used to analyze medium-term and long-term changes in atmospheric conditions, refine the results obtained by traditional methods of mathematical statistics, analyze and predict data flows in mobile communication networks, as well as in other areas of human activity.

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Egger, Joseph, and Joachim Pelkowski. "The first mathematical models of dynamic meteorology: The Berlin prize contest of 1746." Meteorologische Zeitschrift 17, no. 1 (February 26, 2008): 83–91. http://dx.doi.org/10.1127/0941-2948/2008/0261.

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Marshak, A., Y. Knyazikhin, J. C. Chiu, and W. J. Wiscombe. "Spectrally Invariant Approximation within Atmospheric Radiative Transfer." Journal of the Atmospheric Sciences 68, no. 12 (December 1, 2011): 3094–111. http://dx.doi.org/10.1175/jas-d-11-060.1.

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Abstract Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These “spectrally invariant relationships” are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

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Lucarini, Valerio, and Andrey Gritsun. "A new mathematical framework for atmospheric blocking events." Climate Dynamics 54, no. 1-2 (November 1, 2019): 575–98. http://dx.doi.org/10.1007/s00382-019-05018-2.

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Abstract We use a simple yet Earth-like hemispheric atmospheric model to propose a new framework for the mathematical properties of blocking events. Using finite-time Lyapunov exponents, we show that the occurrence of blockings is associated with conditions featuring anomalously high instability. Longer-lived blockings are very rare and have typically higher instability. In the case of Atlantic blockings, predictability is especially reduced at the onset and decay of the blocking event, while a relative increase of predictability is found in the mature phase. The opposite holds for Pacific blockings, for which predictability is lowest in the mature phase. Blockings are realised when the trajectory of the system is in the neighbourhood of a specific class of unstable periodic orbits (UPOs), natural modes of variability that cover the attractor the system. UPOs corresponding to blockings have, indeed, a higher degree of instability compared to UPOs associated with zonal flow. Our results provide a rigorous justification for the classical Markov chains-based analysis of transitions between weather regimes. The analysis of UPOs elucidates that the model features a very severe violation of hyperbolicity, due to the presence of a substantial variability in the number of unstable dimensions, which explains why atmospheric states can differ a lot in term of their predictability. Additionally, such a variability explains the need for performing data assimilation in a state space that includes not only the unstable and neutral subspaces, but also some stable modes. The lack of robustness associated with the violation of hyperbolicity might be a basic cause contributing to the difficulty in representing blockings in numerical models and in predicting how their statistics will change as a result of climate change. This corresponds to fundamental issues limiting our ability to construct very accurate numerical models of the atmosphere, in term of predictability of the both the first and of the second kind in the sense of Lorenz.

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Kovalnogov, Vladislav N., Yuriy A. Khakhalev, Ekaterina V. Tsvetova, and Larisa V. Khakhaleva. "MATHEMATICAL MODELING AND NUMERICAL STUDY OF ATMOSPHERIC BOUNDARY LAYER NEAR WINDFARMS." Автоматизация процессов управления 3, no. 65 (2021): 33–40. http://dx.doi.org/10.35752/1991-2927-2021-3-65-33-40.

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The article analyzes Russian and foreign sources relating to the interaction of wind turbines with the surface layers of the atmosphere. It specifies the main problems of mathematical modeling of the atmospheric boundary layer near the wind farms due to adverse meteorological conditions, in particular, constant zero crossings in the autumn-winter period, various precipitation, a wide time range, air parameters, terrain and other features. The authors analyze the evolution of mathematical models of turbulence to describe the boundary layer near wind turbines from earlier to rapidly developing and currently used. To achieve greater accuracy and naturalism, it is proposed to use high-performance efficient algorithms based on combining scales and physics of phenomena. The authors propose a mathematical model for studying the state of the atmospheric polydisperse boundary layer under conditions of the Ulyanovsk wind farm, taking into account the dispersed particles in the flow, surface curvature, pressure gradient and other influences.

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Du, Hailiang, and Leonard A. Smith. "Pseudo-Orbit Data Assimilation. Part II: Assimilation with Imperfect Models." Journal of the Atmospheric Sciences 71, no. 2 (January 31, 2014): 483–95. http://dx.doi.org/10.1175/jas-d-13-033.1.

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Abstract Data assimilation and state estimation for nonlinear models is a challenging task mathematically. Performing this task in real time, as in operational weather forecasting, is even more challenging as the models are imperfect: the mathematical system that generated the observations (if such a thing exists) is not a member of the available model class (i.e., the set of mathematical structures admitted as potential models). To the extent that traditional approaches address structural model error at all, most fail to produce consistent treatments. This results in questionable estimates both of the model state and of its uncertainty. A promising alternative approach is proposed to produce more consistent estimates of the model state and to estimate the (state dependent) model error simultaneously. This alternative consists of pseudo-orbit data assimilation with a stopping criterion. It is argued to be more efficient and more coherent than one alternative variational approach [a version of weak-constraint four-dimensional variational data assimilation (4DVAR)]. Results that demonstrate the pseudo-orbit data assimilation approach can also outperform an ensemble Kalman filter approach are presented. Both comparisons are made in the context of the 18-dimensional Lorenz96 flow and the two-dimensional Ikeda map. Many challenges remain outside the perfect model scenario, both in defining the goals of data assimilation and in achieving high-quality state estimation. The pseudo-orbit data assimilation approach provides a new tool for approaching this open problem.

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Da’ie, Abdul Basit. "Developing mathematical models for global solar radiation intensity estimation at Shakardara, Kabul." International Journal of Innovative Research and Scientific Studies 4, no. 2 (March 30, 2021): 133–38. http://dx.doi.org/10.53894/ijirss.v4i2.68.

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Solar energy properties such as Global Solar Radiation (GSR) intensity could be determined in either methods, experimentally or theoretically. Unfortunately, in most countries including Afghanistan, the first method which is more acceptable, but due to the high cost, maintenance and calibration requirements is not available. Therefore, an alternative widely used way is the second one which is model developments based on the meteorological (atmospheric) data; specially the sunny hours. The aim of this study at Shakardara area is to estimate atmospheric transparency percentage on 2017, determining the angstrom model coefficients and to introduce a suitable model for global solar radiation prediction. The hourly observed solar radiation intensity H (WHm-2 ) and sunshine hours S (

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Venkatram, Akula, and Christian Seigneur. "Review of mathematical models for health risk assessment: II. Atmospheric chemical concentrations." Environmental Software 8, no. 2 (1993): 75–90. http://dx.doi.org/10.1016/0266-9838(93)90018-d.

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Guseynov, Sharif, and Eugene Kopytov. "Complex Mathematical Models for Analysis, Evaluation and Prediction of Aqueous and Atmospheric Environment of Latvia." Transport and Telecommunication Journal 13, no. 1 (January 1, 2012): 57–74. http://dx.doi.org/10.2478/v10244-012-0006-8.

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Complex Mathematical Models for Analysis, Evaluation and Prediction of Aqueous and Atmospheric Environment of Latvia In present paper the authors consider the complete statements of initial-boundary problems for the modelling of various aspects of aqueous (3 models) and atmospheric systems (2 models) in Latvia. All the proposed models are described in terms of differential equations theory (using both ordinary differential equations and partial differential equations) and are regarded to be the evolutional models. Two of the three aqueous system models being studied are intended to describe the natural aquatic media ecosystems while the other models are aimed at studying environmental pollution processes.

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Scotton, Jaque W., Zardo Becker, Darci L. Savicki, and Antonio Goulart. "Mathematical Modeling and Numerical Simulation of Atmospheric Pollutant Dispersion." Defect and Diffusion Forum 372 (March 2017): 180–87. http://dx.doi.org/10.4028/www.scientific.net/ddf.372.180.

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This work presents a mathematical modeling and numerical solution of dispersion of pollutants in the atmosphere. The equations of conservation of mass, amount of movement, energy and a chemical species are solved by the Finite Volume Method in Cartesian coordinates and the turbulence closure is based on the Reynolds averages (RANS models), using the model k-ε for the determination of the fields of velocity, temperature and, in a specific case, concentration of pollutant. The numerical results are compared with data from the classic Prairie Grass experiment, showing excellent agreement.

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Vasilevich and Nikanorova. "ANALYTICAL MATHEMATICAL MODELS OF THE POPULATION OF ARTHROPODS IN THE NON-BLACK EARTH ZONE." THEORY AND PRACTICE OF PARASITIC DISEASE CONTROL, no. 22 (May 19, 2021): 128–32. http://dx.doi.org/10.31016/978-5-6046256-1-3.2021.22.128-132.

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The article provides an example of mathematical analytical modeling of the population size of blood-sucking arthropods on the example of mosquitoes and ixodid ticks that inhabit the Kaluga Region. The presented analytical mathematical models make it possible to clearly assess the influence of environmental factors on parasite populations. The following factors were taken into account: average temperature (monthly and yearly, t, oС); average precipitation (monthly and yearly, S, mm); mean atmospheric pressure (P, mm Hg) for mosquitoes, and monthly average temperature (t, o С), monthly mean relative humidity (Q, %), and mean atmospheric pressure (P, mm Hg) for ixodid ticks. The analysis of the obtained models shows that under weather conditions when monthly mean values of the considered factors are at a zero level, the estimated number of ixodid ticks and mosquitoes will be 1150 and 1529 individuals in the control area per year. The population of ixodid ticks is most significantly influenced by the mean atmospheric pressure; its influence is twice as strong as monthly mean humidity and 6.4 times stronger than the influence of monthly average temperature. The "+" sign indicates that the higher the atmospheric pressure is, the more active ticks are observed. Monthly average precipitation has the greatest effect on the mosquito population.

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Alkinani, Sadeem S., Mohamed F. El-Amin, and Tayeb Brahimi. "Numerical Modeling and Analysis of Harvesting Atmospheric Water Using Porous Materials." Separations 9, no. 11 (November 10, 2022): 364. http://dx.doi.org/10.3390/separations9110364.

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Nowadays, harvesting water from the atmosphere is becoming a new alternative for generating fresh water. To the author’s best knowledge, no mathematical model has been established to describe the process of harvesting water from the atmosphere using porous materials. This research seeks to develop a new mathematical model for water moisture absorption in porous materials to simulate and assess harvesting atmospheric water. The mathematical model consists of a set of governing partial differential equations, including mass conservation equation, momentum equation, associated parameterizations, and initial/boundary conditions. Moreover, the model represents a two-phase fluid flow that contains phase-change gas–liquid physics. A dataset has been collected from the literature containing five porous materials that have been experimentally used in water generation from the air. The five porous materials include copper chloride, copper sulfate, magnesium sulfate, manganese oxides, and crystallites of lithium bromide. A group of empirical models to relate the relative humidity and water content have been suggested and combined with the governing to close the mathematical system. The mathematical model has been solved numerically for different times, thicknesses, and other critical parameters. A comparison with experimental findings was made to demonstrate the validity of the simulation model. The results show that the proposed mathematical model precisely predicts the water content during the absorption process. In addition, the simulation results show that; during the absorption process, when the depth is smaller, the water content reaches a higher saturation point quickly and at a lower time, i.e., quick process. Finally, the highest average error of the harvesting atmospheric water model is around 1.9% compared to experimental data observed in manganese oxides.

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Liu, Xin'an, Bolum Wang, and Guirui Yu. "Mathematical Models for Light Distribution in Rice Canopy." Journal of Agricultural Meteorology 48, no. 5 (1993): 751–54. http://dx.doi.org/10.2480/agrmet.48.751.

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Li, Zhuolin, Dongmei Fu, and Zibo Pei. "Modeling research of initial atmospheric corrosion of Q235 carbon steel based on electrical resistance probe." Anti-Corrosion Methods and Materials 68, no. 2 (April 5, 2021): 45–52. http://dx.doi.org/10.1108/acmm-04-2020-2295.

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Purpose This paper aims to discover the mathematical model for Q235 carbon steel corrosion date acquired in the initial stage of atmospheric corrosion using electrical resistance probe. Design/methodology/approach In this paper, mathematical approaches are used to construct a classification model for atmospheric environmental elements and material corrosion rates. Findings Results of the experiment show that the corrosion data can be converted into corrosion depth for calculating corrosion rate to obtain corrosion kinetics model and conform corrosion acceleration phase. Combined with corresponding atmospheric environmental elements, a real time grade subdivision model for corrosion rate can be constructed. Originality/value These mathematical models constructed by real time corrosion data can be well used to research the characteristics about initial atmospheric corrosion of Q235 carbon steel.

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Widmann, J. F., and E. J. Davis. "Mathematical models of the uptake of ClONO2 and other gases by atmospheric aerosols." Journal of Aerosol Science 28, no. 1 (January 1997): 87–106. http://dx.doi.org/10.1016/s0021-8502(96)00060-2.

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Wang, A. P. "Correction of atmospheric effects on remote sensing (new mathematical models and approximation solutions)." Mathematical Modelling 9, no. 2 (1987): 117–24. http://dx.doi.org/10.1016/0270-0255(87)90520-3.

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Biliaiev, M., I. Kalashnikov, V. Kozachina, and O. Berlov. "Mathematical and descrete models in the tasks of emergency pollution of atmospheric air." Collection of Research Papers of the National Mining University 57 (March 30, 2019): 149–57. http://dx.doi.org/10.33271/crpnmu/57.149.

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Popov, O., A. Iatsyshyn, V. Kovach, V. Artemchuk, D. Taraduda, V. Sobyna, D. Sokolov, et al. "Physical Features of Pollutants Spread in the Air During the Emergency at NPPs." Nuclear and Radiation Safety, no. 4(84) (December 19, 2019): 88–98. http://dx.doi.org/10.32918/nrs.2019.4(84).11.

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The authors carried out a thorough study of the features of the spread of hazardous chemicals in the surface layer of the atmosphere in the event of an emergency at the site of a nuclear power plant. In order to ensure the continuous operation of the stations in their territories, various ancillary technogenic facilities are located and operate, which release emissions of non-radiation pollutants into the atmosphere. Under various negative circumstances of a technical and natural nature, emergencies may occur due to significant chemical pollution of the atmospheric air in and outside the sanitary protection zone. The prevention of such emergencies is based on environmental monitoring in the locations of man-made objects and their preventive forecast. Implementation of these measures is not possible without the use of effective methods based on mathematical models of environmental pollution by anthropogenic objects, and the hardware and software that implement these methods. The main stages of the development of information and technical methods of prevention of such emergencies are given and described. Different scenarios of emergencies are described as a result of the release of chemicals into the atmosphere at these sites. A conceptual scheme for the distribution of impurities in the atmosphere due to man-made emissions has been developed. The peculiarities of atmospheric air propagation under stationary and non-stationary emission conditions are described in detail. It is established that the most determinants of influence on the concentration distribution of impurities are: mode and conditions of emission, type of source, direction, and velocity of the wind, state of the atmosphere, chemical interaction with other substances in the atmospheric air, gravitational deposition, leaching of sediments, absorption of the underlying surface. surface, terrain. The results obtained will be used in the process of developing mathematical models for the propagation of pollutants in the atmospheric air from the emissions of nuclear power plants during relevant emergencies.

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Pandžić, K., I. Šimunić, F. Tomić, S. Husnjak, T. Likso, and D. Petošić. "Comparison of three mathematical models for the estimation of 10-day drain discharge." Theoretical and Applied Climatology 85, no. 1-2 (December 22, 2005): 107–15. http://dx.doi.org/10.1007/s00704-005-0165-9.

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Nikezić, Dušan P., Uzahir R. Ramadani, Dušan S. Radivojević, Ivan M. Lazović, and Nikola S. Mirkov. "Deep Learning Model for Global Spatio-Temporal Image Prediction." Mathematics 10, no. 18 (September 19, 2022): 3392. http://dx.doi.org/10.3390/math10183392.

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Mathematical methods are the basis of most models that describe the natural phenomena around us. However, the well-known conventional mathematical models for atmospheric modeling have some limitations. Machine learning with Big Data is also based on mathematics but offers a new approach for modeling. There are two methodologies to develop deep learning models for spatio-temporal image prediction. On these bases, two models were built—ConvLSTM and CNN-LSTM—with two types of predictions, i.e., sequence-to-sequence and sequence-to-one, in order to forecast Aerosol Optical Thickness sequences. The input dataset for training was NASA satellite imagery MODAL2_E_AER_OD from Terra/MODIS satellites, which presents global Aerosol Optical Thickness with an 8 day temporal resolution from 2000 to the present. The obtained results show that the ConvLSTM sequence-to-one model had the lowest RMSE error and the highest Cosine Similarity value. The advantages of the developed DL models are that they can be executed in milliseconds on a PC, can be used for global-scale Earth observations, and can serve as tracers to study how the Earth’s atmosphere moves. The developed models can be used as transfer learning for similar image time-series forecasting models.

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AbdelMeguid, Hossam, Piotr Skworcow, and Bogumil Ulanicki. "Mathematical modelling of a hydraulic controller for PRV flow modulation." Journal of Hydroinformatics 13, no. 3 (January 6, 2011): 374–89. http://dx.doi.org/10.2166/hydro.2011.024.

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This paper describes the development of mathematical models, which represent static and dynamic properties of the AQUAI-MOD® hydraulic controller coupled with a standard pressure reducing valve (PRV) as well as a new experimental set-up for testing the controller and calibrating and validating the models. The purpose of the AQUAI-MOD® controller is to modulate the PRV outlet pressure according to the valve flow. The controller has been experimentally tested to assess its operation in different conditions and operating ranges and in all cases showed good performance. The mathematical models of the PRV and its controller have been developed and solved using the Mathematica software package to represent both steady state and dynamics conditions. The numerical results of simulation of the mathematical model have been compared with experimental data and showed a good agreement in magnitude and trends. The model can be used to simulate the behaviour of the PRV and the AQUAI-MOD® hydraulic controller in typical network applications. It can also be used at the design stage to size the controller components and to compute the required set points for the minimum and the maximum pressure before installing the controller in the field.

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Chen, Xin, Prateek Bahl, Charitha de Silva, David Heslop, Con Doolan, Samsung Lim, and C. Raina MacIntyre. "Systematic Review and Evaluation of Mathematical Attack Models of Human Inhalational Anthrax for Supporting Public Health Decision Making and Response." Prehospital and Disaster Medicine 35, no. 4 (June 4, 2020): 412–19. http://dx.doi.org/10.1017/s1049023x20000734.

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AbstractBackground:Anthrax is a potential biological weapon and can be used in an air-borne or mail attack, such as in the attack in the United States in 2001. Planning for such an event requires the best available science. Since large-scale experiments are not feasible, mathematical modelling is a crucial tool to inform planning. The aim of this study is to systematically review and evaluate the approaches to mathematical modelling of inhalational anthrax attack to support public health decision making and response.Methods:A systematic review of inhalational anthrax attack models was conducted using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) criteria. The models were reviewed based on a set of defined criteria, including the inclusion of atmospheric dispersion component and capacity for real-time decision support.Results:Of 13 mathematical modelling studies of human inhalational anthrax attacks, there were six studies that took atmospheric dispersion of anthrax spores into account. Further, only two modelling studies had potential utility for real-time decision support, and only one model was validated using real data.Conclusion:The limited modelling studies available use widely varying methods, assumptions, and data. Estimation of attack size using different models may be quite different, and is likely to be under-estimated by models which do not consider weather conditions. Validation with available data is crucial and may improve models. Further, there is a need for both complex models that can provide accurate atmospheric dispersion modelling, as well as for simpler modelling tools that provide real-time decision support for epidemic response.

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Aydossov, А. А., R. U. Bayamirova, A. R. Togasheva, and А. Т. Zholbassarova. "Mathematical models of atmospheric transport of reactive pollutants emitted by oil and gas fisheries." Vestnik KazNRTU 138, no. 2 (2020): 799–805. http://dx.doi.org/10.51301/vest.su.2020.v138.i2.140.

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Mukhartova, Iuliia, Alexander Krupenko, Polina Mangura, and Alexander Olchev. "Mathematical Modeling of Vegetation Heterogeneity and Complex Topography Effects on Turbulent Exchange of GHG within the Atmospheric Surface Layer." Proceedings 2, no. 20 (October 17, 2018): 1310. http://dx.doi.org/10.3390/proceedings2201310.

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The local-scale 2D and 3D models of greenhouse gases (GHG) exchange between a non-uniform land surface and the atmosphere were developed. They are based on solution of the system of averaged Navier-Stokes, continuity and diffusion-advection equations. For numerical solution of the differential equations the stable finite-difference schemes were suggested. The models were applied to derive effects of complex topography and vegetation heterogeneity on 2D-3D air flow patterns, as well as on CO2 exchange within the atmospheric surface layer. Several numerical experiments were also provided to describe the air-flow re-establishing after its interaction with some obstacle (e.g., forest edge). Quantitative criteria for selection of the experimental sites for continuous eddy covariance flux measurements characterized by minimum effects of horizontal advection on measured fluxes were suggested.

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Soldatenko, Sergei A., and Rafael M. Yusupov. "The Determination of Feasible Control Variables for Geoengineering and Weather Modification Based on the Theory of Sensitivity in Dynamical Systems." Journal of Control Science and Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/1547462.

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Geophysical cybernetics allows for exploring weather and climate modification (geoengineering) as an optimal control problem in which the Earth’s climate system is considered as a control system and the role of controller is given to human operators. In mathematical models used in climate studies control actions that manipulate the weather and climate can be expressed via variations in model parameters that act as controls. In this paper, we propose the “instability-sensitivity” approach that allows for determining feasible control variables in geoengineering. The method is based on the sensitivity analysis of mathematical models that describe various types of natural instability phenomena. The applicability of this technique is illustrated by a model of atmospheric baroclinic instability since this physical mechanism plays a significant role in the general circulation of the atmosphere and, consequently, in climate formation. The growth rate of baroclinic unstable waves is taken as an indicator of control manipulations. The information obtained via calculated sensitivity coefficients is very beneficial for assessing the physical feasibility of methods of control of the large-scale atmospheric dynamics and for designing optimal control systems for climatic processes. It also provides insight into potential future changes in baroclinic waves, as a result of a changing climate.

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Cai, Yikun, Yuanming Xu, Yu Zhao, and Xiaobing Ma. "Atmospheric corrosion prediction: a review." Corrosion Reviews 38, no. 4 (August 27, 2020): 299–321. http://dx.doi.org/10.1515/corrrev-2019-0100.

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AbstractThe atmospheric corrosion of metallic materials causes great economic loss every year worldwide. Thus, it is meaningful to predict the corrosion loss in different field environments. Generally, the corrosion prediction method includes three parts of work: the modelling of the corrosive environment, the calibration of the corrosion effects, and the establishment of the corrosion kinetics. This paper gives an overview of the existing methods as well as promising tools and technologies which can be used in corrosion prediction. The basic corrosion kinetic model is the power function model and it is accurate for short-term corrosion process. As for the long-term corrosion process, the general linear models are more appropriate as they consider the protective effect of the corrosion products. Most corrosion effect models correlate the environmental variables, which are characterized by the annual average value in most cases, with corrosion parameters by linear equations which is known as the dose-response function. Apart from these conventional methods, some mathematical and numerical methods are also appropriate for corrosion prediction. The corrosive environment can be described by statistical distributions, time-varying functions and even geographic information system (GIS), while the corrosion effect can be captured via response surface models and statistical learning methods.

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Sednev, I., and S. Menon. "Analyzing numerics of bulk microphysics schemes in community models: warm rain processes." Geoscientific Model Development 5, no. 4 (August 3, 2012): 975–87. http://dx.doi.org/10.5194/gmd-5-975-2012.

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Abstract. Implementation of bulk cloud microphysics (BLK) parameterizations in atmospheric models of different scales has gained momentum in the last two decades. Utilization of these parameterizations in cloud-resolving models when timesteps used for the host model integration are a few seconds or less is justified from the point of view of cloud physics. However, mechanistic extrapolation of the applicability of BLK schemes to the regional or global scales and the utilization of timesteps of hundreds up to thousands of seconds affect both physics and numerics. We focus on the mathematical aspects of BLK schemes, such as stability and positive-definiteness. We provide a strict mathematical definition for the problem of warm rain formation. We also derive a general analytical condition (SM-criterion) that remains valid regardless of parameterizations for warm rain processes in an explicit Eulerian time integration framework used to advanced finite-difference equations, which govern warm rain formation processes in microphysics packages in the Community Atmosphere Model and the Weather Research and Forecasting model. The SM-criterion allows for the existence of a unique positive-definite stable mass-conserving numerical solution, imposes an additional constraint on the timestep permitted due to the microphysics (like the Courant-Friedrichs-Lewy condition for the advection equation), and prohibits use of any additional assumptions not included in the strict mathematical definition of the problem under consideration. By analyzing the numerics of warm rain processes in source codes of BLK schemes implemented in community models we provide general guidelines regarding the appropriate choice of time steps in these models.

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Stamou, A. I., M. Latsa, and D. Assimacopoulos. "Design of two-storey final settling tanks using mathematical models." Journal of Hydroinformatics 2, no. 4 (October 1, 2000): 235–45. http://dx.doi.org/10.2166/hydro.2000.0021.

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A mathematical model is applied to the design of two-storey final settling tanks. Computations show that the flow and suspended solids (SS) concentration fields for the upper and bottom tanks are similar. The flow field has the ‘two-layer’ structure, observed in real and laboratory settling tanks, consisting of a bottom current and a free surface return current with approximately equal heights. The SS concentration field is governed by the flow field (and vice versa). The SS concentration profiles are uniform in the major part of the tanks. The hydraulic and SS removal efficiencies improve with decreasing flow rate. In both tanks the outlet SS concentrations are lower than the maximum permissible value (20 mg l−1), with the upper tank showing a better performance than the bottom tank.

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Kolb, C. E., D. R. Worsnop, J. T. Jayne, and P. Davidovits. "Comment on mathematical models of the uptake of ClONO2 and other gases by atmospheric aerosols." Journal of Aerosol Science 29, no. 7 (August 1998): 893–97. http://dx.doi.org/10.1016/s0021-8502(97)10022-2.

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Degond, Pierre, and Brigitte Lucquin Desreux. "Mathematical models of electrical discharges in air at atmospheric pressure: a derivation from asymptotic analysis." International Journal of Computing Science and Mathematics 1, no. 1 (2007): 58. http://dx.doi.org/10.1504/ijcsm.2007.013764.

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Agarkov, N. M., M. I. Churnosov, O. A. Osipova, O. V. Sharapova, A. A. Modestov, E. N. Korovin, and N. V. Eckert. "Effect of Anthropogenic Atmospheric Pollutants on the Prevalence of Congenital Malformations in Newborns." Rossiyskiy Vestnik Perinatologii i Pediatrii (Russian Bulletin of Perinatology and Pediatrics) 65, no. 6 (January 22, 2021): 34–41. http://dx.doi.org/10.21508/1027-4065-2020-65-6-34-41.

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Rationale. The congenital malformations are the important indicator of the environmental condition, and the anthropogenic pollution of the atmosphere effects strongly the incidence of malformations in the newborns. Purpose of the Study. It is the study of the cause-and-effect relationship between the incidence of malformations in newborns and anthropogenic atmospheric pollutants using the correlation and variance methods, and the development of the mathematical models to predict the formation of the congenital malformations depending on the specific pollutants. Material and methods. The correlation and variance methods were used to study the relationships of the main anthropogenic atmospheric pollutants with the incidence of the congenital malformations in all newborns in Belgorod city in 2000–2015. The predictive models were developed based on the regression method. Results. The most effect of the excess of the maximum allowable average daily concentrations of ammonia and carbon monoxide in the atmosphere on the prevalence of the congenital malformations of various systems and organs was determined with 11 reliable correlations with the congenital malformations studied and those in general. According to the results of the analysis of variance, the maximum level of the combined effect of the anthropogenic air pollutants was revealed for the congenital malformations of the musculoskeletal system (95.69%), face and neck (94.66%), central nervous system (92.31%), digestive system (93.76%). Conclusion. The regression models created at the level required assure the prediction of the various forms of the congenital malformations depending on the anthropogenic pollutants.

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Guergachi, A. Aziz, and Gilles G. Patry. "Identification, verification and validation of process models in wastewater engineering: a critical review." Journal of Hydroinformatics 5, no. 3 (July 1, 2003): 181–88. http://dx.doi.org/10.2166/hydro.2003.0014.

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This article presents a critical review of the existing methodologies for process mathematical modelling in the area of wastewater engineering. It is argued that model identifiability is not a major issue in mathematical modelling. Model verifiability is a very demanding criterion that can be replaced by a less stringent one: model observability. The issue of ‘complex models versus reduced-order models’ is to be resolved by introducing a new concept: optimal model complexity. The traditional procedures of model validation are not adequate and a mathematical framework for model quality evaluation is needed.

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Vasilevich, F. I., V. V. Kalmykov, A. M. Nikanorova, and E. V. Koroleva. "Mathematical modeling of ixodid ticks depending on three climatic factors." IOP Conference Series: Earth and Environmental Science 839, no. 3 (September 1, 2021): 032009. http://dx.doi.org/10.1088/1755-1315/839/3/032009.

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Abstract The article deals with the regulation of the number of ixodid ticks in the Non-Chernozem zone using mathematical modeling of ixodid ticks that live in the Kaluga region of the Russian Federation. Statistical data is taken for the period of the decade of the research. In the Kaluga Region, two species of ixodid ticks are presented, which are Ixodes ricinus (European forest) and Dermacentor reticulatus (pasture), both demonstrating two regular peaks of their activity in spring and autumn. Analytical and calculated mathematical models of the population of ixodid ticks are obtained based on the composition of three or four factors, including: average monthly air temperature per year, average monthly relative humidity per year, average atmospheric pressure per year. The analysis of the results shows that it makes sense to take into account the composition of the first three factors, excluding cloud cover, as long as the cloud value is minimal is minimal in the Kaluga Region and thus cannot affect the results of the mathematical calculations. There are theories which are based on the hypothesis that both the temperature and humidity have an effect on the size of the ixodid ticks’ population. The obtained models presented in the article prove strong influence of these parameters, but moreover accents the monthly average atmospheric pressure having the greatest influence on the parasites’ population.

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Santana, Juan J., Alejandro Ramos, Alejandro Rodriguez-Gonzalez, Helena C. Vasconcelos, Vicente Mena, Bibiana M. Fernández-Pérez, and Ricardo M. Souto. "Shortcomings of International Standard ISO 9223 for the Classification, Determination, and Estimation of Atmosphere Corrosivities in Subtropical Archipelagic Conditions—The Case of the Canary Islands (Spain)." Metals 9, no. 10 (October 15, 2019): 1105. http://dx.doi.org/10.3390/met9101105.

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The classification, assessment, and estimation of the atmospheric corrosivity are fixed by the ISO 9223 standard. Its recent second edition introduced a new corrosivity category for extreme environments CX, and defined mathematical models that contain dose–response functions for normative corrosivity estimations. It is shown here that application of the ISO 9223 standard to archipelagic subtropical areas exhibits major shortcomings. Firstly, the corrosion rates of zinc and copper exceed the range employed to define the CX category. Secondly, normative corrosivity estimation would require the mathematical models to be redefined introducing the time of wetness and a new set of operation constants.

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Yakovleva, Valentina, Aleksey Zelinskiy, Roman Parovik, Grigorii Yakovlev, and Aleksey Kobzev. "Model for Reconstruction of γ-Background during Liquid Atmospheric Precipitation." Mathematics 9, no. 14 (July 11, 2021): 1636. http://dx.doi.org/10.3390/math9141636.

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With regard to reconstructing the gamma background dose rate, existing models are either empirical with limited applicability or have many unknown input parameters, which complicates their application in practice. Due to this, there is a need to search for a new approach and build a convenient, easily applicable and universal model. The paper proposes a mathematical model for reconstructing the temporal evolution of the ambient equivalent γ-radiation dose rate during rain episodes, depending on the density of radon flux from the soil surface, as well as the duration and intensity of rain. The efficiency of the model is confirmed by the high coefficient of determination (R2 = 0.81–0.99) between the measured and reconstructed ambient equivalent dose rate during periods of rain, the simulation of which was performed using Wolfram Mathematica. An algorithm was developed for restoring the dynamics of the ambient equivalent γ-radiation dose rate during rainfall. Based on the results obtained, assumptions were made where the washout of radionuclides originates. The influence of the radionuclides ratio on the increase in the total γ-radiation dose rate was investigated.

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Pooja, S. B., and Siva R. V. Balan. "An Investigation Study on Clustering and Classification Techniques for Weather Forecasting." Journal of Computational and Theoretical Nanoscience 16, no. 2 (February 1, 2019): 417–21. http://dx.doi.org/10.1166/jctn.2019.7742.

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Weather forecasting is the prediction of atmosphere state for particular location by using principles of physics provided by many statistical and empirical techniques. Weather forecasts are frequently made by collecting quantitative data about current state of atmosphere through scientific understanding of atmospheric processes to illustrate how atmosphere changes in future. Current weather conditions are collected through the observation from the ground, ships, aircraft, radio sounds and satellites. The information is transmitted to the meteorological centers where the data are collected and examined for prediction. There are diverse techniques included in weather forecasting, from relatively simple observation of sky to complex computerized mathematical models. But, the existing techniques failed to predict the weather with higher accuracy and lesser time. In order to improve the prediction performance, the machine learning and ensemble techniques are introduced.

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Cheng, Jianwei, Xixi Zhang, and Apurna Ghosh. "Explosion risk assessment model for underground mine atmosphere." Journal of Fire Sciences 35, no. 1 (December 14, 2016): 21–35. http://dx.doi.org/10.1177/0734904116676495.

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In the coal mining industry, explosions or mine fires present the most hazardous safety threats for coal miners or mine rescue members. Hence, the determination of the mine atmosphere explosibility and its evolution are critical for the success of mine rescues or controlling the severity of a mine accident. However, although there are numbers of methods which can be used to identify the explosibility, none of them could well indicate the change to the explosion risk time evolution. The reason is that the underground sealed atmospheric compositions are so complicated and their dynamical changes are also affected by various influence factors. There is no one method that could well handle all such considerations. Therefore, accurately knowing the mine atmospheric status is still a complicated problem for mining engineers. Method of analyzing the explosion safety margin for an underground sealed atmosphere is urgently desired. This article is going to propose a series of theoretical explosion risk assessment models to fully analyze the evolution of explosion risk in an underground mine atmosphere. Models are based on characteristics of the Coward explosibility diagram with combining mathematical analyzing approaches to address following problems: (1) for an “not-explosive” atmosphere, judging the evolution of explosion risk and estimating the change-of-state time span from “not-explosive” to “explosive” and (2) for an “explosive” atmosphere, estimating the “critical” time span of moving out of explosive zone and stating the best risk mitigation strategy. Such research efforts could not only help mine operators understand the explosibility risk of a sealed mine atmosphere but also provide a useful tool to wisely control explosive atmosphere away from any dangers. In order to demonstrate research findings, case studies for derived models are shown and are also used to instruct readers how to apply them. The results provide useful information for effectively controlling an explosive underground sealed atmosphere.

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Jaoua, Nizar. "Climate mitigation mathematical models consistent with the 2015 Paris Agreement." International Journal of Global Warming 21, no. 3 (2020): 294. http://dx.doi.org/10.1504/ijgw.2020.10030530.

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Jaoua, Nizar. "Climate mitigation mathematical models consistent with the 2015 Paris Agreement." International Journal of Global Warming 21, no. 3 (2020): 287. http://dx.doi.org/10.1504/ijgw.2020.108677.

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Potempski, S., and S. Galmarini. "<i>Est modus in rebus</i>: analytical properties of multi-model ensembles." Atmospheric Chemistry and Physics 9, no. 24 (December 16, 2009): 9471–89. http://dx.doi.org/10.5194/acp-9-9471-2009.

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Abstract. In this paper we investigate some basic properties of the multi-model ensemble systems, which can be deduced from a general characteristic of statistical distributions of the ensemble members with the help of mathematical tools. In particular we show how to find optimal linear combination of model results, which minimizes the mean square error both in the case of uncorrelated and correlated models. By proving basic estimations we try to deduce general properties describing multi-model ensemble systems. We show also how mathematical formalism can be used for investigation of the characteristics of such systems.

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Santana, Juan J., Víctor Cano, Helena C. Vasconcelos, and Ricardo M. Souto. "The Influence of Test-Panel Orientation and Exposure Angle on the Corrosion Rate of Carbon Steel. Mathematical Modelling." Metals 10, no. 2 (January 29, 2020): 196. http://dx.doi.org/10.3390/met10020196.

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The effects of both test-panel orientation and exposure angle on the atmospheric corrosion rates of carbon steel probes exposed to a marine atmosphere were investigated. Test samples were exposed in a tree-shape metallic frame with either three exposure angles of 30°, 45° and 60° and orientation north-northeast (N-NE), or eight different orientation angles around a circumference. It was found that the experimental corrosion rates of carbon steel decreased for the specimens exposed with greater exposure angles, whereas the highest corrosion rates were found for those oriented to N-NE due to the influence of the prevailing winds. The obtained data obtained were fitted using the bi-logarithmic law and its variations as to take in account the amounts of pollutants and the time of wetness (TOW) for each particular case with somewhat good agreement, although these models failed when all the effects were considered simultaneously. In this work, we propose a new mathematical model including qualitative variables to account for the effects of both exposure and orientation angles while producing the highest quality fits. The goodness of the fit was used to determine the performance of the mathematical models.

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Volkov, A. V., and A. A. Khadartsev. "THE HYPOTHESIS OF TWO-DIMENSIONAL REGULARITY OF ATMOSPHERIC STATE INDEX FIELDS AND ITS EMPIRICAL JUSTIFICATION." News of the Tula state university. Sciences of Earth 4, no. 1 (2021): 34–45. http://dx.doi.org/10.46689/2218-5194-2021-4-1-34-45.

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The paper discusses the empirical foundations and the results of two-dimensional approximation of the diagnostic components of the atmospheric indices - its dispersion poten-tials (DP) and pollution by mathematical models. A hypothesis is formulated about the pres-ence of features of the possible self-organization of the studied fields by the energy-informational influences of the Sun. Key words: analysis of empirical data, spatial and temporal patterns of field chang-es, dispersion and atmospheric pollution potentials, diagnostic component of the field, two-dimensional waves, self-organization.

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Amundson, N. R., A. Caboussat, J. W. He, A. V. Martynenko, V. B. Savarin, J. H. Seinfeld, and K. Y. Yoo. "A computationally efficient inorganic atmospheric aerosol phase equilibrium model (UHAERO)." Atmospheric Chemistry and Physics Discussions 5, no. 5 (September 28, 2005): 9291–324. http://dx.doi.org/10.5194/acpd-5-9291-2005.

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Abstract. A variety of thermodynamic models have been developed to predict inorganic gas-aerosol equilibrium. To achieve computational efficiency a number of the models rely on a priori specification of the phases present in certain relative humidity regimes. Presented here is a new computational model, named UHAERO, that is both efficient and rigorously computes phase behavior without any a priori specification. The computational implementation is based on minimization of the Gibbs free energy using a primal-dual method, coupled to a Newton iteration. The mathematical details of the solution are given elsewhere. The model also computes deliquescence and crystallization behavior without any a priori specification of the relative humidities of deliquescence or crystallization. Detailed phase diagrams of the sulfate/nitrate/ammonium/water system are presented as a function of relative humidity at 298.15 K over the complete space of composition.

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Amundson, N. R., A. Caboussat, J. W. He, A. V. Martynenko, V. B. Savarin, J. H. Seinfeld, and K. Y. Yoo. "A new inorganic atmospheric aerosol phase equilibrium model (UHAERO)." Atmospheric Chemistry and Physics 6, no. 4 (March 28, 2006): 975–92. http://dx.doi.org/10.5194/acp-6-975-2006.

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Abstract. A variety of thermodynamic models have been developed to predict inorganic gas-aerosol equilibrium. To achieve computational efficiency a number of the models rely on a priori specification of the phases present in certain relative humidity regimes. Presented here is a new computational model, named UHAERO, that is both efficient and rigorously computes phase behavior without any a priori specification. The computational implementation is based on minimization of the Gibbs free energy using a primal-dual method, coupled to a Newton iteration. The mathematical details of the solution are given elsewhere. The model computes deliquescence behavior without any a priori specification of the relative humidities of deliquescence. Also included in the model is a formulation based on classical theory of nucleation kinetics that predicts crystallization behavior. Detailed phase diagrams of the sulfate/nitrate/ammonium/water system are presented as a function of relative humidity at 298.15 K over the complete space of composition.

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Journal articles on the topic 'Atmospheric Mathematical models'

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