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- Author or Editor: Rich F. Coleman x
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Abstract
A new formulation of the equations describing the conditions necessary for aircraft exhaust contrail formation is derived from the fundamental necessary condition. First, the original solution of Appleman is derived from the necessary condition to illustrate the continuity of the new formulation. Then the new formulation offers an analytic solution for the critical temperature Tc expressed in terms of water vapor mixing ratio and atmospheric pressure, rather than in terms of relative humidity and pressure, thus avoiding potential forecast errors associated with the temperature sensitivity inherent in relative humidity. A variety of results is presented, including a comparison with the seminal results of Appleman, a comparison of the sensitivity of Tc to perturbations in relative humidity versus perturbations in mixing ratio, and some typical results for actual atmospheric conditions. The clear superiority of a formulation based on mixing ratio rather than relative humidity is seen in the reduced sensitivity of c , to errors or uncertainties in the input atmospheric variables.
Abstract
A new formulation of the equations describing the conditions necessary for aircraft exhaust contrail formation is derived from the fundamental necessary condition. First, the original solution of Appleman is derived from the necessary condition to illustrate the continuity of the new formulation. Then the new formulation offers an analytic solution for the critical temperature Tc expressed in terms of water vapor mixing ratio and atmospheric pressure, rather than in terms of relative humidity and pressure, thus avoiding potential forecast errors associated with the temperature sensitivity inherent in relative humidity. A variety of results is presented, including a comparison with the seminal results of Appleman, a comparison of the sensitivity of Tc to perturbations in relative humidity versus perturbations in mixing ratio, and some typical results for actual atmospheric conditions. The clear superiority of a formulation based on mixing ratio rather than relative humidity is seen in the reduced sensitivity of c , to errors or uncertainties in the input atmospheric variables.
Abstract
A complete and traceable geometric ray-tracing solution for finite hexagonal columns and plates arbitrarily oriented in space has been developed by means of analytic geometry. In addition, an analytic expression for the cross-sectional area for arbitrarily oriented hexagons also has been derived based on which Fraunhofer diffraction and extinction and scattering cross sections in the limit of geometric optics can be computed exactly. The program involving geometrical reflection and refraction and Fraunhofer diffraction was used to compute the scattered intensities corresponding to two components of polarization for randomly oriented columns and plates in a horizontal plane and three-dimensional space. The scattered intensities were subsequently normalized to yield the nondimensional phase function commonly used in radiative transfer analyses. Numerical computations have been performed to study the effects of size, shape, orientation, and absorption on the scattering phase function and linear polarization. We show that the scattering phase functions for columns and plates, having approximately the same value, are quite similar except columns have a broader 22° halo pattern. The polarization patterns for these two shapes as well as for spheres and circular cylinders, however, are distinctly different, especially between 30 and 60° and between 130 and 140° scattering angles. We also show that hexagonal columns and plates randomly oriented in a horizontal plane do not generate a full scattering pattern of significant magnitude for an obliquely incident beam, and that the scattering patterns vary significantly with the oblique angle of the incident beam. At the 10.6 μm infrared wavelength, because of the strong absorption of ice, the scattering pattern is basically attributed to diffraction and external reflection but with a noticeable 7° halo maximum due to two refractions. Comparisons with experimental results for plates having a mode radius of 20 μm reveal a general agreement in regions from about 30–160° scattering angles.
Abstract
A complete and traceable geometric ray-tracing solution for finite hexagonal columns and plates arbitrarily oriented in space has been developed by means of analytic geometry. In addition, an analytic expression for the cross-sectional area for arbitrarily oriented hexagons also has been derived based on which Fraunhofer diffraction and extinction and scattering cross sections in the limit of geometric optics can be computed exactly. The program involving geometrical reflection and refraction and Fraunhofer diffraction was used to compute the scattered intensities corresponding to two components of polarization for randomly oriented columns and plates in a horizontal plane and three-dimensional space. The scattered intensities were subsequently normalized to yield the nondimensional phase function commonly used in radiative transfer analyses. Numerical computations have been performed to study the effects of size, shape, orientation, and absorption on the scattering phase function and linear polarization. We show that the scattering phase functions for columns and plates, having approximately the same value, are quite similar except columns have a broader 22° halo pattern. The polarization patterns for these two shapes as well as for spheres and circular cylinders, however, are distinctly different, especially between 30 and 60° and between 130 and 140° scattering angles. We also show that hexagonal columns and plates randomly oriented in a horizontal plane do not generate a full scattering pattern of significant magnitude for an obliquely incident beam, and that the scattering patterns vary significantly with the oblique angle of the incident beam. At the 10.6 μm infrared wavelength, because of the strong absorption of ice, the scattering pattern is basically attributed to diffraction and external reflection but with a noticeable 7° halo maximum due to two refractions. Comparisons with experimental results for plates having a mode radius of 20 μm reveal a general agreement in regions from about 30–160° scattering angles.
Abstract
Mesoscale forecasts for the Los Angeles basin made with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) exhibited a moderate to substantial warm temperature bias for extended periods in the summer months. A similar bias also was thought to exist in forecasts made using version 2.2 of the Weather Research and Forecasting Model (WRF v2.2). To address these biases, two sources of anthropogenic moisture were analyzed: commercial irrigation and outdoor domestic water use. These represent substantial amounts of equivalent precipitation that are not accounted for in normal WRF execution. This is especially true for the summer months when little or no precipitation occurs in the area. A method for estimating the temporal and spatial distributions of these two sources was developed and the resulting database was applied to model runs. The addition of these anthropogenic moisture sources is an important source of enthalpy, which results in significant cooling in WRF. However, in the course of the analysis it was determined that the biases in WRF were much smaller than had been thought. Also, despite producing significant cooling, the addition of anthropogenic moisture made only modest improvements in forecast skill, and only for some hours of the day, indicating that more research is necessary on how the physical processes are handled in WRF, and how the anthropogenic moisture is distributed during the forecast period.
Abstract
Mesoscale forecasts for the Los Angeles basin made with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) exhibited a moderate to substantial warm temperature bias for extended periods in the summer months. A similar bias also was thought to exist in forecasts made using version 2.2 of the Weather Research and Forecasting Model (WRF v2.2). To address these biases, two sources of anthropogenic moisture were analyzed: commercial irrigation and outdoor domestic water use. These represent substantial amounts of equivalent precipitation that are not accounted for in normal WRF execution. This is especially true for the summer months when little or no precipitation occurs in the area. A method for estimating the temporal and spatial distributions of these two sources was developed and the resulting database was applied to model runs. The addition of these anthropogenic moisture sources is an important source of enthalpy, which results in significant cooling in WRF. However, in the course of the analysis it was determined that the biases in WRF were much smaller than had been thought. Also, despite producing significant cooling, the addition of anthropogenic moisture made only modest improvements in forecast skill, and only for some hours of the day, indicating that more research is necessary on how the physical processes are handled in WRF, and how the anthropogenic moisture is distributed during the forecast period.
