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 m...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 approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.展开更多
Kozeny-Carman(KC) equation is a well-known relation between hydraulic conductivity and pore properties in porous material. The applications of KC equation to predicting saturated hydraulic conductivities of sands and ...Kozeny-Carman(KC) equation is a well-known relation between hydraulic conductivity and pore properties in porous material. The applications of KC equation to predicting saturated hydraulic conductivities of sands and non-expansive soils are well documented. However, KC equation is incapable of predicting saturated hydraulic conductivity of expansive soil(e.g. bentonite) well. Based on a new dualpore system, this study modified KC equation for improving the prediction of saturated hydraulic conductivities of bentonites. In this study, an assumption that inter-layer space(micropore) has limited effect on fluid flow performance of compacted bentonite was adopted. The critical parameters including total porosity and total tortuosity in conventional KC equation were replaced by macroporosity and tortuosity of macropore, respectively. Macroporosity and microporosity were calculated by basal spacing of compacted bentonite, which was estimated by assuming that specific surface area is changeable during saturation process. A comprehensive comparison of bentonite’s saturated hydraulic conductivity predictions, including modified KC equation proposed in this study, conventional KC equation, and prediction method based on diffuse double layer(DDL) theory, was carried out. It was found that the predicted saturated hydraulic conductivity of bentonites calculated using modified KC equation fitted the experimental data better than others to a certain extent.展开更多
The saturated hydraulic conductivity of a soil is the main parameter for modeling the water flow through the soil and determination of seepage losses. In addition, hydraulic conductivity of compacted soil layers is cr...The saturated hydraulic conductivity of a soil is the main parameter for modeling the water flow through the soil and determination of seepage losses. In addition, hydraulic conductivity of compacted soil layers is critical component for designing liner and cover systems for waste landfills. Hydraulic conductivity can be predicted using empirical relationships, capillary models, statistical models and hydraulic radius theories [1]. In the current research work the reliability of Kozeny-Carman equation for the determination of the hydraulic conductivity of compacted clayey soils, is evaluated. The relationship between the liquid limit and the specific surface of the tested samples is also investigated. The resulting equation gives the ability for quick estimation of specific surface and hydraulic conductivity of the compacted clayey samples. The results presented here show that the Kozeny-Carman equation provides good predictions of the hydraulic conductivity of homogenized clayey soils compacted under given compactive effort, despite the consensus set out in the literature.展开更多
Anthropometric measurements, e.g., body weight （BW）, body mass index （BMI）, as well as serum prostate-specific antigen （PSA） and percent-free PSA （%fPSA） have been shown to have positive correlations with tota...Anthropometric measurements, e.g., body weight （BW）, body mass index （BMI）, as well as serum prostate-specific antigen （PSA） and percent-free PSA （%fPSA） have been shown to have positive correlations with total prostate volume （TPV）. We developed an equation and nomogram for estimating TPV, incorporating these predictors in men with benign prostatic hyperplasia （BPH）. A total of 1852 men, including 1113 at Tokyo Medical and Dental University （TMDU） Hospital as a training set and 739 at Cancer Institute Hospital （CIH） as a validation set, with PSA levels of up to 20 ng m1-1, who underwent extended prostate biopsy and were proved to have BPH, were enrolled in this study. We developed an equation for continuously coded TPV and a logistic regression-based nomogram for estimating a TPV grater than 40 mh Predictive accuracy and performance characteristics were assessed using an area under the receiver operating characteristics curve （AUC） and calibration plots. The final linear regression model indicated age, PSA, %fPSA and BW as independent predictors of continuously coded TPV. For predictions in the training set, the multiple correlation coefficient was increased from 0.38 for PSA alone to 0.60 in the final model. We developed a novel nomogram incorporating age, PSA, %fPSA and BW for estimating TPV greater than 40 mh External validation confirmed its predictive accuracy, with AUC value of 0.764. Calibration plots showed good agreement between predicted probability and observed proportion. In conclusion, TPV can be easily estimated using these four independent predictors.展开更多
文摘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 approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.
基金support from the Ministry of Economy, Trade, and Industry (METI) of Japanfunding support from Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX21_0122)
文摘Kozeny-Carman(KC) equation is a well-known relation between hydraulic conductivity and pore properties in porous material. The applications of KC equation to predicting saturated hydraulic conductivities of sands and non-expansive soils are well documented. However, KC equation is incapable of predicting saturated hydraulic conductivity of expansive soil(e.g. bentonite) well. Based on a new dualpore system, this study modified KC equation for improving the prediction of saturated hydraulic conductivities of bentonites. In this study, an assumption that inter-layer space(micropore) has limited effect on fluid flow performance of compacted bentonite was adopted. The critical parameters including total porosity and total tortuosity in conventional KC equation were replaced by macroporosity and tortuosity of macropore, respectively. Macroporosity and microporosity were calculated by basal spacing of compacted bentonite, which was estimated by assuming that specific surface area is changeable during saturation process. A comprehensive comparison of bentonite’s saturated hydraulic conductivity predictions, including modified KC equation proposed in this study, conventional KC equation, and prediction method based on diffuse double layer(DDL) theory, was carried out. It was found that the predicted saturated hydraulic conductivity of bentonites calculated using modified KC equation fitted the experimental data better than others to a certain extent.
文摘The saturated hydraulic conductivity of a soil is the main parameter for modeling the water flow through the soil and determination of seepage losses. In addition, hydraulic conductivity of compacted soil layers is critical component for designing liner and cover systems for waste landfills. Hydraulic conductivity can be predicted using empirical relationships, capillary models, statistical models and hydraulic radius theories [1]. In the current research work the reliability of Kozeny-Carman equation for the determination of the hydraulic conductivity of compacted clayey soils, is evaluated. The relationship between the liquid limit and the specific surface of the tested samples is also investigated. The resulting equation gives the ability for quick estimation of specific surface and hydraulic conductivity of the compacted clayey samples. The results presented here show that the Kozeny-Carman equation provides good predictions of the hydraulic conductivity of homogenized clayey soils compacted under given compactive effort, despite the consensus set out in the literature.
文摘Anthropometric measurements, e.g., body weight （BW）, body mass index （BMI）, as well as serum prostate-specific antigen （PSA） and percent-free PSA （%fPSA） have been shown to have positive correlations with total prostate volume （TPV）. We developed an equation and nomogram for estimating TPV, incorporating these predictors in men with benign prostatic hyperplasia （BPH）. A total of 1852 men, including 1113 at Tokyo Medical and Dental University （TMDU） Hospital as a training set and 739 at Cancer Institute Hospital （CIH） as a validation set, with PSA levels of up to 20 ng m1-1, who underwent extended prostate biopsy and were proved to have BPH, were enrolled in this study. We developed an equation for continuously coded TPV and a logistic regression-based nomogram for estimating a TPV grater than 40 mh Predictive accuracy and performance characteristics were assessed using an area under the receiver operating characteristics curve （AUC） and calibration plots. The final linear regression model indicated age, PSA, %fPSA and BW as independent predictors of continuously coded TPV. For predictions in the training set, the multiple correlation coefficient was increased from 0.38 for PSA alone to 0.60 in the final model. We developed a novel nomogram incorporating age, PSA, %fPSA and BW for estimating TPV greater than 40 mh External validation confirmed its predictive accuracy, with AUC value of 0.764. Calibration plots showed good agreement between predicted probability and observed proportion. In conclusion, TPV can be easily estimated using these four independent predictors.
