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Scale-Dependent Bedform Migration and Deformation in the Physical and Spectral Domains

Multi-scale bathymetries observed in laboratory channels and natural rivers have posed several challenges to the description of bedform geometry and kinematics. To better quantify scale-dependent migration velocity, high resolution spatio-temporal bed evolution data are analyzed using three independent methods: (i) a bedform tracking method that identifies individual bedforms in longitudinal bed elevation profiles, (ii) a cross-correlation based, image matching technique in consecutive bathymetry scans similar to Particle Image Velocimetry, and (iii) two-dimensional frequency-wavenumber spectra marking a dispersion relation between bedform period and length, allowing estimation of Fourier-based, scale-dependent migration velocities. The comparative studies show that the spectral and bedform tracking methods present small differences in the migration velocity of medium-large bedforms. However, significant deviations occur in the small bedforms, mostly due to bedform sheltering or amplified exposure to the flow, which also contribute to their enhanced scale-dependent deformation. The analysis also shows that some form of scale separation is needed to extract the large and slowly migrating bedforms as they are masked by secondary features when several bedform orders coexist. Bathymetric Image Velocimetry reasonably estimates the averaged migration velocity and exhibits potential to study relations between spanwise bed surface velocity and local bedform kinematics.

58 GEOSCIENCES↗

Techno-economic analysis of advanced small modular nuclear reactors

Here, small modular nuclear reactors (SMRs) represent a robust opportunity to develop low-carbon and reliable power with the potential to meet cost parity with conventional power systems. This study presents a detailed, bottom-up economic evaluation of a 12 × 77 MW e (924 MW e total) light-water SMR (LW-SMR) plant, a 4 × 262 MW e (1,048 MW e ) gas-cooled SMR (GC-SMR) plant, and a 5 × 200 MW e (1,000 MW e total) molten salt SMR (MS-SMR) plant. Cost estimates are derived from equipment costs, labor hours, material inputs, and process-engineering models. The advanced SMRs are compared to natural gas combined cycle plants with and without post-combustion carbon capture and a conventional large nuclear reactor. Overnight capital cost (OCC) and levelized cost of energy (LCOE) estimates are developed. The OCC of the LW-SMR, GC-SMR, and MS-SMR are found to be $\$4,844$/kW, $\$4,355$/kW, and $\$3,985$/kW respectively. The LCOE of the LW-SMR, GC-SMR, and MS-SMR are found to be $\$89.6$/MWh, $\$81.5$/MWh, and $\$80.6$/MWh respectively. A Monte Carlo analysis is performed, for which the OCC and construction time of the LW-SMR is found to have a lower mean and standard deviation than a conventional large reactor. The LW-SMR OCC is found to have a mean of $\$5,233$/kW with a standard deviation of $\$658$/kW and a 90 % probability of remaining between $\$4,254$/kW and $\$6,399$/kW, while the construction duration is found to have a mean of 4.5 years with a standard deviation of 0.8 years and a 90 % probability of remaining between 3.4 and 6.0 years. The economic impact of economies of scale, simplification, modularization, and construction time for SMRs are discussed. Additionally, policy implications for direct SMR capital subsidies and the impact of a carbon tax on natural gas emissions are explored.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

SU-E-J-22: A Feasibility Study On KV-Based Whole Breast Radiation Patient Setup

Purpose: In room kilovoltage x-ray (kV) imaging provides higher contrast than Megavoltage (MV) imaging with faster acquisition time compared with on-board cone-beam computed tomography (CBCT), thus improving patient setup accuracy and efficiency. In this study we evaluated the clinical feasibility of utilizing kV imaging for whole breast radiation patient setup. Methods: For six breast cancer patients with whole breast treatment plans using two opposed tangential fields, MV-based patient setup was conducted by aligning patient markers with in room lasers and MV portal images. Beam-eye viewed kV images were acquired using Varian OBI system after the set up process. In house software was developed to transfer MLC blocks information overlaying onto kV images to demonstrate the field shape for verification. KV-based patient digital shift was derived by performing rigid registration between kV image and the digitally reconstructed radiography (DRR) to align the bony structure. This digital shift between kV-based and MV-based setup was defined as setup deviation. Results: Six sets of kV images were acquired for breast patients. The mean setup deviation was 2.3mm, 2.2mm and 1.8mm for anterior-posterior, superior-inferior and left-right direction respectively. The average setup deviation magnitude was 4.3±1.7mm for six patients. Patient with large breast had a larger setup deviation (4.4–6.2mm). There was no strong correlation between MV-based shift and setup deviation. Conclusion: A preliminary clinical workflow for kV-based whole breast radiation setup was established and tested. We observed setup deviation of the magnitude below than 5mm. With the benefit of providing higher contrast and MLC block overlaid on the images for treatment field verification, it is feasible to use kV imaging for breast patient setup.

60 APPLIED LIFE SCIENCES↗

Convection-permitting hindcasting of diurnal variation of Mei-yu rainfall over East China with a global variable-resolution model

Two sets of 48-hr hindcast experiments for Mei-yu season using non-hydrostatic global variable-resolution model (MPAS-Atmosphere) with regional refinement at 4km resolution (V4km) and uniform 60km resolution (U60km) are first-time conducted to attempt at simulating the Mei-yu rainfall in 2015 over East China. The analysis focuses on the seasonal average of diurnal variation of precipitation amount (PA), intensity (PI), and frequency (PF). Both simulations reasonably reproduce the spatial distribution of PA. V4km is more skillful in simulating the spatial distributions and magnitudes of PF and PI. The diurnal cycle of Mei-yu rainfall shows a major early morning peak and a minor afternoon peak, contributed by precipitation during two sub-periods with distinct synoptic circulations. With strong Mei-yu in the first sub-period, the diurnal variation of PA is controlled by nocturnal southwesterly jet. V4km overestimates the morning peak mainly due to its bias in simulating boundary layer inertial oscillation. Although differences in PA between the simulations are small, U60km overestimates PF and underestimates PI. With weak Mei-yu in the second sub-period, the diurnal variation of PA is controlled by both synoptic circulation and local convection. At both resolutions, deviations in the large-scale circulation modulated by a few typhoons lead to positive biases in the morning peak of PA. After removing the typhoon impacts, V4km captures the observed diurnal cycle of PA well, while U60km significantly underestimates PA and PI particularly in the afternoon. Future studies focusing on advancing modeling of southwesterly jet and typhoons may further improve convection permitting simulation of Mei-yu rainfall.

Xu, Mingyue↗

r 2 SCAN-D4: Dispersion corrected meta-generalized gradient approximation for general chemical applications

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r 2 SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, and non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal–organic systems transfers to condensed systems, where lattice energies of molecular crystals are within the chemical accuracy (errors <1 kcal/mol).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Joint analysis of 6dFGS and SDSS peculiar velocities for the growth rate of cosmic structure and tests of gravity

ABSTRACT Measurement of peculiar velocities by combining redshifts and distance indicators is a powerful way to measure the growth rate of a cosmic structure and test theories of gravity at low redshift. Here we constrain the growth rate of the structure by comparing observed Fundamental Plane peculiar velocities for 15 894 galaxies from the 6dF Galaxy Survey (6dFGS) and Sloan Digital Sky Survey (SDSS) with predicted velocities and densities from the 2M++ redshift survey. We measure the velocity scale parameter $\beta \equiv {\Omega _{\rm m}^\gamma }/b = 0.372^{+0.034}_{-0.050}$ and $0.314^{+0.031}_{-0.047}$ for 6dFGS and SDSS, respectively, where Ωm is the mass density parameter, γ is the growth index, and b is the bias parameter normalized to the characteristic luminosity of galaxies, L*. Combining 6dFGS and SDSS, we obtain β = 0.341 ± 0.024, implying that the amplitude of the product of the growth rate and the mass fluctuation amplitude is fσ8 = 0.338 ± 0.027 at an effective redshift z = 0.035. Adopting Ωm = 0.315 ± 0.007, as favoured by Planck and using γ = 6/11 for General Relativity and γ = 11/16 for DGP gravity, we get $S_8(z=0) = \sigma _8 \sqrt{\Omega _{\rm m}/0.3} =0.637 \pm 0.054$ and 0.741 ± 0.062 for GR and DGP, respectively. This measurement agrees with other low-redshift probes of large-scale structure but deviates by more than 3σ from the latest Planck CMB measurement. Our results favour values of the growth index γ > 6/11 or a Hubble constant H0 > 70 km s−1 Mpc−1 or a fluctuation amplitude σ8 < 0.8 or some combination of these. Imminent redshift surveys such as Taipan, DESI, WALLABY, and SKA1-MID will help to resolve this tension by measuring the growth rate of cosmic structure to 1 per cent in the redshift range 0 < z < 1.

Said, Khaled↗

Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach

In this work, we investigate the scattering of a quark on a heavy nucleus at high energies using the time-dependent basis light-front quantization (tBLFQ) formalism, which is the first application of the tBLFQ formalism in QCD. We present the real-time evolution of the quark wave function in a strong classical color field of the relativistic nucleus, described as the color glass condensate. The quark and the nucleus color field are simulated in the QCD SU(3) color space. We calculate the total and the differential cross sections, and the quark distribution in coordinate and color spaces using the tBLFQ approach. We recover the eikonal cross sections in the eikonal limit. We find that the differential cross section from the tBLFQ simulation is in agreement with a perturbative calculation at large $p_⊥$, and it deviates from the perturbative calculation at small $p_⊥$ due to higher-order contributions. In particular, we relax the eikonal limit by letting the quark carry realistic finite longitudinal momenta. We study the sub-eikonal effect on the quark through the transverse coordinate distribution of the quark with different longitudinal momentum, and we find the sub-eikonal effect to be sizable. Our results can significantly reduce the theoretical uncertainties in small $p_⊥$ region which has important implications to the phenomenology of the hadron-nucleus and deep inelastic scattering at high energies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Learning unknown physics of non-Newtonian fluids

Here, we use physics-informed neural networks (PINNs) to learn viscosity models of two non-Newtonian systems (polymer melts and suspensions of particles) using only velocity measurements. For synthetic velocity data generated with the power-law viscosity model, the PINN-inferred viscosity model agrees with the analytical model for shear rates with large absolute values but deviates for shear rates near zero where the analytical model has an unphysical singularity. Once the viscosity model is learned the PINN method can solve the momentum conservation equation using only the boundary conditions.

42 ENGINEERING↗

Centrality-Dependent Modification of Jet-Production Rates in Deuteron-Gold Collisions at s N N = 200 GeV

We measured jet production rates in p+p and d+Au collisions at s N N = 200 GeV recorded in 2008 with the PHENIX detector at the Relativistic Heavy Ion Collider. Jets are reconstructed using the R=0.3 anti-k t algorithm from energy deposits in the electromagnetic calorimeter and charged tracks in multiwire proportional chambers, and the jet transverse momentum (p T ) spectra are corrected for the detector response. Spectra are reported for jets with 12 T <50 GeV/c, within a pseudorapidity acceptance of |η|<0.3. The nuclear-modification factor (R dAu ) values for 0%–100% d+Au events are found to be consistent with unity, constraining the role of initial state effects on jet production. Nonetheless, the centrality-selected R dAu values and central-to-peripheral ratios (R CP ) show large, p T -dependent deviations from unity, challenging the conventional models that relate hard-process rates and soft-particle production in collisions involving nuclei.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A General Method for Estimating Bulk 2D Projections of Ice Particle Shape: Theory and Applications

The orientation of falling ice particles directly influences estimates of microphysical and radiative bulk quantities as well as in situ retrievals of size, shape, and mass. However, retrieval efforts and bulk calculations often incorporate very basic orientations or ignore these effects altogether. To address this deficiency, this study develops a general method for projecting bulk distributions of particle shape for arbitrary orientations. The Amoroso distribution provides the most general bulk aspect ratio distribution for gamma-distributed particle axis lengths. The parameters that govern the behavior of this aspect ratio distribution depend on the assumed relationship between mass, maximum dimension, and aspect ratio. Individual spheroidal geometry allows for eccentricity quantities to linearly map onto ellipse analogs, whereas aspect ratio quantities map nonlinearly. For particles viewed from their side, this analytic distinction leads to substantially larger errors in projected aspect ratio than for projected eccentricity. Distribution transformations using these mapping equations and numerical integration of projection kernels show that both truncation of size distributions and changes in Gaussian dispersion can alter the modality and shape of projection distributions. As a result, the projection process can more than triple the relative entropy between the spheroidal and projection distributions for commonly assumed model and orientation parameters. This shape uncertainty is maximized for distributions of highly eccentric particles and for particles like aggregates that are thought to fall with large canting-angle deviations. As a result, the methods used to report projected aspect ratios and the corresponding values should be questioned.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Insights into Earth’s Energy Imbalance from Multiple Sources

The current Earth’s energy imbalance (EEI) can best be estimated from changes in ocean heat content (OHC), complemented by top-of-atmosphere (TOA) radiation measurements and an assessment of the small non-ocean components. Sustained observations from the Argo array of autonomous profiling floats enable near-global estimates of OHC since 2005, which reveal considerable cancellation of variations in the upper 300 m. An analysis of the monthly contributions to EEI from non-ocean components (land and ice) using the Community Earth System Model (CESM) Large Ensemble reveals standard deviations of 0.3–0.4 W m -2 (global); largest values occur in August, but values are below 0.75 W m -2 greater than 95% of the time. Global standard deviations of EEI of 0.64 W m -2 based on top-of-atmosphere observations therefore substantially constrain ocean contributions, given by the tendencies of OHC. Instead, monthly standard deviations of many Argo-based OHC tendencies are 6–13 W m -2 , and nonphysical fluctuations are clearly evident. It is shown that an ocean reanalysis with multivariate dynamical data assimilation features much better agreement with TOA radiation, and 44% of the vertically integrated short-term OHC trend for 2005–14 of 0.8 ± 0.2 W m -2 (globally) occurs below 700-m depth. Largest warming occurs from 20° to 50°S, especially over the southern oceans, and near 40°N in all ocean analyses. The EEI is estimated to be 0.9 ± 0.3 W m -2 for 2005–14.

54 ENVIRONMENTAL SCIENCES↗

Radiometric correction of LANDSAT data

The author has identified the following significant results. The six independent sensors of the multispectral band scanner are supposed to be identical; however, in actual practice, they may have different gain settings and offset factors, which result in the effect known as stripping (black lines at regular intervals) of the imagery. A simple two parameter method to correct the gain settings and offset factors of each of the sensors with respect to one sensor, taken as reference, was developed. This method assumes: (1) the response of a detector varies linearly with the radiance of radiation received, and (2) the means, as well as the standard deviations, of a reasonably large number of pixels, in a given wavelength band, are equal for each of the detectors for the radiometrically corrected data.

Dejesusparada, N.↗

Stratospheric temperature increases due to Pinatubo aerosols

Northern-Hemisphere stratospheric temperatures at 30 and 50 mb beginning in June 1991 are compared with 20-year (1965-1984) and 26-year (1964-1989) monthly means. Significant temperature increases are shown in July, August, September, and October for latitudes from approximately 30 deg N to the equator. In September and October deviations are observed for large areas between the equator and 30 deg N, with temperature increases as high as + 3.5 C occurring at some locations. The monthly averaged zonal mean 30-mb temperatures at 20 deg N in September and October were approximately 2.5 C higher that the 26-year mean, with some daily zonal mean increases of almost 3 C. Higher values occurred equatorward of 20 deg N. These warmings are due to absorption of radiation by the aerosols produced from the June eruptions of the volcano Pinatubo (15.1 deg N, 120.4 deg E) in the Philippines. Stratospheric warmings are expected to be occurring simultaneously at southern latitudes, especially from the equator to about 20 deg S, based on satellite and lidar measurements of the locations of the new aerosol layers. These localized temperature increases should decrease in magnitude and become more global as the cloud disperses globally and spreads in altitude.

Labitzke, K.↗

The Cirrus Parcel Model Comparison Project

The cirrus Parcel Model Comparison Project involves the systematic comparison of current models of ice crystal nucleation and growth for specified, typical, cirrus cloud environments. In Phase 1 of the project reported here, simulated cirrus cloud microphysical properties are compared for situations of "warm" (-40 C) and "cold" (-60 C) cirrus subject to updrafts of 4, 20 and 100 centimeters per second, respectively. Five models are participating in the project. These models employ explicit microphysical schemes wherein the size distribution of each class of particles (aerosols and ice crystals) is resolved into bins. Simulations are made including both homogeneous and heterogeneous ice nucleation mechanisms. A single initial aerosol population of sulfuric acid particles is prescribed for all simulations. To isolate the treatment of the homogeneous freezing (of haze drops) nucleation process, the heterogeneous nucleation mechanism is disabled for a second parallel set of simulations. Qualitative agreement is found amongst the models for the homogeneous-nucleation-only simulations, e.g., the number density of nucleated ice crystals increases with the strength of the prescribed updraft. However, non-negligible quantitative differences are found. Systematic bias exists between results of a model based on a modified classical theory approach and models using an effective freezing temperature approach to the treatment of nucleation. Each approach is constrained by critical freezing data from laboratory studies. This information is necessary, but not sufficient, to construct consistent formulae for the two approaches. Large haze particles may deviate considerably from equilibrium size in moderate to strong updrafts (20-100 centimeters per second) at -60 C when the commonly invoked equilibrium assumption is lifted. The resulting difference in particle-size-dependent solution concentration of haze particles may significantly affect the ice nucleation rate during the initial nucleation interval. The uptake rate for water vapor excess by ice crystals is another key component regulating the total number of nucleated ice crystals. This rate, the product of ice number concentration and ice crystal diffusional growth rate, partially controls the peak nucleation rate achieved in an air parcel and the duration of the active nucleation time period.

Lin, Ruei-Fong↗

GCSS Cirrus Parcel Model Comparison Project

The Cirrus Parcel Model Comparison Project, a project of GCSS Working Group on Cirrus Cloud Systems (WG2), involves the systematic comparison of current models of ice crystal nucleation and growth for specified, typical, cirrus cloud environments. The goal of this project is to document and understand the factors resulting in significant inter-model differences. The intent is to foment research leading to model improvement and validation. In Phase 1 of the project reported here, simulated cirrus cloud microphysical properties are compared for situations of "warm" (-40 C) and "cold" (-60 C) cirrus subject to updrafts of 4, 20 and 100 cm/s, respectively. Five models participated. These models employ explicit microphysical schemes wherein the size distribution of each class of particles (aerosols and ice crystals) is resolved into bins. Simulations are made including both homogeneous and heterogeneous ice nucleation mechanisms. A single initial aerosol population of sulfuric acid particles is prescribed for all simulations. To isolate the treatment of the homogeneous freezing (of haze drops) nucleation process, the heterogeneous nucleation mechanism is disabled for a second parallel set of simulations. Qualitative agreement is found for the homogeneous-nucleation-only simulations, e.g., the number density of nucleated ice crystals increases with the strength of the prescribed updraft. However, non-negligible quantitative differences are found. Detailed analysis reveals that the homogeneous nucleation formulation, aerosol size, ice crystal growth rate (particularly the deposition coefficient), and water vapor uptake rate are critical components that lead to differences in predicted microphysics. Systematic bias exists between results based on a modified classical theory approach and models using an effective freezing temperature approach to the treatment of nucleation. Each approach is constrained by critical freezing data from laboratory studies, but each includes assumptions that can only be justified by further laboratory data. Consequently, it is not yet clear if the two approaches can be made consistent. Large haze particles may deviate considerably from equilibrium size in moderate to strong updrafts (20-100 cm/s) at -60 C when the commonly invoked equilibrium assumption is lifted. The resulting difference in particle-size-dependent solution concentration of haze particles may significantly affect the ice nucleation rate during the initial nucleation interval. The uptake rate for water vapor excess by ice crystals is another key component regulating the total number of nucleated ice crystals. This rate, the product of ice number concentration and ice crystal diffusional growth rate, which is sensitive to the deposition coefficient when ice particles are small, partially controls the peak nucleation rate achieved in an air parcel and the duration of the active nucleation time period. The effects of heterogeneous nucleation are most pronounced in weak updraft situations. Vapor competition by the nucleated (heterogeneous) ice crystals limits the achieved ice supersaturation and thus suppresses the contribution of homogeneous nucleation. Correspondingly, ice crystal number density is markedly reduced. Definitive laboratory and atmospheric benchmark data are needed for the heterogeneous nucleation process. Inter-model differences are correspondingly greater than in the case of the homogeneous nucleation process acting alone.

Lin, Ruei-Fong↗

Cirrus Parcel Model Comparison Project: The Critical Components to Simulate Cirrus Initiation Explicitly - Phase 1

The Cirrus Parcel Model Comparison Project, a project of the GCSS (GEWEX Cloud System Studies) Working Group on Cirrus Cloud Systems, involves the systematic comparison of current models of ice crystal nucleation and growth for specified, typical, cirrus cloud environments. In Phase I of the project reported here, simulated cirrus cloud microphysical properties are compared for situations of "warm" (40 C) and "cold" (-60 C) cirrus, both subject to updrafts of 4, 20 and 100 centimeters per second. Five models participated. The various models employ explicit microphysical schemes wherein the size distribution of each class of particles (aerosols and ice crystals) is resolved into bins or treated separately. Simulations are made including both the homogeneous and heterogeneous ice nucleation mechanisms. A single initial aerosol population of sulfuric acid particles is prescribed for all simulations. To isolate the treatment of the homogeneous freezing (of haze droplets) nucleation process, the heterogeneous nucleation mechanism is disabled for a second parallel set of simulations. Qualitative agreement is found for the homogeneous-nucleation- only simulations, e.g., the number density of nucleated ice crystals increases with the strength of the prescribed updraft. However, significant quantitative differences are found. Detailed analysis reveals that the homogeneous nucleation rate, haze particle solution concentration, and water vapor uptake rate by ice crystal growth (particularly as controlled by the deposition coefficient) are critical components that lead to differences in predicted microphysics. Systematic bias exists between results based on a modified classical theory approach and models using an effective freezing temperature approach to the treatment of nucleation. Each approach is constrained by critical freezing data from laboratory studies, but each includes assumptions that can only be justified by further laboratory research. Consequently, it is not yet clear if the two approaches can be made consistent. Large haze particles may deviate considerably from equilibrium size in moderate to strong updrafts (20-100 centimeters per second) at -60 C when the commonly invoked equilibrium assumption is lifted. The resulting difference in particle-size- dependent solution concentration of haze particles may significantly affect the ice particle formation rate during the initial nucleation interval. The uptake rate for water vapor excess by ice crystals is another key component regulating the total number of nucleated ice crystals. This rate, the product of particle number concentration and ice crystal diffusional growth rate, which is particularly sensitive to the deposition coefficient when ice particles are small, modulates the peak particle formation rate achieved in an air parcel and the duration of the active nucleation time period. The effects of heterogeneous nucleation are most pronounced in weak updraft situations. Vapor competition by the heterogeneously nucleated ice crystals may limit the achieved ice supersaturation and thus suppresses the contribution of homogeneous nucleation. Correspondingly, ice crystal number density is markedly reduced. Definitive laboratory and atmospheric benchmark data are needed for the heterogeneous nucleation process. Inter-model differences are correspondingly greater than in the case of the homogeneous nucleation process acting alone.

Lin, Ruei-Fong↗

A Method for Obtaining the Nonlinear Aerodynamic Stability Characteristics of Bodies of Revolution from Free-Flight Tests

A method is presented for obtaining the nonlinear aerodynamic stability characteristics of bodies of revolution from free-flight test.s The necessary conditions for the application of this method are: (1) that the roll rate and damping encountered in a single cycle of oscillation be small, and (2) that the resulting motion be reasonably planar. Four approximations to the nonlinear restoring moment are considered and solutions are obtained in closed form: 1. A single-term polynomial in an arbitrary power of the angle of attack. 2. A two-term polynomial having linear and cubic terms. 3. A three-term polynomial having linear, quadratic, and cubic terms. 4. A three-term polynomial having linear, quadratic, and cubic terms. An iteration procedure is formulated to allow the use of each of these approximations for obtaining the aerodynamic coefficients of bodies of revolution from free-flight test data. It is found that although the equations that are solved pertain strictly to planar motion, the solutions are applicable to motions that deviate to a fairly large degree from planar motion.

Kirk, Donn B.↗

Investigating Sources of Variability and Error in Simulations of Carbon Dioxide in an Urban Region

Greenhouse gas (GHG) emissions estimation methods that use atmospheric trace gas observations, including inverse modeling techniques, perform better when carbon dioxide (CO2) fluxes are more accurately transported and dispersed in the atmosphere by a numerical model. In urban areas, transport and dispersion is particularly difficult to simulate using current mesoscale meteorological models due, in part, to added complexity from surface heterogeneity and fine spatial/temporal scales. It is generally assumed that the errors in GHG estimation methods in urban areas are dominated by errors in transport and dispersion. Other significant errors include, but are not limited to, those from assumed emissions magnitude and spatial distribution. To assess the predictability of simulated trace gas mole fractions in urban observing systems using a numerical weather prediction model, we employ an Eulerian model that combines traditional meteorological variables with multiple passive tracers of atmospheric CO2 from anthropogenic inventories and a biospheric model. The predictability of the Eulerian model is assessed by comparing simulated atmospheric CO2 mole fractions to observations from four in situ tower sites (three urban and one rural) in the Washington DC/Baltimore, MD area for February 2016. Four different gridded fossil fuel emissions inventories along with a biospheric flux model are used to create an ensemble of simulated atmospheric CO2 observations within the model. These ensembles help to evaluate whether the modeled observations are impacted more by the underlying emissions or transport. The spread of modeled observations using the four emission fields indicates the model's ability to distinguish between the different inventories under various meteorological conditions. Overall, the Eulerian model performs well; simulated and observed average CO2 mole fractions agree within 1% when averaged at the three urban sites across the month. However, there can be differences greater than 10% at any given hour, which are attributed to complex meteorological conditions rather than differences in the inventories themselves. On average, the mean absolute error of the simulated compared to actual observations is generally twice as large as the standard deviation of the modeled mole fractions across the four emission inventories. This result supports the assumption, in urban domains, that the predicted mole fraction error relative to observations is dominated by errors in model meteorology rather than errors in the underlying fluxes in winter months. As such, minimizing errors associated with atmospheric transport and dispersion may help improve the performance of GHG estimation models more so than improving flux priors in the winter months. We also find that the errors associated with atmospheric transport in urban domains are not restricted to certain times of day. This suggests that atmospheric inversions should use CO2 observations that have been filtered using meteorological observations rather than assuming that meteorological modeling is most accurate at certain times of day (such as using only mid-afternoon observations).

CO2↗