A finite element-spherical harmonics model for radiative transfer in inhomogeneous clouds. Part II. some applications

EVENT has been used to examine the effects of 3D cloud structure, distribution, and inhomogeneity on the scattering of visible solar radiation and the resulting 3D radiation field. Large eddy simulation and aircraft measurements are used to create realistic cloud fields which are continuous or broken with smooth or uneven tops. The values, patterns and variance in the resulting downwelling and upwelling radiation from incident visible solar radiation at different angles are then examined and compared to measurements. The results from EVENT confirm that 3D cloud structure is important in determining the visible radiation field, and that these results are strongly influenced by the solar zenith angle. The results match those from other models using visible solar radiation, and are supported by aircraft measurements of visible radiation, providing confidence in the new model.

The diurnal cycle of convection and atmospheric tides in an aquaplanet

The diurnal cycle of tropical convection and its relationship to the atmospheric tides is investigated using an aquaplanet GCM. The diurnal and semidiurnal harmonics of precipitation are both found to contribute significantly to the total diurnal variability of precipitation in the model, which is broadly consistent with observations of the diurnal cycle of convection over the open ocean. The semidiurnal tide is found to be the dominant forcing for the semidiurnal harmonic of precipitation. In contrast the diurnal tide plays only a small role in forcing the diurnal harmonic of precipitation, which is dominated by the variations in shortwave and longwave heating. In both the diurnal and semidiurnal harmonics, the feedback onto the convection by the humidity tendencies due to the convection is found to be important in determining the phase of the harmonics. Further experiments show that the diurnal cycle of precipitation is sensitive to the choice of closure in the convection scheme. While the surface pressure signal of the simulated atmospheric tides in the model agree well with both theory and observations in their magnitude and phase, sensitivity experiments suggest that the role of the stratospheric ozone in forcing the semidiurnal tide is much reduced compared to theoretical predictions. Furthermore, the influence of the cloud radiative effects seems small. It is suggested that the radiative heating profile in the troposphere, associated primarily with the water vapor distribution, is more important than previously thought for driving the semidiurnal tide. However, this result may be sensitive to the vertical resolution and extent of the model.

Wave functions for the methane molecule

If the potential field due to the nuclei in the methane molecule is expanded in terms of a set of spherical harmonics about the carbon nucleus, only the terms involving s, f, and higher harmonic functions differ from zero in the equilibrium configuration. Wave functions have been calculated for the equilibrium configuration, first including only the spherically symmetric s term in the potential, and secondly including both the s and the f terms. In the first calculation the complete Hartree-Fock S.C.F. wave functions were determined; in the second calculation a variation method was used to determine the best form of the wave function involving f harmonics. The resulting wave functions and electron density functions are presented and discussed

Vibrational intensities in methane

The absorption intensities of the two infra-red active vibrations in methane have been obtained from a perturbation calculation on the equilibrium wave functions derived in the preceding paper. The perturbation field is the change in the potential field due to the nuclei which results from moving the nuclei in the vibrational coordinate concerned, and a simplified form of second order perturbation theory, developed by Pople and Schofield, is used for the calculation. The main approximation involved is the neglect of f and higher harmonics in the spherical harmonic expansion of the nuclear field. The resulting dipole moment derivatives are approximately three times larger than the experimental values, but they show qualitative features and sign relationships which are significant.

Self-consistent field theory for diblock copolymers grafted to a sphere

An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.

The determination of molecular orientation in uniaxially compressed PMMA by X-ray scattering

A procedure is presented for obtaining full molecular orientation information from wide angle X-ray scattering patterns of deformed non-crystalline polymers. The method is based on the analysis of experimental and calculated scattering patterns into their spherical harmonics. The results obtained for PMMA are compared with values predicted by the pseudo affine and affine deformation schemes.