Numerical Modeling of Temporal Trends Warming Climate on Experimental Base Data in Change of Ingredient Composition Earth’s Atmosphere

Nikolay MoskalenkoKazan State Power Engineering University, Kazan, Russia, ORCID: [0000–0003–1807–078X]

Yana SafiullinaKazan State Power Engineering University, Kazan, Russia,

Azat AkhmetshinKazan State Power Engineering University, Kazan, Russia, ORCID: [0000–0003–4424–7761]

Maryana HamidullinaKazan State Power Engineering University, Kazan, Russia,

Abstract  Numerical modeling of complicated radiate heat exchange in system “Sun-atmosphere-­earth underlying surface” are made on base experimental data in change of gradient composition atmosphere temporal trend of climate changes Earth are predicted.

Keywords: radiate heat exchange, underlying surface, ingredient, composition of atmosphere

© The Authors, published by CULTURAL-EDUCATIONAL CENTER, LLC, 2020

This work is licensed under Attribution-NonCommercial 4.0 International

I. Introduction

The increasing scale of human economic activity is attracting increasing attention to estimates of possible anthropogenic climate factors [1–4].

Studies published over the past decades have shed light on a variety of complexities with realistic estimates of the effects of changes in atmospheric composition on climate change. In this paper, we consider the numerical modeling of climate and the time trends of its change.

In recent years the possible effects of deforestation and biomass burning in the tropics (forests, shrubs, grass) as an anthropogenic source of small gas components in the atmosphere have attracted much attention: H2, CH4, N2O, NO, NO2, N2O4, COS, CH3Cl, HNO3, H2O2, COOH, heavy hydrocarbons.

Some of them (N2O, CH4) make a significant contribution to climate change, while others determine the interactions between the rapid succession of various components in the atmosphere.

The most important components that determine the greenhouse effect of the atmosphere are vapors of H2O, CO2, O3, N2O, CH4, atmospheric aerosol, and multi-­tiered cloud cover. Temporal trends in changes in the concentration of gas components, chemical composition and optical density of atmospheric aerosol and its microstructure, temporal variations in cloud cover structure determine temporal trends in climate change [4, 5].

The spectral optical characteristics of clouds and atmospheric aerosol formations (effective absorption and scattering cross sections, scattering indicatrix) are modeled as superpositions of the gamma functions of their microstructure [6–8].

The spectral transmission functions for the ingredients of the gaseous phase of the atmosphere are calculated by the two-parameter equivalent mass method [6].

Algorithms for calculating heat influx to the underlying surface and outgoing thermal radiation for zonal modeling of the greenhouse effect of the atmosphere are considered in [1, 2, 11].

II. Optical-Electronic Complexes for Measurements of the Ingredient Composition of the Atmosphere

the first measurements of the atmospheric ingredient composition were carried out on an optoelectronic complex with a multi-pass gas cuvette and medium resolution spectrometer  = 5–10 cm–1 in 1964 using the method of atmospheric compression to a pressure of P = 3 · 106 Pa with an optical path length of L up to 40 meters in a compressed atmosphere.

Subsequently, this complex was modernized using an internal and external heating system for measuring the ingredient composition of the combustion products of energy fuels and air emissions from automobile and air transport.

Since 1970, thin-structure high-resolution spectrometry has been used to analyze the ingredient composition of anthropogenic emissions into the atmosphere. The identification of the ingredients was determined by the fine structure of the absorption spectra (the position of the spectral lines), and the concentration of the ingredients was determined by the absorption of radiation in the centers of the spectral lines.

To reduce the measurement noise, the spectrum was processed by a spline in the form of a polynomial of the 5th degree [10]. The absorption spectrum of the medium under study was divided into the contours of individual spectral lines by the differential moment method with the subsequent restoration of their true contours on the influence of the spectrometer apparatus function.

For measuring of the atmospheric ingredient composition fine-structure spectrometry of the incoming solar radiation was also used. The concentration of the ingredients of the atmospheric gas phase was determined by spectral lines using the data of radio sounding of the altitude profile of the temperature and humidity of the atmosphere from a nearby weather station.

For an example in fig. 1 shows the absorption spectrum of the atmosphere of solar radiation in the spectral range of 4990–5020 cm–1. In the spectral range of 5000–5005 cm–1, spectral absorption lines of atmospheric CO2 are observed, which are used to determine the concentration CO2 in the atmosphere.

Figure 1. Spectrograms of solar radiation for spectral regions 4990–5030 cm–1.

To determine the atmospheric ingredient composition, a spectral setup with a multi-way cell of a variable base was developed, which allows one to study the atmospheric ingredient composition on paths from 16 meters up to 1000 meters long with a pressure up to 2 · 106 Pa [8].

A fast cryogenic setup for measuring the absorption spectra of a radiation propagation medium at low temperatures of 180–300 K at pressures of 100 – 5 · 106 Pa with a high spectral resolution was developed in [12]. The spectral range of the installation using the modernized monochromator IKM-31 is 0.1–6 microns.

To measure the CO2 concentration, we used a two-beam measuring system with a two-beam multi-path cell and deffusiometer based on the IKS-24 spectrophotometer [16], which allows measuring the CO2 concentration with a relative error:


when using an deffusiometer, to equalize the concentration in the measuring and control channels by dosing CO2 from a metering device with pure CO2.

CO2 consumption from the dispenser is controlled by a mercury monometer with an error:


The concentration of CO2 is determined from the ratio:


where  is the volume of the dispenser,  is the volume of the cuvette channel with the optical path length L in the first and second channels of the multi-way cuvette (L1 = L2),  is the pressure change in the dispenser when the concentration of ingredient i in the control channel is equalized.

To measure the concentration of CH4, N2O, we used the method of compression air in a high-pressure unit [8, 14, 15].

At high pressures, the spectral transmission functions in the vibrational-­rotational bands are described by Bouguer’s law:

, (1)

which makes it possible to determine the concentration  of components with high accuracy for a known optical path length and absorption coefficient  (T is the temperature of the medium in the cell), is the number of the component.

III. The Method of Fine-Structural Spectrometry for Determining the Ingredient Composition of the Atmosphere

The most promising method for determining the atmospheric ingredient composition is the method of fine-structure spectrometry, which allows one to determine the concentration of various ingredients on the fine structure of the absorption spectra of high spectral resolution.

The spectral transmission function is determined from the measured spectrograms by the formula:


where  is the baseline.

In spectral regions where there are no spectral lines (transparency windows), the spectral transmission functions are determined only by attenuation of radiation by the dispersed phase, and the  microstructure of the volatile sol is determined from the transparency windows.

The radiation attenuation spectrum for determining the microstructure should be measured in a wide spectral range of 0.2–14 μm [17].

For apparatus function :

, (2)

where  is the function of spectral attenuation of radiation, taking into account molecular absorption and attenuation of radiation by aerosol; is function of attenuation of radiation by aerosol.

For a multi-­component environment:

, (3)

where  are the spectral transmission functions for the i-th component of the gas phase of the radiation propagation medium.

In the case of high spectral resolution the function:


decompose on the contour of individual spectral lines using the differential moment method. For this purpose, the measured spectra are partitioned with a step Δ/5, where Δ is the spectral resolution of the spectrometer. The reduction of random noise is achieved by a five-point spline smoothing procedure in the form of a polynomial of the 5th degree.

The spectrum obtained in digital form is decomposed into individual line components:

, (4)

where  is the maximum intensity of the m-th component,  are the coefficients of the generalized contour

. (5)

The characteristics  give complete information about the individual contours of the spectral lines and are defined as the coefficients of the expansion in a Taylor series of a function  describing the m-th contour:

. (6)

The value  is the maximum amplitude of the loop. The center  is determined from the condition that the coefficient  is equal to zero, the half-width of the m-th line:

. (7)

The spectral line profiles obtained in this way are restored to the influence of the spectrometer apparatus function.

So, we have separate function  contours with centers  that are identified by ingredients based on a priori information on the centers of their spectral lines. The identified lines are denoted by i-the ingredient numbers, and their centers, contours, half-widths contain information on the concentration of the ingredient.

Valid for the Lorentz contour:


line intensity:

, (8)


where  is the intensity of the m-th line of ingredient i is the absorption coefficient in the center of the line,  is the volume concentration of ingredient i,


where is the effective pressure in the working chamber,  is the half-width of the line at a standard pressure P (N2) = 105 Pa.

Many molecules of the spectroscopy of weakly volatile hydrocarbons have diffuse spectrums and spectral transmittance functions for them are determined by relation (1). Effective pressure for component i:


where  is the broadening factor in collisions of molecules of ingredients i-k.

The experimental data on the parameters of the spectral lines are converted to the temperature of the working chamber according to the spectroscopic relations presented in [1, 6].

Determination of the concentration of the ingredient from the solar absorption spectra of radiation of atmospheric concentration i is carried out by absorption in the centers of the spectral absorption lines using a priori information on the experimental intensities , half-widths  centers of the absorption spectral lines of ingredient i.

If is the apparatus function of the spectrometer, then the concentration  of component i is determined from the condition that the calculated function of the spectral transmission of the atmosphere in the calibration channel is equal to the experimental value of ingredient i in the centers of the spectral lines k:


where  are the spectral transmission functions of the atmosphere for monochromatic radiation,  are the absorption spectral lines centers of ingredient i,


where  is the contour of the absorption spectral lines k of the i-th ingredient, is the optical path, h is the height above the underlying surface,  is the zenith angle. For the Lorentz contour of the absorption spectral lines:

, (12)

where  is the effective pressure of ingredient i in the atmosphere,  is the half-width of the spectral line at a height h in the atmosphere. The effective pressure  is determined by the formula (9).

In calculating the absorption coefficient of radiation at atmospheric pressures P < 1 · 104 Pa, the Voigt contour for spectral absorption lines was used.

The temperature dependence of the half-width of the absorption spectral lines is determined by the relation [17]:


where  are the experimental data on the half-width of the spectral absorption lines at a temperature  = 296 K.

The temperature dependence of the intensity of the spectral absorption lines is determined by the ratio:


where  = 1,439,  is the height of the lower energy level for the transition.

The relation by formula (10) is valid when normalizing the spectrometer apparatus function:


The calibration dependences  according to formula (10) for nonoverlapping spectral absorption lines were calculated for CH4, N2O, CO2, and CO and used to determine their concentration in the atmosphere.

А method was developed in [17–19] for determining the microstructure of carbon black sol from the data of numerical modeling of the optical characteristics of polydisperse formations. Estimates showed that soot sol during combustion of wood contains ≈ 20% by weight of the soluble fraction, and soot sol of combustion products of gas fuels contains ≈ 10% of the soluble fraction. For many fractions of soot sol, optical characteristics were calculated when the relative humidity f of the atmosphere changed in limits , which allows us to estimate the greenhouse effect of atmospheric emissions of soot sol.

In fig. 2 shows an example of the microstructure of the dispersed phase of combustion products in atmospheric emissions of gasoline and diesel engines. The microstructure of the dispersed phase  is normalized:


where r — radius of particles.

Figure 2. The distribution function f (r) of the number of particles in size for the products of combustion: 1 — gasoline engine; 2 — diesel engine.

IV. Research Results

the results obtained in this work on the effects of anthropogenic emissions of optically active small and trace components into the atmosphere indicate a temporary trend in increasing their concentration, which leads to global warming of the Earth’s climate and especially in the Arctic zone [13].

In this work, to determine the atmospheric ingredient composition and anthropogenic emissions into the atmosphere, we used the method of spectral analysis of high-resolution spectra and the method of spectral analysis of the compressed atmosphere up to elevated pressures (20–70) 105 Pa, with the aim of increasing the ultimate sensitivity of measurements of the concentration of the ingredient.

For an example in fig. 3 shows the time trend and measurement of CH4 concentration over a period of time from 1964 up to 2015 years. The results of methane concentration measurements by different methods correlate well with each other. Table 1 presents numerical data on the time dependence of the volume concentration of CO2 and N2O over Kazan.

Figure 3. The temporary trend of changes in the concentration of CH4.

(1 — data of changes by the method of atmospheric compression, 2 — measurements by solar spectra, 3 — data [15]).

Table 1. Numerical Data on the Time Dependence of the Volume Concentration of CO2 and N2O Over Kazan


The data obtained were used to calculate changes in temperature at the Earth’s surface by the zonal modeling method [2].

The temporal trend of climate warming  is described by the relation:


where  is the change in the greenhouse effect of the atmosphere with an increase in the concentration of the component of the gas phase i with an increase in its concentration by a factor of two compared with the concentration in 1964 year,  is the concentration of the component in 1964 year,  is the change in concentration with time (year),  is the parameter for component i, is multiplier for enhancing the greenhouse effect with water vapor due to an increase in atmospheric moisture content with an increase in surface temperature.

For models of the structural characteristics of the atmosphere [1], the values  for the northern hemisphere accounts 2.1, 1.9, 1.6 for the tropics, moderate latitudes, arctic regions, accordingly.

For СО2 = 2.7 К, = 0.7. For СН4= 0,74,  = 0.57. For N2= 0.98, = 0.60.

The greenhouse effect for the components of CO2, CH4, N2O for the period from 1964 up to 2019 years leads to a warming  of 0.39, 0.67, and 0.364 K, respectively. The total value  of the change due to an increase in the atmospheric concentration of CO2, CH4, N2O from 1964 up to 2019 years is = 1,568 K.

If we assume that the relative humidity of the atmosphere remained constant, then due to an increase in the moisture content (H2O vapor) in the atmosphere with an average coefficient  = 1.9, it will be  ≈3 K.

The actual value  can range from 1.568 up to 3 K, depending on the processes of water vapor evaporation by the oceans, the intensity of cloud formation, the change in the optical characteristics of the aerosol due to increased emissions of anthropogenic (soot) aerosol into the atmosphere by motor vehicles, aerotransport and industrial enterprises of the power industry and electric power industry.

The capture by the clouds of the lower tier of soot sol for the layered cloud microstructure model leads to a warming of 0.763 K at a volume concentration of soot in the droplets of 1 · 10–5.

For the clouds of the lower and middle tiers, the greenhouse effect  for the average global atmosphere can be calculated:

 К (16),

where  is the mass concentration of soot in water droplets. However, it should be noted that with an increase  in the absorption of solar radiation by a drop, the water droplets dry out with the formation of a coarse fraction of soot sol [20].

The coarse fraction of the resulting soot sol falls on the underlying surface, and the finely dispersed sol fraction serves as nuclei of condensation of water vapor to form a new cloud. Thus, the cloudiness of the lower tier is an important factor for the purification of the atmosphere from anthropogenic sol. It is also important to consider the leaching of anthropogenic sol by precipitation, especially in the vicinity of large cities. The drying of particles of anthropogenically disturbed clouds leads to a reduction in their lifetime, which should lead to a decrease in the overlap of the Earth’s surface by clouds and a change in the greenhouse effect of the atmosphere.

Emissions of combustion products by air carriers [17] serve as nuclei of condensation of water vapor in the upper atmosphere and stratosphere, which leads to the formation of ice clouds, which reduce the greenhouse effect of the atmosphere. At the same time, in connection with the increase in population over time the economic activity of mankind intensifies.

Thus, an increase in the concentration of CO2 leads to an increase in the spectral albedo of the underlying surface, caused by a more intensive development of the vegetation cover with an increase in the concentration of CO2 and an increase in the area of agricultural land use, which leads to an anti-greenhouse effect. It can be expected that with increasing temperature the average wind speed will increase, which causes an increase in the albedo of the planet, leading to a decrease in the greenhouse effect of the atmosphere.

For the environmentally sustainable development of life on earth, environmental sustainability is required as a functions of all living organisms in the global biosphere, including humans.

The growth of anthropogenic environmental impacts caused by the growing population of planet Earth, in all their diversity, necessitates the development of a numerical modeling of the processes of the dynamics of the atmosphere and the biosphere based on experimental data on the state of the environment and its change over time. An analysis of the aggregate data performed in [1–7,9] allows us to conclude that a new era has come in the development of new methods for predicting climate changes near the Earth’s surface over time based on electronic databases on the state of the environment of existing weather stations and space weather observations from satellites.

V. Conclusion

Optoelectronic systems have been developed for studying the atmospheric composition and anthropogenic emissions into the atmosphere, including the gas and dispersed phases, and experimental data have been obtained on changes in the atmospheric composition since 1964 for CO2, N2O, CH4. Calculations of changes in the temperature of the atmosphere at the underlying surface due to changes in their concentration are performed. The possible warming of the Earth’s climate was estimated, which in the period from 1964 up to 2019 years can range from 1.57 to 3 K. The multifactorial nature of the greenhouse effect problem and possible correlations of the effects of various processes of heat transfer in the atmosphere and heat transfer as a result of circulation of the atmosphere and the ocean. Man-made environmental disturbances are the main cause of modern climate change. The strongest temporal trends of climate change are observed in the Arctic zone due to the removal of anthropogenic sol from the industrially developed regions of the Earth and its runoff on snow and ice. The latter leads to a significant decrease in the albedo of the underlying surface and a decrease in the ice cover, which is accompanied by a decrease in the albedo of the Earth’s polar zone during the solstice.

Climate change observations indicate the complexity of the separation of natural and human-­induced climate changes. So at the condensation of water vapor and its freezing produces a large amount of heat, which affects the climate. The moisture content in the atmosphere is determined by the temperature of the surface waters of the oceans, which increases with time due to the absorption of solar radiation by the waters of the oceans. Changes in the Earth’s climate are influenced by such factors as temporary variations in solar activity and the Earth’s magnetic field as planets. The development of methods for numerical modeling of the Earth’s climate, taking into account all natural and anthropogenic factors, remains to be done in the future. The global average increase in atmospheric temperature at the surface of planet Earth due to the greenhouse effect currently lies in the range of 0.0285–0.0545 K / year.


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