scholarly journals Relativistic Milne-Eddington Type Solutions with a Variable Eddington Factor for Relativistic Spherical Winds

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Jun Fukue
Keyword(s):  
Optical Depth ◽  
Power Law ◽  
Source Function ◽  
Flow Speed ◽  
Radiative Flux ◽  
Exponential Behavior ◽  
Background Density ◽  
Relativistic Treatment ◽  
Parallel Case ◽  
Expansion Effect

Relativistic radiative transfer in a relativistic spherical flow is examined in the fully special relativistic treatment. Under the assumption of a constant flow speed and using a variable (prescribed) Eddington factor, we analytically solve the relativistic moment equations in the comoving frame for several restricted cases, and obtain relativistic Milne-Eddington type solutions. In contrast to the plane-parallel case where the solutions exhibit the exponential behavior on the optical depth, the solutions have power-law forms. In the case of the radiative equilibrium, for example, the radiative flux has a power-law term multiplied by the exponential term. In the case of the local thermodynamic equilibrium with a uniform source function in the comoving frame, the radiative flux has a power-law form on the optical depth. This is because there is an expansion effect (curvature effect) in the spherical wind and the background density decreases as the radius increases.

scholarly journals Wind Speed Influences on Marine Aerosol Optical Depth

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Colin O'Dowd ◽  
Claire Scannell ◽  
Jane Mulcahy ◽  
S. Gerard Jennings
Keyword(s):  
Wind Speed ◽  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Power Law ◽  
Anthropogenic Pollution ◽  
Open Ocean ◽  
Marine Aerosol ◽  
Wind Speeds ◽  
General Power ◽  
Relationship Of

The Mulcahy (Mulcahy et al., 2008) power-law parameterization, derived at the coastal Atlantic station Mace Head, between clean marine aerosol optical depth (AOD) and wind speed is compared to open ocean MODIS-derived AOD versus wind speed. The reported AOD versus wind speed (U) was a function of ∼U2. The open ocean MODIS-derived AOD at 550 nm and 860 nm wavelengths, while in good agreement with the general magnitude of the Mulcahy parameterization, follows a power-law with the exponent ranging from 0.72 to 2.47 for a wind speed range of 2–18 m s−1. For the four cases examined, some MODIS cases underestimated AOD while other cases overestimated AOD relative to the Mulcahy scheme. Overall, the results from MODIS support the general power-law relationship of Mulcahy, although some linear cases were also encountered in the MODIS dataset. Deviations also arise between MODIS and Mulcahy at higher wind speeds (>15 m s−1), where MODIS-derived AOD returns lower values as compared to Mulcahy. The results also support the suggestion than wind generated sea spray, under moderately high winds, can rival anthropogenic pollution plumes advecting out into marine environments with wind driven AOD contributing to AOD values approaching 0.3.

The parameterisation of the atmospheric aerosol optical depth using the Ångström power law

Solar Energy ◽  
1998 ◽  
Vol 63 (5) ◽  
pp. 303-311 ◽  
Author(s):  
J.A. Martı́nez-Lozano ◽  
M.P. Utrillas ◽  
F. Tena ◽  
V.E. Cachorro
Keyword(s):  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Power Law ◽  
Atmospheric Aerosol

scholarly journals Planck 2018 results

2020 ◽  
Vol 641 ◽  
pp. A6 ◽  
Author(s):  
◽  
N. Aghanim ◽  
Y. Akrami ◽  
M. Ashdown ◽  
J. Aumont ◽  
...  
Keyword(s):  
Dark Energy ◽  
Optical Depth ◽  
Power Law ◽  
Hubble Constant ◽  
Big Bang ◽  
Matter Density ◽  
Small Scale ◽  
Density Parameter ◽  
Λcdm Model ◽  
Correlated Parameters

We present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ωch2 = 0.120 ± 0.001, baryon density Ωbh2 = 0.0224 ± 0.0001, scalar spectral index ns = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100θ* = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H0 = (67.4 ± 0.5)  km s−1 Mpc−1; matter density parameter Ωm = 0.315 ± 0.007; and matter fluctuation amplitude σ8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be Neff = 2.99 ± 0.17, in agreement with the Standard Model prediction Neff = 3.046, and find that the neutrino mass is tightly constrained to ∑mν <  0.12  eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, ΩK = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = −1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r0.002 <  0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6σ, tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.

scholarly journals The Truncated Geometric Approximation and the Size Distribution of Small Atmospheric Particles

2011 ◽  
Vol 28 (6) ◽  
pp. 779-786 ◽  
Author(s):  
J. G. DeVore
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Optical Depth ◽  
Power Law ◽  
Spherical Particles ◽  
Simple Relationship ◽  
Nasa Goddard Space ◽  
Geometric Approximation ◽  
Power Law Function

Abstract This paper describes a simple relationship between the slope of particulate optical depth as a function of wavelength and the size distribution of spherical particles. It is based on approximating extinction using a truncated geometric optics relationship and is applicable when optical depth decreases with wavelength. The new relationship suggests that extinction versus wavelength measurements are most sensitive to particles that are comparable in size to the wavelength. When optical depth is expressed as a power-law function of wavelength, the resulting particle size distribution is also a power-law function of size, with the two exponents reproducing the well-known relationship between the Ångström and Junge exponents. Examples of applying the new relationship are shown using both numerical calculations based on Mie theory and measurements from the Aerosol Robotic Network (AERONET) sun photometer at NASA Goddard Space Flight Center (GSFC). Since the truncated geometric approximation makes no assumptions per se concerning the form of the particle size distribution, it may find application in supplementing solar aureole profile measurements in retrieving the size distributions of particles in thin clouds—for example, cirrus—or when they are present.

scholarly journals Computation of longwave radiative flux and vertical heating rate with 4A-Flux v1.0 as integral part of the radiative transfer code 4A/OP v1.5

2021 ◽  
Author(s):  
Yoann Tellier ◽  
Cyril Crevoisier ◽  
Raymond Armante ◽  
Jean-Louis Dufresne ◽  
Nicolas Meilhac
Keyword(s):  
Radiative Transfer ◽  
Heating Rate ◽  
Optical Depth ◽  
Radiative Forcing ◽  
Specular Reflection ◽  
Radiative Flux ◽  
High Spectral Resolution ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Very High

Abstract. Based on advanced spectroscopic databases, line-by-line and layer-by-layer radiative transfer codes numerically solve the radiative transfer equation with a very high accuracy. Taking advantage of its pre-calculated optical depth look-up table, the fast and accurate radiative transfer model Automatized Atmospheric Absorption Atlas OPerational (4A/OP) calculates the transmission and radiance spectra for a user defined layered atmospheric model. Here we present a module, called 4A-Flux, developed and implemented into 4A/OP in order to include the calculation of the clear-sky longwave radiative flux profiles and heating rate profiles at a very high spectral resolution. Calculations are performed under the assumption of local thermodynamic equilibrium, plane-parallel atmosphere and specular reflection on the surface. The computation takes advantage of pre-tabulated exponential integral functions that are used instead of a classic angular quadrature. Furthermore, the sublayer variation of the Planck function is implemented to better represent the emission of layers with a high optical depth. Thanks to the implementation of 4A-Flux, 4A/OP model have participated in the Radiative Forcing Model Intercomparison Project (RFMIP-IRF) along with other state-of-the-art radiative transfer models. 4A/OP hemispheric flux profiles are compared to other models over the 1800 representative atmospheric situations of RFMIP, yielding an Outgoing Longwave Radiation (OLR) mean difference between 4A/OP and other models of −0.148 W .m−2 and a mean standard deviation of 0.218 W .m−2, showing a good agreement between 4A/OP and other models. 4A/OP is applied to the Thermodynamic Initial Guess Retrieval (TIGR) atmospheric database to analyze the response of the OLR and vertical heating rate to several perturbations of temperature or gas concentration. This work shows that 4A/OP with 4A-Flux module can successfully be used to simulate accurate flux and heating rate profiles and provide useful sensitivity studies including sensitivities to minor trace gases such as HFC134a, HCFC22 and CFC113. We also highlight the interest for the modeling community to extend intercomparison between models to comparisons between spectroscopic databases and modelling to improve the confidence in model simulations.

scholarly journals Gaussian Process Reconstruction of Reionization History

2021 ◽  
Vol 922 (2) ◽  
pp. 95
Author(s):  
Aditi Krishak ◽  
Dhiraj Kumar Hazra
Keyword(s):  
Gaussian Process ◽  
Optical Depth ◽  
Power Law ◽  
Source Term ◽  
Gamma Ray ◽  
High Redshift ◽  
Gaussian Process Regression ◽  
Joint Analysis ◽  
Data Compilation ◽  
History Of

Abstract We reconstruct the history of reionization using Gaussian process regression. Using the UV luminosity data compilation from Hubble Frontiers Fields we reconstruct the redshift evolution of UV luminosity density and thereby the evolution of the source term in the ionization equation. This model-independent reconstruction rules out single power-law evolution of the luminosity density but supports the logarithmic double power-law parameterization. We obtain reionization history by integrating ionization equations with the reconstructed source term. Using the optical depth constraint from Planck cosmic microwave background observation, measurement of UV luminosity function integrated until truncation magnitude of −17 and −15, and derived ionization fraction from high redshift quasar, galaxies, and gamma-ray burst observations, we constrain the history of reionization. In the conservative case we find the constraint on the optical depth as τ = 0.052 ± 0.001 ± 0.002 at 68% and 95% confidence intervals. We find the redshift duration between 10% and 90% ionization to be 2.05 − 0.21 − 0.30 + 0.11 + 0.37 . Longer duration of reionization is supported if UV luminosity density data with truncation magnitude of −15 is used in the joint analysis. Our results point out that even in a conservative reconstruction, a combination of cosmological and astrophysical observations can provide stringent constraints on the epoch of reionization.

scholarly journals Parameterization of The Single-Scattering Properties of Dust Aerosols in Radiative Flux Calculations

Atmosphere ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 728 ◽  
Author(s):  
Meihua Wang ◽  
Jing Su ◽  
Xugang Li ◽  
Chen Wang ◽  
Jinming Ge
Keyword(s):  
Optical Depth ◽  
Radiative Forcing ◽  
Climate Model ◽  
Single Scattering ◽  
Radiative Flux ◽  
Dust Particles ◽  
Nonspherical Particle ◽  
Parameterization Schemes ◽  
Relative Errors ◽  
The Impact

In this study, we present parameterization schemes of dust single-scattering properties (SSPs) in order to establish a fast and accurate way to obtain the SSPs for dust shortwave radiative flux calculation. Based on the assumption that dust particles are spheroids, we represent a single nonspherical particle with a collection of monodisperse spheres that contain the same total surface area and volume as the original particle to convert the spheroid to a sphere. The SSPs of dust particles were parameterized in terms of the effective radius ( R e ) and imaginary part of the refractive index ( M i ). The averaged relative errors of the parameterized to the “exact” single-scattering properties, which refer to the results from the Mie theory program, are below 1.5%. To further quantify the impact of parametrization on the radiative flux simulation, we computed the radiative fluxes at both the top of the atmosphere (TOA) and the surface by using SSPs from the parameterization and the “exact”, respectively. The maximum relative errors were below 1% at both the TOA and the surface, proving that the SSPs of dust calculated by our parameterization schemes are well suited for radiative flux calculations. This parameterization differs from previous works by being formulated not only with R e but also with M i . We also investigated the sensitivity of dust-aerosol forcing to R e , M i , optical depth (τ), and solar zenith angle (SZA). The results show that the value of shortwave (SW) radiative forcing (RF) at the TOA changes from negative to positive as the M i is increasing, which means that, as the absorption of dust particles becomes stronger, more energy is kept in the atmosphere to heat the earth–atmosphere system. The SW RF gradually becomes less negative at the TOA and more negative at the surface with increasing R e , due to the decreases of reflection and transmission along with the single-scattering albedo decreasing. As the optical depth increases, the values of the SW RF decrease because of the strong attenuation for heavy loading. When SZA increases, the SW RF becomes more negative at both the TOA and the surface due to the long optical path at a large SZA. The errors induced from the parameterized SSPs of dust in the SW RF calculation are very small, which are less than 2.1%, demonstrating the accuracy of the parameterization and its reliability for climate model applications.

scholarly journals Modeling the South American regional smoke plume: aerosol optical depth variability and surface shortwave flux perturbation

2013 ◽  
Vol 13 (6) ◽  
pp. 2923-2938 ◽  
Author(s):  
N. E. Rosário ◽  
K. M. Longo ◽  
S. R. Freitas ◽  
M. A. Yamasoe ◽  
R. M. Fonseca
Keyword(s):  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Biomass Burning ◽  
Solar Irradiance ◽  
Amazon Basin ◽  
Radiative Flux ◽  
Smoke Plume ◽  
Aerosol Loading ◽  
Coarse Mode ◽  
Flux Perturbation

Abstract. Intra-seasonal variability of smoke aerosol optical depth (AOD) and downwelling solar irradiance at the surface during the 2002 biomass burning season in South America was modeled using the Coupled Chemistry-Aerosol-Tracers Transport model with the Brazilian developments on the Regional Atmospheric Modeling System (CCATT-BRAMS). Measurements of total and fine mode fraction (FMF) AOD from the AErosol RObotic NETwork (AERONET) and solar irradiance at the surface from the Solar Radiation Network (SolRad-NET) were used to evaluate model results. In general, the major features associated with AOD evolution over the southern part of the Amazon basin and cerrado ecosystem are captured by the model. The main discrepancies were found for high aerosol loading events. In the northeastern portion of the Amazon basin the model systematically underestimated total AOD, as expected, since smoke contribution is not dominant as it is in the southern portion and emissions other than smoke were not considered in the simulation. Better agreement was obtained comparing the model results with observed FMF AOD, which pointed out the relevance of coarse mode aerosol emission in that region. Likewise, major discrepancies over cerrado during high AOD events were found to be associated with coarse mode aerosol omission in our model. The issue of high aerosol loading events in the southern part of the Amazon was related to difficulties in predicting the smoke AOD field, which was discussed in the context of emissions shortcomings. The Cuiabá cerrado site was the only one where the highest quality AERONET data were unavailable for both total and FMF AOD. Thus, lower quality data were used. Root-mean-square error (RMSE) between the model and observed FMF AOD decreased from 0.34 to 0.19 when extreme AOD events (FMF AOD550 nm ≥ 1.0) and Cuiabá were excluded from the analysis. Downward surface solar irradiance comparisons also followed similar trends when extreme AOD were excluded. This highlights the need to improve modelling of the regional smoke plume in order to enhance the accuracy of the radiative energy budget. An aerosol optical model based on the mean intensive properties of smoke from the southern part of the Amazon basin produced a radiative flux perturbation efficiency (RFPE) of −158 Wm−2/AOD550 nm at noon. This value falls between −154 Wm−2/AOD550 nm and −187 Wm−2/AOD550 nm, the range obtained when spatially varying optical models were considered. The 24 h average surface radiative flux perturbation over the biomass burning season varied from −55 Wm−2 close to smoke sources in the southern part of the Amazon basin and cerrado to −10 Wm−2 in remote regions of the southeast Brazilian coast.

Sign in / Sign up

Export Citation Format

Share Document