Simulation of atmospheric effect on the emergent radiation over a circular lake

The upwelling radiation at the top of the atmosphere is computed over a circular lake which is located in the uniform Lambert surface, using a modified version of the doubling-adding method. The radiance over the lake is discussed with respect to the atmospheric effect. The radius of the lake is assumed to be 0.5, 1, and 3 km. The observational site is located at altitude 30 km. The zenith of the observational site is located in the plane which is determined by the zenith of the center of the lake and incident solar direction. The zenith angle of the observational site to the center of the lake is fixed to 6.28°. The atmosphere is assumed to be homogeneous, which is composed of aerosol and molecule, where the model aerosol is of the oceanic or the water soluble types.Numerical simulation exhibits an extraordinary effect near the lake. The radiance of the lake against the surrounding depends upon the albedo of the surrounding surface. It increases with the increase of the size of the lake and decreases with the optical thickness. At large optical depth, the radiance depends upon the aerosol characteristics. It shows little dependence on the solar zenith angle if less than 60°.     

Atmospheric effect on the upwelling radiation at the top of the atmosphere over a stream

A new version is adopted for the evaluation of the upwelling radiation from atmosphere bounded by the surface, where the surface is composed of two half semi-infinite Lambert surfaces and a stream is inserted between them. The contrast of the stream is discussed with respect to the atmospheric effect. The width of the stream is considered to be 0.5, 1, and 3km; The solar and observational direction is located in the normal plane to the stream. The observational site is located at altitude 30km. The horizontal distance of observational site to the stream is fixed to 6.28 . The atmosphere is assumed to be homogeneous, which is composed of aerosol and molecules, where the model aerosol is of the oceanic type.In the computational procedure, a probability of radiation interacting with respective half surfaces and the stream are calculated based on the assumption of single scattering in the atmosphere, where isotropic scattering is undertaken. By use of this probability, the emergent radiation at the top of the atmosphere is calculated approximately by considering the radiative interactions between atmosphere and surfaces up to twice. The numerical simulation exhibits the extraordinary effect near the stream. The contrast of the stream depends upon the albedo of the surrounding surfaces. It increases with the increase of the stream width and decreases with the optical thickness.     

Emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo,II

For the evaluation of the effect of the non-uniform surface albedo on the emergent radiation from the atmosphere, the emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo is computed. This paper is the improved version of the previous paper (Takashima and Masuda, 1991). The atmosphere is assumed to be homogeneous, which is composed of aerosol, molecules, and absorbent gases. Their optical thicknesses are (1) 0.25, 0.23, and 0.02, and (2) 0.75, 0.23, and 0.02, respectively. The model aerosol is of the oceanic and water soluble types.In the computational procedure, the emergent radiation is calculated approximately by the contributions due to the multiple scattering in the atmosphere, and due to the diffusely or directly transmitted radiation through the atmosphere which is reflected by the surfaces once (4 interactive radiative modes between atmosphere and surface). Furthermore, to perform the hemispherical integration processing the radiative interaction, the transmission function based on the single scattering in the atmosphere is introduced and then the transmission function is averaged over the hemisphere with weighting function. The numerical simulation exhibits the extraordinary effect near the two half surface boundary of different albedoes. The effect decreases exponentially with the distance from the boundary. The effect depends on the atmospheric aerosol type, optical thickness, and surface albedo. The present version enables us to quantitatively discuss the radiative transfer trend near the boundary of two half surfaces. The upward radiance would simply be evaluated using the present scattering approximation method if the surface albedo is less than 0.3. The present method is thought of as a first step extending the one-dimensional radiative transfer model to two-dimensional using the doubling-adding method.     

Emergent radiation from the atmosphere bounded by the two halves of the Lambert surface with different albedos

For the evaluation of the effect of the nonuniform surface albedo to the emergent radiation from the atmosphere, the emergent radiation from the atmosphere bounded by the two-halves of the Lambert surface with different albedos is computed. The principal plane is assumed to be perpendicular to the boundary of surfaces. The atmosphere is assumed to be homogeneous, which is composed of aerosol, molecules, and absorbent gases. Their optical thicknesses are 0.25, 0.23, and 0.02, respectively. The model aerosol is of the oceanic and water soluble types.In the computational procedure, the emergent radiation is approximated by the contributions due to the multiple scattering in the atmosphere, directly attenuated radiation, and radiation due to single scattering in the atmosphere which is reflected by the Lambert surface (up to 4 interactive radiative modes between atmosphere and surface). For quantitative analysis, results are compared with those of the atmosphere-uniform surface model, where the multiple scattering is considered. The numerical simulation exhibits the extraordinary effect near the surface boundary of different albedos. The effect decreases exponentially with the distance from the boundary. It is a function of the observational position, difference of surface albedos, optical thickness and aerosol type.The upward radiance would simply be evaluated using the present scattering approximation method if the atmosphere is in clear condition. Whereas in hazy condition, the effect of multiple scattering in the atmosphere should be considered more precisely, since the upward radiance exhibit a strong dependence on observational nadir angles due to multiple scattering in the atmosphere. Furthermore, it depends on the optical characteristics of aerosols.     

A new approach to evaluation of the effect of the two half-Lambert surfaces composed of different albedoes on the emergent radiation at the top of the atmosphere

A new way is adopted for the evaluation of the upwelling radiation from atmosphere bounded by two half-Lambert surfaces. The atmosphere is assumed to be homogeneous, and is composed of aerosol, molecules, and absorbent gases, where the model aerosol is of the oceanic and water soluble types.In the computational procedure, an iterative doubling-adding equation is expanded into a series of the radiative interaction modes between atmosphere and surface. Next, a probability of radiation interacting with respective half surfaces is calculated based on the assumption of single-scattering in the atmosphere. On the basis of this probability, the emergent radiation at the top of the atmosphere is approximately calculated by considering the radiative intractions to be twice as large. The effect of the multiple-scattering is fully taken into account. A numerical simulation exhibits the extraordinary effect near the two half-surface boundary of different albedoes. The effect of the other half-surface on the radiance decreases monotonically with the distance from the boundary. The present new version enable us to quantitatively discuss radiative transfer near the boundary of two half-surfaces even if the optical thickness is large and (or) surface albedo is great.     

Diffusion of radiation in planetary atmospheres

The problem of interaction of the solar radiation with the turbid Earth atmosphere, containing complicated polydispersive aerosol systems, is discussed in this paper. Equations for computing the angular functions ofn-th order scattering are derived. On the basis of these functions the spectral radiance, radiation flows and radiation balance of the atmosphere in the short-wave spectral range are calculated. The relations obtained can be used to calculate the complex index of refraction, distribution function and other characteristics of the submicron aerosol fraction, by solving the inverse problems.     

The troposphere-stratosphere radiation field at twilight: A spherical model

Time-dependent calculations of trace constituent distributions require as input the dissociating radiation field as a function of altitude and solar zenith angle. An isotropic, spherical, multiple scattering model of the radiation field has been developed to determine the radiation field at twilight. Comparison of the spherical model with a plane parallel model at twilight shows that: (1) for solar zenith angles less than 92°, plane parallel solutions for the source function are suitable if the initial deposition of solar energy is calculated for a spherical atmosphere; (2) for solar zenith angles greater than 92°, the plane parallel radiation field can be several orders of magnitude smaller than that calculated with the spherical model; (3) at altitudes above 40 km and at all solar zenith angles, the spherical model predicts 10–20% less radiation than the radiation field calculated with the plane parallel model. Calculations of the rate of photodissociation of NO₂ in the troposphere and stratosphere show that the spherical model yields significantly higher values at solar zenith angles greater than 92°.     

A spherical model for computing polarized radiation in Titan's atmosphere

The Huygens descent through Titan's atmosphere in January 2005 will provide invaluable information about Titan's atmospheric composition and aerosol properties. The Descent Imager/Spectral Radiometer (DISR) will perform upward and downward looking radiation observations at various spectral ranges and spatial resolutions. To prepare the DISR data interpretation we have developed a new model for radiation transfer in Titan's atmosphere. The model solves for the full three-dimensional polarized radiation field in spherical geometry. However, the atmosphere itself is assumed to be spherically symmetric. The model is initialized with a fast-to-compute plane–parallel solution based on the doubling and adding algorithm that incorporates a spherical correction for the incoming direct solar beam. The full three-dimensional problem is then solved using the characteristics method combined with the Picard iterative approximation as described in Rozanov et al. (J. Quant. Spectrosc. Radiat. Transfer 69 (2001) 491). Aerosol scattering properties are calculated with a new microphysical model. In this formulation, aerosols are assumed to be fractal aggregates and include methane gas absorption embedded into the extinction coefficient. The resulting radiance of the model atmosphere's internal field is presented for two prescribed DISR wavelengths.     

Theory of optical identification of submicron particles in high atmosphere

Interaction between planetary atmospheres and small bodies is connected with radiation effects. Submicron particles in the Earth's upper atmosphere strongly influence the scattering of the shortwave solar radiation. Based on the mutual connection between the environmental and radiation field structures it is possible to determine the physical characteristics of the particle set in this environment. Generaly, the diffused radiation field in the real atmosphere is given by a sum of elementary and multiple scattering components. Solving the inverse problems always leads to complicated integral equations. A major part of the diffused radiation field in the upper atmosphere is due to the first order scattering. The paper presents a new method for determination of the effective complex refractive index and size distribution of the particles based on the radiance data. The solution of integral equations is to be found in the space of quadratically integrable and continuous functionsf L ₂.     

Airborne total eclipse observation of the extreme solar limb at 400 μm

The total solar eclipse of February 26, 1979 was monitored at far infrared wavelengths from the NASA Lear Jet Observatory flying at 12.9 km in the eclipse shadow. The resultant eclipse curve for radiation within a bandwidth of 20 cm^–1 centered upon 25 cm^–1 (400 m) was measured and analysed at an equivalent angular resolution of 1 arc sec over a 100 arc sec region adjacent to the limb to provide information on the intensity distribution of continuum radiation close to this limb. The curve has been compared to predictions derived from models of the solar atmosphere for the specific geometry of this eclipse, and is shown to match most closely that derived from a uniform distribution of radiation across the disk. This is in distinct contrast to the result obtained in the only other comparable experiment, carried out over Africa in 1973 from a supersonic Concorde aircraft, in which an intense but narrow spike of far infrared radiation at the extreme solar limb was inferred from the data. The absence also in the present observations of the significant limb brightening predicted by the HSRA model (in which homogeneity within the source region is assumed) is in substantial agreement with lower resolution results from mountain altitudes. This result is interpreted as further evidence for the presence in the Sun's lower chromosphere of significant inhomogeneity with a scale size of at least 1000 km at this depth.     

The interpretation of velocity filtergrams

The paper describes a numerical experiment in which the effect of an assumed velocity distribution in the solar atmosphere on the intensity difference between a blue- and a red-wing filter-gram is derived. This results in the effective optical depth at which the velocity is measured. It is shown that this _eff strongly depends on the assumed velocity distribution.     

High altitude haze: Influence of monomer particles on Titan’s temperature profile

The present study investigates the role of high altitude monomer particles in the energy balance of Titan’s upper atmosphere above an assumed low and high aggregate formation altitude of 385 km and 535 km. A ‘single particle approach’ was applied, where the starting point is the energy balance of an individual aerosol. In our analysis 0.01–0.06 μm radius aerosol particles were chosen for the proposed monomer formation regions. These particles absorb solar radiation, emit in the infrared, and are energetically linked to the surrounding gas by thermal conduction. To compute the monomer particle heating effect, the aerosols are assumed to radiate directly to space. We found that high altitude monomers may affect the profile of Titan’s thermosphere from 2 to 20 K depending on the formation altitude of fluffy non-spherical aggregates, the monomer size and distribution. The actual Titan temperature profile in this altitude range including all heating effects will be measured by the HASI instrument during the descent of the Huygens probe.     

Turbulence in the troposphere of Venus: Refined characteristics and new estimates

Based on spaceborne experimental data, characteristics of turbulence are calculated for the Venusian troposphere under conditions corresponding to the planet-averaged flux of solar radiation, which is equal to its value at a solar zenith angle of 66°. Additionally, given experimental data on radiation fluxes and their numerical calculations, turbulence characteristics were calculated for a solar zenith angle of 45°. The turbulence pattern is significantly different for small and large solar zenith angles. At large solar zenith angles, there exist an anomalous downward turbulent heat flux above 7–10 km and a normal upward flux at lower heights. At small zenith angles, the turbulent flux is normal throughout the entire troposphere. The dissipation of turbulent energy contributes significantly to the atmospheric heating in a wide range of altitudes. The spectrum of the time and space scales of dissipative processes in the troposphere is very wide and changes with height.Translated from Astronomicheskii Vestnik, Vol. 39, No. 1, 2005, pp. 38–50.Original Russian Text Copyright © 2005 by Izakov.     

Daytime ionosphere of Venus as studied with Veneras 9 and 10 dual-frequency radio occultation experiments

We present results of the dual-frequency radio sounding of the Venusian ionosphere carried out by the Venera 9 and 10 satellites in 1975. Thirteen height profiles of electron density for different solar zenith angles varying from 10 to 87° have been obtained by analyzing the refraction bending of radiorays in the sounded ionssphere. The main maximum of electron density at a height of 140–150 km depends on the solar zenith angle and is 1.4 to 5 × 10⁵ cm^?3. The lower maximum is determined definitely to be at ～130 km high. In the main and lower maxima the electron density variations with solar zenith angle are in good agreement with the Chapman layer theory. For the first time it is found that the height of the upper boundary for the daytime ionosphere (h_i) depends regularly on the solar zenith angle. At Z_⊙ < 60°, h_i does not exceed 300 km while at Z_⊙ > 60°, it increases with Z_⊙ and comes up to ～ 600 km at Z_⊙ ～ 80°.     

A model of Titan's aerosols based on measurements made inside the atmosphere

The descent imager/spectral radiometer (DISR) instrument aboard the Huygens probe into the atmosphere of Titan measured the brightness of sunlight using a complement of spectrometers, photometers, and cameras that covered the spectral range from 350 to 1600 nm, looked both upward and downward, and made measurements at altitudes from 150 km to the surface. Measurements from the upward-looking visible and infrared spectrometers are described in Tomasko et al. [2008a. Measurements of methane absorption by the descent imager/spectral radiometer (DISR) during its descent through Titan's atmosphere. Planet. Space Sci., this volume]. Here, we very briefly review the measurements by the violet photometers, the downward-looking visible and infrared spectrometers, and the upward-looking solar aureole (SA) camera. Taken together, the DISR measurements constrain the vertical distribution and wavelength dependence of opacity, single-scattering albedo, and phase function of the aerosols in Titan's atmosphere.Comparison of the inferred aerosol properties with computations of scattering from fractal aggregate particles indicates the size and shape of the aerosols. We find that the aggregates require monomers of radius 0.05 μm or smaller and that the number of monomers in the loose aggregates is roughly 3000 above 60 km. The single-scattering albedo of the aerosols above 140 km altitude is similar to that predicted for some tholins measured in laboratory experiments, although we find that the single-scattering albedo of the aerosols increases with depth into the atmosphere between 140 and 80 km altitude, possibly due to condensation of other gases on the haze particles. The number density of aerosols is about 5/cm³ at 80 km altitude, and decreases with a scale height of 65 km to higher altitudes. The aerosol opacity above 80 km varies as the wavelength to the −2.34 power between 350 and 1600 nm.Between 80 and 30 km the cumulative aerosol opacity increases linearly with increasing depth in the atmosphere. The total aerosol opacity in this altitude range varies as the wavelength to the −1.41 power. The single-scattering phase function of the aerosols in this region is also consistent with the fractal particles found above 60 km.In the lower 30 km of the atmosphere, the wavelength dependence of the aerosol opacity varies as the wavelength to the −0.97 power, much less than at higher altitudes. This suggests that the aerosols here grow to still larger sizes, possibly by incorporation of methane into the aerosols. Here the cumulative opacity also increases linearly with depth, but at some wavelengths the rate is slightly different than above 30 km altitude.For purely fractal particles in the lowest few km, the intensity looking upward opposite to the azimuth of the sun decreases with increasing zenith angle faster than the observations in red light if the single-scattering albedo is assumed constant with altitude at these low altitudes. This discrepancy can be decreased if the single-scattering albedo decreases with altitude in this region. A possible explanation is that the brightest aerosols near 30 km altitude contain significant amounts of methane, and that the decreasing albedo at lower altitudes may reflect the evaporation of some of the methane as the aerosols fall into dryer layers of the atmosphere. An alternative explanation is that there may be spherical particles in the bottom few kilometers of the atmosphere.     

Solar Occultation Measurements of the Martian Atmosphere on the Phobos Spacecraft: Water Vapor Profile,Aerosol Parameters,and Other Results

The Auguste experiment onboard the Phobos spacecraft was devoted to solar occultation spectroscopy of the Martian atmosphere in the ultraviolet through infrared wavelength region. Despite the short duration of the space mission and problems associated largely with a fault in the solar pointing system, data have been obtained on the chemical composition and aerosol content in the atmosphere of Mars at sunset early in the summer at equatorial latitudes (in the northern hemisphere). This paper presents a somewhat detailed review of the experiment performed, the data obtained, and their interpretation, and compares these data with new results. Ozone traces were detected at altitudes of 40–60 km, and, in one case, an ozone profile was obtained. Nine profiles of water vapor content at altitudes between 12 and 50 km were obtained from absorption data in the 1.87-m band. At altitudes of 23–25 km, the mean H₂O concentration profile falls steeply to the value of 3 ppm, but at lower altitudes the relative H₂O content is approximately constant (130 ppm). The overall content of water vapor is estimated as 8.3^+2.5 _-1.5 m of settled water. The temperature profile for the saturated atmosphere yields a cooling rate of 2 ± 1 K/km at altitudes from 25 to 35 km. The atmospheric extinction profiles were measured at altitudes from 10 to 50 km at the wavelengths 1.9 and 3.7 m. The atmosphere is transparent up to 25–33 km; below this level radiation is attenuated by dust; it is also possible that a layer of water ice clouds is present at altitudes of 20–25 km. High-altitude transparent ( 0.03) clouds consisting supposedly of water ice were observed in 5 of 38 cases at altitudes z 50 km. The optical depth ₀ of the atmosphere was estimated to be 0.2 ± 0.1, and constraints on the form of the size distribution of dust particles were established. Spectral features in the 3.7 m range have been previously attributed to formaldehyde; its content is substantially higher than the limits deduced from new ground-based observations. The spectrum in the 3.7 m range is discussed and other unsettled problems are pointed out.     

Formation of spectral lines in a dynamically active stochastic and multicomponent atmosphere

This paper is devoted to a determination of the statistical mean quantities describing spectral line radiation of dynamically active stochastic and multicomponent atmospheres. The lines in LTE are considered so that the effects of multiple scattering can be neglected. Two types of problem are discussed. In the first it is assumed that the realization of one or another type of nonthermal motion depends on the type of structural element and in the other this type of dependence is absent, i.e., it is supposed that the assumed random values of the velocity are distributed according to a law that is common to all the components. Particular attention is paid to a determination of the relative mean square deviation of the intensity of the observed radiation. It appears that the distinctive feature of the relative mean square deviation of the radiation in a line formed in a dynamically active stochastic atmosphere is local “spikes” (maxima) in the wings of the line. The theoretical results in this paper are compared with spectral observations of quiescent solar prominences obtained in framework of the SOHO space mission. __________ Translated from Astrofizika, Vol. 50, No. 1, pp. 121–134 (February 2007).     

Ionization by cosmic rays of the atmosphere of Titan

Cosmic ray radiation is the main mechanism for ionizing the lower atmosphere of Titan. Their higher penetration power, in comparison with solar photons, allows cosmic rays to penetrate deep into the atmosphere of Titan, ionizing the neutral molecules and generating an ionosphere with an electron density peak, placed at around 90 km, similar in magnitude to the ionospheric peak produced by solar radiation in the upper atmosphere. In the lower atmosphere, the electron density profile, in the absence of a magnetic field, depends mainly on the modulation of cosmic rays by the solar wind and on the nature of the ionizable particles. We present here the first results of a new numerical model developed to calculate the concentration of electrons and most abundant ions in the Titan lower atmosphere. The present knowledge of Titan’s atmosphere permits us to include new neutral and ionic species, such as oxygen derivates, in a more detailed ion-chemistry calculation than previous lower ionospheric models of Titan. The electron density peaks at 90 km with a magnitude of 2150 cm⁻³. The ion distribution obtained predicts that cluster cations and hydrocarbon cations are the most abundant ions below and above the electron density peak, respectively. We also discuss the effect of solar activity at the distance of the Saturn orbit on the spectrum of the cosmic particles. We obtain that from solar minimum to solar maximum the ionization rate at the energy deposition peak changes by a factor of 1.2 at 70 km, and by a factor of 2.6 at altitudes as high as 400 km. The electron density at the concentration peak changes by a factor of 1.1 at 90 km, and by a factor of 1.6 at 400 km.     

Heat balance in Titan's atmosphere

The recent measurements of the vertical distribution and optical properties of haze aerosols as well as of the absorption coefficients for methane at long paths and cold temperatures by the Huygens entry probe of Titan permit the computation of the solar heating rate on Titan with greater certainty than heretofore. We use the haze model derived from the Descent Imager/Spectral Radiometer (DISR) instrument on the Huygens probe [Tomasko, M.G., Doose, L., Engel, S., Dafoe, L.E., West, R., Lemmon, M., Karkoschka, E., See, C., 2008a. A model of Titan's aerosols based on measurements made inside the atmosphere. Planet. Space Sci., this issue, doi:10.1016/j.pss.2007.11.019] to evaluate the variation in solar heating rate with altitude and solar zenith angle in Titan's atmosphere. We find the disk-averaged solar energy deposition profile to be in remarkably good agreement with earlier estimates using very different aerosol distributions and optical properties. We also evaluated the radiative cooling rate using measurements of the thermal emission spectrum by the Cassini Composite Infrared Spectrometer (CIRS) around the latitude of the Huygens site. The thermal flux was calculated as a function of altitude using temperature, gas, and haze profiles derived from Huygens and Cassini/CIRS data. We find that the cooling rate profile is in good agreement with the solar heating profile averaged over the planet if the haze structure is assumed the same at all latitudes. We also computed the solar energy deposition profile at the 10°S latitude of the probe-landing site averaged over one Titan day. We find that some 80% of the sunlight that strikes the top of the atmosphere at this latitude is absorbed in all, with 60% of the incident solar energy absorbed below 150 km, 40% below 80 km, and 11% at the surface at the time of the Huygens landing near the beginning of summer in the southern hemisphere. We compare the radiative cooling rate with the solar heating rate near the Huygens landing site averaging over all longitudes. At this location, we find that the solar heating rate exceeds the radiative cooling rate by a maximum of 0.5 K/Titan day near 120 km altitude and decreases strongly above and below this altitude. Since there is no evidence that the temperature structure at this latitude is changing, the general circulation must redistribute this heat to higher latitudes.     

Distribution of HCN in Titan’s upper atmosphere from Cassini/VIMS observations at 3 μm

Cassini/VIMS limb observations have been used to retrieve vertical profiles of hydrogen cyanide (HCN) from its 3 μm emission in the region from 600 to 1100 km altitude at daytime. While the daytime emission is large up to about 1100 km, it vanishes at nighttime at very low altitudes, suggesting that the daytime emission originates under non-LTE conditions. The spectrally integrated radiances around 3.0 μm shows a monotonically decrease with tangent altitude, and a slight increase with solar zenith angle in the 40-80° interval around 800 km.A sophisticated non-LTE model of HCN energy levels has been developed in order to retrieve the HCN abundance. The population of the HCN 0 0⁰ 1 energy level, that contributes mostly to the 3.0 μm limb radiance, has been shown to change significantly with the solar zenith angle (SZA) and HCN abundance. Also its population varies with the collisional rate coefficients, whose uncertainties induced errors in the retrieved HCN of about 10% at 600-800 km and about 5% above. HCN concentrations have been retrieved from a set of spectra profiles, covering a wide range of latitudes and solar zenith angles, by applying a line-by-line inversion code. The results show a significant atmospheric variability above ∼800 km with larger values for weaker solar illumination. The HCN shows a very good correlation with solar zenith angles, irrespective of latitude and local time, suggesting that HCN at these high altitudes is in or close to photochemical equilibrium. A comparison with UVS and UVIS measurements show that these are close to the lower limit (smaller SZAs) of the VIMS observations above 750 km. However, they are in reasonable agreement when combining the rather large UV measurement errors and the atmospheric variability observed in VIMS. A comparison of the mean profile derived here with the widely used profile reported by Yelle and Griffith (Yelle R.V., Griffith, C.A. [2003]. Icarus 166, 107-115) shows a good agreement for altitudes ranging from 850 to 1050 km, while below these altitudes our result exhibits higher concentrations.