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- Author or Editor: Wilford Zdunkowski x
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Abstract
Abstract
Abstract
A radiation model is constructed as part of a general prediction system of the polluted atmospheric boundary layer assumed to extend to a height of 3 km. The radiative treatment comprises the solar and infrared spectrum, ranging from 0.29 to 100 µm. In the solar spectral range the absorption by water vapor, nitrogen dioxide and industrial haze is fully accounted for in addition to multiple scattering by air molecules and haze particles. Cloud effects are ignored in the present investigation, since cloudiness is normally absent in strongly polluted air. The influence of relative humidity on the particle size distribution function and on the complex index of refraction of the aerosol particles is included in all calculations. This implies that not only the attenuation coefficients are height-dependent but also the phase function. The computations are carried out by means of the spherical harmonics method which is based on the exact form of the radiative transfer equation. The atmosphere is subdivided into homogeneous layers and intensifies are matched at the interfaces.
In the spectral region of the strong absorption bands of the infrared emission spectrum the effect of aerosol is very small and is disregarded. The emissivity method is applied here, allowing full treatment of the overlapping effects of the water vapor and carbon dioxide bands. In the window region of the infrared spectrum the effect of aerosol and water vapor absorption and emission is accounted for, in addition to multiple scattering by aerosol particles. The spherical harmonic method mentioned above is applied here also, but the temperature is permitted to vary linearly through the otherwise homogeneous atmospheric layers.
It is found that solar radiation may heat the boundary layer in excess of 4°C h−1 in the case of a strongly polluted inversion layer for a zenith angle of 45°. Corresponding infrared cooling rates may exceed 0.25°C h−1 at normally observed lapse rates. The presence of strong air pollution decreases the global radiation substantially at the earth's surface, while the infrared downward radiation is significantly increased.
Abstract
A radiation model is constructed as part of a general prediction system of the polluted atmospheric boundary layer assumed to extend to a height of 3 km. The radiative treatment comprises the solar and infrared spectrum, ranging from 0.29 to 100 µm. In the solar spectral range the absorption by water vapor, nitrogen dioxide and industrial haze is fully accounted for in addition to multiple scattering by air molecules and haze particles. Cloud effects are ignored in the present investigation, since cloudiness is normally absent in strongly polluted air. The influence of relative humidity on the particle size distribution function and on the complex index of refraction of the aerosol particles is included in all calculations. This implies that not only the attenuation coefficients are height-dependent but also the phase function. The computations are carried out by means of the spherical harmonics method which is based on the exact form of the radiative transfer equation. The atmosphere is subdivided into homogeneous layers and intensifies are matched at the interfaces.
In the spectral region of the strong absorption bands of the infrared emission spectrum the effect of aerosol is very small and is disregarded. The emissivity method is applied here, allowing full treatment of the overlapping effects of the water vapor and carbon dioxide bands. In the window region of the infrared spectrum the effect of aerosol and water vapor absorption and emission is accounted for, in addition to multiple scattering by aerosol particles. The spherical harmonic method mentioned above is applied here also, but the temperature is permitted to vary linearly through the otherwise homogeneous atmospheric layers.
It is found that solar radiation may heat the boundary layer in excess of 4°C h−1 in the case of a strongly polluted inversion layer for a zenith angle of 45°. Corresponding infrared cooling rates may exceed 0.25°C h−1 at normally observed lapse rates. The presence of strong air pollution decreases the global radiation substantially at the earth's surface, while the infrared downward radiation is significantly increased.
Abstract
For a calm night, nocturnal temperature profiles pertaining to various soil types are computed for the entire boundary layer. The mathematical analysis is based upon a numerical solution of the equations of motion, heat conduction and radiative transfer. The effect of radiative temperature change upon the total cooling rate is investigated. Some other interesting quantities associated with the distribution of the exchange coefficient and wind velocity components as a function of height and time are also calculated.
Solutions are presented in graphical format. All results such as temperature profiles, inversion heights and wind spirals seem to be in reasonable agreement with theoretical and observational deductions.
Abstract
For a calm night, nocturnal temperature profiles pertaining to various soil types are computed for the entire boundary layer. The mathematical analysis is based upon a numerical solution of the equations of motion, heat conduction and radiative transfer. The effect of radiative temperature change upon the total cooling rate is investigated. Some other interesting quantities associated with the distribution of the exchange coefficient and wind velocity components as a function of height and time are also calculated.
Solutions are presented in graphical format. All results such as temperature profiles, inversion heights and wind spirals seem to be in reasonable agreement with theoretical and observational deductions.
Abstract
This paper presents some sample computations of infrared radiative flux divergence due to atmospheric water vapor. These calculations are based upon newly constructed radiation tables which were obtained from the radiometersonde observations of P.M. Kuhn. The results are compared with the findings of other investigators. The importance of the surface-air temperature discontinuity is demonstrated.
Abstract
This paper presents some sample computations of infrared radiative flux divergence due to atmospheric water vapor. These calculations are based upon newly constructed radiation tables which were obtained from the radiometersonde observations of P.M. Kuhn. The results are compared with the findings of other investigators. The importance of the surface-air temperature discontinuity is demonstrated.
Abstract
The radiative flux divergence is computed for the lower few centimeters of the atmosphere assuming a water vapor-haze mixture. Some additional computations are made for higher altitudes also. The haze model, based on Deirmendjian's formulation, is used to obtain the scattering and absorption coefficients from Mie theory, which are employed in radiative transfer equations. This new formulation of the radiative transfer equation takes into consideration the combined effects of water vapor and particle absorption, as well as primary particle scattering. The influence of the albedo of the earth and the interface temperature discontinuity is taken into consideration. Results show that the incorporation of a reasonable interface temperature discontinuity of the earth's surface is of higher order of importance than the haze influence near the surface.
Abstract
The radiative flux divergence is computed for the lower few centimeters of the atmosphere assuming a water vapor-haze mixture. Some additional computations are made for higher altitudes also. The haze model, based on Deirmendjian's formulation, is used to obtain the scattering and absorption coefficients from Mie theory, which are employed in radiative transfer equations. This new formulation of the radiative transfer equation takes into consideration the combined effects of water vapor and particle absorption, as well as primary particle scattering. The influence of the albedo of the earth and the interface temperature discontinuity is taken into consideration. Results show that the incorporation of a reasonable interface temperature discontinuity of the earth's surface is of higher order of importance than the haze influence near the surface.
Abstract
The Crank-Nicholson method may not give useful results in detailed prediction of the thermal planetary boundary layer unless tune steps on the order of 10 s are used. In similar problems, lower order time differencing methods give reasonable results with time steps as large as 300 s. The reason for the superior behavior of the lower order schemes relative to straightforward application of the Crank-Nicholson technique is due to a better treatment of short waves which appear to be critically important in nonlinear terms.
Abstract
The Crank-Nicholson method may not give useful results in detailed prediction of the thermal planetary boundary layer unless tune steps on the order of 10 s are used. In similar problems, lower order time differencing methods give reasonable results with time steps as large as 300 s. The reason for the superior behavior of the lower order schemes relative to straightforward application of the Crank-Nicholson technique is due to a better treatment of short waves which appear to be critically important in nonlinear terms.
Abstract
A dynamic-numerical model is utilized to study the impact of air pollution on the temperature and wind distributions of the planetary boundary layer. The mathematical model uses a rather complete radiative treatment which comprises the entire solar and infrared spectrum ranging from 0.29 to 100 µm. In the solar spectral range, the absorption by water vapor, nitrogen dioxide and industrial haze is fully accounted for in addition to multiple scattering by air molecules and haze particles. In the spectral region of the strong absorption hands of the infrared emission spectrum, the effect of aerosol is very small and is disregarded. The emissivity method is applied here, allowing full treatment of the overlapping effects of water vapor and carbon dioxide. In the window region, however, the effect of aerosol and water vapor absorption and emission is taken into account in addition to multiple scattering by aerosol particles. The radiative treatment accounts for the influence of relative humidity on the particle distribution function and on the complex index of refraction of the aerosol. The spherical harmonic method is used to handle the scattering problem.
The dynamical part of the analysis consists of the numerical solution of a coupled system of partial differential equations comprising the equation of horizontal mean motion, the thermodynamic equations of the air and the soil, and the transport equations of moisture and pollution. Various models of the exchange coefficient are used to study the impact of model assumptions on the computed distributions of temperature, pollutant material and wind. It is found that the choice of the exchange model is not critical but has some effect on the model computations. The present calculations show that the maximum impact of air pollution on the evolution of temperature and wind profiles is highly significant, thus verifying the previous conclusions of Zdunkowski and McQuage (1972).
Abstract
A dynamic-numerical model is utilized to study the impact of air pollution on the temperature and wind distributions of the planetary boundary layer. The mathematical model uses a rather complete radiative treatment which comprises the entire solar and infrared spectrum ranging from 0.29 to 100 µm. In the solar spectral range, the absorption by water vapor, nitrogen dioxide and industrial haze is fully accounted for in addition to multiple scattering by air molecules and haze particles. In the spectral region of the strong absorption hands of the infrared emission spectrum, the effect of aerosol is very small and is disregarded. The emissivity method is applied here, allowing full treatment of the overlapping effects of water vapor and carbon dioxide. In the window region, however, the effect of aerosol and water vapor absorption and emission is taken into account in addition to multiple scattering by aerosol particles. The radiative treatment accounts for the influence of relative humidity on the particle distribution function and on the complex index of refraction of the aerosol. The spherical harmonic method is used to handle the scattering problem.
The dynamical part of the analysis consists of the numerical solution of a coupled system of partial differential equations comprising the equation of horizontal mean motion, the thermodynamic equations of the air and the soil, and the transport equations of moisture and pollution. Various models of the exchange coefficient are used to study the impact of model assumptions on the computed distributions of temperature, pollutant material and wind. It is found that the choice of the exchange model is not critical but has some effect on the model computations. The present calculations show that the maximum impact of air pollution on the evolution of temperature and wind profiles is highly significant, thus verifying the previous conclusions of Zdunkowski and McQuage (1972).
