Toward Cloud Tomography from Space Using MISR and MODIS: Locating the “Veiled Core” in Opaque Convective Clouds

For passive satellite imagers, current retrievals of cloud optical thickness and effective particle size fail for convective clouds with 3D morphology. Indeed, being based on 1D radiative transfer (RT) theory, they work well only for horizontally homogeneous clouds. A promising approach for treating clouds as fully 3D objects is cloud tomography, which has been demonstrated for airborne observations. However, more efficient forward 3D RT solvers are required for cloud tomography from space. Here, we present a path forward by acknowledging that optically thick clouds have “veiled cores” (VCs). Sunlight scattered into and out of this deep region does not contribute significant information about the inner structure of the cloud to the spatially detailed imagery. We investigate the VC location for the MISR and MODIS imagers. While MISR provides multiangle imagery in the visible and near-infrared (IR), MODIS includes channels in the shortwave IR, albeit at a single view angle. This combination will enable future 3D retrievals to disentangle the cloud’s effective particle size and extinction fields. We find that, in practice, the VC is located at an optical distance of ~5, starting from the cloud boundary along the line of sight. For MODIS’s absorbing wavelengths the VC covers a larger volume, starting at smaller optical distances. This concept will not only lead to a reduction in the number of unknowns for the tomographic reconstruction but also significantly increase the speed and efficiency of the 3D RT solver at the heart of the algorithm by applying, say, the photon diffusion approximation inside the VC.

Statistics of Saturn Ring Occultations

<p>We calculate the excess variance, excess skewness and excess kurtosis including the effects of cylindrical shadows, along with gaps, ghosts and clumps (all calculated for the granola bar model for rectangular clumps and gaps). The widths and separation of the clumps play an analogous role to the relative size of the particle shadows, <strong>δ</strong>. Wherever the rings have significant gaps or clumps, those will dominate the statistics over the individual ring particles shadow contribution. In the first model considered, our calculations are based on the moments of the transparency <strong>T</strong> in that part of the ring sampled by the occultation, thus extending the work of  Showalter and Nicholson (1990) to larger <strong>τ</strong> and <strong>δ</strong>, and to higher central moments, without their simplifying assumptions. We also calculate these statistics using an approach based on the autocovariance, autocoskewness and autocokurtosis. This  may be more intuitive, and can be extended to other transparency distributions, e.g., those provided by gaps, ghosts, clumps and granola bars. In a third method, we have refined an overlap correction for multiple shadows, which is important for larger optical depth. This correction is calculated by summing a geometric series, and is similar to the empirical formula, eq. (22) in Colwell et al (2018). These 3 new approaches compare well to the formula for excess variance from Showalter and Nicholson in the region where all are accurate, that is <strong>δτ</strong><strong>≪</strong><strong>1</strong>. Skewness for small <strong>τ </strong>has a different sign for transparent and opaque structures, and can distinguish gaps from clumps. The higher order central moments are more sensitive to the extremes of the size distribution and opacity.</p> <p>As a check, we can explain the upward curvature of the dependence of normalized excess variance for Saturn’s background C ring by the observation of Jerousek etal (2018) that the increased optical depth is directly correlated with effective particle size. For a linear dependence <strong>R<sub>eff</sub> = 12 * (τ – 0.08) + 1.8m</strong> from Jerousek’s results, we match both the curvature of normalized excess variance and the skewness in the region between 78,000 and 84,600km from Saturn. This explanation has no free parameters and requires no gaps or ghosts (Baillie etal 2013) in this region of Saturn’s C ring.</p>

Identifying and Characterizing Local Gaps in Saturn’s Rings from Skewness of Cassini UVIS Stellar Occultation Data

<p>The Ultraviolet Imaging Spectrograph (UVIS) high-speed photometer (HSP) aboard the Cassini spacecraft collected stellar occultation data for stars of various brightness and viewing geometries as they were occulted by Saturn’s rings. We calculate the variance and skewness of the occultation light curves, and we analyze these statistical moments as functions of both optical depth and ring plane radius. Typical radial resolution of the occultations is 10-20 meters allowing for statistical moments to be calculated from 1000 points at 10 km radial sampling in the rings. We derived an analytic expression for skewness (S) as a function of optical depth assuming a ring composed of identical spherical particles, analogous to the normalized excess variance (E) relationship to optical depth used by Showalter and Nicholson (1990) and Colwell et al. (2018) to determine an effective particle size across the rings. We compared the results for effective particle size derived from S and E. Some regions, such as the inner B ring, return similar R-effective values, while others, such as the C ring plateaus, show distinctly different values. Skewness is a measure of the asymmetry of the distribution of photon counts in a measurement sample, while the variance is related to the spread of the distribution. Thus, agreement in the derived values of R-effective from S and E indicates an absence of clumps or local holes (nicknamed “ghosts”) in the rings that would lead to unusually small or large values of S, respectively. Regions of the rings where the values of R-effective from skewness (R_S) disagree with those derived from E (R_E) thus indicate the presence of ghosts or clumps that skew the distribution of photon counts in those regions. We use Monte-Carlo simulations of a simplified ring system composed of identical spherical particles interspersed with clumps and ghosts to determine the effects of these phenomena on S and compare to data. We also use simulated occultations through N-body simulations of the rings to calculate E and S where ghosts due to small moonlets or boulders are prevalent. We find variations in the suggested number of ghosts, presumed to be openings due to the same phenomena that create propeller structures in the A ring, across the rings, including in regions where there are no obvious optical depth signatures. </p>

Statistics of Saturn Ring occultations

<p>We give calculations for the excess variance, excess skewness and excess kurtosis with formulas that combine the effects of cylindrical shadows, along with gaps, ghosts and clumps (all calculated for the granola bar model for rectangular clumps and gaps). Wherever the rings have significant gaps or clumps, those will dominate the statistics over the individual ring particles contribution. We have refined an overlap correction for multiple shadows, which is important for larger optical depth. This correction results from summing a geometric series, and is similar to the empirical formula, eq. (22) in Colwell et al (2018). The comparison to Monte Carlo calculations is improved for large particle size by including the edge effects when large particles cross the edges of the viewing area A in Cassini UVIS occultations. As a check, we can explain the upward curvature of the dependence of normalized excess variance for Saturn’s background C ring by the observation of Jerousek etal (2018) that the increased optical depth is directly correlated with effective particle size. Assuming a linear dependence R<sub>eff</sub> = 12 * (tau – 0.08) + 1.8m, we match both the curvature of excess variance E and the skewness Gamma in the region between 78,000 and 84,600km from Saturn. This explanation requires no gaps or ghosts (Baillie etal 2013) in this region of Saturn’s C ring.</p>

PARTICLE DYNAMICS WITH A VISCOUS LIQUID THROUGH A POROUS MEDIUM CELL WITH A PRESSURE GRADIENT

On the basis of the previously developed mathematical model, the dynamics of the flow of a viscous liquid with particles in a porous medium is studied. The model takes into account the hydrodynamic interaction of all particles, both moving and stationary. For computer simulation of particle dynamics in such currents, a developed software package is used. A numerical calculation of the dynamics of a viscous liquid with particles at a given pressure gradient in two model structures of a porous medium, formed respectively of 450 and 478 particles of effective size is carried out. The dimensions of the dispersed particle placed in a viscous liquid were 0.3 and 0.2 of the effective particle size. The flow of a viscous liquid with a pressure gradient was specified. It is found that in the presence of a pressure gradient, the movement of the dispersed particle in the porous structure has a component directed against the flow of liquid outside the structure.

Thermal-Hydraulic Performance of SiC-Water and Al2O3-Water Nanofluids in the Minichannel

The single-phase flow and heat transfer behaviors of SiC and Al2O3 nanoparticles dispersed in water were studied experimentally in a multiport minichannel flat tube (MMFT). The volume concentrations of the two nanofluids ranged from 0.001% to 1%. Their effective particle sizes, thermal conductivities, and viscosities were also measured. Results indicated that these nanofluids as a working fluid could enhance heat transfer but increase pressure drop and the Nusselt number by up to 85%. The two nanofluids exhibited a common optimal volume concentration of 0.01% for heat transfer. Effective particle size was also found to have a significant effect on heat transfer.

Identification of Slope Debris Flow Based on Fisher Discriminated Criterion

On the basis of analyzing formation condition of slope debris flow, optimize four indexes as the discriminated factors: the loose material reserves weighted by area (),effective particle size of the loose material ,geomorphic super entropy (),meteorological and hydrological index which is composed of indirect and direct antecedent precipitation and short duration rainfall (),use the basic data of slope debris flow in Beishan of Longnan City, build the Fisher discriminated analysis model , find out the discriminated function of debris flow and non-debris flow on slope is,critical value is 1.305,give the new method of identification on the slope debris flow.