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Two-Stream Approximation to the Radiative Transfer Equation:A New Improvement and Comparative Accuracy with Existing Methods

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Advances in Atmospheric Sciences 2024年第2期41卷 278-292页

作者： F.Momo TEMGOUA l.akana nguimdo DNJOMO Environmental Energy Technologies laboratory(EETl) Faculty of SciencesUniversity of YaoundéPO Box 812 YaoundéCameroon Department of Electrical and Electronic Engineering Faculty of Engineering and TechnologyUniversity of BueaPO Box 63 BueaCameroon

Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of app

关键词： Radiative Transfer Equation two-stream method legendre polynomial optical thickness moments of specific intensity conversion function transmittance reflectance

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Shortwave Cloud and Aerosol Radiative Forcings and Their Effects on the Vertical local Heating/Cooling Rates

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Atmospheric and Climate Sciences 2013年第3期3卷 337-347页

作者： l. akana nguimdo D. Njomo Department of Electrical and Electronic Engineering University of Buea Buea Cameroun. Environmental Energy Technologies laboratory (EETl) Faculty of Sciences University of Yaoundé 1 Yaoundé Cameroon

An analysis of atmospheric SW-radiative forcing and local heating/cooling rate is made using a one year temporal and vertical profiles of aerosol and cloud over Yaoundé (11.51°E, 3.83°N). It appears that the direct influence of aerosols on the surface compared to the TOA can be 3 times larger. Annual mean value obtained at 559 mb altitude is +27.74 W/m2 with range from 0 to +43 W/m2. At 904 mb, we obtained an annual mean of ﹣46.22 W/m2 with range from ﹣65 to ﹣9 W/m2. Frequency distribution indicates that more than 95% of ARF are between +10 and +70 W/m2 at 559 mb (upper limit of Ul), and more than 85% of ARF are between ﹣70 and ﹣10 W/m2 at 904 mb (upper limit of PBl). This sign change is explained by the fact that the backscattering peaks at the upper limit of the aerosol PBl layer. The maximum CRF is noted at TOA where it reaches ﹣600 W/m2 based on the time interval and the structure of clouds. The highest values occur between 11.50 and 13.50 lST. Clouds lead to a general heating of the entire atmospheric column with a much greater effect near the surface. Aerosols effect on the heating rate profile show strong cooling during the day for the lower atmosphere, with slight heating at the upper atmosphere. This cooling contribution generally increases from the surface and peacks at the upper boundary of aerosol layer where reflectivity is the most important. Depending on the moment of the day, average heating effect of clouds peacks at surface or within the middle troposphere due to the absorption by clouds particles. Vertical profiles deeply evolve exhibiting differences that exceed ﹣3 K/day according to altitude from one hour to another during a given mean solar day.

关键词： Planetary Boundary layer Upper layer Clear Sky Flux All-Sky Flux Net Downward Flux Radiative Forcing Heating/Cooling Rates

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Parameterized Transmittance Model for Atmospheric and Surface Solar Radiations

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Atmospheric and Climate Sciences 2020年第1期10卷 81-99页

作者： J. Djampou Tchouankap l. akana nguimdo Environmental Energy Technologies laboratory (EETl) Faculty of Sciences University of Yaoundé Yaoundé Cameroon Department of Electrical and Electronic Engineering Faculty of Engineering and Technology University of Buéa Buéa Cameroon

This work describes a transmittance model that evaluates global solar irradiation through the atmospheric column and at surface. The model is based on appropriate determination of the transmission coefficients of the different atmospheric constituents in a plane parallel layers frame and estimates the downward solar fluxes from the upper limit of the atmosphere. In testing this model, we first considered the purely molecular atmosphere to parameterize descending solar fluxes, which allowed us to estimate the attenuation due to atmospheric gases at specific times of the day when the irradiation at ground level is known. The results thus obtained show that the molecular atmosphere has a maximum reduction rate of incident flux (at the Top Of Atmosphere) of 20% with daily profiles that are homogeneous with extraterrestrial fluxes. Considering the turbid and cloudy atmosphere in which the multiple scattering phenomenon is taken into account, we obtain at ground level fluctuating profiles with attenuation rates reaching 64% depending on the time instant in the day. The comparison of our results with the experimental data obtained at the Yaoundé site on one hand and with the results of the ClIRAD-SW model on the other hand shows at monthly scale high correlation, of the order of 0.998. Moreover at monthly time scale, the precision which for some hourly values is relatively low tends towards a net improvement on the seasonal scale where it extends over a narrow domain ranging from 0.02% to 1.66%.

关键词： Scattering Absorption Transmittance Extraterrestrial Fluxes Solar Irradiation

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