The applicability of physical optics in the millimetre and sub-millimetre spectral region. Part II: Application to a three-component model of ice cloud and its evaluation against the bulk single-scattering properties of various other aggregate models

The bulk single-scattering properties of various randomly oriented aggregate ice crystal models are com- pared and contrasted at a number of frequencies between 89 and 874 GHz. The model ice particles consist of the ten-branched plate aggregate, five-branched plate aggregate, eight-branched hexagonal aggregate, Voronoi ice aggregate, six-branched hollow bullet rosette, hexagonal column of aspect ratio unity, and the ten-branched hexagonal aggregate. The bulk single-scattering properties of the latter two ice particle models have been calculated using the light scattering methods described in Part I, which represent the two most extreme members of an ensemble model of cirrus ice crystals. In Part I, it was shown that the method of physical optics could be combined with the T-matrix at a size parameter of about 18 to compute the bulk integral ice optical properties and the phase function in the microwave to sufficient ac- curacy to be of practical value. Here, the bulk single-scattering properties predicted by the two ensemble model members and the Voronoi model are shown to generally bound those of all other models at fre- quencies between 89 and 874 GHz, thus representing a three-component model of ice cloud that can be generally applied to the microwave, rather than using many differing ice particle models. Moreover, the Voronoi model and hollow bullet rosette scatter similarly to each other in the microwave. Furthermore, from the various comparisons, the importance of assumed shapes of the particle size distribution as well as cm-sized ice aggregates is demonstrated.Peer reviewedFinal Accepted Versio

Cloud chamber laboratory investigations into scattering properties of hollow ice particles

Copyright 2015 The Authors. Published by Elsevier Ltd.This is an open access article under the CC-BY license (http://creativecommons.org/licenses/by/4.0/). Date of Acceptance: 16/02/2015Measurements are presented of the phase function, P11, and asymmetry parameter, g, of five ice clouds created in a laboratory cloud chamber. At −7 °C, two clouds were created: one comprised entirely of solid columns, and one comprised entirely of hollow columns. Similarly at −15 °C, two clouds were created: one consisting of solid plates and one consisting of hollow plates. At −30 °C, only hollow particles could be created within the constraints of the experiment. The resulting cloud at −30 °C contained short hollow columns and thick hollow plates. During the course of each experiment, the cloud properties were monitored using a Cloud Particle Imager (CPI). In addition to this, ice crystal replicas were created using formvar resin. By examining the replicas under an optical microscope, two different internal structures were identified. The internal and external facets were measured and used to create geometric particle models with realistic internal structures. Theoretical results were calculated using both Ray Tracing (RT) and Ray Tracing with Diffraction on Facets (RTDF). Experimental and theoretical results are compared to assess the impact of internal structure on P11 and g and the applicability of RT and RTDF for hollow columns.Peer reviewe

The applicability of physical optics in the millimetre and sub-millimetre spectral region. : Part I: The ray tracing with diffraction on facets method

This document is the Accepted Manuscript version of the following article: A. J. Baran, Evelyn Hesse, and Odran Sourdeval, ‘ The applicability of physical optics in the millimetre and sub-millimetre spectral region. Part I: The ray tracing with diffraction on facets method’, Journal of Quantitative Spectroscopy & Radiative Transfer, Vol. 190, (2017), pp. 13-25, first published online on 3 January 2017. The version of record is available online at doi: http://dx.doi.org/10.1016/j.jqsrt.2016.12.030 Crown Copyright © 2016 Published by Elsevier Ltd. All rights reserved.Future satellite missions, from 2022 onwards, will obtain near-global measurements of cirrus at microwave and sub-millimetre frequencies. To realise the potential of these observations, fast and accurate light-scattering methods are required to calculate scattered millimetre and sub-millimetre intensities from complex ice crystals. Here, the applicability of the ray tracing with diffraction on facets method (RTDF) in predicting the bulk scalar optical properties and phase functions of randomly oriented hexagonal ice columns and hexagonal ice aggregates at millimetre frequencies is investigated. The applicability of RTDF is shown to be acceptable down to size parameters of about 18, between the frequencies of 243 and 874 GHz. It is demonstrated that RTDF is generally well within about 10% of T-matrix solutions obtained for the scalar optical properties assuming hexagonal ice columns. Moreover, on replacing electromagnetic scalar optical property solutions obtained for the hexagonal ice aggregate with the RTDF counterparts at size parameter values of about 18 or greater, the bulk scalar optical properties can be calculated to generally well within ±5% of an electromagnetic-based database. The RTDF-derived bulk scalar optical properties result in brightness temperature errors to generally within about ±4 K at 874 GHz. Differing microphysics assumptions can easily exceed such errors. Similar findings are found for the bulk scattering phase functions. This finding is owing to the scattering solutions being dominated by the processes of diffraction and reflection, both being well described by RTDF. The impact of centimetre-sized complex ice crystals on interpreting cirrus polarisation measurements at sub-millimetre frequencies is discussed.Peer reviewe

A coupled cloud physics–radiation parameterization of the bulk optical properties of cirrus and its impact on the Met Office unified model global atmosphere 5.0 configuration

A new coupled cloud physics–radiation parameterization of the bulk optical properties of ice clouds is presented. The parameterization is consistent with assumptions in the cloud physics scheme regarding particle size distributions (PSDs) and mass–dimensional relationships. The parameterization is based on a weighted ice crystal habit mixture model, and its bulk optical properties are parameterized as simple functions of wavelength and ice water content (IWC). This approach directly couples IWC to the bulk optical properties, negating the need for diagnosed variables, such as the ice crystal effective dimension. The parameterization is implemented into the Met Office Unified Model Global Atmosphere 5.0 (GA5) configuration. The GA5 configuration is used to simulate the annual 20-yr shortwave (SW) and longwave (LW) fluxes at the top of the atmosphere (TOA), as well as the temperature structure of the atmosphere, under various microphysical assumptions. The coupled parameterization is directly compared against the current operational radiation parameterization, while maintaining the same cloud physics assumptions. In this experiment, the impacts of the two parameterizations on the SW and LW radiative effects at TOA are also investigated and compared against observations. The 20-yr simulations are compared against the latest observations of the atmospheric temperature and radiative fluxes at TOA. The comparisons demonstrate that the choice of PSD and the assumed ice crystal shape distribution are as important as each other. Moreover, the consistent radiation parameterization removes a long-standing tropical troposphere cold temperature bias but slightly warms the southern midlatitudes by about 0.5 K

Conservation in signal processing systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 205-209).Conservation principles have played a key role in the development and analysis of many existing engineering systems and algorithms. In electrical network theory for example, many of the useful theorems regarding the stability, robustness, and variational properties of circuits can be derived in terms of Tellegen's theorem, which states that a wide range of quantities, including power, are conserved. Conservation principles also lay the groundwork for a number of results related to control theory, algorithms for optimization, and efficient filter implementations, suggesting potential opportunity in developing a cohesive signal processing framework within which to view these principles. This thesis makes progress toward that goal, providing a unified treatment of a class of conservation principles that occur in signal processing systems. The main contributions in the thesis can be broadly categorized as pertaining to a mathematical formulation of a class of conservation principles, the synthesis and identification of these principles in signal processing systems, a variational interpretation of these principles, and the use of these principles in designing and gaining insight into various algorithms. In illustrating the use of the framework, examples related to linear and nonlinear signal-flow graph analysis, robust filter architectures, and algorithms for distributed control are provided.by Thomas A. Baran.Ph.D

Design and implementation of discrete-time filters for efficient sampling rate conversion

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 63-64).Rate-conversion systems are used in an array of applications, including the oversampled audio and video CODECs often found in entertainment and communications systems. It is common practice for many such systems to sample signals at rates which are much faster than the minimum required to represent some bandwidth of interest, and high-quality filters are often implemented at this fast rate. Therefore, their designs tend to be computationally expensive. A number of structures have been proposed to address this, including polyphase implementations and folded structures for linear-phase FIR filters. In this thesis, techniques which combine benefits from both classes of structures are discussed, and an efficient class of structures is proposed. The Generalized Transposition Theorem is also reviewed to demonstrate that an efficient downsampling structure also implies an equally efficient, closely-related upsampling structure. Techniques are investigated for designing minimum multiply filters for the class of structures presented, and methods are discussed for designing filters that, for a given set of frequency domain filter specifications, often require fewer multipliers and have smaller maximum error than Parks-McClellan designs.by Thomas A. Baran.S.M

Using laboratory and field measurements to constrain a single habit shortwave optical parameterization for cirrus

A single habit parameterization for the shortwave optical properties of cirrus is presented. The parameterization utilizes a hollow particle geometry, with stepped internal cavities as identified in laboratory and field studies. This particular habit was chosen as both experimental and theoretical results show that the particle exhibits lower asymmetry parameters when compared to solid crystals of the same aspect ratio. The aspect ratio of the particle was varied as a function of maximum dimension, D, in order to adhere to the same physical relationships assumed in the microphysical scheme in a configuration of the Met Office atmosphere-only global model, concerning particle mass, size and effective density. Single scattering properties were then computed using T-Matrix, Ray Tracing with Diffraction on Facets (RTDF) and Ray Tracing (RT) for small, medium, and large size parameters respectively. The scattering properties were integrated over 28 particle size distributions as used in the microphysical scheme. The fits were then parameterized as simple functions of Ice Water Content (IWC) for 6 shortwave bands. The parameterization was implemented into the GA6 configuration of the Met Office Unified Model along with the current operational long-wave parameterization. The GA6 configuration is used to simulate the annual twenty-year short-wave (SW) fluxes at top-of-atmosphere (TOA) and also the temperature and humidity structure of the atmosphere. The parameterization presented here is compared against the current operational model and a more recent habit mixture model

Accelerated Calder\'on preconditioning for Maxwell transmission problems

We investigate a range of techniques for the acceleration of Calder\'on (operator) preconditioning in the context of boundary integral equation methods for electromagnetic transmission problems. Our objective is to mitigate as far as possible the high computational cost of the barycentrically-refined meshes necessary for the stable discretisation of operator products. Our focus is on the well-known PMCHWT formulation, but the techniques we introduce can be applied generically. By using barycentric meshes only for the preconditioner and not for the original boundary integral operator, we achieve significant reductions in computational cost by (i) using "reduced" Calder\'on preconditioners obtained by discarding constituent boundary integral operators that are not essential for regularisation, and (ii) adopting a ``bi-parametric'' approach in which we use a lower quality (cheaper) $\mathcal{H}$-matrix assembly routine for the preconditioner than for the original operator, including a novel approach of discarding far-field interactions in the preconditioner. Using the boundary element software Bempp (www.bempp.com), we compare the performance of different combinations of these techniques in the context of scattering by multiple dielectric particles. Applying our accelerated implementation to 3D electromagnetic scattering by an aggregate consisting of 8 monomer ice crystals of overall diameter 1cm at 664GHz leads to a 99% reduction in memory cost and at least a 75% reduction in total computation time compared to a non-accelerated implementation

The impact of two coupled cirrus microphysics-radiation parameterizations on the temperature and specific humidity biases in the tropical tropopause layer in a climate model

The impact of two different coupled cirrus microphysics-radiation parameterizations on the zonally averaged temperature and humidity biases in the tropical tropopause layer (TTL) of a Met Office climate model configuration is assessed. One parameterization is based on a linear coupling between a model prognostic variable, the ice mass mixing ratio, qi, and the integral optical properties. The second is based on the integral optical properties being parameterized as functions of qi and temperature, Tc, where the mass coefficients (i.e. scattering and extinction) are parameterized as nonlinear functions of the ratio between qi and Tc. The cirrus microphysics parameterization is based on a moment estimation parameterization of the particle size distribution (PSD), which relates the mass moment (i.e. second moment if mass is proportional to size raised to the power of 2 ) of the PSD to all other PSD moments through the magnitude of the second moment and Tc. This same microphysics PSD parameterization is applied to calculate the integral optical properties used in both radiation parameterizations and, thus, ensures PSD and mass consistency between the cirrus microphysics and radiation schemes. In this paper, the temperature-non-dependent and temperature-dependent parameterizations are shown to increase and decrease the zonally averaged temperature biases in the TTL by about 1 K, respectively. The temperature-dependent radiation parameterization is further demonstrated to have a positive impact on the specific humidity biases in the TTL, as well as decreasing the shortwave and longwave biases in the cloudy radiative effect. The temperature-dependent radiation parameterization is shown to be more consistent with TTL and global radiation observations

A New Parameterization of Single Scattering Solar Radiative Properties for Tropical Anvils Using Observed Ice Crystal Size and Shape Distributions

Parameterizations of single scattering properties currently used in cloud resolving and general circulation models are somewhat limited in that they typically assume the presence of single particle habits, do not adequately account for the numbers of ice crystals with diameters smaller than 100 mm, and contain no information about the variance of parameterization coefficients. Here, new parameterizations of mean single scattering properties (e.g., single scatter albedo, asymmetry parameter, and extinction efficiency) for distributions of ice crystals in tropical anvils are developed. Using information about the size and shape of ice crystals acquired by a two-dimensional cloud probe during the Central Equatorial Pacific Experiment (CEPEX), a self-organized neural network defines shape based on simulations of how the particle maximum dimension and area ratio (ratio of projected area to that of circumscribed circle with maximum dimension) vary for random orientations of different idealized shapes (i.e., columns, bullet rosettes, rough aggregates, and particles represented by Chebyshev poly-nomials). The size distributions for ice crystals smaller than 100 mm are based on parameterizations developed using representative samples of 11 633 crystals imaged by a video ice particle sampler (VIPS). The mean-scattering properties for distributions of ice crystals are then determined by weighting the single scattering properties of individual ice crystals, determined using an improved geometric ray-tracing method, according t