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At least 955 records · Page 53

SU-F-J-99: Dose Accumulation and Evaluation in Lung SBRT Among All Phases of Respiration

Purpose: To calculate the total planning dose on lung tumors (GTV) by accumulating the dose received in all respiration phases. Methods: A patient 4D planning CT (phase-binned, from a Siemens Somatom CT) was used to locate the GTV of a lung tumor in all respiratory phases with Pinnacle (v9.10). GTV contours defined in all phases were projected to the reference phase, where the ITV was defined. Centroids were calculated for all the GTV projections. No deformation or rotation was taken into account. The only GTV contour as defined in the reference phase was voxelized to track each voxel individually. We accumulated the absorbed dose in different phases on each voxel. A 3DCRT and a VMAT plan were designed on the reference phase fulfilling the ITV dosimetric requirements, using the 10MV FFF photon model from an Elekta Versa linac. ITV-to-PTV margins were set to 5mm. In-house developed MATLAB code was used for tumor voxeling and dose accumulation, assuming that the dose distribution planned in the reference phase behaved as a “dose-cloud” during patient breathing. Results: We tested the method on a patient 4DCT set of images exhibiting limited tumor motion (<5mm). For the 3DCRT plan, D95 was calculated for the GTV with motion and for the ITV, showing an agreement of 0.04%. For the VMAT plan, we calculated the D95 for every phase as if the GTV in that phase had received the whole treatment. Differences in D95 for all phases are within 1%, and estimate the potential interplay effect during delivery. Conclusion: A method for dose accumulation and assessment was developed that can compare GTV motion with ITV dosage, and estimate the potential interplay effect for VMAT plans. Work in progress includes the incorporation of deformable image registration and 4D CBCT dose calculation for dose reconstruction and assessment during treatment.

60 APPLIED LIFE SCIENCES↗

Summary of results and conclusions based on analysis of volume imaging and high spectral resolution lidar data acquired during FIRE phase 1, part 1

The collection of long term global statistics on cloud cover may be most easily accomplished with satellite based observations; however, measurements derived from passive satellite retrieval methods must be calibrated and verified by in situ or ground based remote sensor observations. Verification is not straight forward, however, because the highly variable nature of cloud altitude, morphology, and optical characteristics complicates the scaling of point measurements to satellite footprint sized areas. This is particularly evident for cirrus clouds which may be organized on horizontal scales of 10's of meters to 8 km or more, and have optical depths ranging from less than .003 to greater than 3. Cirrus clouds can strongly influence earths' radiative balance, but, because they are often transmissive, cirrus clouds are difficult to detect and characterize from satellite measurements. Because of its precise ranging capabilities, spatial resolution and sensitivity, lidar observations have played an important role in the detection, depiction, and characterization of cirrus clouds. Some of the characteristics of cirrus clouds are summarized which observed the High Spectral Resolution and Volume Imaging Lidars during the phase 1 IFO and ETO periods.

Grund, Christian J.↗

Global and Regional Impacts of HONO on the Chemical Composition of Clouds and Aerosols

Recently, realistic simulation of nitrous acid (HONO) based on the HONO / NOx ratio of 0.02 was found to have a significant impact on the global budgets of HOx (OH + HO2) and gas phase oxidation products in polluted regions, especially in winter when other photolytic sources are of minor importance. It has been reported that chemistry-transport models underestimate sulphate concentrations, mostly during winter. Here we show that simulating realistic HONO levels can significantly enhance aerosol sulphate (S(VI)) due to the increased formation of H2SO4. Even though in-cloud aqueous phase oxidation of dissolved SO2 (S(IV)) is the main source of S(VI), it appears that HONO related enhancement of H2O2 does not significantly affect sulphate because of the predominantly S(IV) limited conditions, except over eastern Asia. Nitrate is also increased via enhanced gaseous HNO3 formation and N2O5 hydrolysis on aerosol particles. Ammonium nitrate is enhanced in ammonia-rich regions but not under ammonia-limited conditions. Furthermore, particle number concentrations are also higher, accompanied by the transfer from hydrophobic to hydrophilic aerosol modes. This implies a significant impact on the particle lifetime and cloud nucleating properties. The HONO induced enhancements of all species studied are relatively strong in winter though negligible in summer. Simulating realistic HONO levels is found to improve the model measurement agreement of sulphate aerosols, most apparent over the US. Our results underscore the importance of HONO for the atmospheric oxidizing capacity and corroborate the central role of cloud chemical processing in S(IV) formation

Global and regional impacts↗

On the interpretation of the 'inverse phase effect' for CO2 equivalent widths on Venus

Computations of the equivalent widths of absorption lines as a function of planetary phase angle are made for a homogeneous cloud with particles having the properties (shape, refractive index, and size distribution) deduced from polarimetry of Venus. The computed equivalent widths show an 'inverse phase effect' comparable to that which is observed for CO2 lines on Venus. This result verifies a recent suggestion of Regas et al. that the existence of an inverse phase effect does not by itself imply the presence of multiple layers of scattering particles in the atmosphere of Venus.

Whitehill, L. P.↗

The 1996 Subsonic Aircraft: Contrail and Cloud Effects Special Study

During April 1996 NASA, in conjunction with the DOE, will sponsor a multi-aircraft field campaign to better understand the microphysical and radiative properties of cirrus clouds, the origins of ice nuclei and cloud condensation nuclei in the upper troposphere, and the possible role that the commercial subsonic aircraft fleet might play in altering cloud or aerosol properties. The NASA ER-2 aircraft will be used as a remote sensing platform, while the NASA DC-8 aircraft will be used as an in situ measurement platform. In situ observations will include a full set of size distribution measurements from nano-meter to millimeter sizes, ice water content measurements, gas phase and condensed phase chemical measurements, ice crystal optical phase function measurements, lidar observations of cloud top and cloud base, and atmospheric state measurement. The ER-2 will have lidar, microwave ice water path measurements, as well as visible and infrared spectral measurement. In this presentation the highlights of the mission will be presented. The goal will be to address fundamental questions such as the mode of nucleation of cirrus clouds, the composition of the nuclei on which cirrus form, the degree to which aircraft impact cirrus cloud properties.

Toon, Owen B.↗

The Relation of Environmental Conditions With Charge Structure in Central Argentina Thunderstorms

In this study we explored the environmental conditions hypothesized to induce a dominant charge structure in thunderstorms in the province of Cordoba, Argentina, during the RELAMPAGO-CACTI (Remote sensing of Electrification, Lightning, And Mesoscale/microscale Processes with Adaptive Ground Observations-Clouds, Aerosols, Complex Terrain Interactions) field campaigns. Hypothesized environmental conditions are thought to be related to small warm cloud residence time and warm rain growth suppression, which lead to high cloud liquid water contents in the mixed-phase zone, contributing to positive charging of graupel and anomalous charge structure storms. Data from radiosondes, a cloud condensation nuclei (CCN) ground-based instrument and reanalysis were used to characterize the proximity inflow air of storms with anomalous and normal charge structures. Consistent with the initial hypothesis, anomalous storms had small warm cloud depth caused by dry low-level humidity and low 0°C height. Anomalous storms were associated with lower CCN concentrations than normal storms, an opposite result to the initial expectation. High CAPE is not an important condition for the development of anomalous storms in Argentina, as no clear pattern could be found among the different parameters calculated for updraft proxy that would be consistent with the initial hypothesis.

54 ENVIRONMENTAL SCIENCES↗

Anomalous Distributions of Primary Cosmic Rays as Evidence for Time-dependent Particle Acceleration in Supernova Remnants

Recent precise measurements of cosmic-ray (CR) spectra show that the energy distribution of protons is softer than those of heavier nuclei, and there are spectral hardenings for all nuclear compositions above ∼200 GV. Models proposed for these anomalies generally assume steady-state solutions of the particle acceleration process. We show that if the diffusion coefficient has a weak dependence on the particle rigidity near shock fronts of supernova remnants (SNRs), time-dependent solutions of the linear diffusive shock acceleration at two stages of SNR evolution can naturally account for these anomalies. The high-energy component of CRs is dominated by acceleration in the free expansion and adiabatic phases with enriched heavy elements and a high shock speed. The low-energy component may be attributed to acceleration by slow shocks propagating in dense molecular clouds with low metallicity in the radiative phase. Instead of a single power-law distribution, the spectra of time-dependent solutions soften gradually with the increase of energy, which may be responsible for the “knee” of CRs.

79 ASTRONOMY AND ASTROPHYSICS↗

Revisiting the Phase Curves of WASP-43b: Confronting Re-analyzed Spitzer Data with Cloudy Atmospheres

Recently acquired Hubble and Spitzer phase curves of the short-period hot Jupiter WASP-43b make it an ideal target for confronting theory with data. On the observational front, we re-analyze the 3.6 and 4.5 μm Spitzer phase curves and demonstrate that our improved analysis better removes residual red noise due to intra-pixel sensitivity, which leads to greater fluxes emanating from the nightside of WASP-43b, thus reducing the tension between theory and data. On the theoretical front, we construct cloud-free and cloudy atmospheres of WASP-43b using our Global Circulation Model (GCM), THOR, which solves the non-hydrostatic Euler equations (compared to GCMs that typically solve the hydrostatic primitive equations). The cloud-free atmosphere produces a reasonable fit to the dayside emission spectrum. The multi-phase emission spectra constrain the cloud deck to be confined to the nightside and have a finite cloud-top pressure. The multi-wavelength phase curves are naturally consistent with our cloudy atmospheres, except for the 4.5 μm phase curve, which requires the presence of enhanced carbon dioxide in the atmosphere of WASP-43b. Multi-phase emission spectra at higher spectral resolution, as may be obtained using the James Webb Space Telescope, and a reflected-light phase curve at visible wavelengths would further constrain the properties of clouds in WASP-43b.

79 ASTRONOMY AND ASTROPHYSICS↗

The vertical structure of Jupiter's equatorial and tropical regions

The equatorial and tropical regions of Jupiter are presently treated in light of an inhomogeneous atmospheric model that encompasses both polarizing aerosols and methane gas, in keeping with Pioneer polarimetry and photometry data as well as the methane band data obtained by West (1979). The relative strengths of weak and strong methane bands are addressed by a two-cloud model with overlying stratospheric haze. For all the regions considered, the best fit for polarization measurements is a negatively polarizing ammonia cloud beneath a positively polarizing haze. Unlike the nearby features, the equatorial region and the Great Red Spot have a negative polarization at 80-deg phase angle, implying less gas above the clouds in these regions.

Smith, P. H.↗

Field Validation of Cloud Properties Sensor Field Campaign Report

The purpose of this campaign is to deploy Aerodyne Research Inc.’s extended wavelength cloud optical properties sensor (TWST-EN) in an operationally relevant environment with co-located, validated sensors. The Atmospheric Radiation Measurement (ARM) user facility’s Southern Great Plains (SGP) observatory is ideal for this deployment because of the variety of operational sensors that can measure some of the same cloud properties using different modalities. While cloud property sensors have long existed, they tend to be costly to produce and maintain. Our sensor measures absolute spectral radiance in the two bands and will retrieve cloud optical depth (COD), droplet effective radius, and thermodynamic phase. Our prototype is built predominantly from off-the-shelf components and uses uncooled spectrometers. A lower-cost, easy-to-use sensor such as this could allow deployment at many more sites for greater spatial coverage. Analysis and retrieval algorithm development using the data from this deployment has been a central technical objective of our U.S. Department of Energy Small Business Innovative Research (SBIR) Phase 2 contract (DE-SC0020473: Low-Cost Shortwave Spectroradiometer for Retrieval of Cloud Properties).

54 ENVIRONMENTAL SCIENCES↗

Fluctuations of high clouds and 500-mb geopotential heights in baroclinic waveguides

The spatial phase relationship between the atmospheric circulation and the bandpass fluctuations in cloudiness are investigated using satellite retrievals of high cloud areas reported by Stowe et al. (1988, 1989) NMC 500-mb geopotential heights in northern extratropics. Results of the analysis suggest that the high-cloud structures of baroclinic waves are less spatially coherent than the internal geopotential-height structures. It is shown that over the North Pacific, small-scale (latitudinal wavenumber 13-18) fluctuations in geopotential play a greater role in forcing high cloudiness than do medium-scale (latitudinal wavenumber 7-12) fluctuations in geopotential.

Charlock, Thomas P.↗

A Melting Layer Model for Passive/Active Microwave Remote Sensing Applications: Simulation of TRMM Observations - Part 2

The one-dimensional, steady-state melting layer model developed in Part I of this study is used to calculate both the microphysical and radiative properties of melting precipitation, based upon the computed concentrations of snow and graupel just above the freezing level at applicable horizontal gridpoints of 3-dimensional cloud resolving model simulations. The modified 3-dimensional distributions of precipitation properties serve as input to radiative transfer calculations of upwelling radiances and radar extinction/reflectivities at the TRMM Microwave Imager (TMI) and Precipitation Radar (PR) frequencies, respectively. At the resolution of the cloud resolving model grids (approx. 1 km), upwelling radiances generally increase if mixed-phase precipitation is included in the model atmosphere. The magnitude of the increase depends upon the optical thickness of the cloud and precipitation, as well as the scattering characteristics of ice-phase precipitation aloft. Over the set of cloud resolving model simulations utilized in this study, maximum radiance increases of 43, 28, 18, and 10 K are simulated at 10.65, 19.35 GHz, 37.0, and 85.5 GHz, respectively. The impact of melting on TMI-measured radiances is determined not only by the physics of the melting particles but also by the horizontal extent of the melting precipitation, since the lower-frequency channels have footprints that extend over 10''s of kilometers. At TMI resolution, the maximum radiance increases are 16, 15, 12, and 9 K at the same frequencies. Simulated PR extinction and reflectivities in the melting layer can increase dramatically if mixed-phase precipitation is included, a result consistent with previous studies. Maximum increases of 0.46 (-2 dB) in extinction optical depth and 5 dBZ in reflectivity are simulated based upon the set of cloud resolving model simulations.

Olson, William S.↗

Global and Regional Impacts of HONO on the Chemical Composition of Clouds and Aerosols

Recently, realistic simulation of nitrous acid (HONO) based on the HONO/NO(sub x) ratio of 0.02 was found to have a significant impact on the global budgets of HO(sub x) (OH + HO2) and gas phase oxidation products in polluted regions, especially in winter when other photolytic sources are of minor importance. It has been reported that chemistry-transport models underestimate sulphate concentrations, mostly during winter. Here we show that simulating realistic HONO levels can significantly enhance aerosol sulphate (S(VI)) due to the increased formation of H2SO4. Even though in-cloud aqueous phase oxidation of dissolved SO2 (S(IV)) is the main source of S(VI), it appears that HONO related enhancement of H2O2 does not significantly affect sulphate because of the predominantly S(IV) limited conditions, except over eastern Asia. Nitrate is also increased via enhanced gaseous HNO3 formation and N2O5 hydrolysis on aerosol particles. Ammonium nitrate is enhanced in ammonia-rich regions but not under ammonia-limited conditions. Furthermore, particle number concentrations are also higher, accompanied by the transfer from hydrophobic to hydrophilic aerosol modes. This implies a significant impact on the particle lifetime and cloud nucleating properties. The HONO induced enhancements of all species studied are relatively strong in winter though negligible in summer. Simulating realistic HONO levels is found to improve the model measurement agreement of sulphate aerosols, most apparent over the US. Our results underscore the importance of HONO for the atmospheric oxidizing capacity and corroborate the central role of cloud chemical processing in S(IV) formation.

HONO↗

Chandra X-ray Observation of a Mature Cloud-Shock Interaction in the Bright Eastern Knot of Puppis A

We present Chandra X-ray images and spectra of the most prominent cloud-shock interaction region in the Puppis A supernova remnant. The Bright Eastern Knot (BEK) has two main morphological components: (1) a bright compact knot that lies directly behind the apex of an indentation in the eastern X-ray boundary and (2) lying 1 westward behind the shock, a curved vertical structure (bar) that is separated from a smaller bright cloud (cap) by faint diffuse emission. Based on hardness images and spectra, we identify the bar and cap as a single shocked interstellar cloud. Its morphology strongly resembles the "voided sphere" structures seen at late times in Klein et al. experimental simulat.ions of cloud-shock interactions, when the crushing of the cloud by shear instabilities is well underway. We infer an intera.ction time of roughly cloud-crushing timescales, which translates to 2000-4000 years, based on the X-ray temperature, physical size, and estimated expansion of the shocked cloud. This is the first X-ray identified example of a cloud-shock interaction in this advanced phase. Closer t o the shock front, the X-ray emission of the compact knot in the eastern part of the BEK region implies a recent interaction with relatively denser gas, some of which lies in front of the remnant. The complex spatial relationship of the X-ray emission of the compact knot to optical [O III] emission suggests that there are multiple cloud interactions occurring along the line of sight.

Hwang, Una↗

Interannual Variations in Aerosol Sources and Their Impact on Orographic Precipitation Over California's Central Sierra Nevada

Aerosols that serve as cloud condensation nuclei (CCN) and ice nuclei (IN) have the potential to profoundly influence precipitation processes. Furthermore, changes in orographic precipitation have broad implications for reservoir storage and flood risks. As part of the CalWater I field campaign (2009-2011), the impacts of aerosol sources on precipitation were investigated in the California Sierra Nevada. In 2009, the precipitation collected on the ground was influenced by both local biomass burning (up to 79% of the insoluble residues found in precipitation) and long-range transported dust and biological particles (up to 80% combined), while in 2010, by mostly local sources of biomass burning and pollution (30-79% combined), and in 2011 by mostly long-range transport from distant sources (up to 100% dust and biological). Although vast differences in the source of residues was observed from year-to-year, dust and biological residues were omnipresent (on average, 55% of the total residues combined) and were associated with storms consisting of deep convective cloud systems and larger quantities of precipitation initiated in the ice phase. Further, biological residues were dominant during storms with relatively warm cloud temperatures (up to -15 C), suggesting these particles were more efficient IN compared to mineral dust. On the other hand, lower percentages of residues from local biomass burning and pollution were observed (on average 31% and 9%, respectively), yet these residues potentially served as CCN at the base of shallow cloud systems when precipitation quantities were low. The direct connection of the source of aerosols within clouds and precipitation type and quantity can be used in models to better assess how local emissions versus long-range transported dust and biological aerosols play a role in impacting regional weather and climate, ultimately with the goal of more accurate predictive weather forecast models and water resource management.

Creamean, J. M.↗

The Use of the BSRN Data as A Benchmark for the POWER Hourly DHI and DNI and In Validating Derived Hourly GTI

The satellite-based CERES SYN1deg hourly data is the source data of the POWER GIS solar data that covers 2001 to near present. The SYN1deg(Ed4.1) hourly GHI agrees well with the BSRN data, but the hourly DHI and DirHI (Direct Horizontal Irradiance) are positively and negatively, respectively, biased with appreciable magnitudes. The hourly DNI, derived by dividing the DirHI by cos(SZA), or the cosine of the solar zenith angle, is therefore negatively biased. Based on the statistics of comparisons with the BSRN data, we performed bias corrections on the hourly DHI and DNI. The corrections were executed in the 3-D phase space of latitude, cos(SZA), and cloud fraction (CLFR). The isotropic model is then used to derive the hourly global tilted irradiance (GTI). For validation purpose, we applied the isotropic model to the BSRN data at the original 1-, 2-, 3- or 5-minute interval. The satellite-based hourly GTI shows good agreement with their BSRN counterpart. We also examined two monthly-mean-based methods that empirically derive monthly mean GTI and DNI from monthly mean GHI and from both monthly mean GHI and DHI. The monthly-mean-based results compare favorably with the hourly-mean-based results. The GEWEX SRB (V4-IP) provides POWER with daily mean GHI for the years before the CERES era, and the data were corrected using quantile mapping by referencing the CERES SYN1deg data. We used the Kolmogorov -Smirnov test (K-S test) and Cramer-von Mises test to examine how well the results agree with the BSRN data. We found that if we set the lower limit for the daily mean GHI to 30 W m-2, the data can pass the K-S test at 0.01 significance level and the Cramer-von Mises test at 0.001 significance level. If no lower limit is set on the daily means, the data fail both tests. The satellite-based CERES SYN1deg hourly data is the source data of the POWER GIS solar data that covers 2001 to near present. The SYN1deg(Ed4.1) hourly GHI agrees well with the BSRN data, but the hourly DHI and DirHI (Direct Horizontal Irradiance) are positively and negatively, respectively, biased with appreciable magnitudes. The hourly DNI, derived by dividing the DirHI by cos(SZA), or the cosine of the solar zenith angle, is therefore negatively biased. Based on the statistics of comparisons with the BSRN data, we performed bias corrections on the hourly DHI and DNI. The corrections were executed in the 3-D phase space of latitude, cos(SZA), and cloud fraction (CLFR). The isotropic model is then used to derive the hourly global tilted irradiance (GTI). For validation purpose, we applied the isotropic model to the BSRN data at the original 1-, 2-, 3- or 5-minute interval. The satellite-based hourly GTI shows good agreement with their BSRN counterpart. We also examined two monthly-mean-based methods that empirically derive monthly mean GTI and DNI from monthly mean GHI and from both monthly mean GHI and DHI. The monthly-mean-based results compare favorably with the hourly-mean-based results. The GEWEX SRB (V4-IP) provides POWER with daily mean GHI for the years before the CERES era, and the data were corrected using quantile mapping by referencing the CERES SYN1deg data. We used the Kolmogorov -Smirnov test (K-S test) and Cramer-von Mises test to examine how well the results agree with the BSRN data. We found that if we set the lower limit for the daily mean GHI to 30 W m-2, the data can pass the K-S test at 0.01 significance level and the Cramer-von Mises test at 0.001 significance level. If no lower limit is set on the daily means, the data fail both tests.

Taiping Zhang↗

Forecasting Lightning Threat using Cloud-Resolving Model Simulations

Two new approaches are proposed and developed for making time and space dependent, quantitative short-term forecasts of lightning threat, and a blend of these approaches is devised that capitalizes on the strengths of each. The new methods are distinctive in that they are based entirely on the ice-phase hydrometeor fields generated by regional cloud-resolving numerical simulations, such as those produced by the WRF model. These methods are justified by established observational evidence linking aspects of the precipitating ice hydrometeor fields to total flash rates. The methods are straightforward and easy to implement, and offer an effective near-term alternative to the incorporation of complex and costly cloud electrification schemes into numerical models. One method is based on upward fluxes of precipitating ice hydrometeors in the mixed phase region at the-15 C level, while the second method is based on the vertically integrated amounts of ice hydrometeors in each model grid column. Each method can be calibrated by comparing domain-wide statistics of the peak values of simulated flash rate proxy fields against domain-wide peak total lightning flash rate density data from observations. Tests show that the first method is able to capture much of the temporal variability of the lightning threat, while the second method does a better job of depicting the areal coverage of the threat. Our blended solution is designed to retain most of the temporal sensitivity of the first method, while adding the improved spatial coverage of the second. Exploratory tests for selected North Alabama cases show that, because WRF can distinguish the general character of most convective events, our methods show promise as a means of generating quantitatively realistic fields of lightning threat. However, because the models tend to have more difficulty in predicting the instantaneous placement of storms, forecasts of the detailed location of the lightning threat based on single simulations can be in error. Although these model shortcomings presently limit the precision of lightning threat forecasts from individual runs of current generation models,the techniques proposed herein should continue to be applicable as newer and more accurate physically-based model versions, physical parameterizations, initialization techniques and ensembles of forecasts become available.

McCaul, Eugene W., Jr.↗

Information Content Analysis for Selection of Optimal JWST Observing Modes for Transiting Exoplanet Atmospheres

The James Webb Space Telescope ( JWST ) is nearing its launch date of 2018, and is expected to revolutionize our knowledge of exoplanet atmospheres. In order to specifically identify which observing modes will be most useful for characterizing a diverse range of exoplanetary atmospheres, we use an information content (IC) based approach commonly used in the studies of solar system atmospheres. We develop a system based upon these IC methods to trace the instrumental and atmospheric model phase space in order to identify which observing modes are best suited for particular classes of planets, focusing on transmission spectra. Specifically, the atmospheric parameter space we cover is T = 600–1800 K, C/O = 0.55–1, [M/H] = 1–100 × Solar for an R = 1.39 R{sub J}, M = 0.59 M{sub J} planet orbiting a WASP-62-like star. We also explore the influence of a simplified opaque gray cloud on the IC. We find that obtaining broader wavelength coverage over multiple modes is preferred over higher precision in a single mode given the same amount of observing time. Regardless of the planet temperature and composition, the best modes for constraining terminator temperatures, C/O ratios, and metallicity are NIRISS SOSS+NIRSpec G395. If the target’s host star is dim enough such that the NIRSpec prism is applicable, then it can be used instead of NIRISS SOSS+NIRSpec G395. Lastly, observations that use more than two modes should be carefully analyzed because sometimes the addition of a third mode results in no gain of information. In these cases, higher precision in the original two modes is favorable.

79 ASTRONOMY AND ASTROPHYSICS↗